Document [original]

Fluidic Ultrasound Generation for

Nondestructive Testing

vorgelegt von

M. Sc.

Benjamin B¨uhling

ORCID: 0000-0002-6775-7118

an der Fakult¨at V – Verkehrs- und Maschinensysteme

der Technischen Universit¨at Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften

– Dr.-Ing. –

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr.-Ing. Markus Hecht

Gutachter: Prof. Dr.-Ing. Ennes Sarradj

Gutachterin: Prof. Dr.-Ing. Ute Rabe

Gutachter: Dr.-Ing. Christoph Strangfeld

Gutachter: Dr.-Ing. Stefan Maack

Tag der wissenschaftlichen Aussprache: 27. Februar 2024

Berlin 2024

Acknowledgments

I would like to express my deepest gratitude for my supervisors Christoph Strangfeld and

Stefan Maack who invited me to work on this research project at BAM Division 8.2 and sup-

ported me over the course of the whole project and beyond. Their passion for the topic, their

trust in my abilities and the freedom they gave me to follow new approaches were invaluable to

this thesis. Their honest feedback and our numerous discussions greatly shaped my research.

I am thankful to Ernst Niederleithinger, who supported me in extending my stay at BAM

Division 8.2 to pursue projects beyond my thesis research. Special thanks should also go to

Heiko Stolpe for being approachable and willing to share his knowledge of measurement tech-

nology and Labview. I am also grateful for the many enjoyable conversations with Stefan

K¨uttenbaum, Niklas Epple and Jens W¨ostmann, be it work-related or not. Many problems

were solved. Also thanks to my various office neighbors over time, Kerstin Borchardt-Giers,

Chun-Man Liao and Vera Lay, with whom it was always nice to chat for the pleasant office

vibes. I am also grateful to Marco Lange and Sean Smith who always offered help and guidance

in practical issues of specimen manufacturing and handling. All of my other colleagues at BAM

Division 8.2 were also always approachable and helped in many different ways over the course

of this thesis, which I am grateful for.

I am deeply indebted to Stefan Facius of BAM Division 9.2, whose outstanding craftsmanship

was integral for the project and whose enthusiasm was infectious. Talking and working with you

was always a pleasure. You will be missed.

I would also like to thank Thorge Schweitzer, Bernhard Bobusch and Oliver Kr¨uger of FDX

Fluid Dynamix GmbH, who shared their experience fluidics development and design, which

was essential for the success of my research. Thanks should also go to Navid Nayeri and

Sascha Martinke of the Hermann-F¨ottinger-Institut at TU Berlin, who facilitated the use of

their measurement equipment without complications and helped me setting up my measure-

ments.

I would like to extend my gratitude to Prof. Ennes Sarradj, who gave me the opportunity

to graduate at the Department of Engineering Acoustics of the Institute of Fluid Dynamics

and Engineering Acoustics at TU Berlin and was always available to discuss any questions

regarding my research. I would also like to thank Prof. Ute Rabe of the Fraunhofer Institute

for Non-Destructive Testing IZFP and the Department of Materials Science and Engineering at

the Saarland University, who kindly accepted to be part of the doctoral committee. I am also

thankful to Prof. Markus Hecht of the Department of Rail Vehicles of the Institute of Land and

Sea Transport Systems at TU Berlin for accepting to be the committee chair of my doctoral

thesis defense. I am honored to have a group of such distinguished researchers constituting my

doctoral committee.

I am extremely grateful for the support of parents, my grandparents and my brother, who

always encouraged me in my academic work and are always there to help with all the challenges

in life.

Finally, I would like to thank my wife, Theresa. Words cannot express my gratitude. Her

unwavering support, her understanding and her motivation were vital for this work. I could not

have completed this research without her always having my back.

iii

Abstract

Ultrasonic testing has become an indispensable method for verifying integrity, dimensional ac-

curacy and material properties in numerous technical domains. Air-coupled ultrasound offers

advantages in terms of measurement flexibility and reduced measurement time, but also presents

challenges due to limitations in transmitted sound pressure amplitude and sensor positioning.

Due to the high impedance mismatch at the interfaces between the transducer, air, and speci-

men, only a fraction of the generated sound pressure interacts with the specimen and is received

by a sensor. To reduce these losses, a novel fluidic ultrasonic transducer is presented. This

device produces a transient triggered ultrasound pulse based on aeroacoustic sound generation

mechanisms in a bistable fluidic amplifier. Little is known about its performance characteristics

and suitability for nondestructive testing (NDT). The publications included in this thesis are the

first to present a transient aeroacoustic ultrasonic generator using a bistable fluidic amplifier.

This dissertation demonstrates that such a fluidic ultrasonic transducer is applicable for com-

mon measurement tasks in NDT. By disseminating the acoustic and flow characteristics of the

device, the resulting challenges and opportunities concerning its applicability to NDT tasks are

identified and addressed. It is found that the generated pulse contains frequency components

below 60 kHz, fluctuating in amplitude and phase delay, and is accompanied by a high velocity

free jet that partially interacts with the sound pulses. In order to prevent interaction between

the jet and the specimen surface and to increase transducer directivity, the attachment of sonic

crystals and an exponential horn were successfully tested. The distinct spectral characteris-

tics of each ultrasonic pulse were exploited to develop a signal processing approach that allows

better differentiation between two pulses received in quick succession. This improved the usabil-

ity of the fluidic transducer in multiple-input multiple-output (MIMO) setups. To address the

stochastic ultrasound generation behavior, a novel, fully non-contact through-transmission mea-

surement setup is presented that allows time-of-flight measurements without prior knowledge

of trigger time, pulse shape, or distance between the transducer and the specimen. Successful

measurement of longitudinal propagation velocity in various materials demonstrates that the

fluidic transducer is capable of nondestructively measuring a variety of geometric and material

properties. Thus, a new type of ultrasonic transducer has been established and its applicability

to common NDT tasks has been demonstrated. The usability of these novel procedures extends

beyond fluidic ultrasonic testing and can also be employed to improve conventional air-coupled

ultrasonic measurements. The results presented not only offer the amplifier-based fluidic trans-

ducer as a robust alternative ultrasound source for NDT, especially in civil engineering, but

also raise a number of research questions related to the use of aeroacoustic transducers as an

alternative to conventional air-coupled ultrasonic devices.

Zusammenfassung

Die Ultraschallpr¨ufung hat sich in vielen technischen Bereichen zu einer unverzichtbaren Meth-

ode zur ¨

Uberpr¨ufung von Bauteilintegrit¨at, Maßhaltigkeit und Materialeigenschaften entwickelt.

Luftgekoppelter Ultraschall bietet Vorteile im Hinblick auf Flexibilit¨at in der Durchf¨uhrung der

Messung und in der Verringerung der Messdauer. Herausforderungen bestehen hingegen sowohl

aufgrund der geringeren eingebrachten Schalldruckamplituden als auch der erforderlichen Posi-

tionierungsgenauigkeit der Sensorik. Auf Grund des großen Unterschieds der spezifischen Schal-

limpedanzen an den ¨

Uberg¨angen zwischen Schallwandler, Luft und Pr¨ufk¨orper interagiert nur

Bruchteil des erzeugten Schalldrucks mit dem Pr¨ufk¨orper und wird im Anschluss vom Schallsen-

sor empfangen. Um diese Verluste zu reduzieren, wird ein neuartiger fluidischer Ultraschall-

wandler vorgestellt. Basierend auf der aeroakustischen Schallerzeugung in einem fluidischen

bistabilen Haftstrahlelement erzeugt dieses Ger¨at einen gesteuerten transienten Ultraschallpuls.

Weder dessen Schallcharakteristik noch die Eignung zur zerst¨orungsfreien Pr¨ufung (ZfP) wurden

bisher erforscht. Die Publikationen dieser Dissertation sind die ersten, die Luftschallerzeugung

durch fluidische Wandstrahlelemente untersuchen und die transiente Signalerzeugung mit Hilfe

aeroakustischer Ultraschallwandler zeigen. In dieser Dissertation wird gezeigt, dass der fluidische

Ultraschallwandler f¨ur ¨ubliche ZfP-Messverfahren geeignet ist. Mit der Untersuchung der Schall-

und Str¨omungseigenschaften des Wandlers werden die M¨oglichkeiten und Herausforderungen

f¨ur ZfP-Anwendungen herausgearbeitet. Es wird gezeigt, dass der durch den fluidischen Wan-

dler erzeugte Puls dominante Frequenzen unter 60 kHz erzeugt, die stochastisch in Ampli-

tude und Phase variieren, und mit einem Freistrahl nahe der Schallgeschwindigkeit einhergeht,

der mit nachfolgenden Schallpulsen interagiert. Um die Interaktion dieses Freistrahls mit der

Oberfl¨ache eines Probek¨orpers zu verhindern und um die Richtcharakteristik des Wandlers zu

verbessern, wurden das Anbringen eines Exponentialtrichters und der Einsatz sonischer Kristalle

erfolgreich untersucht. Die spezifischen spektralen Eigenschaften der einzelnen Ultraschallpulse

werden genutzt, um eine Signalverarbeitungsmethode zu entwickeln, durch die mehrere kurz

aufeinanderfolgende Pulse besser unterschieden werden k¨onnen und so Multiple-input Multiple-

output (MIMO) Anwendungen mit Hilfe des fluidischen Wandlers m¨oglich werden. Um dem

stochastischen Verhalten des Schallerzeugungsmechanismus zu begegnen, wird ein neuartiger

komplett ber¨uhrungsloser Durchschallungspr¨ufstand vorgestellt, der erlaubt, die Laufzeit eines

Ultraschallsignals zu messen, ohne dass der Trigger-Zeitpunkt, die Pulsform oder der Abstand

zwischen Wandler und Probek¨orper bekannt sein m¨ussen. Durch die erfolgreiche Messung der

Longitudinalwellengeschwindigkeit in verschiedenen Materialien wird gezeigt, dass der fluidis-

che Wandler geeignet ist, eine Reihe von Geometrie- und Materialeigenschaften zerst¨orungsfrei

zu untersuchen. In dieser Arbeit wird damit ein neuer Typ von luftgekoppelten Ultraschall-

wandlern vorgestellt und deren Einsetzbarkeit in typischen ZfP-Anwendungen nachgewiesen.

Die ben¨otigten neuen Verfahren reichen ¨uber die fluidische Ultraschallerzeugung hinaus und

k¨onnen auch in konventionellen Luftultraschall-Anwendungen eingesetzt werden. Die vorgestell-

ten Ergebnisse zeigen nicht nur, dass ein Wandler auf Basis eines fluidischen Wandstrahlele-

ments eine robuste alternative Ultraschallquelle f¨ur die zerst¨orungsfreie Pr¨ufung - insbesondere

im Bauwesen - sein kann, sondern er¨offnen allgemein das Forschungsfeld der aeroakustischen

Wandler als Alternative zu konventionellen Ger¨aten f¨ur die Erzeugung von luftgekoppeltem Ul-

traschall.

vii

Table of Contents

ListofFigures ........................................ xi

ListofSymbols........................................ xiii

1 Introduction 1

1.1 BackgroundandAim.................................. 1

1.2 UltrasonicTesting ................................... 2

1.3 Air-Coupled Ultrasonic Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Aeroacoustic Sound Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 Fluidics ......................................... 10

1.6 ResearchQuestions................................... 14

2 Publications 17

2.1 Publication I: Experimental analysis of the acoustic field of an ultrasonic pulse

inducedbyafluidicswitch............................... 17

2.2 Publication II: Using sonic crystals to separate the acoustic from the flow field of

afluidictransducer................................... 27

2.3 Publication III: Enhancing the spectral signatures of ultrasonic fluidic transducer

pulses for improved time-of-flight measurements . . . . . . . . . . . . . . . . . . . 35

2.4 Publication IV: Development of an Accurate and Robust Air-Coupled Ultrasonic

Time-of-Flight Measurement Technique . . . . . . . . . . . . . . . . . . . . . . . 49

2.5 Publication V: Fluidic Ultrasound Generation for Non-Destructive Testing . . . . 67

3 Results and Discussion 91

3.1 Transducer and Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.2 Signal Characteristics and Flow-Sound Interactions . . . . . . . . . . . . . . . . . 92

3.3 Separation of Flow and Sound Fields . . . . . . . . . . . . . . . . . . . . . . . . . 96

3.4 Utilizing the Inherent Signal Characteristics . . . . . . . . . . . . . . . . . . . . . 98

3.5 Development of a Fully Non-Contact ToF Measurement Setup . . . . . . . . . . . 100

3.6 Application to ToF Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.7 Limitations and Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4 Conclusions 107

References 109

Associated Publications 127

List of Figures

1.1 Transducer arrangements for ultrasonic testing . . . . . . . . . . . . . . . . . . . 3

1.2 Schematic of a supersonic free jet spectrum . . . . . . . . . . . . . . . . . . . . . 9

1.3 Schematic and switching process of a bistable fluidic amplifier . . . . . . . . . . . 13

3.1 Schematic contextualization of the publications in relation to the final measure-

mentsetup ....................................... 91

3.2 Versions of the fluidic transducer . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.3 Operating procedure of the fluidic transducer . . . . . . . . . . . . . . . . . . . . 93

3.4 Sound characteristics of the fluidic transducer. . . . . . . . . . . . . . . . . . . . 94

3.5 Supply pressure dependence of pulse characteristics in bistable operation . . . . . 96

3.6 Effect of sonic crystal on the transducer sound field . . . . . . . . . . . . . . . . . 97

3.7 Accuracy in semi-synthetic MIMO experiments . . . . . . . . . . . . . . . . . . . 100

3.8 Schematic and performance of the novel through-transmission ToF setup . . . . . 101

3.9 Measurement results of the fluidic transducer compared to the piezoelectric ACU

andcontacttransducers ................................ 103

3.10 Preliminary tests of a down-scaled oscillator-based fluidic transducer . . . . . . . 106

List of Symbols

Acronyms

ACU Air-coupled ultrasound

BAM Bundesanstalt f¨ur Materialforschung und -pr¨ufung

CMUT Capacitive micromachined ultrasonic transducer

EU European Union

LDV Laser Doppler vibrometer

MEMS Microelectromechanical systems

MIMO Multiple-input multiple-output

NDT Nondestructive testing

NDT-CE Nondestructive testing for civil engineering

P2P Peak-to-peak ratio

PuC Pulse compression

RV Refracto-vibrometry

Rx Receiver

SAFT Synthetic aperture focusing technique

SC Sonic crystal

SNR Signal-to-noise ratio

ToE Time of entry

ToF Time of flight

Tx Transmitter

U.S. United States of America

UES Unit envelope signal

UT Ultrasonic testing

UWR Ultrasonic wave reflection method

ZfP Zerst¨orungsfreie Pr¨ufung

Symbols

A(t) Amplitude modulation function

aSonic crystal lattice constant [m]

cSound speed [m s−1]

cLSound speed of longitudinal waves [m s−1]

DCharacteristic jet diameter [m]

dCharacteristic discontinuity size [m]

fFrequency [Hz]

g(t) Angle modulation function

kWave number [m−1]

St Strouhal number [-]

ℓCharacteristic piston dimension [m]

m˙sPoint mass source [kg m−3s−1]

xiii

pˆ Mean absolute peak sound pressure [Pa]

pin Inlet pressure from air supply [Pa]

RReflection coefficient [-]

s(t) Time signal function

sPropagation path length [m]

TTransmission coefficient [-]

tTime [s]

uFlow velocity [m s−1]

ujJet flow velocity [m s−1]

ZFSpecific acoustic impedance [Pa s m−1]

θcr Critical angle [°]

λWavelength [m]

ρDensity [kg m−3]

τtof Time of flight [s]

ϕ0Phase shift [-]

ϕ(t) Phase modulation function

˙(t) Frequency modulation function

ω0Angular frequency [Hz]

xiv

List of Included Publications

This cumulative dissertation contains the following five research papers, of which four had al-

ready been published after peer-reviewed and the final one is still under review at the time of

submission.

Section 2.1:

B. B¨uhling, C. Strangfeld, S. Maack, and T. Schweitzer. “Experimental analysis of the acoustic

field of an ultrasonic pulse induced by a fluidic switch”. Journal of the Acoustical Society of

America 149.4 (2021), 2150–2158. doi:10.1121/10.0003937

Version: Publisher’s version

Section 2.2:

B. B¨uhling, S. Maack, and C. Strangfeld. “Using sonic crystals to separate the acoustic from

the flow field of a fluidic transducer”. Applied Acoustics 189 (2022), 108608. doi:10.1016/j.

apacoust.2021.108608

Version: Publisher’s version

Section 2.3:

B. B¨uhling, S. Maack, T. Schweitzer, and C. Strangfeld. “Enhancing the spectral signatures of

ultrasonic fluidic transducer pulses for improved time-of-flight measurements”. Ultrasonics 119

(2022), 106612. doi:10.1016/j.ultras.2021.106612

Version: Publisher’s version

Section 2.4:

B. B¨uhling, S. K¨uttenbaum, S. Maack, and C. Strangfeld. “Development of an Accurate and

Robust Air-Coupled Ultrasonic Time-of-Flight Measurement Technique”. Sensors 22.6 (2022),

2135. doi:10.3390/s22062135

Version: Publisher’s version

Section 2.5:

B. B¨uhling, S. Maack, and C. Strangfeld. “Fluidic Ultrasound Generation for Non-Destructive

Testing”. Advanced Materials (2024), 2311724. doi:10.1002/adma.202311724

Version: Preprint

1 Introduction

1.1 Background and Aim

Materials testing is an essential activity throughout the life cycle of many structures and man-

ufactured products. It is used to determine the properties of raw and processed materials, to

assess the structural properties of intermediate and final products, and to examine their integrity

[6]. While destructive testing methods allow direct measurement of material properties, they

render the test object unusable after testing. They are therefore best suited for large batch

sizes, where the properties of the remaining products can be inferred from the testing of in-

dividual specimens. In contrast, nondestructive testing (NDT) allows specimens to be tested

while retaining their serviceability. This enables testing of small series or unique products, as

well as regular or even continuous monitoring of critical structures and products throughout

their service life. The incentive for applying nondestructive testing to in-service structures is

primarily to avoid personal injury and, furthermore, to reduce economic costs due to failures

and thereby ecological damage by extending service life [7]. Beginning with the industrial ap-

plication of X-ray testing in the 1930s, various nondestructive methods based on magnetism,

eddy current, ultrasound, and numerous other mechanisms have been employed to inspect the

subsurface properties of structures [8]. The improvement and development of NDT methods

continues to be an active field of research as both the materials under test and the understand-

ing of the physical phenomena of the measurement techniques have evolved over time, facilitated

by improved measurement and processing equipment.

The construction industry is one sector that can benefit greatly from NDT. With an average

age of multiple decades and a projected lifespan reaching up to a century, civil structures require

monitoring to ensure their operability [9]. The civil infrastructure of industrialized countries

constitutes a large part of their national wealth [10, 11], with annual operation and maintenance

costs for the EU’s road infrastructure alone amounting to 38 billion euros in 2016 [12]. The

production of building materials, mainly cement and steel, is responsible for 10 % of global

carbon dioxide emissions [13]. At the same time, the construction industry is also one the

largest producers of waste through scrap and demolition [14]. By extending the service life of

civil structures and thus reducing the need for demolition and reconstruction, NDT benefits

both infrastructure owners and the general public.

Ultrasonic testing (UT) is a category of NDT methods that uses acoustic waves, usually

with a frequency above 20 kHz, for examining specimens. It is used for a multitude of testing

tasks related to structural properties (e.g., thickness, cracks, voids, inclusions) and material

properties (e.g., density, strength, degree of cure) [7]. UT can be applied to any material, but

different materials and settings can impose different requirements on the measurement system.

For instance, the signal frequency influences the detectability of small inclusions in a specimen

[15, 16]. Furthermore, the acoustic signal needs to be coupled into the specimen effectively

enough to allow fast measurements when larger areas are inspected.

There are several challenges in non-destructive testing for civil engineering (NDT-CE), where

UT can be employed to serve a wide range of measurement tasks [17]. Since concrete, the most

common building material, is inhomogeneous and contains aggregates several millimeters in di-

ameter, signals with frequencies below 200 kHz and high amplitudes that can propagate through

1 Introduction

thick structures are usually required [18]. The rugged surface makes it challenging to couple

a transducer to it using a liquid. In addition, the size of the civil structure compared to the

transducer size prevents large-scale measurements from being performed manually in an eco-

nomical manner [18–20]. Furthermore, the measurement system for in-situ measurements must

be resilient to various ambient conditions such as changes in temperature, moisture, vibration,

and dust.

The goal of this dissertation is to address these challenges by developing a method for non-

contact ultrasonic measurements that is facilitated by a novel high sound pressure source and

is applicable in harsh environments. Fluidics, a technology from the 1960s and 1970s, is used

as a platform for a transducer that satisfies these requirements. Since the research presented

was conducted in Division 8.2 – Non-destructive Testing Methods for Civil Engineering of the

German Federal Institute for Materials Research and Testing (BAM), the method development

focused on civil engineering applications. However, literature references and potential use cases

of the presented methods are included that go beyond this specialized field of application. The

following sections briefly review the fundamentals of ultrasonic testing in general (Section 1.2)

and challenges of air-coupled ultrasonic testing in particular (Section 1.3). Concepts of aeroa-

coustic sound generation are then outlined in Section 1.4 and linked to theory of fluidics in

Section 1.5. After presenting the publications that are part of this dissertation in Chapter 2,

their results are summarized and discussed comprehensively in Chapter 3.

1.2 Ultrasonic Testing

Acoustic signals are mechanical waves that are locally excited in an elastic medium and propagate

by exchange of energy. Their frequency fand wavelength λare related by the sound speed c:

c=fλ (1.1)

Ultrasound includes waves with frequencies above human hearing threshold, which is usually

20 kHz [21]. In NDT, ultrasonic waves generally propagate through solid media in which multiple

wave types can be excited and exist simultaneously. Ultrasonic testing came into industrial use

in the 1940s and was aided by the rapid development of electronics, fueled by radar development

for air surveillance. Fast electronics allowed to measure the transit time of ultrasound signals

and relate them to material or structural properties. Although the use of ultrasound for self-

localization of bats was hypothesized decades earlier and various continuous wave techniques

were invented in the 1930s, it was the feasibility of pulsed signal processing that enabled UT.

Several authors have provided a very comprehensive historical overview of the development of

ultrasonic testing [8, 22, 23].

The most commonly used wave types in NDT are pressure, shear, surface and plate waves, all

of which have different propagation speeds [24]. In pressure or longitudinal waves, the particles

inside a medium oscillate along the axis of sound propagation, which is perpendicular to the

wave front. In shear or transverse waves, particle oscillations are directed perpendicular to

the propagation direction because shear forces are transmitted. These two types of waves are

subsumed under the term bulk waves and can penetrate deeply into a specimen. Surface waves,

which include Rayleigh and Love waves, propagate along phase boundaries and penetrate a

body only to a depth of about one wavelength. Plate waves, also called Lamb or guided waves,

require a plate to propagate. Since they propagate dispersively, there are an infinite number of

symmetric and asymmetric modes for any material and thickness.

In NDT-CE, all of these wave types are used for different measurement tasks. The best known

use of Lamb waves is the impact echo technique [25, 26], although the acoustic frequencies used

are usually in the audible frequency range. Rayleigh waves have proven to be a useful tool to

1.2 Ultrasonic Testing

find surface cracks in concrete [27]. Both longitudinal and shear waves are used primarily to find

and quantify internal features of a specimen [28]. However, shear waves are generally preferred

because they are less likely to be converted to other wave types upon reflection if the proper

polarization is chosen [29].

When an acoustic wave encounters a material interface, some sound pressure is usually re-

flected due to differences in the specific acoustic impedance ZFof the propagation media. This

impedance is a function of the material density ρand the sound speed c:

ZF=ρc (1.2)

The portion of reflected sound pressure between two media, described by the reflection coef-

ficient R, is a function of the impedances ZF,1and ZF,2[24]:

R=ZF,2−ZF,1

ZF,2+ZF,1

(1.3)

Conversely, the transmission coefficient is

T=2ZF,2

ZF,2+ZF,1

(1.4)

The reflection of ultrasonic waves at boundaries is a key concept for most UT methods aimed

at detecting large discontinuities with a characteristic size d≫λ. For discontinuities that have a

smaller characteristic size, wave diffraction becomes significant. The resulting scattering, which

is a mixture of reflection and diffraction, is thus more diffuse than pure reflection and contains

components in all spatial directions [30]. For inhomogeneous materials containing inclusions

with d≪λ, scattering is a source of signal attenuation in addition to material attenuation

properties [31].

UT generally uses three different setups, which are sketched in Figure 1.1. They can be

generally divided into pulse-echo techniques and through-transmission techniques. In a pulse-

echo setup, the ultrasonic pulse is emitted into a specimen by a transmitter (Tx), and its echo,

which is scattered by an impedance difference, is subsequently sensed by a receiver (Rx). This

can be done either by the same transducer (see Fig. 1.1a) with normal wave incidence, or

multiple transducers are used in an oblique pitch-catch arrangement (see Fig. 1.1b). In pitch-

catch setups, the time of flight (ToF) of a pulse between Tx and Rx can be used to infer the

depth of a scatterer, since the ToF τtof is related to the propagation path length svia the sound

speed calong the path:

Figure 1.1: Transducer arrangements for ultrasonic testing: (a) single-transducer pitch-catch setup; (b) double-

transducer pitch-catch setup; (c) through-transmission setup. Transmitters and receivers are denoted

Tx and Rx, respectively.

1 Introduction

c=s/τtof (1.5)

While this method allows measurements with only one-sided access to a specimen, it creates

adead zone. This prevents scatterer detection near to the surface because large amplitude

surface vibrations mask incoming echoes. Pulse-echo ToF measurement setups have been used

successfully with all of the previously mentioned wave types [32, 33].

In a through-transmission setup (see Fig. 1.1c), two transducers are located on opposite sides

of a specimen to transmit and receive bulk waves. The ToF of the waves propagating from Tx

to Rx depends on the material thickness and the propagation velocity and can be used infer

either of them. If an inclusion is located on the sound path, the reflection or scattering of the

wave causes a reduction in the received sound pressure and a delayed ToF due to an increase

in the propagation path around the obstacle. While this can be used to indicate an inclusion,

it is not possible to quantify its depth with a through-transmission setup. Unlike the previous

transducer arrangements, this method requires access to two opposing faces of a specimen.

While a known speed can be used to determine specimen thickness, inferring the propagation

speed for a known thickness may yield information about a variety of material properties. For

instance, ToF has been shown to be related to the strength of materials [34, 35], their curing

state [36, 37], their porosity [38], stiffness [39], or fiber orientation [40]].

Apart from ToF measurements, mechanical properties can also be determined by inspecting

additional ultrasonic properties in either pulse-echo or through-transmission mode. For example,

the ultrasonic wave reflection (UWR) method measures the amount of sound pressure reflected

from a surface to infer the specific acoustic impedance (see Eq. (1.3)) and thereby the curing state

of a material [41]. The attenuation of a signal passing through a material can give indications

of the permeability of membranes [42]. Acoustic dispersivity has been used to characterize the

bond between two plates [43]. The elastic moduli of a specimen can be reconstructed from its

frequency response [44].

In ToF measurements, material properties, transducer properties, and the measurement proce-

dure affect the quality of the result. The depth resolution of pulse-echo measurements increases

with bandwidth and center frequency of ultrasonic bursts, which determine whether multiple

reflected pulses are distinguishable from each other [31]. Lateral resolution, the ability to distin-

guish closely spaced features, is limited to half of the acoustic wavelength, known as the Rayleigh

criterion, and the divergence of the transducer’s sound field. Sensitivity, referring to the smallest

detectable feature, is not subject to the Rayleigh criterion. However, it is still influenced by the

wavelength, which defines the dominant scattering regime for different sizes of reflectors and thus

the scattering amplitude and shadowing behavior in pulse-echo and through-transmission mea-

surements, respectively [15]. Small scale scattering from material inhomogeneities reduces the

usable acoustic energy for ToF measurements and adds unwanted bursts to the received signal

[45]. While increasing the transmitted acoustic pressure compensates for material attenuation,

the attenuation due to scattering is scaled accordingly and can only be decreased by lowering

the signal frequency [31]. For UT in concrete, this requires a compromise: the frequency of the

emitted pulse needs to be high enough to faithfully resolve the features of interest, but not so

high as to cause strong scattering from the contained aggregates. Usually, signals with frequen-

cies below 200 kHz are used for ToF measurements using bulk waves [18], and frequencies of up

to 1 MHz have been used for attenuation measurements [36, 46].

Additionally, small lateral specimen dimensions can cause erroneous measurements by pro-

ducing unwanted wave reflections from sidewalls that interfere with the main pulse.

The coupling of the transducers to the material also has a significant effect on the signal

quality [47], as the interface between the transducer and the specimen surface is also subject

to sound reflection (Eqs. (1.2) to (1.4)). If the transducer face is not fully in contact with the

1.2 Ultrasonic Testing

specimen surface, e.g. due to surface roughness or curvature, the sound waves must pass through

the ambient air before entering the specimen, reducing signal transmission almost entirely [47].

It is common to either use a direct coupling transducer or to use a liquid coupling agent at the

interface with ZFclose to the transducer and the specimen to ensure optimal acoustic pressure

transfer. Several fluids are used as a couplant, e.g. petroleum jelly or water [48, 49]. While the

former is generally applied as a thin film between the transducer and the specimen, the latter

is used in settings requiring a larger distance between the two. Measurements with a specimen

immersed in a water tank enables high versatility in transducer positioning without delaying the

measurement time due to the need to manually adjust the coupling.

The ToF is generally assessed by comparing the received pulse with a reference pulse that

has not passed a specimen. A specific feature of the pulse can be selected as a reference, the

occurrence of which in the time signal is then used to mark the arrival of the pulse at the sensor.

These include the first maximum, the first zero-crossing, the envelope maximum or the signal

onset [50, 51]. Another approach is using cross-correlation between the received pulse and a

reference pulse to determine the ToF. The reference pulse can either be measured directly or

calculated based on knowledge about the transducer’s impulse response. This technique, taking

into account the full phase and amplitude information of the pulse, has been shown to give more

exact results than focusing on one single feature and is considered optimal for ToF applications

[52].

The cross-correlation approach also enables the use of pulse compression of the ultrasonic

signal. This technique, which dates back to advances in radar applications in the 1970s [53,

54], uses amplitude, frequency or phase modulation to encode the signal [55, 56]. The modu-

lation techniques allow embedding of additional information into these properties of the signal.

This information can be considered as the signature of an ultrasonic pulse, which increases its

detectability in a noisy signal. A modulated signal s(t) can be expressed as [57]:

s(t) = A(t) cos(ω0t+ϕ0+ϕ(t)) = A(t)g(t),(1.6)

where A(t) is the amplitude modulation function and g(t) contains the angular information.

The carrier signal has a constant frequency ω0and a phase offset ϕ0. Angular modulation

comprises both phase and frequency modulation, which can be achieved by defining ϕ(t) or its

time derivative ϕ

˙(τ), where ϕ(t) = ∫︁t

0ϕ

˙(τ)dτ. Pulse compression schemes using both continuous

and discrete level modulation functions are frequently used in NDT, e.g., chirp signals [58, 59]

or binary codes [60, 61].

If ToF measurements are conducted to determine material or structural properties along a

specified sound path, the ToF information acquired by the above methods may be used directly.

If spatial information is required, the measurement needs to be conducted along a measure-

ment grid. The waveforms recorded at individual measurement points (A-Scans) can then be

concatenated into a B-Scan or further processed using reconstruction algorithms such as syn-

thetic aperture focusing technique (SAFT) [62, 63] or even more advanced techniques [64, 65].

In addition, the simultaneous use of multiple transducers allows beam steering using phased

array technology [66, 67]. However, given the size of civil structures and the considerable time

required to place the transducer on the area to be surveyed, it is only economically feasible to

conduct planar sampling on a fraction of the total surface area. Using air as a coupling agent

would provide the versatility of an automated, contact-free measurement setup in an immersion

tank and would also reduce the measurement time. Besides the aforementioned large impedance

contrast of air and solids, air-coupled ultrasound (ACU) poses several other challenges that will

be discussed in the following section.

1 Introduction

1.3 Air-Coupled Ultrasonic Testing

While water immersion offers enormous flexibility in transducer positioning, it can only be

used if the specimen is not damaged or its properties altered by water contact, which excludes,

for example, many porous materials [68] and art works [69]. Water immersion testing is also

unsuitable for assembled transport vehicles [70] and most civil structures, since they can hardly

be moved or do not fit into immersion tanks. Therefore, it seems advantageous to use as

the immersion medium the medium that usually surrounds these test specimens. In many

applications, this medium is air.

Since the specific acoustic impedance of air (ZF,air = 407 Ns/m3at a temperature of 22 °C

and a static pressure of 1 bar [71]) is usually four to five orders of magnitude below that of

solids [72], almost all acoustic pressure encountered at an air-solid interface is reflected (see

Eq. (1.3)). While this behavior is beneficial in sonar-ultrasound applications, where ultrasound

echoes are used for in-air ranging [73], it poses severe challenges in NDT where the amount of

sound pressure transmitted to the solid is essential. Furthermore, this issue is not limited to

the interface between air and specimen, but also leads to inefficient sound transmission from

the transducer to the air. In addition, in bulk wave ToF measurement, the ultrasonic signal

needs to pass each air-solid interface twice. Thus, reducing impedance losses at these interfaces

is important to increase the signal-to-noise ratio (SNR) of the received signal.

Much of the ACU research is focused on improving the coupling between air and piezoelectric

or capacitive transducers [74], as these types are conventionally used for ultrasound generation

and detection. Piezoelectric transducers make use of the piezoelectric effect, by which certain

materials deform when a voltage is applied to them. By applying a well-defined source signal

to this material, a wide range of ultrasonic frequencies can be produced. Since its inception,

ultrasonics research has been dominated by piezoelectric transducers [23], which includes ACU

applications. However, piezoelectric transducers require a matching layer between the vibrat-

ing surface and the surrounding air. The search for improved materials and designs for the

matching layer is an ongoing research effort, resulting in one-way insertion losses as low as

8.75 dB for a current experimental piezoelectric transducer [75]. Interest in capacitive trans-

ducers, which work by actuating a membrane via electrostatic transduction, as an alternative

to piezoelectric transducers has been fueled by advanced manufacturing capabilities that allow

the production of capacitive micromachined ultrasonic transducers (CMUTs). CMUTs offer

higher bandwidth and better integration with microelectronics than piezoelectric transducers,

while their low-impedance membrane eliminates the need for impedance matching layers [76].

However, the technology is not yet considered mature as it lacks long-term reliability and has

lower transmission efficiency than comparable piezoelectric transducers [77, 78]. Compared to

the aforementioned technologies, alternative non-contact sound generation methods that do not

depend on an oscillating solid and therefore allow for zero insertion loss are comparatively under-

researched. These methods either generate sound at a transducer separated from the specimen

by an air gap, similar to conventional ACU transducers, or aim at generating ultrasound directly

in the specimen material itself. An example for the former sound generation method is the use

of thermoacoustic sources [79]. Ohmic heating of an electrically conductive film causes the air

to expand rapidly locally, leading to an ultrasonic pulse with a main frequency of over 300 kHz.

This signal is generated in the air itself and therefore does not suffer from impedance mismatch.

Transducers using electric discharges generate additional dominant frequencies below 100 kHz

due to ionic winds acting on the surrounding air [80]. These methods require high voltage supply

for ultrasound generation. Methods that induce ultrasound directly at the specimen surface use

electromagnetic waves to transfer the required energy to the specimen, where it is converted to

elastic waves. This eliminates not only the impedance mismatch at the transducer-air interface,

1.3 Air-Coupled Ultrasonic Testing

but also at the air-specimen interface. Methods include laser heating [81–83], microwave excita-

tion [84, 85], and X-ray excitation [86, 87]. Research on these non-contact ultrasound methods

is mainly concerned with medical applications, as they generate high-frequency ultrasound and

come with their own safety concerns. Unlike piezoelectric and capacitive transducers, these

alternative transducers also require their own receiving device, as they are pure transmitters.

Various receiving devices are used to detect ultrasonic signals in double-transducer pitch-

catch setups and through-transmission setups. Aside from microphones, optical methods can be

used to omit impedance mismatches encountered when a pulse exits a specimen. While in-air

interferometric methods remove the interface between the receiving transducer and the air from

the setup [88, 89], the use of a laser Doppler vibrometer (LDV) aimed at the specimen surface

leads to signal detection directly at the specimen-air interface [90, 91], additionally avoiding

transmission loss due to impedance mismatch of the ultrasonic signal leaving the specimen.

Aiming at further SNR improvement beyond the coupling improvements already mentioned,

established methods from contact ultrasound are transferred to the air-coupled domain, such as

pulse compression [92, 93] or the use of transducer arrays for beam steering of the transmitter

[94] and beam forming of the receiver [95].

While sound pressure loss is a prominent drawback of ACU, the different material properties

of the surrounding air and solid specimens have a number of unfavorable implications, especially

for bulk wave techniques. Since the speed of sound in air is an order of magnitude less than

in most solids, the critical angle of the incident ultrasonic wave is narrow. Following Snell’s

law [24], the critical angle θcr is calculated from the ratio of the propagation velocities of the

respective media:

sin θcr =cair

csol

(1.7)

For air-coupled bulk wave testing, the critical angle of longitudinal waves θcr,L is most relevant

since air supports the propagation of pressure waves only. Entering an example concrete with

longitudinal wave velocity cL= 4500 m/s, waves are transmitted only up to θcr,L <4.4°.

Although it has been shown that θcr can be slightly larger than Snell’s law indicates for common

transducers [96], this generally small range of useful incident angles for bulk wave testing shows

that ACU transducers require high directivity to ensure that a large portion of the generated

sound is able to pass the air-specimen interface. The directivity of a transducer can be modeled

as a piston in an infinite baffle [97] and depends on the relation kℓ of the oscillation wavenumber

k= 2π/λ and the characteristic dimension of the piston ℓ. Thus, to obtain a highly directional

sound field, a transducer surface must be used that is large compared to the wavelength. Still,

any finite transducer will generate a non-planar wavefield, which will result in mode conversion

between longitudinal and transverse waves inside the specimen. The resulting mode-converted

waves may be picked up by the ultrasonic receiver and complicate signal analysis.

The difference in propagation velocities between air and solid further restricts the arrangement

of transducers in a pitch-catch setup for ToF measurements. In most applications, the ToF inside

a specimen is much shorter than the incident pulse length, including the following ringing.

Thus, the signal exiting the specimen is superimposed on the signal reflected from the surface.

Since the surface reflection has a significantly higher amplitude (see Eq. (1.3)) than the signal

exiting the specimen, the latter is masked. For this reason, normal incidence single-sided ACU

was designated as infeasible [98]. Yet, oblique longitudinal wave pitch-catch setups have been

presented in which the incidence and exit angles are meticulously chosen and the direct in-air

sound paths are shielded so that superposition is avoided [99, 100].

Due to these restrictions, most applications of ACU ToF measurements involve excitation of

either surface waves and Lamb waves in a pitch-catch [90, 101, 102] or through-transmission

1 Introduction

setup [89, 103]. In NDT-CE, ACU are therefore mainly used to detect surface cracks using

surface waves in-situ [27, 104] or in a more controlled environment to measure material and

structural properties of smaller specimens [105–108]. A review of ACU applications in NDT-CE

up to 2015, with a focus on concrete, was presented by Kaczmarek et al. [109]. Many laboratory

applications of ACU, even outside of civil engineering, involve attenuation [98] or resonance [110]

measurements, which are easier to implement and sufficient for the often thin specimens [111].

As shown in this section, there are still some challenges to enable the use of ACU bulk wave

techniques in NDT. In this thesis, the challenge of acoustic impedance mismatch in ultrasound

generation is addressed. Instead of reducing this mismatch at the transducer-air interface, it is

removed altogether. This is done by generating the ultrasound using airflow instabilities instead

of vibrating surfaces, so that the interface between the generator and the ambience vanishes,

and with it the impedance mismatch.

1.4 Aeroacoustic Sound Sources

In this thesis, the novel approach to produce ultrasound for NDT is based on aeroacoustic

sound generation by a fluidic device. This purposeful use of aeroacoustics is in contrast to

most treatments outside of musical applications, since aeroacoustic sound sources are typically

considered noise. Here, a concise overview of aeroacoustic sound generation mechanisms is

provided, focusing on the known mechanisms for generating ultrasound and their respective

applications.

A basic sound source model is a monopole source, usually inserted as a concentrated fluctu-

ating mass source term m˙son the right-hand side of the linearized mass conversion equation

[112]. The linearized wave equation then becomes inhomogeneous [112, 113]:

∂2p′

∂t2− ∇2p′=∂m˙s

∂t ,(1.8)

where p′is a pressure disturbance. It follows from Eq. (1.8) that aeroacoustic waves are

generated only in case of a fluctuating mass flow injection, as a continuous mass flow injection

with constant m˙swould vanish. Furthermore, Rienstra points out that sound generation in mass

injection is primarily caused by the displacement of the ambient fluid, so that the density of the

injected flow should have little influence on the sound generation [113].

A prominent example of the technical use of mass injection for sound generation is the siren,

in which a rotating plate causes a regular interruption of a static mass flow, causing a continuous

single-frequency sound. Although used primarily for warning purposes [23], an ultrasonic siren

has been developed that reaches frequencies of up to 35 kHz [114].

Furthermore, free jets have frequently been used to generate ultrasound by reinforcing their

instability using aeroacoustic feedback mechanisms. By coupling the instability of the free jet to

the sound generated by its vortices downstream via a sufficiently strong feedback mechanism, a

self-sustaining loop can be created. This feedback loop then amplifies a narrow-band tone related

to the instability mode, flow velocity, and geometric parameters. Since the jet mode needs to be

synchronized with the acoustic wave generated downstream, multiple possible instability stages

can be forced, related to phase shifted integer multiples of the acoustic wavelength. Subsonic

jets require interaction with a solid boundary to establish a feedback loop. While a large

number of subsonic feedback sound generators have been presented [23, 115–118], only edge

tone oscillators have been used to generate ultrasound. They are based on the excitation of an

asymmetric instability mode by the interaction of a jet with a wedge located on the jet axis.

Due to the instability, the jet oscillates over the edge tip and sheds vortices alternately on both

sides of the edge, resulting in a dipole sound field [119]. With this simple arrangement, it is

1.4 Aeroacoustic Sound Sources

possible to generate loud tones with reported frequencies up to 200 kHz [120].

Supersonic jets have been shown to be even more effective sound generators. Given this type

of flow is highly relevant in disciplines such as aerospace engineering, it is still a very active field

of research. Comprehensive review papers on the topic have been published in the past decades

[124–129].

In the case of imperfectly expanded supersonic free jets, the flow directly downstream of the

nozzle is dominated by a pattern of shocks, compression and expansion fans. The two major

sound sources that contribute to the overall sound generation, in addition to the turbulent

mixing sound, are directly linked to this pattern. These sound sources are the broadband shock-

associated sound and the screech, both of which can reach ultrasonic frequencies. Figure 1.2

shows an example of the spectrum of sound generated by a supersonic jet. The broadband

shock-associated sound is the result of the interaction of large-scale turbulence with the tips

of the oblique shocks in imperfectly expanded supersonic flows. Further interactions of Kelvin-

Helmholtz wave packets in the shear layer with the quasi-periodic flow structure can be strong

enough to additionally maintain a feedback loop by enhancing various jet modes at the nozzle

lip, which is called jet screech [130].

When a supersonic jet impinges on a solid wall, additional feedback mechanisms are created

that cause a high-intensity impingement sound [127, 129, 131, 132] with frequencies that are

close to, but distinguishable from, screeching [133]. This impingement sound complements the

sound sources of the free supersonic jet and can also reach ultrasonic frequencies. When the jet

impinges perpendicularly, a stand-off shock develops parallel to the plate wall, while the mass

flow is redirected along the wall. Inside this wall flow, other weak shocks may develop. The

sound-producing mechanisms are believed to originate in the impingement region, where large

vortices and the stand-off shock interact, and in the wall jet region, where vortices interact with

transient shock structures [134, 135]. When the jet is inclined relative to the surface normal of

the plate, no feedback and discrete tone generation were observed, only broadband sound [136,

137]. When the supersonic jet instead emerges along a Coand˘a surface, vortices propagating

in the free shear layer have been shown to interact with oblique shocks formed at a separation

bubble, forming a feedback loop [138, 139].

Supersonic jets impinging on solids were used as sound generators in various types of whistles

Figure 1.2: Schematic of the supersonic free jet spectrum. SPL is the sound pressure level and St =fD/u is the

Strouhal number, composed of the frequency f, the characteristic diameter Dand the flow velocity

u. Figure is based on references [121–123].

1 Introduction

such as the Galton whistle [140, 141] or the Hartmann whistle [142, 143]. The Hartmann whistle,

developed in 1916 [142], is still considered the most effective aeroacoustic sound generating device

[144]. By letting the supersonic flow impinge on a cavity, a resonator is added to the system,

while the stand-off shock at the mouth of the cavity remains and interacts with both the main

flow from a nozzle and the periodic outflow from the resonator. Similar to a jet impinging on a

wall, multiple frequencies can be generated depending on geometry and mode of operation [145,

146]. Frequencies of up to 126 kHz have been obtained in air [147].

Recently, it was shown that it is possible to use the continuous acoustic signal of a Hartmann

whistle for ToF measurements in gas [148, 149]. However, using cross-correlation of a continuous

sinusoidal signal to determine the ToF results in a fairly low signal-to-noise ratio. There is also

the risk of creating standing waves in the specimen when applied to solid specimens, causing

erroneous results [150]. This makes the use of the abovementioned sound generation mechanisms

for ToF measurements for NDT challenging, since they have been described as continuous and

the deviced based on them have also been operated in a continuous sound generation mode.

To improve signal-to-noise ratio and prevent the generation of standing waves, it is necessary

to generate a transient acoustic signal, which requires control of sound-generating fluid flow

in the millisecond to microsecond range. It was precisely this pursuit of high-frequency flow

control that was a thriving field of research in the 1960s and 1970s, termed fluidics. In the

following section, the basics of fluidics and fluidic devices will be briefly explained before linking

the findings from this field to the aim of using an aeroacoustic ultrasound generator for NDT.

1.5 Fluidics

1.5.1 Overview

Fluidics is the “branch of the control technology which uses streams of gas or liquid to sense,

compute, perform logic, and control” [151]. Contrary to conventional flow engineering, fluidics

not only uses the fluid power, but also transmits information via the working fluid. Low response

times and high reliability are aspired to by largely omitting moving parts and instead using

fluid dynamic phenomena for operation [152]. Although devices later referred to as fluidic

were mentioned earlier, [153, 154], the development of a novel fluid amplifier at the Diamond

Ordnance Fuze Laboratories in 1959 is considered the starting point of fluidics technology [155].

Initially referred to as fluid amplification, the term fluidics was coined in 1964 as a combination

of the words fluid and logic [156, 157]. Later, an additional term fluerics was defined to describe

devices that do not contain any moving parts [158, 159] and thus represent a subset of fluidics

that includes membranes or peripherals with moving parts. Since the term fluerics is outdated

and most applications require moving part peripherals, only the more general term fluidics will

be used below.

When fluidics research began, its devices were introduced as an alternative to electronic de-

vices, which were then quite sensitive and expensive [151, 160]. The general idea was to use

a fluid flow in carefully designed channels instead of electrons in a wire to transmit informa-

tion and also to use the mass flow at the system output if necessary. The idea of eliminating

moving parts from fluid handling and replacing electronic circuits with fluidic ones had sparked

the creativity of researchers [155, 161] and still resonates with the unconventional computing

community [162]. This enthusiasm was fueled by the advantages of fluidics technology [155,

163]:

•Fluidic elements can be designed to prevent structural failure due to environmental condi-

tions. Since the components and systems consist largely of channels and cavities in a solid

material, this material can be chosen to withstand harsh conditions. These conditions can

1.5 Fluidics

be extreme temperatures, pressures and vibrations, but also nuclear or electromagnetic

radiation.

•The above advantage also applies to the working fluid. Fluidics can be operated using any

type of fluid, although most applications use air. The use of more demanding fluids, such

as corrosive substances or high-temperature gases, can be facilitated by the choice of an

appropriate material.

•Fluidic elements without moving parts are considered to be virtually maintenance-free,

since no wear occurs on the components, given an appropriate material was chosen.

•Compared to conventional mechanical or electromechanical valves, shorter switching times

are achieved with fluidic controls.

•Fluidic devices do not require explosion proofing for operation in explosive atmospheres

because a hazard of excessive heating due to electrical discharges cannot occur in the event

of malfunction. An exception to this property is the deliberate use of heating in a Hartman

generator to ignite rocket propellants and bombs [164].

In the U.S., fluidics development focused on military and aerospace applications, where dura-

bility in harsh environments was particularly important [165]. Building on the digital fluidic

amplifier, elaborate circuits that could perform complex operations were soon introduced [166–

168]. In the years that followed, numerous other devices were developed for sensing and control

of machinery, as well as for handling hazardous fluids [169, 170]. Although many engineers were

engaged to fluidics research, the technology did not mature fast enough to meet the demands

of the time. Public and private research spending declined [151, 161]. Nonetheless, as research

continued, progress was made in understanding and modelling complex fluidic systems [152,

171]. A second generation of fluidic devices was proclaimed [155] that worked primarily with

laminar flow, contrary to the first generation devices that mainly used turbulent flow. However,

the increased predictability and better signal-to-noise ratio did not help fluidics prevail over

electronic systems, as a number of disadvantages remained [155, 163, 165, 170, 172, 173]:

•Fluidics, being a relatively new technology, could not keep pace with the development of

electronics in terms of reliability, size, and cost with the development of electronics, which

was fueled by the rapid advances in manufacturing capabilities.

•The response of fluidic systems is inherently slower than that of electronic system. In

electronics, the information is transmitted at the electromagnetic wave propagation speed,

while in fluidics it is limited to the speed of sound.

•Most fluidic devices, especially those without moving parts, require constant fluid flow for

operation. This can lead not only to an unpleasant acoustic exposure for operators, but

also to high power consumption.

•Although fluidic devices can be designed to be structurally resistant to harsh environments

and demanding working fluids, their operation characteristics may still be influenced by

factors such as temperature or vibration. Especially for devices based on laminar flow, the

possibility of a laminar-turbulent transition is a hard limit for the operating conditions.

•Second generation fluidics were often analog devices with channels at millimeter scale. This

type of device is prone to strong performance losses in case of clogging due to particles in

the working fluid. The issue of always ensuring adequate air conditioning in an industrial

setting even led the East German VEB Reglerwerke Dresden to completely abandon its

proportional amplifier program in favor of fluidic elements with moving parts [174].

1 Introduction

•The ruggedness of fluidic components does not necessarily apply to peripheral instruments.

In many applications, interfacing the fluidic component to electromechanical or electronic

devices for flow regulation or for processing analog output values is essential.

In general, industrial and academic interest in fluidics faded as its performance gap to electron-

ics grew larger. However, in Eastern Europe, where the electronics industry lagged somewhat

behind the U.S. and Western Europe, moving-part fluidics continued to be used for process con-

trol until the 1980s [152, 174]. Concepts based on power fluidics are also still used in hydraulic

and sanitary engineering for large-scale control of fluid flows [160, 175]. Today, research in flu-

idics is mostly concerned with the use of fluidic oscillators for flow control, e.g., to reduce drag

in automotive [176, 177], aerospace [178, 179], and wind power engineering [180], or to enhance

mixing in combustion processes [181]. In the last two decades, a new branch of fluidics has

emerged: microfluidics. However, since microfluidics is mainly concerned with two-phase flows

at nanometer to micrometer scale, it has its roots in inkjet printing and mass spectroscopy [182,

183]. For the purposes of this work, however, only “millimeter to macroscale fluidic” systems

[184] will be considered.

1.5.2 The Bistable Wall-Attachment Amplifier

One of the many fluid mechanic effects on which fluidic devices are based [152, 165, 171, 185–

187] is the Coand˘a effect [188, 189]. It is essential for the operating principle of the bistable

wall-attachment amplifier, which is mainly used in this work, as it provides fast switching times

of gas flows. The Coand˘a effect describes the deflection of a jet adjacent to a lateral wall. When

a jet is ejected from an orifice into a quiescent environment, it entrains the previously stationary

ambient fluid and creates a secondary flow in the radial direction that feeds the main flow [187,

190, 191]. When a lateral wall is placed close to the jet, the entrainment of the fluid between the

wall and the jet is limited, causing a decrease of static pressure in this area. Due to the emerging

pressure gradient between the two sides of the jet, the jet is redirected toward the wall, where it

subsequently attaches and forms a recirculation bubble between the jet exit and the attachment

point. Using a convex shaped lateral wall, it is then possible to guide the jet along the wall

to change its direction. If the jet is confined by two parallel, equidistant walls, the pressure

difference between the two sides of the jet vanishes and the jet is not attracted to either wall.

If a sufficiently large disturbance is introduced into the flow field, e.g. by turbulence, the flow

may attach to one of the walls and remain there even if the disturbance has dissipated. This

memory property of the Coand˘a effect is exploited in the bistable wall-attachment amplifier.

Figure 1.3a shows the most common internal geometry of bistable wall-attachment amplifiers.

This type of amplifier is also termed a fluidic switch. Both terms are used interchangeably in

this dissertation. The general behavior of these devices can be found in any fluidics textbook,

e.g. in references [152, 171, 187], and is summarized below. The geometry contains a main flow

inlet into which the main flow, also called power jet, is introduced into the device. The flow exits

the device through one of the outlet channels, which are branched off from the main interaction

region using a splitter geometry. Which channel the flow exits through is determined by the

active control inlets through which extra fluid is introduced into the device. When the device

is used as part of a fluidic system, the flow outlets are usually connected to additional fluidic

elements. In this case, additional outlets, called vents or bleeds, are usually branched off from

the main outlets and connected to the ambience to provide stable switching.

For the mainly applied mass flow switching mechanism inside a bistable wall-attachment

amplifier, the recirculation bubble inside the interaction region plays a key role. This bubble is

formed when the power jet attaches to one of the walls due to the Coand˘a effect (see Fig. 1.3b).

The fluid in this bubble is entrained by the power jet, which in turn feeds the bubble with the

1.5 Fluidics

fluid diverging off at the reattachment point, so that equilibrium is established. As additional

fluid is introduced to the system through the control inlets, this recirculation bubble grows

until the main flow is fully detached from the wall (see Fig. 1.3c). As a result, the main flow

moves toward the opposite wall, where it reattaches (see Fig. 1.3d). Due to the Coand˘a effect,

it remains stably attached to this wall even when the control flow is turned off (see Fig. 1.3e).

When the flow exits the device through one of the outlets, a small inward mass flow is generated

through the other outlet due to entrainment effects on the unconfined side of the jet. Several

detailed switching models have been proposed [188, 192–195], but, as Drzewiecki resumed in a

conference discussion: “No matter what kind of device you have or what kind of switch you

have, you must always fill the bubble and you must always pierce the bubble” [196].

The overall response time of bistable wall-attachment amplifiers from the entry of the control

flow into the interaction zone to reaching a stable outflow from the opposite outlet is the sum

of the time intervals required for the three switching phases and the transport time required

for a fluid particle to travel from the power nozzle to the device outlet [197]. In practice, the

response time is about four to ten times the transport time [198]. While mass flow switching

requires the control mass flow to be only a fraction of the power jet’s mass flow in the order of

10 % [186, 194], momentum switching may be achieved if higher control mass flows are applied

[193, 197]. In this case, the momentum of the control flow is sufficient to switch the power

jet past the splitter completely from one attachment wall to the other without requiring to

fill the recirculation bubble. By omitting the recirculation bubble feed, switching occurs faster

than with mass flow switching and approaches the transport time of the fluid through amplifier.

Switching times of less than 50 µs have been reported for amplifiers that use pressure shocks for

switching [197].

The fast and reliable bistable switching was used to develop fluidic oscillators, in which the

flow constantly switches between both outlets. Over the years, numerous oscillator designs have

been presented [199]. One of the most prominent is a modified bistable amplifier in which

Figure 1.3: Schematic and switching process of a bistable fluidic amplifier. (a) 2D sketch of the amplifier with:

S – pressure supply port or main flow inlet, C1 – control port 1, C2 – control port 2, O1 – outlet 1,

O2 – outlet 2, IR – interaction region. (b)-(d) Switching process: (b) in the initial stable state, (c)

recirculation bubble grows when control flow is applied, (d) main flow is fully switched to opposite

outlet, (e) control flow is turned off and flow reaches second stable state.

1 Introduction

the control ports are converted to feedback tubes. The resulting feedback flow alternately

destabilizes the main flow and causes it to switch back and forth between outlets. Similar to

the bistable amplifier, the switching time is a function of fluid properties, flow velocity and fluid

travel path.

1.5.3 Acoustics in Fluidics

Fluidic devices have been used to receive and act on acoustic inputs and generate sounds using

the aeroacoustic mechanisms outlined in Section 1.4 which do not violate the definition of fluidics,

except for the siren.

Examples of binary fluidic devices for acoustic waves sensing are the turbulence amplifier

or the acoustically driven bistable wall-attachment amplifier [200–202]. In the former case, a

laminar-turbulent transition of a free jet is induced by sound exposure to obtain binary states

[203]. In the latter, the switching is induced acoustically by adjusting the input frequency to

the shear layer roll-up frequency of the power jet. Furthermore, analog fluidic elements have

been used to transmit and amplify audible sound as part of an intercom [204, 205]. Ultrasonic

signal generators have been presented for object detection, distance measurements, ignition, and

sensing. To generate a continuous ultrasonic signal, aeroacoustic sound generation mechanisms

have been used, most frequently edge tone generators with one [206] or two edges [206–209] for

sound generation, which have recently been revisited [210]. A different approach employed a

Hartmann generator to produce ultrasound [206]. Taking advantage of the heating effects that

can occur during operation of a Hartmann generator due to acoustic resonances, fluidic devices

have been presented for bomb fuzes and rocket engine ignitions [164]. Hartmann generators

were also used to harvest the energy required for arming bombs [211].

Devices have been developed both for temperature and gas composition measurement, based

on fluidic oscillators whose oscillation frequency changes with the change of fluid properties

[212]. A fluidic oscillator can be considered as a static siren when the outflow is forced to

oscillate between multiple outlets. Few research papers have been published concerning the

sound field of a fluidic oscillator, finding a dipole behavior [213, 214]. In a scaling study on

a specific fluidic oscillator type, a so-called feedback-free oscillator, Tomac and Gregory [215]

provide the only reference of a fluidic transducer that operates stably in the ultrasonic frequency

range.

All of these acoustic fluidics applications rely on continuous waves. An important measure-

ment technique in NDT and the most important technique in NDT-CE is ToF measurement. As

described in the previous section, ToF techniques mainly rely on correlation approaches, which

only give distinct results for transient acoustic signals. The bistable wall-attachment amplifier is

proposed in this work for sound generation as it is designed to trigger singular flow operations,

which in turn can generate a transient ultrasound signal.

1.6 Research Questions

In the previous sections, the main concepts of ultrasonic testing, aeroacoustics, and fluidics were

briefly explained. It is hypothesized that the use of fluidics for ultrasound generation will allow

air-coupled ultrasonic measurements for NDT while avoiding excessive losses due to impedance

mismatch at the transducer-air interface. The bistable wall-attachment amplifier was chosen as

the platform for a fluidic transducer. The concept of using fluidic devices for NDT applications

is novel. Thus, it is necessary to thoroughly analyze its characteristics, explore other ways in

which it might differ from conventional transducers, and compare it to these transducers in a

standard NDT use case. Given its dominant use in NDT-CE, this use case was chosen to be a

1.6 Research Questions

ToF arrangement. The research presented focuses on the application of the fluidic transducer

and leaves aside a detailed investigation of the aeroacoustic mechanisms inside the fluidic switch.

This is treated as a gray box for now, and only knowledge of the internal flow mechanisms of

the device is used. Against this background, the following research questions are addressed

concerning the fluidic transducer:

A. What are the characteristics of the generated signal? It is necessary to first investigate

the acoustic output of the transducer. This concerns characteristics in the time and fre-

quency domains, but also the propagation properties. In addition, since the acoustic signal

generation is accompanied by a transient flow, it is necessary to investigate the interaction

between the two.

B. Can the sound field and flow field be separated? Contrary to most aeroacoustic research,

flow-induced sound generation is desirable in this particular application, while the flow

field may cause issues in the application of the transducer. Thus, a strategy for separating

the sound field from the flow field may improve the transducer performance.

C. Can signal characteristics be used to improve measurement results? Fluidic sound gener-

ation follows mechanisms that are fundamentally different from the principles of conven-

tional ACU generation. Thus, the fluidically generated signal may have properties that set

it apart from those previously investigated and render known signal processing methods

inapplicable. Rather than viewing this as a restriction, it needs to be investigated if the

fluidic signal characteristics can be used to improve measurement results in a way that is

not possible with conventional ACU pulses.

D. What ToF sensing concept can be used in conjunction with the transducer? The fluidic

transducer described in this thesis is a pure actuator and cannot be used to sense ultrasonic

signals. This prohibits measurement setups that are often used in conventional applications

where sensors of the same build are used as transmitters and receivers. Thus, an alternative

sensing setup needs to be conceptualized and tested.

E. Can the transducer be used for measurement tasks in NDT? Finally, it is required to syn-

thesize the previous findings. The applicability of the fluidic transducer for NDT tasks

needs to be proven and compared to conventional transducers.

2 Publications

2.1 Publication I: Experimental analysis of the acoustic field of an

ultrasonic pulse induced by a fluidic switch

Bibliographic Data:

B. B¨uhling, C. Strangfeld, S. Maack, and T. Schweitzer. “Experimental analysis of the acoustic

field of an ultrasonic pulse induced by a fluidic switch”. Journal of the Acoustical Society of

America 149.4 (2021), 2150–2158. doi:10.1121/10.0003937

Version:

Publisher’s version. All article content, except where otherwise noted, is licensed under a Cre-

ative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.

0/).

Experimental analysis of the acoustic field of an ultrasonic

pulse induced by a fluidic switch

Benjamin B€

uhling,

1,a)

Christoph Strangfeld,

Stefan Maack,

and Thorge Schweitzer

Bundesanstalt f€

ur Materialforschung und -pr€

ufung (BAM), Unter den Eichen 87, 12205 Berlin, Germany

FDX Fluid Dynamix GmbH, Rohrdamm 88, 13629 Berlin, Germany

ABSTRACT:

Ultrasonic inspection is a common tool for non-destructive testing in civil engineering (NDT-CE). Currently, trans-

ducers are coupled directly to the specimen surface, which makes the inspection time-consuming. Air-coupled ultra-

sound (ACU) transducers are more time-efficient but need a high pressure amplitude as the impedance mismatch

between the air and the concrete is high and large penetration depth is needed for the inspection. Current approaches

aim at eliminating the impedance mismatch between the transducer and the air to gain amplitude; however, they

hardly fulfill the NDT-CE requirements. In this study, an alternative approach for ultrasound generation is presented:

the signal is generated by a fluidic switch that rapidly injects a mass flow into the ambience. The acoustic field, the

flow field, and their interaction are investigated. It is shown that the signal has dominant frequencies in the range of

35–60 kHz, and the amplitude is comparable to that of a commercial ACU transducer.

C2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons

Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).https://doi.org/10.1121/10.0003937

(Received 11 November 2020; revised 5 March 2021; accepted 8 March 2021; published online 1 April 2021)

[Editor: Michael R. Haberman] Pages: 2150–2158

I. INTRODUCTION

Today, civil infrastructure is estimated to account for

50% of industrialized countries’ assets (Long et al., 2008).

Nevertheless, these structures suffer from aging and degen-

eration, including yearly repair costs of 8.3 10

dollars

only for highway bridges in the United States and 13 10

euros for the whole German transport infrastructure (Koch

et al., 2002;Kunert and Link, 2013). Thus, infrastructure

needs to be inspected regularly for proper maintenance.

Methods for non-destructive testing in civil engineering

(NDT-CE) include, e.g., ground penetrating radar, thermog-

raphy, ultrasonic techniques, etc. (Maierhofer et al., 2010).

Ultrasonic inspection using body waves is commonly and

successfully used to detect damages, determine material prop-

erties, and locate reinforcements in reinforced concrete.

Measurements require a high pressure amplitude to penetrate

specimens in centimeter-to-meter scale. Center frequencies of

less than 100 kHz are typically used to avoid scattering by

aggregates added to the cement (Krautkr€

amer and

Krautkr€

amer, 1990;Popovics et al., 2000), although use of

higher frequencies has been reported (Jacobs and Whitcomb,

1997;Popovics et al.,2000). In industrial practice, an investi-

gator examines critical locations of a structure with a handheld

ultrasonic device that is pressed against a concrete surface for

direct coupling (Schickert and Krause, 2010). While being

commercially available and providing useful high-quality

three-dimensional information of the specimen, this procedure

is time consuming, and thus only selected areas are investi-

gated. Extensive measurements of entire structures are there-

fore too expensive to be economically feasible.

To lift this limitation, air-coupled ultrasound (ACU)

methods are being developed, which would enable fast and

automatable non-contact measurements (Gr€

afe and Krause,

2006). The main challenge in generating ACU is the enormous

amplitude loss of the signal. As a very compliant medium, air

has an acoustic impedance that is about three orders of magni-

tude lower compared to the material of the transducer and that

of the specimen. This leads to high amplitude losses at the

transducer-air and air-specimen interfaces. While the losses at

the latter are a result of the ACU setup itself, losses at the

transducer have been the subject of research since ACU meth-

ods were first applied to non-destructive testing (NDT) in the

early 1970s (Luukkala et al., 1971).

In practice, piezoelectric and capacitive transducers are

most commonly used to generate ACU signals (Chimenti,

2014). Both use pressure-volume work to generate sound.

Piezoelectric transducers use piezoelectric crystals coated

with thin layers for acoustic impedance matching, whereas

capacitive transducers use electrostatically excited mem-

branes to perform this work. Commercially available trans-

ducers suffer a transmission loss of 98.2% of the sound

pressure (Gr€

afe, 2009). While these types of actuators are

still being improved (Hansen et al., 1999;



Alvarez-Arenas

and D

ıez, 2013;Qiu et al., 2015), a third type of resonant

transducers based on ferroelectrets has emerged recently.

These transducers provide low acoustic impedance but have

their optimum center frequency at 250 kHz (Bovtun et al.,

Electronic mail: [email protected]

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ARTICLE

...................................

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2 Publications

2007;Gaal et al., 2019), which is too high for most mea-

surement tasks in civil engineering.

In the past ten years, novel techniques have emerged

aiming at ACU generation without any vibrating surfaces by

utilizing the thermoacoustic effect. Daschewski et al. (2013)

pursued a concept proposed by Shinoda et al. (1999) to gen-

erate ultrasonic pulses by Ohmic heating of an electrically

conductive film results in a single broadband ultrasonic

pulse ranging from 1.2 kHz to 1 MHz (Bente et al., 2018).

By applying an electrode voltage of 1.5 kV, a sound pressure

level of 115 dB is reached at a frequency of 50 kHz

(Daschewski et al., 2013). Kotschate et al. (2018a,b) pro-

posed to combine pressure-volume work with the thermo-

acoustic effect for sound generation by utilizing plasma

discharges. Generating pulses with dominant frequencies

below 100 kHz, this type of transducer reaches up to 137 dB

SPL when operated at a peak-to-peak voltage of 4 kV.

Dai et al. (2013) used a spark source to generate a broad-

band low frequency ultrasonic pulse for impact-echo mea-

surements, reaching 450 Pa when unmodified and more than

3000 Pa when focused using an elliptic reflector.

Further research has used short pulsed lasers to generate

broadband acoustic waves by various mechanisms directly

at the specimen surface, which avoids transmission loss

(Hutchins, 1988) and has also been shown to work for trans-

mission measurements in concrete (Jacobs and Whitcomb,

1997). A drawback of the method is material ablation that

may occur due to the high power laser needed (Davies et al.,

1993). A high power microwave source has also been used

to achieve ultrasonic excitation by local heating (Hosten and

Bernard, 1998;Hosten et al., 2002). X-ray induced ultra-

sound offers another mechanism for non-contact ultrasound

generation (Kim and Sachse, 1983;Tang et al., 2018;

Robertson et al., 2020). Here, the ultrasonic waves are gen-

erated by heating at the defect location itself and therefore

have a shorter travel time in the specimen, decreasing their

damping. The method promises high resolution imaging;

however, high levels of X-ray energy are needed in low

ultrasonic regimes, which may damage the equipment.

In addition to increasing the signal strength for

increased performance of ultrasonic testing, progress has

been made in terms of pulse compression (Purnell et al.,

2004;Berriman et al., 2006;Hutchins et al., 2014;Laureti

et al., 2018) and reconstruction techniques (Mayer et al.,

1990;Schickert et al., 2003;Asadollahi and Khazanovich,

2018), which allow for a strong increase in signal-to-noise

ratio without increasing the emitted pressure amplitude.

The research presented here aims at providing insight

into the sound field of the novel fluidic ultrasonic trans-

ducers. Similar to thermoacoustic and plasma transducers,

fluidic transducers aim at generating ACU without an

impedance mismatch between transducer and the surround-

ing air. However, the working principle is based solely on

volume work and does not require any high voltage supply,

laser safety precautions, and does not cause material abla-

tion or potentially harmful radiation, which may restrict the

use outside a lab environment.

The knowledge about the acoustic characteristics

presented in this study lays the ground work for the develop-

ment of a full NDT system for concrete specimens and fur-

ther development of fluidic transducers for other fields of

application. In Sec. II, fluidics technology is outlined with a

focus on the fluidic switch, which is used in this study to

generate ultrasound, and its properties, that make it particu-

larly suitable for NDT-CE. Section III describes the mea-

surement design that is used to characterize the fluidic

transducer. In Sec. IV, the measured acoustic and flow fields

and their interaction are discussed. The results are compared

to a commercial ACU transducer, which has been used in

NDT-CE in previous studies (Gr€

afe, 2009;Maack, 2012).

II. THEORY

Fluidic devices, although developed in the 1960s

(Warren, 1962a,b;Spyropoulos, 1964), have offered possi-

ble solutions to many modern engineering problems. They

are used in active flow control (Woszidlo and Wygnanski,

2011;Gregory and Tomac, 2013) and research has been

done in the realization of the shockless explosion combus-

tion (Bobusch, 2015) or the generation of microbubbles in

bioreactors (Tesa

r, 2002). Extensive information, history of

fluidic devices, and further examples can be found in the

works of Gregory and Tomac (2013),Tesa

r (2007),

Kirshner and Katz (1975),orBobusch et al. (2013). It has

been shown that fluidic elements may produce significant

characteristic acoustic pressures (Hirsch and Gharib, 2018),

which, however, are considered to be a secondary effect.

While using steady jet noise for ultrasound generation has

been described by McBride and Hutchison (1976), the idea

to generate ultrasound with a controllable frequency content

was patented by Strangfeld and Maack (2018). The first

approach to utilize sound generated by fluidic oscillators in

NDT was presented by B€

uhling et al. (2019).

The fluidic transducer used in this study to generate an

acoustic signal is a bistable fluidic switch (Warren, 1962b).

It allows the rapid switching of a large mass flow of pressur-

ized air (S) between two outlets (O1, O2) by applying sig-

nificantly smaller mass flows at the control ports (C1, C2).

The working principle of the device is presented in Fig. 1.If

a constant supply pressure is applied only to S, the flow will

attach to one of the outlet channels due to the Coand

a effect.

To determine the initial switching state with outflow through

O1, a control pressure is applied to C1 [Fig. 1(a)]. The flow

is then in a stable state that is preserved even when the con-

trol port is turned off [Fig. 1(b)]. To switch the state, the C2

needs to be activated. The main flow from S is then

deflected [Fig. 1(c)] and reaches a new stable state exiting

through the O2 [Fig. 1(d)]. The time that it takes the flow to

switch between the stable states is the switching time ts.Itis

mainly determined by the geometry of the switch, the inter-

nal flow velocity and the pressure applied to the control

ports (Kirshner and Katz, 1975;Rechten, 1976). Thereby,

the influence of the control pressure decreases asymptoti-

cally with the increasing pressure. The pressurized air

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2.1 Publication I

applied to the control ports is regulated by external valves.

The switching time of these valves does not influence ts.

Once the pressure exceeds the threshold needed to detach

the flow from one wall and push it to the opposite one, ts

depends only on the switching behavior of the fluidic switch.

Thus, tsis only limited by the maximum internal flow veloc-

ity that can be achieved and by the size of the device.

Since a fluidic switch allows for rapid switching of

mass flow, it may be used as an ultrasonic generator. When

the outlet ports start to lead the flow into ambient air, the

switching initiates fast insertion of mass. This process is

modelled as an acoustic point mass source. According to

Pierce (2019), the acoustic pressure pat a time tof such

source can be described as

p¼1

4pr

mtr



dt ;(1)

where ris the radial distance from the source, cis the speed

of sound, and _

ðÞis the inserted mass flow function. The

change of mass flow d_

m=dt only takes nonzero values

during the switching process, thus p/1=tsfor a fixed _

and p/_

mfor a fixed ts. The generated acoustic frequency

fdepends on the frequency of _

mðtÞ. During both switching

events, pressure pulses are generated. Switching on produ-

ces a positive mass flow to the ambient air, switching off

produces a negative flow. If we expand this model to a finite

piston in a rigid baffle, we can observe the spherical wave

radiation shifting towards a higher directivity as ka increases

(Pierce, 2007), where k¼2pf=cis the wavenumber and ais

the piston radius.

The wide range of frequencies that are possible to pro-

duce and the absence of an impedance mismatch are the

acoustic advantages of fluidic switches over the existing

transducer technologies for ultrasound generation. Fluidic

devices have further properties that make them suitable for

ACU applications, especially in civil engineering: Fluidic

elements are shock resistant and contain no electrical com-

ponents thus they are well suited for use in harsh environ-

ments. Moreover, they are insensitive to radiation;

temperature changes, however, may affect the switching

properties but not the functionality of the device. As long as

the supplied gas is clean, fluidic switches are also insensitive

to contamination (on a construction site, for example).

Additionally, they are maintenance free due to the absence

of moving parts. No high voltages are needed to generate

high amplitude ultrasound as the device is only powered by

pressurized air.

III. MATERIALS AND METHODS

The fluidic switch studied here was designed by the

company FDX Fluid Dynamix based on the bistable fluidic

amplifier by Bobusch (2015) and manufactured at BAM

(Fig. 2). Static pressures of 1.85 and 1.2 bar were applied

continuously to the S and C2, respectively, pushing the flow

to O2. The pressure applied to C1 was switched between

zero-pressure and 1.4 bar. This configuration enables an

automatic switch back to O1 as soon as the pressure at C1 is

removed. To control the pressure at C1 a Festo MHJ10 sole-

noid valve is used. This device is designed to switch on

within 0.8 ms; however, it has a switching time jitter of

0.24 ms. The pressure on control port 1 was switched on for

a period of 15 ms with a repetition rate of 25 Hz. Only pulses

emitted by switching to outlet 1 are considered here, thus

this state is further referred to as on state. When the flow

goes through outlet 2, it is referred to as the off state. The

complete measurement setup is shown in Fig. 3. The acous-

tic signal was measured using a calibrated 1

=4in. (6.35 mm)

MK301 microphone in combination with a MV302 pre-

amplifier from the company Microtech Gefell, which has an

almost linear impulse response up to 70 kHz and is cali-

brated up to 100 kHz and a sensitivity of 5 mV/Pa. The

expanded uncertainty of the microphone in amplitude and

FIG. 1. (Color online) Switching process of a fluidic switch. The flow is

illustrated in blue. S, pressure supply port; C1, control port 1; C2, control

port 2; O1, outlet 1; O2, outlet 2. The abbreviations apply to all insets.

FIG. 2. (Color online) Fluidic transducer with coordinate system (blue).

Abbreviations as in Fig. 1.

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frequency is 0.15 dB and 0.1 Hz, respectively. As a refer-

ence ultrasound generator, the piezoelectric transducer

NCG100-S63 from the company Ultran Group with active

surface dimensions of 63 63 mm was investigated, which

was driven by an 80 kHz pulse of 100 Vpp. This transducer

uses as a gas matrix piezoelectric composite and is specifi-

cally designed for ACU applications (Kunkle et al., 2006).

Flow measurements were conducted using a one-

dimensional hot-wire from the company Dantec with an

IFA-100 constant temperature anemometer. The hot-wire

was aligned with the z-axis so that the absolute pressure in

the x- and y-direction was measured. Additionally, a Pitot

tube connected to a HDOB005 pressure sensor from the

company First Sensor with a range of 0–5 bar was used for

flow measurement. The Pitot tube was directed in the nega-

tive y-direction so it had a 97.5% accuracy for the mean

flow in the y-direction with a divergence tolerance of 15

(Nitsche and Brunn, 2006). The measurement data were

acquired using a USB-6361 DAQ device from the company

National Instruments. For the measurements, the respective

transducer was moved by an x–y-stage, while keeping the

microphone or the hot-wire probe in the stationary position.

For variations in the z-direction, the microphone was moved

manually.

Microphone measurements were conducted in the nega-

tive z-range since reflectional symmetry was assumed. The

sound measurements of the fluidic transducer had an offset

of z¼20 mm from the acoustical axis. Placing the micro-

phone into regions of high fluid velocities would lead to

damage. The microphone data were corrected for directivity

and frequency response of the measurement system. Flow

measurements were conducted in the z¼0 mm plane only.

The process of switching on and off represents a full

switching cycle, which is repeated 100 times at each mea-

surement position. For the analysis of the acoustic field, four

time intervals containing two switching events and two sta-

ble states were defined. The intervals were held constant for

all cycles at all measurement positions. For switching events

at a certain position, the maximum absolute pressure value ^

was picked from the previously defined intervals and aver-

aged over all cycles. To determine the static noise level, the

standard deviation of the acoustic pressure was calculated

for the stable states, which is defined as

p0¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

i;(2)

where piare the sound pressure amplitudes and Nis the

number of samples. The data shows that 100 repetitions are

sufficient for ^

pand p0to converge.

IV. RESULTS AND DISCUSSION

The setup described above was used to measure the

flow field and the acoustic field of a fluidic transducer. First,

the acoustic field of a commercial piezoelectric transducer is

investigated to provide a reference for the novel transducer

design. Next, the flow field is described, whose characteris-

tics are essential to the following discussion of the acoustic

field of the fluidic transducer.

A. Piezoelectric transducer

An exemplary pulse of the piezo transducer, exhibiting

a40 dB pulse length of 300 ls, is shown in Fig. 4(a). The

ultrasonic pulses have a center frequency of 82 kHz at a

–6 dB bandwidth of 20 kHz, as shown in Fig. 4(b). The pulse

length and bandwidth are in good accordance with previous

measurements (Gr€

afe, 2009). The impulse response of the

transducer exhibits a main lobe and side lobes in the fre-

quency domain, which are not described by Gr€

afe (2009).

This might be a result of the transducer’s aging. Figure 4(c)

shows the acoustic field of the transducer at the center plane

and the sound pressure distribution along the acoustic axis.

The distance of the focal point from the transducer surface

is 220 mm, and the acoustic beam has a divergence of 5,

confirming the results obtained by Gr€

afe (2009) and Maack

(2012). In the focal point the transducer generates a maxi-

mum sound pressure of 155 Pa. The high directivity is

caused by the large transducer area compared to the gener-

ated wavelength of 4 mm.

B. Flow field of the fluidic transducer

The mean flow field of the fluidic switch in the on state

is shown in Fig. 5(a). The maximum velocity of u¼293 m/s

is reached closest to outlet 1, which is presumed to be the jet

exit velocity. Although the inner channel leading to O1 is

perpendicular to the exit plane, the measured jet shows an

inclination of /¼6. This behavior is believed to be a result

of the monostable operation mode and a 4inclination of the

O1 channel with respect to the outlet plane. Nevertheless,

during off state, a lower velocity at O1 is measured, with a

maximum of u¼1.5 m/s, as shown in Fig. 5(b). As known

from literature, this is a suction flow that develops if the flow

is fully switched (Conway, 1971). The omnidirectional dis-

tribution around the outlet supports this assumption (Van

Buren et al., 2017).

C. Acoustic field of the fluidic transducer

Figure 6(a) shows a representative time signal of the

acoustic pressure of two switching cycles, measured at

x;y;z

ðÞ

¼ð0;20;40Þmm. Additionally, four regions of

interest, during both switching periods and in stable states,

are highlighted. Both generated acoustic pulses can be

FIG. 3. (Color online) Experimental setup. Microphone, hot-wire probe,

and Pitot tube were mounted at probe position.

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FIG. 4. (Color online) Acoustic field of the piezoelectric transducer. (a) Impulse response; (b) averaged time signal; (c) acoustic field.

FIG. 5. (Color online) Flow field of the fluidic transducer. (a) On state; (b) off state.

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clearly distinguished from the sound emitted by the jet itself.

Pulses vary in amplitude and location of the peak pressure,

indicating variations in the internal dynamics of the fluidic

switch. The frequency content of the highlighted time inter-

vals averaged over 100 cycles is shown in Fig. 6(b). All

intervals exhibit frequency peaks around 11.5, 17, and

22 kHz, which makes us assume that this is characteristic

noise emitted steadily by the system. In the switching inter-

vals (S1, S2), further frequency peaks are evident around

35, 42, and 56 kHz with bandwidths from 6 to 8 kHz.

Although the pressure amplitude in the range of 30–65 kHz

is slightly raised in the on state, the stationary flow exhibits

no peaks in these intervals. This disparity shows that these

ultrasonic components are only generated during fluidic

switching. The pressure amplitude in the peak frequency

range from 42 to 56 kHz exceeds the static noise in the on

state by 30%–100%.

The acoustic fields of the four regions of interest aver-

aged over 100 actuation cycles are shown in Fig. 7. These

amplitudes are high-pass filtered with a threshold of 20 kHz

to obtain solely the ultrasonic signal. For the switching inter-

vals, the maximum absolute sound pressure ^

pis displayed.

The ultrasonic field of the first pulse [Fig. 7(a)] exhibits

a maximum of ^

p¼162 Pa at 5 mm axial distance from the

outlet in the z¼20 mm plane. Higher values are expected

on the jet axis. The field has a slightly elliptical directivity,

FIG. 6. (Color online) Representative signal generated by the fluidic transducer at (x, y, z)¼(0, 20, 40) mm. (a) Time signal of two switching cycles with

intervals for analysis highlighted; (b) averaged impulse response in the highlighted intervals. S1, switching process 1; S2, switching process 2; On, On state;

Off, Off state.

FIG. 7. (Color online) Averaged acoustic field of the fluidic transducer. (a) Switching process 1; (b) switching process 2; (c) off state; (d) on state. Note that

the color scale for (a) and (b) is different from the color scale for (c) and (d).

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which is consistent with analytical solutions for a finite pis-

ton in a rigid baffle with a ka value from 0.3 to 0.9, where a

is substituted here with the hydraulic radius of the outlet.

The ultrasonic field of the second pulse shown in

Fig. 7(b) exhibits a maximum of ^

p¼121 Pa at 10 mm axial

distance from the outlet in the z¼20 mm plane. Contrary to

the first pulse, the second one exhibits a hollow cone-shaped

directivity. This divergence of the acoustic pressure maxima

is related to the flow field shown in Fig. 5(a) and is consis-

tent with the findings obtained by Choi et al. (2002), who

describe the cone of silence developing when an air jet is

used as an ultrasonic waveguide. A similar situation occurs

when the second pulse is initiated. It is generated if the mass

flow is suddenly switched off and enters the existing flow

field established during the previous switching state. Shin

et al. (2017) have shown that a free jet flow dissipates only

at a timescale of 104s, which is increasing in the flow

direction. Thus, the flow field of the fluidic switch has no

time to fully dissipate during the time of pulse generation.

The speed of sound is not homogenous anymore and

increases radially toward the jet axis. As a result, the ema-

nating ultrasonic pulse diverges from the jet axis, as shown

by Tam and Auriault (1998). In a further development, the

defocusing effect of the jet may be reversed by altering its

density through cooling or the use of a different working

medium as shown by Choi et al. (2002).

Figures 7(c) and 7(d) show the level of static jet noise

in the intervals of the on and off states. The maximum

values are p0

on ¼16 Pa and p0

off ¼14 Pa. When switched off,

the measured acoustic pressure has its maximum region

close to the transducer surface with a slight shift in the

direction of outlet 2. This sound is believed to be the jet

noise emanating from the flow through outlet 2. The acous-

tic field in the on state has a hollow cone-shaped directivity

as seen before in the case of the second pulse. Although the

sound is generated by various mechanisms throughout the

free jet, the same refraction mechanism applies.

V. CONCLUSIONS

This study examines the ultrasonic acoustic field of an

ACU transducer based on a fluidic switch. For the first time,

a pulsed free air jet has been used to generate an ultrasonic

signal. A measurement setup has been designed to investi-

gate both the acoustic field and the flow field throughout the

switching cycle of the device. These results are compared to

a commercial piezoelectric transducer for ACU.

The fluidic transducer generates peak frequencies

around 35, 42, and 56 kHz; however, the generated pulse

shape needs improvement since the non-uniformity of the

peaks complicates precise time-of-flight measurements.

When the mass flow is switched on, the transducer exhibits

an elliptical directivity since its dimensions are of the same

order of magnitude as the generated wavelengths. The ambi-

ent flow is a speed of less than 2 m/s and is directed to the

transducer outlet so that it does not significantly influence

the acoustic directivity. When switching off the transducer,

the ultrasonic signal diverges from the acoustic axis forming

a cone of silence. Here, the ultrasonic signal is ejected in a

decaying free jet with a maximum centerline velocity close

to the speed of sound. The maximum pressure amplitude

generated by the fluidic transducer is slightly higher than the

commercial piezoelectric transducer produces in its focal

point.

The generated frequency range, the amplitude that can

be achieved, and its robustness make the fluidic transducer

presented here a promising tool for ACU inspection in civil

engineering.

ACKNOWLEDGMENTS

The authors would like to thank Navid Nayeri from the

Institute of Fluid Dynamics and Technical Acoustics at TU

Berlin for support with the flow measurements, Mate Gaal

(BAM 8.4) for support with the acoustic measurements,

Stefan Facius (BAM 9.2) for manufacturing fluidic devices,

and Eric Sch€

onsee for helping with the data acquisition.

This work was supported by the German Federal Ministry of

Economics and Technology (BMWi) under the ZIM

(Zentrales Innovationsprogramm Mittelstand) Grant No.

ZF4044222WM7. Concept: B.B., C.S., S.M.; design of

experiment: B.B.; transducer design: T.S.; data acquisition:

B.B.; analysis: B.B.; validation: B.B., C.S., S.M.; original

draft: B.B.; review and editing: C.S., S.M., T.S.;

visualization: B.B.; supervision and administration: C.S.,

S.M.

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2.2 Publication II: Using sonic crystals to separate the acoustic from

the flow field of a fluidic transducer

Bibliographic Data:

B. B¨uhling, S. Maack, and C. Strangfeld. “Using sonic crystals to separate the acoustic from

the flow field of a fluidic transducer”. Applied Acoustics 189 (2022), 108608. doi:10.1016/j.

apacoust.2021.108608

Version:

Publisher’s version. The article is licensed under an Elsevier user license and is protected

by copyright. License information can be found under https://www.elsevier.com/about/

policies/copyright (last accessed November 3, 2023).

Publisher’s link:

https://www.sciencedirect.com/science/article/pii/S0003682X21007027

Technical note

Using sonic crystals to separate the acoustic from the flow field of a

fluidic transducer

Benjamin Bühling

⇑

, Stefan Maack, Christoph Strangfeld

Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12205 Berlin, Germany

article info

Article history:

Received 22 July 2021

Received in revised form 24 November 2021

Accepted 23 December 2021

Keywords:

Air-coupled ultrasound

Sonic crystal

Fluidics

Non-destructive testing

Metamaterial

Bandgap quenching

abstract

Ultrasonic testing is a widely applied measurement method in materials research and medicine.

Commonly, a transducer is coupled to the specimen directly or via a liquid coupling agent. While reduc-

ing acoustic transmission losses significantly, this procedure is time-consuming and cannot be used for

sensitive specimens. Air-coupled ultrasound is a viable alternative in such cases, although suffering from

very high acoustic transmission losses between transducer, air and specimen.

The recently introduced fluidic transducer (FT) generates ultrasound by utilizing the instability of a

supersonic air jet switched inside a fluidic amplifier. Since only air is used as the working medium and

no vibrating surfaces are used for ultrasound generation, the transducer is able to efficiently generate

large acoustic pressure amplitudes. The resulting acoustic field shares its directivity with the ejected

high-velocity air jet. Thus, the acoustic energy needs to be redirected from the jet axis in order to make

the fluidic transducer applicable to sensitive specimens.

In this study, the effectivity of using sonic crystals (SCs) for this redirection is investigated using acous-

tic and flow measurements. SCs are air-permeable while being reflective to large acoustic frequency

bands. It was shown that both a defect waveguide and a mirroring strategy successfully redirected the

acoustic field from the air jet. Furthermore, the interaction of flow and SC showed strong acoustic

quenching if the SC was placed too close to the FT outlet. Blockage of the jet entrainment due to the

SC may result in slightly higher off-axis flow velocities locally, which should be considered in sensitive

applications.

1. Introduction

Ultrasonic testing is a technique widely used in engineering [1]

and medicine [2] to image subsurface structures. When a signal

from an ultrasonic transducer is sent through a material, its

time-of-flight, intensity and spectrum can reveal structural proper-

ties and material parameters. Traditionally, the transducers are

coupled to the specimen directly [3,4] or using gels [1,2] or water

[5,6] to reduce acoustic reflection losses at the interface of the

transducer and specimen. However, the use of a coupling agent

limits the maximum achievable measurement speed and requires

a specimen that allows physical contact with liquids. To overcome

coupling issues and increase testing speed in materials testing, air-

coupled ultrasound (ACU) has been researched since the 1970s,

leading to numerous successful applications [7]. Conventional

ACU methods are based on piezoelectric and capacitive transduc-

ers, which suffer from significant acoustic intensity losses at the

transducer-air interface [7–9]. In recent years, non-contact ultra-

sound based on laser heating has also been applied in medical

research to image bones [10] and tissue layers [11]. While most

applications of ACU concern objects with a resilient surface, such

as engineering materials and to some extent skin, a number of

applications concern fragile or sensitive materials. These include

aerogel plates [12], filter membranes [13,14], textiles [15], art-

works [16], and the human cornea [17]. These applications require

caution since excessive local heating of the specimen may cause

damage to it [11,18].

A novel type of ACU transducer based on fluidics technology

was recently introduced [19–21]. By generating an ultrasonic sig-

nal using a pressurized air flow, it eliminates the intensity loss

encountered when the signal is generated conventionally by a

vibrating surface. It provides high pressure amplitudes without

moving parts or electrical power supply. Furthermore, issues laser

safety and laser heating are eliminated. These advantages over

conventional methods are accompanied by an effect that can con-

stitute a drawback when being applied to soft or sensitive materi-

als: The transducer generates a high-velocity jet when producing

https://doi.org/10.1016/j.apacoust.2021.108608

⇑

Corresponding author.

E-mail address: [email protected] (B. Bühling).

Applied Acoustics 189 (2022) 108608

Contents lists available at ScienceDirect

Applied Acoustics

journal homepage: www.elsevier.com/locate/apacoust

2 Publications

an ultrasonic pulse. While the internal velocity was simulated to

reach 500 m/s [21], a jet velocity of 293 m/s was measured at

the transducer outlet [20], where the sound pressure is also high-

est. This mass flow can affect the properties of fragile specimens

and cause discomfort in medical applications. Due to its aperture,

the ultrasonic field of a fluidic transducer (FT) has a slight directiv-

ity along the flow axis [20]. In order to open a new range of possi-

ble use cases for the FT by making it applicable to sensitive

specimens, the generated acoustic field needs to be deflected from

the flow field.

A conventional setup for deflecting the sound waves would be

the positioning of a sound-hard wall at a desired inclination, which

reflects the waves according to the law of mirrors [22]. This proce-

dure, however, would also deflect the mass flow. A method to

change the acoustic directivity without affecting the flow directiv-

ity is the application of a sonic crystal (SC). Here, the term sonic

crystal is used for an artificial sound hard crystal structure,

immersed in the acoustic working fluid air, to distinguish it from

phononic crystals, in which the crystal matrix is not a fluid [23].

Thus, SCs facilitate that neither does the airborne acoustic signal

cross material boundaries nor does the flow impinge directly on

a straight wall redirecting it. Changing the direction of acoustic

wave propagation can be facilitated by using SC mirrors [24],

defect waveguides [25], or graded SCs [26,27]. Sonic crystal mirrors

behave like rigid mirrors in the sense that most of the acoustic

energy is reflected from the crystal, given the incoming wave cor-

responds to the crystal’s stopband. Defect waveguides allow waves

of the stopband frequency to enter the crystal at the defect location

but force them to follow the defect course, which is highly efficient

[28] and variable [29]. However, the defect width has an impact on

the transmission efficiency and can introduce new stopbands [25].

Graded SCs are structures that have a spatially dependent refrac-

tive index, resulting in a bended plane wave acoustic beam.

The interaction of transient jet flows with SCs has not been well

researched. Only a few studies have been published on SCs in a

steady flow field [30,31], suggesting a bandgap quenching effect

with increasing flow velocity. This quenching effect describes the

decrease in bandgap efficiency due to turbulence induced by the

SC, which creates noise containing frequencies that are supposed

to be filtered out. The sound pressure of such noise can even

exceed the sound pressure reflected from a SC wall, resulting in

negative reflection from the SC.

In this article, experimental research is presented investigating

the possibility of deflecting the propagation direction of ultrasound

from the free jet axis of an FT. The paper focuses only on a two-

dimensional SC mirror and a defective waveguide, since the incom-

ing waves may not be considered as plane waves. In Section 2, the

working principle and signal characteristics of the FT are revisited

before the SC and measurement setup are presented in Section 3.In

Section 4, the experimental results of bandgap quenching, flow

effects, and the redirection characteristics of the SC configurations

are presented and discussed.

2. Fluidic ultrasonic transducer

The FT uses unsteady supersonic airflow to generate ultrasound

and is derived from the fluidic amplifier geometry used by Bobusch

[32].Fig. 1a shows its internal geometry before assembly. The FT

consists of a supply port (S), two control ports (C1 and C2), and

two outlets (O1 and O2). Pressurized air is continuously supplied

into S and exits through one of the two outlet ports at startup.

The flow is attached to the outer wall of the outlet channel and

is in a stable state. The active outlet can be controlled by applying

a mass flow to the corresponding control port. When this control

flow is applied, a recirculation bubble forms in the active outlet

channel, destabilizing the main flow and eventually forcing it into

the opposite outlet channel. There it reattaches to the outer wall

and remains stable even when the initial control flow is turned off.

Fluidic amplifiers were first conceived in the early 1960s [33] to

rapidly switch a fluid mass flow from one outlet to the other,

enabling logic operations using the device’s stable states. In con-

trast, the FT uses the instable process of switching to generate

ultrasound. Fig. 1b shows a representative microphone signal

acquired during one switching cycle. Before the time mark of

t110 ms, the FT is in off state and the flow exits continuously

through O2, resulting in a flow noise with comparatively low

amplitude. When additional pressurized air is applied to C1, the

flow switches and the FT reaches its stable on state. In this state,

the flow noise is increased because the microphone is closer to

O1 than to O2. However, during both switching processes, the

sound pressure reaches peak values exhibiting a characteristic fre-

quency content in the range of 30–60 kHz. The waveforms of the

generated pulses vary randomly for each excitation, giving each

pulse a distinct spectral signature [34]. When switching on, the

ultrasonic pulse is emitted into quiescent air. Given the outlet slit

width L¼4:8 mm, the ratio of wavenumber kand characteristic

length ‘¼L=2 is in the range of k‘¼1:4... 2:7, resulting in an

elliptical directivity if the transducer is modeled as a rectangular

piston in a rigid baffle [35]. When switching off, the ultrasonic

pulse is emitted into the flow field that has been established in

the stable on state. As a result, the acoustic waves propagate away

from the flow axis and the ultrasonic field is defocused [36].A

more detailed discussion of the sound field has been presented in

an earlier study [20]. In the present study, only the undisturbed

signal generated by switching on the FT is considered as its sound

field is independent from the flow field, since the ultrasonic pulse

signal precedes the mass flow [20].

3. Setup

For the SC, 40 mm long circular steel rods were fixed in an alu-

minum plate into which a rectangular grid of blind holes was

drilled to facilitate reassembly for the various deflection configura-

tions. To minimize the influence of out-of-plane reflections in the

two-dimensional setup, the steel rods were fixed to a wall on

one side only. The radius of the steel cylinders was r¼1:5mm

and the lattice constant a¼3:5 mm, leading to a unit cell filling

fraction of ff ¼0:58. The corresponding band structure, calculated

using the plane wave expansion method [37], has a band gap

extending from 45 kHz to 66 kHz.

Mean flow velocities were measured in the constant outflow of

the FT on state. An IFA 100 hotwire anemometer with a custom-

built hotwire probe was used for measurements in x-direction.

The probe was calibrated in a wind tunnel at TU Berlin and time

series of 100 ms at a sampling rate of 1 MS/s were used for averag-

Fig. 1. (a) The internal geometry of the fluidic transducer. S – supply port, C1 –

control port 1, C2 – controlport 2, O1 – outlet 1, O2 – outlet 2. (b) A typical time

signal with the highlighted phases of the switching cycle.

B. Bühling, S. Maack and C. Strangfeld Applied Acoustics 189 (2022) 108608

2.2 Publication II

ing at each position. Flow measurements in y-directions were con-

ducted using a Pitot tube, which is more robust than the hotwire

probe and can be calibrated for higher flow velocities, but is less

accurate for lower flow velocities. More details on the procedure

and the facilities has been published earlier [38]. Sound measure-

ments were conducted using a MK301 measurement microphone

with a MV302 preamplifier (Mictrotech Gefell Company). The mea-

sured sound amplitudes were corrected with the microphone fre-

quency response and bandpass filtered to the 20 kHz–100 kHz

range, which is the calibrated ultrasonic range of the microphone.

The reference case for the various SC configurations was the FT

operated without any interference (configuration A, not depicted).

To assess the influence of a sonic crystal that does not interfere

with the main jet flow, a 3-layer SC wall was positioned parallel

to the main flow direction (configuration B, Fig. 2b). To separate

the acoustic propagation direction from the flow axis, two SC

geometries were placed in front of the FT outlet: first, an SC con-

taining a 90



bent defect waveguide, with a defect width of two

elements (configuration C, Fig. 2c) and second, a 45



mirror (con-

figuration D, Fig. 2d). A photograph of the measurement setup is

shown in Fig. 2e. At every microphone position, N¼60 pulses

were measured and the maximum absolute amplitude is averaged

so that

p¼1

n¼1

maxðjp

jÞ:ð1Þ

The effect of bandgap quenching was investigated by position-

ing the SC lateral wall containing 8 columns and 2 to 4 rows of rods

in front of the transducer outlet (Fig. 3a). The microphone was held

constant at ðx=a;y=aÞ¼ð2;7:7Þwhile the distance in x



-direction

between transducer and SC was varied. The transducer was oper-

ated in steady on state, so that only the sound generated by the

flow and its interaction with the SC was measured. The standard

deviation of the sound pressure was calculated for evaluation.

4. Results and discussion

4.1. Bandgap quenching

Bandgap quenching describes the generation of noise by the

interaction of SC and flow. Given a SC unit cell and steady FT oper-

ating conditions, the only variables that can affect noise generation

are the number of SC rows and the distance x



between FT and SC.

Increasing the number of SC rows increases the flow velocity dissi-

pation inside the SC, while an increased distance broadens and

slows down the jet at impingement. To investigate the bandgap

quenching occurring when an SC is used to redirect the ultrasonic

field of an FT, the microphone was positioned at a fixed position

close to the SC while the number of rows and x



were varied

(Fig. 2a). The results (Fig. 3b) show that the standard deviation of

the noise sound pressure reaches up to 48 Pa and decreases almost

linearly up to a distance of x



=a¼5. For larger distances between

FT outlet and SC, the slope levels off more slowly. Therefore, when

designing an SC for FT applications, it is advisable to position the

first row of elements at least 5aaway from the FT outlet to reduce

bandgap quenching. In configurations C and D, the first row that

the jet impinges on has a distance of x



¼5a, so reduced quenching

effects can be expected. The number of SC layers in axial direction

has no significant effect on the noise level, indicating little contri-

bution from the flow interacting with SC rows 3 and 4.

Fig. 2. Measurement setups. The hotwire probe is moved in the x-direction only,

the Pitot tube is moved in the a-direction only, and the microphone is moved in

both directions. (a) Configuration A: baseline. (b) Configuration B: lateral wall. (c)

Configuration C: waveguide. (d) Configuration D: mirror. (e) Photograph of the

measurement setup in configuration D.

Fig. 3. (a) Setup for evaluation of bandgap quenching. The coloring of the crystal

cells indicates additional layers of the SC. The microphone is held stationary while

the FT is moved away from the SC in x*-direction. (b) Standard deviation of the

acoustic pressure generated by the jet-SC interaction, causing bandgap quenching.

B. Bühling, S. Maack and C. Strangfeld Applied Acoustics 189 (2022) 108608

2 Publications

4.2. Flow velocity

As a reference for the deflection configurations, the flow veloc-

ities along the x-axis at y¼4:4awere measured for the undis-

turbed free jet and an SC wall. The absolute in-plane velocities

are shown in Fig. 4a. For the free jet, the flow velocities are below

¼1:5 m/s, except for an outlier at x=a¼14. This behavior is con-

sistent with the previously measured velocity field [20], which

showed a 6



inclination of the free jet, leaving the surrounding

velocity largely unaffected in the positive y-range.

In configuration B, a velocity of

¼1 m/s was measured close

to the FT outlet plane. It dropped to a minimum of

¼0:5 m/s

at x=a¼2 before climbing to a local maximum of

¼2:3 m/s at

x=a¼6. This velocity distribution was caused by the blockage of

entrainment by the SC. In the x-y-plane, the SC left only a network

of channels with a minimum width of 0:5 mm for the entrained air,

resulting in a pressure loss. Instead of being entrained along the

whole jet axis, the surrounding air was then mainly entrained

through the larger gap between the FT and SC as well as down-

stream of the SC, starting at x=a¼5. The increased velocity com-

pared to the free jet flow, which extended far beyond the last SC

unit cell, indicates that the jet axis has moved in the positive y-

direction while the flow was attached to the SC. This effect coun-

teracted the original jet inclination in the negative y-direction in

the reference case [20].

The flow velocities measured for the deflection configurations

are also shown in Fig. 4a. In configuration D, the flow velocity

was

¼1:6 m/s close to the FT outlet plane and steadily decreased

until it reached a fairly constant value of 0:7 m/s for x=a>9. The

flow did not deviate significantly from the free jet configuration

because the x-coordinate was along the side of the jet that was

not disturbed by the SC mirror. When the flow impinges on the

crystal, it slows down, causing an even lower entrainment, so that

the measured velocity dropped below the reference as the probe

was moved further along x. In configuration C, the flow velocity ini-

tially followed the reference configuration. However, it increased

between 3 <x=a<6 and reached a maximum of 3:4 m/s, which

is more than twice the velocity of the reference configuration.

These coordinates were directly at the outlet of the defect guide,

through which the ambient air was mainly entrained.

To verify that the flow direction was largely unchanged and

only the acoustic propagation was altered, the flow velocity paral-

lel to the FT outlet plane was measured and is shown in Fig. 4b. For

configurations A–C the measurements were conducted along

x¼9aand for configuration D along x¼12a, as the mirror crystal

structure extends further into x-direction. The reference case

shows a typical free jet distribution with a maximum velocity of

80 m/s, shifted by 1:5atowards the negative y-direction. This slight

inclinations is in accordance with earlier results ([20]). The lateral

SC wall interacts with this inclined jet and slows it down to 65 m/s

as a result. When the waveguide SC is placed directly in the path of

the jet, the flow velocity is reduced to only 20% of the reference

case with the characteristic jet distribution still visible. Addition-

ally to the Pitot tube measurements, this configuration was mea-

sured using a hotwire probe, giving comparable results. The axial

velocity measurements behind the mirror configuration shows no

clearly recognizable peak. In this configuration the jet passes one

additional crystal layer, when compared to configuration C, and

the measurement is conducted further downstream. Thus, it is

assumed that the velocity is too slow at this point to be captured

by the Pitot tube, which shows inaccuracies in the single-digit

velocity range for all measurements.

4.3. Acoustic pressure

The resulting ultrasonic fields from the combination of the var-

ious SC arrays are shown in Fig. 6.Fig. 5 presents the maximum

ultrasonic pressure field obtained in previous experiments [20].

These results are qualitatively consistent with the measurements

of the baseline configuration in this study (Fig. 6a). The differences

are attributed to different measurement setups, namely the altered

microphone orientation, the reflection of the SC base plate, and the

measurement plane offset of 20 mm in the previous study.

Since the lateral SC wall has been introduced into the sound

field (Fig. 6b), the acoustic pressure measured behind this wall

was significantly reduced. In the positive y-direction, it was

slightly increased as the undisturbed waves were superimposed

on those reflected at the SC. However, this ultrasonic pressure

increase was small at the investigated measurement positions,

since a large portion of the sound field was reflected undirected

at an obtuse angle to the x-axis. The results show that even a

Fig. 5. Maximum absolute sound pressure amplitudes from previously published

measurements under free-field conditions, acquired in a plane with 20 mm offset to

the outlet plane [20,38]. The colored contours correspond to measurement points in

the x-y-plane that are covered in Fig. 6.

Fig. 4. (a) Absolute flow velocity in the x-direction using only the hotwire

anemometer and (b) in the y-direction using both a hotwire anemometer (solid

lines) and a Pitot tube (dashed lines).

B. Bühling, S. Maack and C. Strangfeld Applied Acoustics 189 (2022) 108608

2.2 Publication II

low number of SC layers can significantly block the propagation

path of the FT signal.

Fig. 6c shows the ultrasonic field when the defect waveguide SC

is placed at the FT outlet. A zone of increased sound pressure was

measured in the negative y-direction, originating in the space

between the FT and SC. The exact cause for this behavior remains

unclear. Unlike the other SC configurations (Figs. 6b and 6d), which

do not exhibit such a prominent secondary lobe, configuration C

contains SC cells in positive y-direction. These are assumed to

cause backscatter of the signal and subsequent leakage in negative

y-direction. In the positive y-direction, the waveguide SC caused a

clear redirection of the acoustic energy. A lobe was formed origi-

nating from the waveguide outlet, which had an inclination of



. This was less than the intended 90



and may be caused by

the low number of SC layers.

When using an SC mirror to redirect the ultrasonic pulse from

the flow (Fig. 6d), the maximum sound pressure exceeded the ref-

erence case while also exhibiting directivity at a 60



inclination.

Here, a larger portion of the acoustic field was directed in the pos-

itive y-direction than in configuration A. Thus, the superposition of

the undisturbed and the redirected portions of the sound field

yields a higher pressure amplitude.

Fig. 7 presents the pulse ultrasonic pressures of all measure-

ment configurations along the coordinate y¼14:5a. The mirror

configuration caused a maximum amplitude increase of 30 % com-

pared to the reference case, while the maximum in the waveguide

configuration was 15 % below the reference. Nonetheless, both

showed a clear directivity that is not evident in the reference case.

5. Conclusions

The fluidic transducer (FT) generates air-coupled ultrasonic

bursts by rapid pulsing of a supersonic air jet. The acoustic field

shares its main axis with the air jet. Thus, the transducer’s usability

in sensitive applications may be limited without further shaping of

the acoustic field. In this study, the use of sonic crystals (SCs) was

proposed to redirect the acoustic field from the jet axis. A defect

waveguide SC and a mirror SC were evaluated concerning their

redirection performance and their interaction with the flow field.

Sound measurements revealed that the ultrasonic pulse is suc-

cessfully redirected off the flow axis by the SCs. The mirror config-

uration increased maximum off-axis sound pressure due to

superposition of the undisturbed and reflected waves. In the defect

waveguide configuration, the ultrasonic pulses were successfully

guided in an off-axis direction by 55



, leading to a more distinct

directivity but lower ultrasonic amplitude than the SC mirror. This

amplitude may be increased in the future by preventing the leak-

age of acoustic energy through the gap between SC and transducer.

When the ultrasonic field was redirected, it was found that an

SC leaves the jet directivity largely unchanged and reduces the

jet axial velocity by 80 %. The radial velocity was reduced where

Fig. 7. Maximum absolute sound pressure amplitudes parallel to the flow axis at

y¼14:5a.

Fig. 6. Maximum absolute sound pressure amplitudes for (a) configuration A, (b)

configuration B, (c) configuration C and (d) configuration D. The dotted lines

indicate the location of the ultrasound pressure profiles shown in Fig. 7.

B. Bühling, S. Maack and C. Strangfeld Applied Acoustics 189 (2022) 108608

2 Publications

the SC blocked entrainment, but increased at SC discontinuities

such as the defect waveguide. At a velocity of 3:4 m/s, this increase

amounts to only 1 % of the undisturbed jet exit velocity. This

flow field behavior suggests that SCs do not significantly deflect

the FT air jet and thus are a suitable means to reshape the ultra-

sonic field of the FT. The noise caused by the interaction of the

jet and SC was found to decrease rapidly as the FT is moved away

from the SC.

Based on these promising results, further research might aim at

increasing the resulting deflection angle of the SC while preserving

high pressure amplitudes. Further SC design optimizations may

account for the influence of the reduced flow velocity on the FT

pulse that is emitted when the flow is switched off and aim utiliz-

ing this pulse as well. Future studies will focus on optimizing the

presented deflection strategies as well as employing advanced 2D

and 3D metamaterials. Achieving a complete decoupling of ultra-

sound and flow directivity will expand the applicability of fluidic

transducers to sensitive specimens such as textiles, art works

and biological tissues.

Declaration of Competing Interest

The authors declare the following financial interests/personal

relationships which may be considered as potential competing

interests: Benjamin Buehling reports financial support was pro-

vided by the German Federal Ministry of Economics and Technology

(BMWi) under the ZIM (Zentrales Innovationsprogramm Mittel-

stand) grant ZF4044222WM7. Christoph Strangfeld has patent

#WO 2018/077759 Al issued to BUNDESREPUBLIK DEUTSCHLAND,

VERTRETEN DURCH DEN BUNDESMINISTER FÜR WIRTSCHAFT

UND ENERGIE, DIESER VERTRETEN DURCH DEN PRÄSIDENTEN

DER BUNDESANSTALT FÜR MATERIALFORSCHUNG UND -

PRÜFUNG, (BAM). Stefan Maack has patent #WO 2018/077759 Al

issued to BUNDESREPUBLIK DEUTSCHLAND, VERTRETEN DURCH

DEN BUNDESMINISTER FÜR WIRTSCHAFT UND ENERGIE, DIESER

VERTRETEN DURCH DEN PRÄSIDENTEN DER BUNDESANSTALT

FÜR MATERIALFORSCHUNG UND -PRÜFUNG, (BAM).

Acknowledgements

The authors would like to thank Navid Nayeri from the Institute

of Fluid Dynamics and Technical Acoustics at TU Berlin for support

with the flow measurements and Mate Gaal (BAM 8.4) for support

with the acoustic measurements. This work was supported by the

German Federal Ministry of Economics and Technology (BMWi)

under the ZIM (Zentrales Innovationsprogramm Mittelstand) grant

ZF4044222WM7.

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B. Bühling, S. Maack and C. Strangfeld Applied Acoustics 189 (2022) 108608

2 Publications

2.3 Publication III: Enhancing the spectral signatures of ultrasonic

fluidic transducer pulses for improved time-of-flight

measurements

Bibliographic Data:

B. B¨uhling, S. Maack, T. Schweitzer, and C. Strangfeld. “Enhancing the spectral signatures of

ultrasonic fluidic transducer pulses for improved time-of-flight measurements”. Ultrasonics 119

(2022), 106612. doi:10.1016/j.ultras.2021.106612

Version:

Publisher’s version. All article content, except where otherwise noted, is licensed under a Cre-

ative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.

0/).

Ultrasonics 119 (2022) 106612

Available online 22 October 2021

Contents lists available at ScienceDirect

Ultrasonics

journal homepage: www.elsevier.com/locate/ultras

Enhancing the spectral signatures of ultrasonic fluidic transducer pulses for

improved time-of-flight measurements

Benjamin Bühlinga,∗, Stefan Maack a, Thorge Schweitzer b, Christoph Strangfeld a

aBundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12205, Berlin, Germany

bFDX Fluid Dynamix GmbH, Rohrdamm 88, 13629, Berlin, Germany

ARTICLE INFO

Keywords:

Air-coupled ultrasound

Fluidics

Signal processing

Pulse compression

MIMO

Hilbert transform

ABSTRACT

Air-coupled ultrasonic (ACU) testing has proven to be a valuable method for increasing the speed in non-

destructive ultrasonic testing and the investigation of sensitive specimens. A major obstacle to implementing

ACU methods is the significant signal power loss at the air–specimen and transducer–air interfaces. The

loss between transducer and air can be eliminated by using recently developed fluidic transducers. These

transducers use pressurized air and a natural flow instability to generate high sound power signals. Due to

this self-excited flow instability, the individual pulses are dissimilar in length, amplitude, and phase. These

amplitude and angle modulated pulses offer the great opportunity to further increase the signal-to-noise ratio

with pulse compression methods.

In practice, multi-input multi-output (MIMO) setups reduce the time required to scan the specimen surface,

but demand high pulse discriminability. By applying envelope removal techniques to the individual pulses, the

pulse discriminability is increased allowing only the remaining phase information to be targeted for analysis.

Finally, semi-synthetic experiments are presented to verify the applicability of the envelope removal method

and highlight the suitability of the fluidic transducer for MIMO setups.

1. Introduction

Ultrasonic measurements are an essential tool in many fields of

science, ranging from medical diagnostics [1] and autonomous vehicle

positioning [2] to non-destructive testing (NDT) of materials. In NDT,

ultrasonic testing (UT) is a common measurement technique used to ob-

tain information about material parameters, structural information, or

to detect flaws [3]. A large number of UT methods have been developed

to this end, involving the measurement of ultrasonic properties such as

amplitude [4–7], spectral information [8–11], attenuation [12–15] or

time-of-flight (TOF) [13,16–18].

In TOF measurements, the time delay of a pulse passing through

a specimen is used to obtain quantitative information about material

properties such as thickness of the specimen or propagation velocity.

While a number of techniques [19–21] have been developed for plate-

like structures to simultaneously measure both thickness and velocity,

in many cases prior knowledge about one is necessary to deduce the

other from the measured TOF. Several factors affect the signal-to-

noise ratio (SNR) of TOF measurements. Besides the absorption in the

material, scattering and dispersion characteristics [22], the transducer

coupling and the signal shape influence the SNR. Coupling directly

affects the transmitted sound intensity, as a significant portion of the

∗Corresponding author.

E-mail address: [email protected] (B. Bühling).

intensity generated by the transducer is reflected at the specimen

surface. To minimize these losses, coupling agents are applied at the

transducer–specimen interface. This preparation is time consuming

and can damage the specimen. Immersing of the entire setup in a

coupling agent, such as water [23], is used to speed up measure-

ments since transducers can then be moved freely to any accessible

surface of the specimen. However, this requires that the specimen be

placed in a water tank and be robust enough not to be affected by

the coupling agent. Such conditions do not exist when testing large

civil structures [18], vehicles [24], or artworks [25]. Regarding time

efficiency and feasibility of immersion, actuating directly into air,

i.e. using air as a couplant, can be considered the optimal choice [26].

Conventional state-of-the-art air-coupled ultrasound (ACU) systems are

based on capacitive and piezoelectric transducers [26]. However, the

sound intensity transmission losses due to impedance mismatches at

both the transducer–air and the air–specimen interfaces are enormous.

For example, the two-way sound pressure insertion loss of a concrete

specimen amounts to −75 dB [27]. The two-way transducer insertion

loss, being −17.5dB for a current experimental transducer [28] or −22.4

for a commercial one [29], is added to that.

https://doi.org/10.1016/j.ultras.2021.106612

Received 9 July 2021; Received in revised form 15 September 2021; Accepted 8 October 2021

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A considerable variety of ultrasound generation approaches have

been proposed to improve or replace capacitive and piezoelectric trans-

ducers. These include improved matching layers [30–32], alternative

transducer materials [33–35], and the use of lasers [36,37], X-rays [38–

40], microwaves [41,42] as well as thermo-acoustic [43–45] or plasma-

acoustic transducers [46,47] for ultrasound generation. Recently, the

fluidic transducer was presented [48,49], which is a completely new

actuation method for ultrasound. The fluidic transducer, based on the

operating principle of a fluidic switch [50,51], generates an acoustic

signal in the low-frequency ultrasound range by rapidly switching

pressurized air from one pressure outlet to another. Generating an

ultrasonic signal using an air flow eliminates the impedance mismatch

between the transducer and the air, offering the potential to achieve

high pressure amplitudes.

A related approach of using continuous flow noise for non-contact

materials testing was presented by McBride and Hutchison [52]. The

signal generated with a fluidic transducer differs in that distinct pulses

with dominant frequency components are generated instead of station-

ary flow noise. Another example of using gas jets in ACU was given by

Choi et al. [53]. They showed that an acoustic signal can be focused

if it propagates inside a jet that has a lower acoustic velocity than

the surrounding air. Applied to the fluidic transducer, this approach

is promising to focus every second pulse generated [48].

The fluidic transducer was originally designed for applications in

NDT of civil structures. In this field, high sound pressures are required

since a high penetration depth is needed for concrete inspection. Fur-

thermore, transducers must be robust against dust, mechanical impacts

and temperature variations, as the measurements are conducted in-situ.

All these requirements are fulfilled by the fluidic transducer [48]. More-

over, the device is robust against electromagnetic fields and radiation,

making it a suitable candidate for ultrasonic applications in further

harsh environments.

The measurement speed, which is the most important parameter for

efficient measurements when using ACU in NDT in civil engineering,

can be further increased by using multi-input multi-output (MIMO)

setups. For this, the signal waveforms need to be quasi-orthogonal so

as not to interfere at the receiver and they should have a high SNR.

However, the SNR of the fluidic transducer signal is in the range of

10 dB, which is comparatively low when the transducer is used in MIMO

mode. Pulse compression (PuC) is a technique that provides both SNR

enhancement and MIMO capabilities.

In first ultrasonic applications of PuC [54–56] in the 1970s, a

random noise signal was used as the coded signal so that correlation

of the input and output signals yielded a peak corresponding to the

time delay. In the early 1980s, it was found that phase modulating

a signal with pseudorandom binary codes, such as Golay codes or

M-sequences [57–59], resulted in more predictable and reduced side-

lobes of the correlation output, with the pulses being repeatable and

quasi-orthogonal. Due to their advantages, binary phase modulation

schemes have been successfully applied and further developed [60–

63]. Other widely used modulation schemes in ultrasonic NDT are

frequency modulated pulses, especially chirped pulses. Linearly increas-

ing or decreasing frequency modulation functions are often used [64],

both in contact [65,66] and air-coupled applications [23,67]. Although

offering an easy envelope and bandwidth control as well as a sharp

correlation peak [64], only two quasi-orthogonal signals can be created,

limiting the applicability of linear chirps in MIMO setups [68]. Given

the widespread availability of chirp generation hardware, Callegari

et al. [68] recently proposed a random frequency modulation method

requiring only minor changes in hardware configuration compared to

a chirp setup. This method essentially refers back to the origins of

pulse compression in ultrasonic testing by correlating a time-limited

noise signal. Additionally, the generated noise-modulated pulses are

quasi-orthogonal, enabling MIMO operation.

The research presented here aims to interpret the signal gener-

ated by a fluidic transducer as a randomly amplitude and frequency

modulated signal and to exploit its intrinsic features for MIMO ap-

plications. In Section 2, the measurement setup is presented and the

signal characteristics of the fluidic transducer are analyzed. Section 3,

the fundamentals of signal modulation are briefly reviewed and the

fluidic transducer signal is discussed in this framework. Based on

this discussion, a signal processing approach is proposed that exploits

the inherent random modulation properties of the fluidic transducer

signal to increase the transducer’s MIMO capabilities. In Section 4,

the performance of the transducer in a realistic measurement setup is

discussed, and a semi-synthetic experiment is performed to assess the

MIMO capabilities of the transducer.

2. Setup, transducer and signal

2.1. Setup

A fluidic transducer is used for the experiments, which has the same

internal geometry as the one used to quantify the acoustic field [48].

The transducer was developed by FDX Fluid Dynamix GmbH (Germany)

and manufactured at the Federal Institute for Materials Research and

Testing (BAM). To increase the signal amplitude, an exponential horn

with a length of 86.6 mm and an exponent 𝜖= 36.6[69] is mounted to

its primary outlet (O1 in Fig. 2). The horn was additively manufactured

using fused deposition modeling. The design goal of the horn was to

improve impedance matching to increase the transducers directivity.

The presented design has a cut-off frequency of 2kHz. Furthermore,

a silencer (AMTE brass silencer by Festo, Germany) is mounted at

the secondary outlet (O2 in Fig. 2) to reduce flow noise when the

transducer is in the off state. The control ports are operated using

fast-switching solenoid valves (MHJ10 by Festo, Germany). The valves

were triggered at a repetition rate of 5 Hz. A calibrated microphone

and an accelerometer were used for the recordings. The frequency

response of the preamplified 1∕4′′ microphone (MK301 and MV302

by Microtech Gefell GmbH, Germany) with a sensitivity of 5mV/Pa

is nearly linear up to 70 kHz and is calibrated up to 100 kHz. The

uniaxial accelerometer (352M66 by PCB Piezotronics, USA) is operated

with a signal conditioner (480B21 by PCB Piezotronics, USA) with a

gain factor of 100 and has a frequency range of up to 60 kHz with a

sensitivity of 11.5 mV/g. For both valve control and data acquisition, a

multifunction I/O device (USB-6361 by National Instruments, USA) is

used. In each setup, 100 pulses were recorded. The data were sampled

at a rate of 500 kS/s.

The experimental investigation is carried out using two setups.

Setup 1 (Fig. 1) is used to obtain the pulse characteristics of the fluidic

transducer, as discussed in Section 2.3. The microphone is placed

directly in the center of the horn mouth to capture the fluidic trans-

ducer signal without defocus effects and with minimal noise. Setup 2

(Fig. 1) is used to evaluate the MIMO capability of the fluidic transducer

in a more realistic setup, discussed in Section 4. The transducer is

directed at a 0.5 mm aluminum sheet. To set up a semi-contact sensor

arrangement [70], an accelerometer is placed on the sheet’s backside

to receive the signal. The reference signal for correlation is acquired by

the microphone, which is located off the acoustic axis to minimize the

interference with the ultrasonic field. The microphone and aluminum

sheet are placed at distances of 70 mm and 255 mm from the horn

mouth.

In both setups, the acquired signals are bandpass filtered with

frequency bounds of (20,100) kHz to capture all ultrasonic components

that can be reliably measured with the microphone, as has been done

previously [48].

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Fig. 1. Setup 1 with microphone directly in front of the horn (a) and setup 2 with microphone off the acoustic axis and accelerometer mounted on an aluminum plate (b).

Fig. 2. Internal geometry of the fluidic transducer used in this study. S — supply port,

C1 — control port 1 (switching on), C2 — control port 2 (switching off ), O1 — outlet

1 (active during on state), O1 — outlet 2 (active during off state).

2.2. Fluidic transducer

The fluidic transducer (Fig. 2) generates an acoustic signal by

causing rapid mass flow variations of pressurized air. Its geometry

comprises a main air supply inlet, two control ports and two outlets.

The supply air inlet operates with constant pressurized air, which leaves

the device through one of the outlets. When an air mass flow is applied

to one of the control ports, the main flow flips to the opposite outlet.

The flow continues to exit through that outlet even when the control

pressure is turned off. The fluidic transducer operates at two stable

states, namely on and off, as well as in the switching of these two states.

The acoustic signal is generated by these switching processes, in which

the mass flow 𝑚 strongly fluctuates when leaving the respective outlet.

Subsequently, this causes pressure fluctuations 𝑝(𝑡, 𝑟)at a radial distance

𝑟as

𝑝(𝑡, 𝑟) = 1

4𝜋𝑟

𝑑 𝑚(𝑡−𝑟

𝑐)

𝑑𝑡 (1)

where c is the propagation velocity [71].

2.3. Signal

Fig. 3(a) shows a representative pulse in the time domain. The

signal is similar to the previously published signal [48] because the

internal geometry of the transducer has changed only slightly and the

horn design dampens only frequencies <2kHz. While the transducer

is stably in off state, the recorded sound pressure consists of low-

amplitude noise induced by the flow exiting through outlet 2. When

the flow is switched to on state, an US peak is measured. The following

higher amplitude noise is caused by the flow exiting through outlet 1

while the on state is stable. After switching off again, the flow returns

to its initial state. Time frames are defined for the on and off states

as well as for the switching process (Fig. 3(a)) The spectra in these

time frames, averaged over all 100 switching processes recorded, are

shown in Fig. 3(b). The generated pulse, covered by the switching

time frame, contains dominant frequencies of around 30.4, 43.1, and

57.4 kHz. These three frequency peaks are distinct compared to the

spectra of the on and off states. This frequency range allows detection

of defects and material parameters at the scale of centimeters in typical

construction materials like concrete or wood [72–74], for which the

fluidic ultrasonic transducer has been developed.

Despite their average characteristic frequency peaks, the individual

pulses generated by the fluidic transducer differ in onset, duration,

and frequency content [48]. Thus, averaging to increase SNR is not

feasible in TOF applications. Additionally, the high amplitude flow

noise generated in the stable states limits the SNR of the pulse. The

extraction of pulse features for TOF estimation, such as the onset or first

maximum [12], is a challenging task under these high noise conditions.

However, using a correlation approach alleviates the difficulties posed

by the aforementioned behavior. Both onset jitter and duration can

be compensated by defining a time window 𝛥𝑡 in which the pulse

is located. It also eliminates the need to pick out pulse features that

may be hidden in the flow noise. The correlation approach is widely

used in PuC methods and provides a framework useful for a deeper

understanding of the fluidic transducer pulses and further utilization

of its characteristic for MIMO applications. Accordingly, the random

behavior of the pulses is interpreted as a non-deterministic amplitude

and angle modulation of the transducer signal, using the framework

provided by earlier studies on random modulation [54–56,68]. Demod-

ulation techniques enable the extraction of unique pulse characteristics

induced by the randomness of the modulation. The quasi-orthogonal

pulses resulting from this signal processing then allow the use of fluidic

transducers in MIMO applications.

3. Signal processing

Given the challenges posed by the previously discussed signal shape,

further signal processing is required to improve TOF results in MIMO

applications. After a brief revision of signal modulation principles and

analytical signals, an envelope extraction method is presented that aims

to reduce the mutual and self-interference of the signal.

3.1. Signal modulation

Commonly, an amplitude and angle modulated signal 𝑠(𝑡)is de-

scribed as

𝑠(𝑡) = 𝐴(𝑡) cos(𝜔0𝑡+𝜙0+𝜙(𝑡)) = 𝐴(𝑡)𝑔(𝑡),(2)

where 𝐴(𝑡)is the amplitude modulation (or signal envelope), 𝜔0the

carrier frequency, 𝜙0the carrier phase shift, and 𝜙(𝑡)is the instanta-

neous phase inducing angle modulation [75]. In audiology, the term

𝑔(𝑡)containing the angle information is called temporal fine structure

(TFS) [76]. Hereafter it will be termed unit envelope signal (UES) as

it is the remainder when the envelope information 𝐴(𝑡)of the signal is

removed. In frequency modulations, such as chirp methods, the angle

modulation is given by the time derivative of instantaneous phase 

𝜙(𝜏),

so that 𝜙(𝑡) = ∫𝑡

0

𝜙(𝜏)𝑑𝜏. Thus, angle modulation includes both phase

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Fig. 3. (a) Microphone time signal of one individual pulse in the time domain and (b) in the frequency domain, averaged over 100 pulses, in setup 1. The colored areas represent

equal length time frames in the on and off states as well as during switching.

and frequency modulation, as one affects the other. In chirp modula-

tions, the signal contains only one frequency component at any instant.

For signals composed of multiple frequency components, the meaning

of instantaneous frequency and phase is not trivial, as presented by

Boashash [77]. One interpretation is that the instantaneous frequency

represents the weighted average of all frequencies 𝑓𝑖that exist at a

given time [78], so that

2𝜋

𝛷(𝑡)

𝑑𝑡 =⟨𝑓𝑖⟩𝑡.(3)

This applies to both negative and positive frequencies, as the energy of

a real signal is equally distributed in positive and negative frequencies.

To find the TOF using a correlation approach, the received signal 𝑠𝑟(𝑡)

is cross-correlated with the transmitted reference signal 𝑠𝑡(𝑡), so that

𝑅𝑡𝑟 =𝑠𝑟(𝑡+𝜏) ∗ 𝑠𝑡(−𝑡)(4)

with

𝑠𝑟(𝑡) = 𝑠𝑡(𝑡) ∗ ℎ(𝑡) + 𝑛(𝑡),(5)

where ∗denotes the convolution operator and 𝑅is the cross-correlation

output. The filter function ℎ(𝑡)contains any filtering along the signal

path (e.g. by the specimen under test or varying frequency responses

of transmitter and receiver) and 𝑛(𝑡)is the channel noise. Neglecting

exterior influences and noise, Eq. (4) reduces to an autocorrelation

𝑅𝑡𝑡 =𝑅𝑡𝑟.

The Wiener–Khintchine theorem states that 𝑅𝑡𝑡 is the inverse Fourier

transform of the power density spectrum of 𝑠𝑡[23]. Thus, the signal

spectrum is shaped in PuC to enhance the correlation result further

by reducing the sidelobe level of the autocorrelation function [23].

If the instantaneous phase or frequency a priori is known, such as in

chirp applications, spectrum shaping can be accomplished by applying

amplitude modulation to the signal. However, if this modulation is

non-deterministic, the envelope of 𝑠𝑡depends fully on the transducer’s

impulse response to an a priori unknown excitation. The envelope can

then have an adverse effect on the correlation output and diminish the

quasi-orthogonality of angle-modulated signals needed to differentiate

between various pulses in MIMO setups (Section 1). Even if the corre-

lation output of the unit envelope signal components 𝑔𝑟(𝑡)and 𝑔𝑡(𝑡)is

small, the correlation of the envelopes side may significantly enhance

the correlation output of the signals in Eq. (4). Inserting Eq. (2) in

Eq. (4), with an envelope function 𝐴(𝑡)that changes much slower than

the respective 𝑔(𝑡), results in [79]:

𝑅𝑡𝑟 =𝑠𝑟∗𝑠𝑡= (𝐴𝑟𝑔𝑟)∗(𝐴𝑡𝑔𝑡) = 𝐴𝑟𝐴𝑡(𝑔𝑟∗𝑔𝑡),(6)

where the time arguments 𝑡and 𝜏of the signal components are omitted

for brevity. Thus, the product of 𝐴𝑡𝐴𝑟can mask a correlation output by

creating secondary peaks where the phase-modulated signal is largely

uncorrelated.

Fig. 4 shows an artificial example of envelope masking. A ran-

dom bandpass signal 𝑔𝑟with an equally distributed spectrum in the

[40,60] kHz interval is amplitude-modulated with a 25 Hz sinusoidal

signal (Fig. 4(a)). When a partition of the unmodulated signal 𝑔𝑟(𝛥𝑡)

is correlated with the whole signal 𝑔𝑟, a clear autocorrelation peak is

found at a time shift of 0 ms (Fig. 4(b)). However, when the modulated

signal is autocorrelated in the same way, the correlation peaks at time

shifts with large envelope amplitude. Assuming that the TOF of a signal

is indicated by the correlation maximum, the amplitude modulation

would lead to a wrong TOF result.

Removing the envelope 𝐴(𝑡)from a signal, i.e. scaling it to unity,

may thus enhance the discrimination of two pulses, which can be

especially useful in random modulation applications. On the other

hand, it may increase the overall noise floor, because the correlation

output of low-amplitude noise is increased relative to high-amplitude

pulse regions. Nevertheless, the pulses’ unique spectral content and the

relations between its components, i.e. the pulse’s spectral signature, re-

mains intact when removing the envelope information. The only linear

operator that leaves the instantaneous phase and frequency unchanged

when the signal power is scaled, e.g. by removing 𝐴(𝑡), is the Hilbert

transform [80].

3.2. Hilbert transform

Following Ktonas and Papp [81], let 𝑠(𝑡)be in the form of Eq. (2).

Since there is an infinite number of pairs of (𝐴(𝑡), 𝜙(𝑡)) satisfying this de-

composition, the concept of analytic signals is introduced. The analytic

signal 𝑧(𝑡)associated with a real signal 𝑠(𝑡)contains only its positive

frequency components and is therefore a complex signal of the form

𝑧(𝑡) = 𝐴(𝑡) exp(𝑖𝜙(𝑡)).(7)

Thus, a unique pair of 𝐴(𝑡) = |𝑧(𝑡)|and 𝜙(𝑡) = arg(𝑧(𝑡)) is obtained, while

the original signal can be fully recovered as 𝑠(𝑡) = Re(𝑧(𝑡)). The Hilbert

transform 𝐻is defined as

𝐻(𝑠(𝑡)) = 1

𝜋∫+∞

−∞

𝑠(𝜏)

𝑡−𝜏d𝑡. (8)

The Hilbert transform is the quadrature component of 𝑠(𝑡)and therefore

eliminates all negative spectral components of 𝑠(𝑡)while doubling

the positive ones. To construct an analytic function 𝑧(𝑡), the Hilbert

transform 𝐻(𝑠(𝑡)) can be used [81], so that

𝑧(𝑡) = 𝑠(𝑡) − 𝑖𝐻(𝑠(𝑡)).(9)

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Fig. 4. Artificial example of envelope masking using a random high frequency bandpass signal and a low frequency envelope (a) and the autocorrelation output of the modulated

and unmodulated signals (b).

Fig. 5. The same signal as in Fig. 3 (top) with its decomposition in envelope

𝐴(𝑡)(middle) and UES 𝑔(𝑡)(bottom).

This relation can then be used to remove the envelope information in

Eq. (2) via Eq. (7), so that

𝑔(𝑡) = cos(arg(𝑧(𝑡))).(10)

Fig. 5 shows the decomposition of the switching region of measured

signal shown in Fig. 3(a) that is acquired by applying the Hilbert

transform. While the signal envelope 𝐴(𝑡)exhibits high amplitudes in

the peak region and lower amplitude in the on and off states, 𝑔(𝑡)is

confined to the amplitude interval [−1,1] since it is defined as a cos

function. Nevertheless, the angle variations manifest in the signal in

𝑔(𝑡)and an abrupt change in angle characteristic can even be observed

visually around the peak region at 𝑡= 173.6 ms.

However, Eq. (9) holds only if the frequency bands of the enve-

lope and phase functions are completely separated, as required by

Bedrosian’s product theorem [77]. If this condition is not met, a unique

analytic signal 𝑧 may still be found as

𝑧(𝑡) = 𝑠(𝑡) − 𝑖𝐻(𝑠(𝑡)) = 

𝐴(𝑡) exp( 

𝜙(𝑡)).(11)

But 

𝐴(𝑡)and 

𝜙(𝑡)must not be considered independent, as it would

be the case for band-separated 𝐴(𝑡)and 𝜙(𝑡). Instantaneous phase and

envelope will overlap and be phase-distorted, and therefore lose their

physical interpretability [77]. Since most measurement signals violate

Bedosian’s theorem, the concept of asymptotic analytic signals was

introduced [82,83]: If the power of the overlapping frequencies become

arbitrarily small, then 𝑧(𝑡)→𝑧(𝑡). This happens when the center

frequency of a tight-band UES 𝑔(𝑡)is sufficiently far away from the band

of lowpass signal envelope 𝐴(𝑡)such that, ideally, 

𝜙(𝑡)→∞[84]. In

practice, however, Hilbert envelope extraction is used even when this

condition is not met [83,85]. This results in mutual information being

contained in 

𝐴(𝑡)and 

𝜙(𝑡)[86,87].

Thus, carrying out a Hilbert demodulation of a measurement signal

to remove envelope masking can be considered a tradeoff between

distortion and possibly improved MIMO capabilities. Hence, Hilbert

demodulation is applied to all recorded fluidic transducer pulses. The

spectral properties of the resulting signal envelope 

𝐴(𝑡)and the UES 𝑔(𝑡)

are evaluated to assess the applicability of Bedrosian’s product theorem.

Fig. 6 shows the average power spectral density (PSD) of 𝑠(𝑡),

𝐴(𝑡)

and 𝑔(𝑡)in the switching region shown in Fig. 3(a), scaled by the

integral signal power. The signal has been lowpass filtered with a lower

bound of 20 kHz before applying the envelope removal. The spectra of

both 

𝐴(𝑡)and 𝑔(𝑡)extend over the whole frequency range, thus violating

Bedrosian’s product theorem. Additionally, the plot shows the relative

cumulative power of 

𝐴(𝑡)and 𝑔(𝑡), with the sum starting at 𝑓= 0 Hz for

the envelope and at the Nyquist frequency 250 kHz for the UES. If the

bands were completely separated, the cumulative powers would have

to touch in their separation interval, since their full cumulative power

would be reached at the band limits. As a result, 𝐴(𝑡)and 𝑔(𝑡)would

not be distorted. In the present case of overlapping bands, there is an

intersection at a frequency of 𝑓𝑐= 27.4kHz at a spectral power of 84%,

meaning that this portion of the spectral powers at 𝑓𝑐is band separated.

Comparing the PSDs of the original signal and the UES, both signals

still show similar frequency peaks, while deviating slightly in amplitude

over the whole frequency range. With a significant amount of power

being band-separated and the frequency peaks of the spectra coincide,

it is concluded that the pulse characteristics are preserved qualitatively

when the signal envelope information is removed.

3.3. Mutual and self-interference

When correlation is applied for TOF estimation in MIMO setups,

both mutual and self-interference of the pulses need to be considered.

Mutual interference describes how similar the generated pulses are. If

they are very similar, like the pulses produced by a capacitive trans-

ducer with no modulation, their cross-correlation is high and successive

pulses are indistinguishable from each other. If the pulses have an

ideally orthogonal basis, a nonzero correlation results only if the sent

and received pulses are the same, i.e., the signal is autocorrelated. If the

cross-correlation is very small compared to the autocorrelation of the

pulse, successive pulses have little mutual interference and are consid-

ered quasi-orthogonal. Self-interference describes how clearly the TOF

can be identified when the received pulse is correlated with the corre-

sponding reference pulse. Small sidelobes indicate low self-interference

as a high peak-to-sidelobe ratio reduces ambiguity concerning the

correlation peak. The effects of Hilbert envelope extraction method on

the mutual and self-interference of the fluidic transducer pulses are thus

investigated.

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Fig. 6. Relative power spectral density and cumulative power averaged over all

recorded pulses.

Fig. 7. Interference of one switching region, the third of the pulse train, with the first

50 switching cycles of the fluidic transducer in setup 1. The plots show the correlation

of the original signal (top), the unit envelope signal (middle) and signal envelope

(bottom).

Fig. 7 shows the correlation outputs of the original signal 𝑠(𝑡),

the signal envelope 

𝐴(𝑡), and the UES 𝑔(𝑡)when the switching region

of a single pulse (which is the 3 ms region highlighted in Fig. 3(a)

and shown in Fig. 5) is correlated with a pulse train containing 50

pulses. The original and envelope correlations show several correlation

peaks at the time of switching. The multiple peaks in the original

signal correlation output also indicate mutual information between

the successive pulses. This is mainly contained in the signal envelope.

While the UES correlation has only a noise floor everywhere except

at the signal location, the envelope correlation has multiple peaks at

all pulse locations. The envelope correlation even exhibits a maximum

at the arrival time of a later pulse, highlighting the effect of envelope

masking on mutual interference as given in Eq. (6).

To obtain more information on the mutual interference statistics of

the signal components, all 100 recorded pulse switching time frames

were individually correlated with the whole signal, as shown in Fig. 7.

A histogram of the maximum mutual correlation amplitudes relative

to their respective auto-correlations is shown in Fig. 8. The lower the

relative correlation maxima, the higher is the orthogonality of the

individual pulses. The original signal has a mean mutual interference of

−8.9dB with a standard deviation of 2dB. The UES has a significantly

lower mean of −11.9dB with a standard deviation of only 0.6 dB. The

envelope signal has the poorest performance with a mean of −1.6dB

and a standard deviation of 1.3 dB. Misidentification of a pulse or its

Fig. 8. Histogram of the maximum dB modulus of all mutual interferences calculated

as shown in Fig. 7.

echoes in a MIMO setup is thus more likely if the original signal or its

envelope is used for correlation rather than its UES.

The averaged correlation output of the peak region signal with the

data of the whole switching cycle (Fig. 9(a)) highlights both adverse

and beneficial effects of envelope masking on the self-interference in

the original signal. While the switch is turned off, the signal received

by the microphone has low amplitude, thus the average correlation

modulus gives low values around −40 dB. It peaks at the pulse arrival

time, as the correlation reduces to the autocorrelation close to 𝑡=𝜏.

While the transducer is in on state, the correlation modulus takes values

<− 30 dB since the average amplitude of the signal is higher than in

the off state. When this amplitude information is removed by envelope

extraction, the state of the fluidic transducer does not influence the

correlation output, giving an average noise floor of around −30 dB. This

output is higher than in the case of correlating the original signal, thus

the inherent envelope masking improves the SNR at large time delays.

Near the autocorrelation peak (Fig. 9(b)), envelope removal increases

SNR, reducing sidelobe amplitude by 1.6 dB. The correlation sidelobe

locations vary slightly between the original and demodulated signal due

to the slight change in frequency content shown in Fig. 6.

4. Results and discussion of multisensor setup

The previous results have shown that interpreting the fluidic trans-

ducer signal as an amplitude and angle modulated signal and re-

moving its envelope yields advantages, concerning both mutual and

self-interference. To assess the effectivity of this approach in a more

realistic setup, the same procedure was applied to the results obtained

using measurement setup 2, which includes a thin aluminum plate as

the specimen and an accelerometer as the receiving sensor. By using

different sensors the performance of the envelope removal method is

investigated, when sensor frequency responses and sensitivities differ.

No measurable TOF change is induced by the aluminum sheet due to

its thickness. A semi-synthetic experiment was then designed using the

measured data to induce a variable artificial time lag and investigate

the performance of the fluidic transducer in MIMO arrangements.

4.1. Pulse characteristics

Although the pulse is clearly distinguishable from the stable states

of the fluidic switch, the SNR of the accelerometer signal is lower than

that of the microphone signal (Fig. 10(a)). This is attributed to various

factors that additionally influence the accelerometer signal: flexural

waves and lamb waves of the aluminum plate as well as the lower

sensitivity compared to the microphone. This behavior also becomes

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Fig. 9. Self-interference in setup 1 (a) through the part of the switching cycle and (b) zoom to the correlation peak area.

Fig. 10. (a) Microphone and accelerometer time signals of one individual pulse in time domain and (b) accelerometer signal in the frequency domain, averaged over 100 pulses,

in setup 2. The colored areas represent equal length time frames in on and off states as well as during switching.

apparent when comparing the frequency domains of the accelerometer

(Fig. 10(b)) and the microphone signal (Fig. 3(b)). While the frequency

peaks are even more distinct in the switching region, their amplitude

difference from the on and off states is reduced in the time signal.

Furthermore, the main part of the additional noise is measured to occur

at frequencies <40 kHz.

While the near sidelobes of the correlation result do not differ

significantly between the original signals and the envelope-extracted

signals, the far sidelobes are successfully attenuated by the reduced

masking of the self-correlation result, as can be seen in Fig. 11(a). The

overall peak-to-sidelobe ratio is significantly reduced compared to the

pure microphone signal in Fig. 9(b). This is a result of the microphone

signal being a sub-optimally matched filter to the accelerometer signal.

The mutual interferences of all pulses are shown in Fig. 11(b). The

results for the signal envelope are omitted as they were shown to

give poor correlation results in Section 3.3. The average correlation

modulus was reduced to −6.5dB and −7.5dB for the original signals

and the UES, respectively. Their standard deviations are 2.3 dB and

0.9 dB, respectively. Thus, the mutual interference of the two signals

in a realistic setup has been increased, while the difference in mean

mutual interference has been decreased, i.e., the benefit of envelope

removal has been reduced. This is attributed to receiver channel noise

and varying sensor cut-off frequencies, which reduce the contribution

of the spectral signature to the correlation output. Nonetheless, even

when using sensors with different frequency responses the source pulse

could be distinguished more clearly from other pulses by using the UES

than by using the original signal for correlation.

4.2. Semi-synthetic experiment

In a MIMO setup, every receiver records a signal 𝑠𝑟(𝑡), which is a

sum of multiple transmitter signals 𝑠𝑟,𝑗 (𝑡). The signals contained in 𝑠𝑟

did not necessarily arrive at the same point in time as different material

properties in their propagation paths, sensor locations, or jitter in the

pulsing may resulted in different TOFs. These same parameters may

also result in attenuation of 𝑠𝑟,𝑖. For the experiment 𝑛= (2,4), the

signals recorded in setup 2 were scaled and time-shifted to generate

these synthetic mixed signals so that

𝑠𝑟(𝑡, 𝛼, 𝜏) = 𝑠𝑟,0(𝑡) + 𝛼

𝑛

∑

𝑗=1

𝑠𝑟,𝑗 (𝑡+𝑗𝜏),(12)

where 𝛼is a scaling factor modeling attenuation, and 𝜏is the time

shift of the added signals. Fig. 12 shows the construction of a signal

according to Eq. (12). In Fig. 12, two signals are added, where the

second is scaled by 𝛼= 0.4. The resulting combined signal shows a

large resemblance to the unattenuated signal component. In Fig. 12(b),

three signals are added, which are time-shifted from their preceding

signal by 𝜏= 0.2 ms. The combined signal shows that time shift makes

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Fig. 11. Self and mutual interference in setup 2. (a) Averaged self-interference zoomed to the correlation peak area. (b) Histogram of the maximum dB modulus of all mutual

interferences.

Fig. 12. Examples of the construction of semi-synthetic MIMO signals. (a) Two signals with different scaling factors 𝛼(top) and the corresponding combined signal (bottom). (b)

Three signals with time shift 𝑗𝜏 (top) and the corresponding combined signal (bottom).

it more difficult to visually identify the first pulse in the combined

signal. To find the TOF of the first arriving pulse, the combined

signal is correlated with the microphone reference signal of the first

pulse so that 

𝑅𝑠𝑡 =𝑠𝑟(𝑡) ∗ 𝑠𝑡,0. To validate that the TOF was found

correctly, the correlation maximum of 

𝑅𝑠𝑡 was compared with the

maximum of the respective unmodified signal pair 𝑅𝑠𝑡,0=𝑠𝑟,0∗𝑠𝑡,0. To

exclude dependence of consecutive pulses, 1000 combinations of 𝑠𝑟,𝑗

were pseudo-randomly sampled. To assess the applicability of fluidic

transducer signals in MIMO setups, the true-false ratio of the correlation

maxima as well as the mean TOF error associated with the erroneous

maxima were compared.

Figs. 13 and 14 show the results of the synthetic MIMO experiments.

The TOF estimation error is highly dependent on the time shift between

the combined signals. For both the original and the envelope-extracted

signals, the number of incorrectly estimated signals was highest at small

time shifts. When 𝑠𝑟(𝑡)contains two signals, the true-false ratio reaches

a minimum of 0.65 for the unmodified signal and 0.83 for the UES

(Fig. 13(a)). For 𝑠𝑟(𝑡)containing four signals, these fractions decreased

to 0.4 and 0.55, respectively (Fig. 14(a)). The fractions increased with

the delay of the successive signals and reached a plateau at time

shifts larger than 1–1.5 ms with values above 0.9, which approximately

represents the duration of the pulse, shown in Fig. 3. At these large

time shifts, the pulse signals superimposed with largely lower ampli-

tudes and different frequency contents, so that there was little mutual

interference. For all time shifts, the true-false ratio decreased further

when the successive pulses were attenuated, reducing their influence in

terms of both spectral signature and amplitude. The TOF error of the

misidentified pulses showed a similar trend. In general, the absolute

errors were higher in the small-shift region, where there was larger

mutual interference between the pulses. For two successive pulses

(Fig. 13(b)), the mean TOF error was below 12 μs for the unmodified

signal and below 6 μs for the UES for all time shifts investigated, except

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Fig. 13. (a) Accuracy for the semi-synthetic experiment using 2 subsequent pulses and (b) mean error of inaccurately identified TOFs.

Fig. 14. (a) Accuracy for the semi-synthetic experiment using 4 subsequent pulses and (b) mean error of inaccurately identified TOFs.

for one outlier. The cause of the spike of the unattenuated original

signal at a shift of 1.44 ms is unclear. As the signal is attenuated, the

mean error reduced. Furthermore, the advantage of correlating the UES

decreased for 𝛼= 0.8and reversed for 𝛼= 0.4at low level. When

a received train of four pulses was synthesized (Fig. 14(b)), the TOF

error of the unmodified signal increased with time shift up to 400 μs

as the following pulses gave higher correlation results than the first,

until a sharp drop at high shifts. When UES was used for correlation,

the TOF error increased even further by an order of magnitude before

dropping to single digits. Even considering the higher true-false ratio,

envelope extraction results in a less accurate TOF estimate in the four-

pulse MIMO setup. Thus the choice of the number of transmitters and

receivers in a MIMO setup is highly dependent on the noise situation

in the application and the required accuracy. If the received pulses

are expected to have similar amplitudes and arrival times, only a few

number of transducers should be used. In case multiple receivers are

placed at a sufficient distance so that the pulse amplitude and TOF

differ largely, more transmitters may be used. In all cases, removing

the envelope causes an increased true-false ratio for small TOF shifts,

compared to the original signal.

5. Conclusions

In this study, the mutual and self-interference characteristics of the

novel fluidic transducer and its suitability for MIMO applications were

investigated. To this end, the fluidic transducer signal was interpreted

as a random amplitude and angle-modulated signal.

Using only the acoustic signal in air, the signal envelope has a signif-

icant influence on the mutual interference of the pulses. Removing the

amplitude information using Hilbert envelope extraction leaves only

the pulses’ spectral signature with a unit envelope. The remaining angle

modulated pulses are quasi-orthogonal. The mean mutual correlation

maximum was reduced by 3dB and its standard deviation by 1.4 dB,

indicating a significant increase in the discriminability between pulses.

Furthermore, the self-interference close to the correlation maximum

was slightly reduced. However, removing the envelope information

resulted in a noise floor increase from −40 dB to −30 dB outside the

peak range of the fluidic transducer signal.

This behavior was confirmed in a second setup. The signal was

transmitted through a thin aluminum sheet, the reference pulse was

measured with a microphone whereas, while the received signal was

recorded with an accelerometer. Significantly less mutual interference

was found. However, the advantages of envelope removal were less-

ened when noise was present in the received signal. Using the same

measurement data, semi-synthetic experiments were realized to simu-

late receiving multiple pulses by the accelerometer in a MIMO setup.

For pulses arriving in close succession, the unit envelope signals consis-

tently had a higher detection rate of the correct correlation maximum.

The results also showed the sensitivity of the UES correlation to channel

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noise, resulting in larger average TOF estimation errors as the number

of received pulses was increased. Thus, depending on the application,

the fluidic transducer is suitable for MIMO applications when the SNR

is high, the number of transmitter–receiver pairs is low, or they are far

enough apart to reduce interference amplitude.

The advanced signal processing presented here increases the signal-

to-noise ratio by an additional 3 dB. Furthermore, the fluidic devices

are very robust, require only pressurized air, are maintenance-free

and thus highly applicable even in harsh environments. These new

transducers in combination with the optimized TOF computation make

it a very promising method for air-coupled ultrasound in NDT. Future

research will investigate the applicability of the fluidic transducer and

the here presented demodulation method to various NDT tasks.

CRediT authorship contribution statement

Benjamin Bühling: Conceptualization, Methodology, Investiga-

tion, Validation, Formal analysis, Visualization, Writing – original

draft, Software, Data curation. Stefan Maack: Supervision, Project

administration, Writing – review & editing, Funding acquisition.

Thorge Schweitzer: Resources, Writing – review & editing.

Christoph Strangfeld: Supervision, Project administration, Writing

– review & editing, Funding acquisition.

Declaration of competing interest

One or more of the authors of this paper have disclosed potential or

pertinent conflicts of interest, which may include receipt of payment,

either direct or indirect, institutional support, or association with an

entity in the biomedical field which may be perceived to have potential

conflict of interest with this work. For full disclosure statements refer

to https://doi.org/10.1016/j.ultras.2021.106612. The Federal Institute

for Materials Research and Testing (BAM), the employer of B. Bühling,

C. Strangfeld, S. Maack, is holding a patent concerning air-coupled ul-

trasound generation using fluidic oscillators [32] of which C. Strangfeld

and S. Maack are the inventors. T. Schweitzer is employed by FDX

Fluid Dynamix GmbH, a company that develops and sells fluidic-based

products.

Acknowledgments

The authors would like to thank Mate Gaal (BAM 8.4) for support

with the acoustic measurements and Christian Köpp (BAM 8.2) for his

helpful feedback.

Funding

This work was supported by the Federal Ministry for Economic

Affairs and Energy (BMWi) under the ZIM (Zentrales Innovationspro-

gramm Mittelstand) Grant No. ZF4044222WM7.

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2.3 Publication III

2.4 Publication IV: Development of an Accurate and Robust

Air-Coupled Ultrasonic Time-of-Flight Measurement Technique

Bibliographic Data:

B. B¨uhling, S. K¨uttenbaum, S. Maack, and C. Strangfeld. “Development of an Accurate and

Robust Air-Coupled Ultrasonic Time-of-Flight Measurement Technique”. Sensors 22.6 (2022),

2135. doi:10.3390/s22062135

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Citation: Bühling, B.; Küttenbaum, S.;

Maack, S.; Strangfeld, C.

Development of an Accurate and

Robust Air-Coupled Ultrasonic

Time-of-Flight Measurement

Technique. Sensors 2022,22, 2135.

https://doi.org/10.3390/s22062135

Academic Editor: Marco Carratù

Received: 8 February 2022

Accepted: 7 March 2022

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sensors

Article

Development of an Accurate and Robust Air-Coupled

Ultrasonic Time-of-Flight Measurement Technique

Benjamin Bühling * , Stefan Küttenbaum , Stefan Maack and Christoph Strangfeld

Bundesanstalt für Materialforschung und -prüfung, Unter den Eichen 87, 12205 Berlin, Germany;

[email protected] (S.K.); [email protected] (S.M.); [email protected] (C.S.)

*Correspondence: [email protected]

Abstract:

Ultrasonic time-of-flight (ToF) measurements enable the non-destructive characterization of

material parameters as well as the reconstruction of scatterers inside a specimen. The time-consuming

and potentially damaging procedure of applying a liquid couplant between specimen and transducer

can be avoided by using air-coupled ultrasound. However, to obtain accurate ToF results, the

waveform and travel time of the acoustic signal through the air, which are influenced by the ambient

conditions, need to be considered. The placement of microphones as signal receivers is restricted

to locations where they do not affect the sound field. This study presents a novel method for in-air

ranging and ToF determination that is non-invasive and robust to changing ambient conditions or

waveform variations. The in-air travel time was determined by utilizing the azimuthal directivity

of a laser Doppler vibrometer operated in refracto-vibrometry (RV) mode. The time of entry of the

acoustic signal was determined using the autocorrelation of the RV signal. The same signal was

further used as a reference for determining the ToF through the specimen in transmission mode

via cross-correlation. The derived signal processing procedure was verified in experiments on a

polyamide specimen. Here, a ranging accuracy of

0.1 mm and a transmission ToF accuracy of 0.3

were achieved. Thus, the proposed method enables fast and accurate non-invasive ToF measurements

that do not require knowledge about transducer characteristics or ambient conditions.

Keywords:

air-coupled ultrasound; laser Doppler vibrometer; refracto-vibrometry; acousto-optic

effect; time-of-flight measurements; in-air ranging; non-destructive testing

1. Introduction

Ultrasonic time-of-flight (ToF) measurements are a common technique in many re-

search and industrial fields, spanning from ranging applications [

–

] to human-computer

interaction [

] to non-destructive testing (NDT) of materials [

–

]. The basic concept of

ultrasonic ToF measurements is that a signal is transmitted from an ultrasonic transducer

and received at a later time by the same or a different transducer. From the time delay

between transmitting and receiving the signal, properties such as the speed of sound or the

distance travelled can be derived. In ranging applications, the main objective is to localize

distant scatterers in front of the transmitter. Thereby, the volume between transmitter and

scatterer is filled with a fluid, usually air or water. Knowing the speed of sound of the

surrounding fluid, its distance can be calculated from the ToF. This setup is adapted in NDT

to investigate solid materials. Instead of a fluid, transmitter and receiver are connected to

a test specimen. ToF measurements of the test specimen can be related to the location of

defects acting as scatterers [

] or changes in material parameters via the calculated

speed of sound [

]. In many cases, the transducers are coupled directly [

] or

with a couplant [

] to the specimen surface to reduce amplitude losses from reflection

at the transducer-specimen interface. To speed up the measurements and avoid the use

of couplant, the specimens are immersed in liquids [

] or air [

–

]. Especially in

air, the increase in measurement flexibility comes with challenges transmitting sufficient

Sensors 2022,22, 2135. https://doi.org/10.3390/s22062135 https://www.mdpi.com/journal/sensors

2 Publications

Sensors 2022,22, 2135 2 of 17

acoustic energy into the air and further into the specimen. These issues are extensively

elaborated on in a number of publications [18,23,25].

The positioning of the transducer at a distance from the specimen surface further

complicates the measurement of the ToF through the specimen, as the travel time of the

ultrasonic signal through the immersion fluid amounts to a non-negligible portion of the

total ToF. Thus, in addition to determining ToF through the specimen, a measurement needs

to be conducted to determine the time delay caused by the immersion. Figure 1shows such

an immersion setup.

Figure 1.

Sketch of a conventional immersed through-transmission setup for ToF measurement.

The ToF through the specimen thickness is the target quantity. For an accurate measurement, knowl-

edge of the transmitter characteristics and either the speed of sound in the immersion fluid and the

immersion distances or the reference distance are required.

Among the methods developed to determine the ToF [

], the correlation approach

is considered statistically optimal [

] because it uses the entire phase and amplitude

information contained in the signal. It requires a reference signal of the immersed trans-

ducer to be correlated with the signal received on the opposite side of the specimen. When

applied to immersion ultrasound, this method poses a number of challenges. The cor-

relation maximum indicates the time of arrival (ToA) of the signal, which includes the

travel time through both the immersion medium and the specimen. The ToF can be de-

termined by subtracting a known time of transmission through the immersion from the

ToA. The required reference signal can be modeled if the trigger time of the transducer

and its impulse response are known. Since most fluid-coupled ultrasound transducers

are triggered electronically, their trigger time can be determined very exactly. However,

this is not always the case, as demonstrated by the recently introduced fluidic ultrasonic

transducer [

]. Although this device is triggered electronically, the sound generation

mechanism is governed by fluid turbulences and cannot be controlled precisely, resulting in

jitter in the 10–100 µs range. Additionally, if the reference signal is insufficiently modeled,

the correlation result gives erroneous information about the actual ToF [

]. Direct

measurement is then the appropriate method for obtaining an accurate reference signal.

If transducers are used that can both transmit and receive, this can be done by recording

one or multiple reflections of the transmitted signal. However, this results in a resolution of

only half a wavelength [

] and long acquisition times since most immersed transducers

are multiple wavelengths away from the specimen. If the transducer does not allow signal

sensing, an additional receiver is required close to the transducer. However, this must

be secluded from the acoustic axis [

], as most sensing devices would interfere with

the generated signal. One method to circumvent this challenge is measuring the signal

with and without specimen in a transmission arrangement. When measuring without a

specimen, the ToA through the reference distance

(Figure 1)

is obtained. By subtracting the

ToA through the specimen from the reference ToA, the ToF can then be calculated [

This differential method requires unchanged environmental conditions, since a change

2.4 Publication IV

Sensors 2022,22, 2135 3 of 17

may result in varying waveforms or varying transmission delays through the immersion

medium [

–

]. In summary, to obtain accurate ToF measurements in a conventional

air-coupled ultrasonic transmission setup, the exact acoustic path length and speed of

sound in the immersion, the trigger time, and the waveform need to be known.

In this paper, we propose a non-contact method for determining the ToF of a specimen

immersed in a fluid that requires no knowledge of these quantities, facilitating measure-

ments in changing environments or using a priori unknown waveforms. This technique

is based on refracto-vibrometry (RV) using a laser Doppler vibrometer (LDV). RV has

been previously used for beamforming [

] and qualitative measurements of 2D sound

fields [

–

]. Tomographic methods have been used to quantitatively reconstruct 3D

sound fields [

–

]. A related acousto-optic approach has been taken by Jia et al. [

] to

perform ranging tasks in a water tank. In RV, the acousto-optic effect is used to measure

sound waves passing perpendicularly through the LDV laser beam. This effect can also be

used to provide a suitable non-contact method for receiving an ultrasonic signal close to

the specimen surface without influencing the sound field.

In the novel measurement technique introduced in this study, the properties of RV

sensing are used for accurate non-contact determination of the immersion-induced time

delay and to obtain a reference signal for correlation approaches. This procedure allows

precise ToF measurements through the specimen for every individual pulse transmitted.

Unlike the previously mentioned approaches, the setup presented here does not require

a priori

knowledge about the exact distance between the transducer and the specimen,

the environmental conditions, the signal waveform or the trigger timing and can be per-

formed using commercially available measurement equipment. Additionally, the method

allows distance measurements between the laser beam and the specimen when the speed

of sound in the immersion fluid is known.

Section 2presents a brief review of the refracto-vibrometric principle and introduces

the theory of the proposed method. In Section 3, the measurement setup used to study

the accuracy of this method is presented. In Section 4, the systematic hardware delay is

estimated and the measurement results are discussed.

2. Theory

The method proposed in this study is based on using the acousto-optic effect to fa-

cilitate non-contact ultrasonic time-of-flight measurements. This section briefly reviews

refracto-vibrometry, proposes a measurement concept that utilizes its characteristic proper-

ties, and explains the relative uncertainty due to misalignment in the setup.

2.1. Refracto-Vibrometry

In RV, the LDV laser beam passes through a sound field and is directed at a static

reflecting target, as shown in Figure 2. The LDV output signal

sRV (t)

is an apparent particle

velocity

vRV (t)

that corresponds to an integral sound pressure

p=p(t

along the laser

beam. The relationship is given by [44,47]:

sRV (t) = vRV(t) = α1

n0∂n

∂pd

dtZLpdl(1)

where

is a directivity factor,

is the length of the laser beam intersecting the sound

field,

(∂n/∂p)

is the piezo-optic coefficient, and

is the refractive index of the immersion

fluid. The acoustic field is modeled as a plane wave propagating perpendicular to the laser

beam [47] at a sound pressure

p(t) = Asin (ωt+ϕ0)(2)

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Sensors 2022,22, 2135 4 of 17

with amplitude

, angular frequency

, and phase

ϕ0

. Inserting Equation (2) into Equa-

tion (1), after integration the output signal is obtained as:

sRV (t) = −αL

n0∂n

∂pAωcos (ωt+ϕ0). (3)

Assuming a fixed setup and a sound pressure much smaller than the atmospheric

pressure,

and

(∂n/∂p)

are constant [

]. The frequency of the output signal then depends

only on the acoustic signal frequency. The amplitude of the output signal depends on the

angle of incidence, the acoustic signal frequency, and the amplitude of the sound pressure

integrated along the laser beam. It has been shown that the directivity

of a LDV in RV

mode can be described by a

sinc

function depending on

, the wave number

, and the

angle of incidence θ[47,48]:

α=|sinc(KL sin θ)|(4)

The resulting directivity for various

is shown in Figure 2b. As the acoustic fre-

quency or beam width increases, the directivity of RV increases. In the case of high-

non-planar waves, this means that the wave components intersecting the laser beam per-

pendicularly have the largest influence on

sRV

. However, this directivity only concerns the

inclination of the acoustic axis relative to the laser axis. The azimuthal directivity of RV for

waves passing the laser from different radial directions is uniform, as shown in Figure 2c.

Only the inclination

influences the directivity factor

. The proposed method is based

on this property as it allows to capture optically both an acoustic wave generated by a

transducer and its reflection by a surface.

Figure 2.

(

) Basic refracto-vibrometry setup using a laser Doppler vibrometer. The arrow indicates

the propagation direction of the sound waves. (

) Directivity of the method for various

. (

) Three-

dimensional rendering of the directivity in one point of the laser beam for KL =10.

2.2. Time-of-Flight Measurements

Figure 3shows a setup that can be used to measure the ToF of an acoustic signal

through two media with different specific acoustic impedances

, one of which needs to

be optically transparent to the LDV laser beam. This is the case in air-coupled ultrasonic

non-destructive testing when the transducer is immersed in ambient air and sends a signal

through a specimen. When the acoustic signal is generated by a transducer, it propagates

through the air at the acoustic velocity cair. It passes the laser beam of the LDV at time

τTL =dTL/cair (5)

where

dTL

is the distance between transducer and laser beam. As the RV is sensitive to all

acoustic signals that pass the laser beam perpendicularly, the LDV also records the signals

reflected from the specimen surface. The reflected waves pass the laser beam at a time

delay of

τ2= (dTL +2dLS)/cair =τTL +2τLS (6)

2.4 Publication IV

Sensors 2022,22, 2135 5 of 17

where

dLS

is the distance between the laser beam and the specimen and

τLS

is the time it

takes the signal to travel this distance. Knowing

τLS

and

cair

, the distance between the laser

beam and the specimen surface can be determined as follows:

dLS =τLScair. (7)

Figure 3.

Sketch of the proposed setup. The arrows indicate the sound path through air (purple)

and through the specimen (yellow), which are used to determine the signal travel time through air

and the specimen. The distances shown are the space between transducer and laser beam (

dTL

the space between laser beam and specimen (

dLS

), and the thickness of the specimen (

). The sketch

additionally shows the speeds of sound (

cair

) of specimen and air, causing the time delays,

and their specific acoustic impedances (

Zair

), causing the partial reflection of the acoustic signal.

In NDT measurements, the time delay

τS

through the specimen with thickness

the quantity of interest, which is given by:

τS=dS/cS=τb−(τ2−τLS)(8)

where

is the longitudinal acoustic velocity of the specimen. The signal reaches the back

surface of the specimen at

τb

, where it is received by a second sensor, such as an additional

LDV. The time of reflection

τLS

is exactly the time delay for the wave to couple into the

specimen after passing the laser beam. The time of entry into the specimen can be found by

autocorrelating sRV. The autocorrelation output R11 is thus

R11(τ) = (sRV ?sRV)(τ)(9)

with

being the correlation operator. The secondary peak of the correlation output,

R11

, is

located at the time delay associated with the arrival of the reflected signal, so that

2τLS =τ(ˆ

R11). (10)

The location of

R11

can be determined by a suitable peak finding algorithm. The RV

signal

sRV (t)

can be further used to find

τS

. This is done by cross-correlating the RV signal

with signal s2(t)from a back wall sensor

R21(τ) = (s2?sRV)(τ). (11)

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Sensors 2022,22, 2135 6 of 17

Then the peak correlation output

τ(ˆ

R21)

occurs at

τLS +τS

. Thus, the ToF can be

determined by using Equations (10) and (11) so that

τS=τ(ˆ

R21)±1

2τ(ˆ

R11)−τh(12)

where

τh

is a delay between the sensors caused by the measurement hardware and the

data acquisition system. In case

sRV (t)

and

s2(t)

represent out-of-phase quantities such

as acceleration and velocity,

τh

also includes the resulting phase shift. The sign of the

second term of Equation (12) depends on whether the first or the second cross-correlation

maximum is chosen, i.e., the cross-correlation result of the back wall signal with the reflected

(+) or the incoming (−) in-air pulse.

Consequently, no information about

cair

dTL

dLS

are required to determine

the ToF

τS

. The time signals

sRV (t)

and

s2(t)

include all the information needed for the

calculation via Equation (12). Due to the relational character of the correlation operation,

possible jitter in the signal generation and variations in environmental conditions between

multiple measurements do not influence the calculated ToF.

2.3. Laser Positioning Error

The theory developed in Section 2is based on the assumption that the laser beam

and acoustic beam axes intersect perfectly. However, errors can occur in the measured

ToF if the positioning of the laser beam does not intersect the sound field in its axis. This

error is modeled geometrically, which is justified by two assumptions: First, the signal

received by the back wall sensor enters the specimen perpendicularly, otherwise it would

be refracted off the direct path to the back wall sensor. Second, only the sound waves

passing perpendicularly through the laser beam significantly influence the RV signal if

in Equation (4) is sufficiently high. This applies to all wave components in the x-z-plane

shown in Figure 4a.

Figure 4.

(

) Sketch of an erroneous laser positioning. The arrows indicate the sound paths. The co-

ordinate system is rotated about the x-axis compared to Figure 3a. (

) Calculated ToF due to laser

positioning errors for distances that are used in experimental verification. Solid lines:

dLS =

20 mm,

dashed lines: dLS =70 mm, dotted lines: dLS =110 mm.

In Figure 4a, the sound paths of the ideal measurement setup are compared with a

setup where the laser beam is off the acoustic axis by a distance

. The signal has to travel a

distance d0

TL before being sensed by the laser. This distance is given by

TL =qd2

TL +a2>dTL (13)

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Thus, the measured time delay

R21

between the signal’s passing through the laser

beam and its sensing by the back wall sensor decreases compared to the ideal case as

τ0

r=dLS −(d0

TL −dTL)

cair

<τLS. (14)

On the other hand, the time delay

τ00

between the initial and reflected waves passing

through the laser beam, calculated using Equation (9), increases since the reflected waves

follow a different propagation path d0

2, given by

2=q(dTL +2dLS)2+a2>dTL +2dLS (15)

In Equation (12), it is assumed that the time delay

τLS

calculated from Equation (10)

represents the wave travel time from the intersection with the laser to the entry into the

specimen. However, if the positioning is incorrect, Equation (10) yields the travel time

τ00

r=τ(ˆ

R11)

2=d0

2−d0

2cair

>τ0

r. (16)

The resulting time delay error subtracted from the ToF

τS

due to positioning errors

can be calculated as

εLS =τ0

r−τ00

r=dLS −(d0

TL −dTL)

2cair

−d0

2−d0

2cair

. (17)

This error has been calculated for various combinations of

dTL

and

dLS

in air, which

have been investigated in this study and are shown in Figure 4b. The negative error caused

by a laser beam

deviating from the direct sound path increases strongly as

dTL

and

dLS

decrease. The resulting underestimation of

causes an erroneously reduced

τS

to be

calculated from Equation (12).

Using similar geometric considerations, the error from inaccurate positioning of the

back wall sensor can be estimated. This error generally increases the calculated

τS

since the

path length through the specimen is increased. However, since the longitudinal propagation

velocity

of the specimen is often much larger than

cair

in NDT applications, this error

can be expected to be significantly smaller than εLS.

The geometrical model used here assumes far-field conditions in which the acoustic

wavefronts propagate spherically [

] and are therefore nonparallel to the specimen surface

at off-axis locations. A smaller angle between the surface and the wavefront would mean

a reduction in

and

. The resulting error estimates can therefore be considered as

upper bounds.

3. Methods and Materials

To verify the performance of the method, a measurement setup was arranged accord-

ing to Figure 3. The NCG100-S63 ultrasonic transducer (Ultran Group, USA) with a center

frequency of 80 kHz was used [

]. Its sound field is shown in Figure 5a. Figure 5b shows

the beam width

, defined by the full width at half maximum (FWHM), which decreases

from 50 mm close the transducer surface to 30 mm in the far field. Conservatively assuming

30 mm for this setup, the resulting aperture of

KL =

44 causes a high directivity of

the RV method, as shown in Figure 2. Therefore, mainly the wavefronts with a direction

perpendicular to the laser beam and the specimen surface contribute to the RV signal.

Larger beam widths

, as measured close to the transducer surface, result in an even larger

directivity. For RV sensing, an OFV 3001 LDV (Polytec, Germany) was aimed at a fixed

aluminum profile at a distance of

L0=

1150 mm from the laser head. The specimen was

a polyamide 6 block with dimensions 206.6

mm ×

262.1

mm ×

311.8 mm, and the signal

was transmitted through the

dS=

206.6 mm wide dimension. Due to its homogeneity,

polyamide is often used as a reference material for bulk wave ultrasonic testing [

–

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A PCB 352M66 accelerometer (PCB Piezotronics, USA) was mounted to the specimen using

1 mm double-sided adhesive tape as the back wall sensor. The signal ToF increase due

to the tape is included in the hardware delay

τh

of Equation (12), cf.

Section 4.2

. A semi-

contact setup using an accelerometer was chosen for its high signal-to-noise ratio, which

provides a good quality verification of the proposed method [

]. The sensor data was

recorded with a M2p5966-x4 measurement card (Spectrum Instrumentation, Germany) at

16 bit resolution using a sample rate of 20 MS/s. The recording was triggered at the same

instance as the signal generator. To cross-validate the ToF measurement results, ranging

measurements were conducted according to Equation (7), using temperature readings from

a WS6750 weather station (Techno Line, Germany). Peak finding was conducted by using

the find_peaks function of the Python SciPy library [

] and subsequently picking the

maximum value of the peaks found.

Figure 5.

(

) Sound field of the Ultran NCG100-S63 transducer in the center plane, where

is the

maximum sound pressure. The pressure data originate from a previous study [

]. (

) The full width

at half maximum (FWHM) along the x-axis.

In refracto-vibrometry, the vibrometer senses the temporal change of the refractive

index

n(t)

, so that

sRV (t) = sRV(∂n/∂t)

. Since

n(t)

can be considered as a linear function

of the acoustic pressure

p(t)

[

] in the pressure range considered here, it follows that

sRV (t) = sRV(∂p/∂t)

. Under far-field conditions, this is in phase with the time derivative

of the particle velocity

∂u(t)/∂t

. The accelerometer measured the particle acceleration at

the specimen surface. Thus,

s2=sacc =sacc(∂u/∂t)

is in phase with

sRV

and the correlation

can be computed according to Equation (12).

4. Results and Discussion

Investigating the accuracy of the proposed method requires a detailed look at the

signal itself, as acquired by the different sensors, and at all the processing steps needed

to compute the result. In this section, after characterizing the signal, the hardware delay

between the accelerometer and the LDV is examined. Then, the results of the different

geometric parameters dTL and dLS are presented and discussed.

4.1. Signal

In this study, the ultrasonic signal generated by the ACU transducer is received by

various devices: the RV-LDV, the accelerometer, and the transducer itself after the signal

is reflected by the specimen surface. Figure 6a shows the waveforms of a single signal,

measured by all three sensors. All of these signals were band-pass filtered in the range of

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[

20,120

]

kHz to capture the whole transducer range but filter out high frequency noise,

especially in the RV signal which has a bandwidth in the MHz range [47].

Figure 6.

One pulse sensed by the various sensors with

dTL =

180 mm and

dLS =

90 mm in

the (

) time domain and (

) frequency domain. For the signal measured by the ACU transducer,

the first reflection was used so that the voltages are not capped. The signals were shifted so that their

maxima coincide.

The acquired waveforms are qualitatively similar having a signal length of about

150

s. However, slight differences appear more distinct in the frequency domain

(Figure 6b)

While the maximum frequency peaks of the RV and the ACU transducers are very close at

79 kHz and 80 kHz, respectively, the maximum frequency measured with the accelerometer

is at 76 kHz. Additionally, a second peak is at 91 kHz for the RV data and at 93 kHz for the

accelerometer data. These different spectra for the same acoustic pressure burst are caused

by the individual frequency responses of the sensors. The piezoelectric transducer itself has

a very narrow bandwidth by design, centered at its operating frequency of about 80 kHz.

The accelerometer was operated out of its nominal bandwidth, so that the frequency re-

sponse is not known, but can be assumed not to be flat. The LDV has a sensitivity that is

linearly increasing with the frequency, as given in Equation (3). While such differences have

little effect in the application of ultrasonic non-destructive testing, they measurably affect

the correlation result of Equation (11). The different spectral energy distributions cause a

difference in the measured signal period lengths and thus in the envelope shapes, with the

latter contributing significantly to the correlation output [

]. This systematic effect is,

however, included in the hardware delay of Equation (12) and can thus be corrected.

4.2. Hardware Delay

The hardware delay

τh

between the sensors was measured by using the LDV in the

common vibrometry mode and aiming it at the back surface at a 10 mm distance from

the center of the accelerometer. The RV signal should be

π/

2 phase shifted with respect

to the accelerometer signal, since the former measures the surface particle velocity and

the latter its derivative. If the phase shift deviates from

π/

2, there is a hardware delay

that needs to be corrected. Since the signals are not monochromatic and furthermore have

slightly varying frequency content (Section 4.1), it is not sufficient to check only whether

the accelerometer signal is

−π/

2 phase shifted from the peak RV signal frequency. All

included frequency components need to be considered. The Wiener–Khintchine theorem

states that the autocorrelation of a signal is the inverse Fourier transform of its power

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density spectrum [

]. Thus, the first zero-crossing of

τ=

s of the autocorrelation

R11

can be assumed as a good estimate of a mean

−π/

2 phase shift of the signal, accounting

for its mean square spectral content [

]. The autocorrelation output of three individual

signals and their zero-crossings indicating a

−π/

2 phase shift are shown in

Figure 7a

Without hardware delay, the cross-correlation maxima of

R21

(Figure 7b) should be at the

location of these zero-crossings. However, the accelerometer signals

sacc

have a positive

delay resulting from varying sensor bandwidth (Section 4.1) as well as internal delays of

the sensors, amplifiers, and transmission lines. Figure 7c shows the total hardware delay

τh

of all individual measurements as well as its estimate of 3.3

s and its uncertainty of 0.3

While the use of a non-contact back wall sensor, such as an additional LDV, is expected

to cause a decrease in signal-to-noise ratio, it could provide a reduced hardware delay

uncertainty since it provides a flat frequency response over a wide range of

frequencies [59]

Figure 7.

Calculation of hardware delay

τh

: (

) shows three autocorrelation outputs of the RV signal,

where

denotes a

−π/

2 phase shift; (

) shows the corresponding cross-correlation outputs of the

RV and accelerometer data, where

◦

denotes the correlation maximum; (

) shows the calculated

τh

for 50 pulses.

The LDV measurements were conducted directly on the specimen, while the ac-

celerometer was mounted on the specimen using double-sided adhesive tape. Therefore,

this calculated hardware delay includes the additional ToF caused by the tape.

4.3. Experimental Verification

With the hardware delay known, the time delay between the laser and the specimen

τLS

as well as the ToF of the signal through the specimen

τS

were calculated according to

Equation (12). This procedure is shown in Figure 8for two individual measurements with

dTL =

180 mm to highlight a number of characteristic signal and correlation properties.

The distances between laser beam and specimen are dLS =5 mm and dLS =105 mm.

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Figure 8.

Measurement procedure for

dTL =

180 mm and two different

dLS

: (

) shows the time signal

from the Ultran piezo transducer as a reference; (

) shows the RV and accelerometer time signals; (

)

shows the autocorrelation results of the RV signals; (d) shows the cross-correlation results of the RV

and accelerometer signals.

Figure 8a shows the time signals acquired with the Ultran piezoelectric transducer.

The voltage of the initial pulse was capped to avoid damaging the data acquisition system.

The ringing of the signal lasted to

250

s, which constitutes the lower time limit for

detecting a reflected signal. Its amplitude was previously much lower than that of the

driving signal and the subsequent ringing. The first reflections of the pulses were received

1100

s and

1670

s, respectively. The secondary reflections, that would be

needed for an accurate determination of the in-air travel time via autocorrelation, are not

shown because their late ToA would render the figure illegible. This illustrates the long

acquisition time required when the same transducer is used for sending and receiving.

Figure 8b shows the time signals acquired by the LDV in RV mode and the accelerom-

eter. Since the distance between the transducer and the laser beam is fixed, the initial

waveforms of the RV signal match from

540

s for both

dLS

. The corresponding

accelerometer signals for both configurations followed some time after the initial signal.

In the

dLS =

5 mm case, the reflected RV signal was received shortly after the incoming

pulse, at

570

s, due to the small distance between the laser and the specimen. Having

a signal length of 150

s (Section 4.1), the incoming and reflected pulse overlap. Since

the time required for the signal to travel back and forth in the air is shorter than to travel

through the specimen, the accelerometer signal arrives after the reflected RV signal. As the

specimen moved away from the laser until

dLS =

105 mm, the reflected pulse was received

later in time, starting at

1140

s. In this case, the signal that had travelled through the

specimen was received in between the in-air signals sensed by RV. Since the RV receives

the in-air pulse much closer to the specimen, a shorter acquisition time is necessary for the

autocorrelation of the signal than by using the piezoelectric transducer, although the same

signals as in Figure 8a were used. The use of an output signal and a reflected signal that are

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close in time not only allows for more economical data handling, but also ensures lower

attenuation on the propagation path resulting in better signal quality.

Figure 8c shows the autocorrelation results of the RV signals obtained from

Equation (9)

Since the transducer signal is periodic, this autocorrelation result

R11

does not show a

singular peak at

R11(τ=

)

, but an envelope with several secondary peaks centered around

τ=

R11

also features a secondary envelope caused by the correlation of the incoming

and reflected in-air signal. By picking the correlation maximum in this secondary envelope,

the two-way travel time of the in-air signal 2

τLS

was found. Since the secondary peaks

inside the first autocorrelation envelope around

τ=

0 can be larger than the maximum of

the secondary envelope, it was necessary to restrict the peak search to time delays larger

than 25

s, which is approximately two periods of the signal. While the primary and

secondary envelopes are clearly separated in the

dLS =

105 mm case, the envelopes overlap

in the

dLS =

5 mm case, which is a result of the overlap in the waveform seen in Figure 8b.

Figure 8d shows the results from cross-correlating the RV signals with the accelerom-

eter signals following Equation (11). The overlap of initial and reflected waves from the

RV signal of the

dLS =

5 mm case is visible in the envelope of the corresponding

R21

in the

interval

[

0,150

]µ

s. The first maximum at

τ=

55.5

s represents the cross-correlation of the

accelerometer signal with the reflected signal, while the global maximum at

τ=

107.8

represents the cross-correlation with the initial signal, as given by

Equation (12)

. Using the

cross-correlation maximum of the initial signal is preferable because the reflected signal may

contain interference caused by the signal overlap, which may cause erroneous correlation

results. If the in-air pulses sensed by RV move further apart, as in the

dLS =

105 mm case,

both correlation maxima may be used equally for determining

τS

. Since the accelerometer

senses the pulse between the initial and received pulse

(Figure 8b)

, the correlation result

corresponding to the reflected pulse moves into the negative

range, which has been

omitted in Figure 8d.

The correlation maxima of

R21

shown in Figure 8d represent the time it took for the

signal to travel from its initial encounter with the laser beam at

τTL

to the specimen surface

τLS

, through it (

τS

), and be received by the accelerometer with a hardware delay

τh

. Since

τh

had been determined earlier, these results were now used to investigate the accuracy of

the proposed method when the specimen was moved away from the laser beam. Following

Equation (12), τLS was determined to calculate τSfor every pulse.

Figure 9a shows the mean calculated time delays

τLS,calc

and distances

dLS,calc

, which

qualitatively agree well with the movement positions of the measurement stage. Only for

the

dLS <

20 mm cases the results do not follow the set distances linearly. This behavior

is caused by the overlap of the autocorrelation envelopes when the laser beam is close to

the specimen surface, and by the small distance between the transducer and the specimen,

which may cause multiple reflections between the surfaces. Both effects hamper the

determination of peak values in the autocorrelation output. Figure 9b shows the absolute

relative errors of the total calculated distance

|εtot|

and of each distance increment by which

the specimen is moved |εi|. These are defined as:

εtot = (dLS,calc −dLS)/dLS = (τLS,calc −τLS)/τLS (18)

εi= (∆dLS,calc −∆dLS)/∆dLS = (∆τLS,calc −∆τLS)/∆τLS (19)

where

∆dLS =

1 mm for the measurements presented here. Given the linear relationship

between time delay and distance travelled from Equation (7), these errors account for both

τLS and dLS.

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Figure 9.

Experimental validation for various

dTL

and

dLS

: (

) shows the mean calculated distance

between laser and specimen as well as the corresponding time delay; (

) shows the error for this

calculated distance for each individual step as well as for the total distance; (

) shows the resulting

ToF

τS

for each individual pulse and their mean values. Published data [

] on longitudinal

acoustic velocity in polyamide were used to calculate the reference ToFs. The calculated

τS

for

dLS

are magnified.

For all

dTL

investigated here, the highest

|εtot|=

0.4 is measured when the laser beam

is closest to the specimen. This error decreased rapidly to be

|εtot|<

0.015 for distances

dLS >

14 mm. The relative total distance error of

dLS =

180 mm dropped at slightly

lower distances than the other dLS configurations, which can be attributed to the multiple

overlapping reflections between transducer and specimen in the latter cases.

In all three

dLS

cases, the incremental error

|εi|

reached values

1 in the same region

where

|εtot|

was elevated. Except for a small number of outliers (less than 10%), this error

dropped below

|εi|=

0.15 as

dLS

increased. A step error of

|εi|=

0.15 is equivalent to 3.5%

of the signal wavelength. This error per wavelength is of the same order as that reported

by Jia et al. [

], who used a comparable method with a higher frequency transducer and

water coupling. These results show that RV can be used to conduct distance measurements

at sub-wavelengths accuracy in air.

As mentioned in Section 2.2, the proposed method neither requires the knowledge of

the exact distance between the laser beam and the specimen surface nor the environmental

conditions to calculate the ToF through the specimen. Thus, measurement errors in the

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distance measurements, such as step losses when traversing

dTL

or in the temperature

measurements, are not propagated into the ToF measurements of the specimen. Only the

travel times

τLS

were used for determining the ToF in NDT applications.

Figure 9c

shows

the

τS

calculated from Equation(12). They were compared with earlier results by Maack [

which served as a reference here. The investigated and reference polyamide block were

made by the same company. The speed of sound in the reference block was

cPA6=

2642 m/s

for signals with a center frequency of 100 kHz. Given the 206.6 mm thickness of the

specimen used in this study, the ToF was

τS=

78.2

s. A further value of

τS=

78.1

using

cPA6=

2645 m/s was included, which was obtained by Zhu et al. [

] using a

2 MHz transducer. Both the maximum parallelism error of the specimen surfaces during

production and the thickness measurement accuracy were 0.05 mm, which corresponds to

ToF accuracy of 0.02

s. Thus, the effect of the thickness measurement error on the accuracy

of the time delay calculation is smaller than the effect of the sampling interval of 0.05

By far the largest error source is the laser positioning error, which has been estimated to

reach up to −1.2 µs for a laser mispositioning of 5 mm.

Similar to the relative distance measurement errors, the calculated ToF deviated consid-

erably when the transducer or the laser beam was close to the specimen surface, i.e., when

the initial signal and one or more reflections significantly overlapped. For distances of

dLS >

20 mm, the ToF deviation from the reference values was below 0.8

s or 1.1%.

Following Section 2.3, these deviations imply a laser mispositioning of about 4 mm, which

appears excessive considering the effort in assembling the measurement setup and implies

that the model employed for the assessment of mispositioning error may need refinement.

As the distance between the transducer and laser beam

dTL

increased, the maximum ToF

deviation from the references decreased to 0.4%. This is significantly lower than the thick-

ness measurement error of 1.2% observed by Jia et al. [

] using a differential measurement

approach, highlighting the obtainable accuracy of the presented method. Furthermore,

a slight increase in ToF with increasing

dLS

was observed for all configurations investigated.

Both behaviors are consistent in amplitude and trend with the errors caused by inaccurate

laser positioning

(Section 2.3)

, which decreased with increasing

dLS

. The only outlier from

that behavior is found in the

dTL =

20 mm case at

dLS =

99 mm, where the deviation of the

individual measurements was about one period of the signal, indicating that a secondary

correlation maximum was higher than the correlation value at the true

τS

. This is an

inherent issue of using correlation methods for undamped narrow-band signals, which are

common for piezoelectric ACU transducers. Although the voltage signal-to-noise ratio is

high, the correlation peak-to-peak ratio may be marginal

(ref. Figure 8d)

. A higher corre-

lation peak-to-peak ratio may be achieved by generating a Dirac-like acoustic

pulse [61]

or by using pulse compression techniques [

] that generate a single peak in the

correlation output.

5. Conclusions

In this study, a novel non-contact method was proposed to provide high-resolution

time-of-flight measurements using air-coupled ultrasonic transducers in a transmission

setup. The results show how an off-the-shelf laser Doppler vibrometer can be used to obtain

accurate ultrasonic time-of-flight measurements. The employed model of the sound paths

implies that no prior knowledge is required about the signal waveform, environmental

conditions, or even the distance between the transducer and the specimen. The only

information needed is the time delay between the sensors used in the setup.

Using a laser Doppler vibrometer, operated in refracto-vibrometry mode as a bidirec-

tional acoustic receiver, the incoming signal and its reflection from a solid specimen surface

in-air are sensed. In the first processing step, these data are used to calculated the signal’s

time of entrance into the specimen. Then, the same data are used to detect the time-of-flight

of the signal through the specimen by cross-correlating it with a signal received on the

opposite side of the specimen.

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To verify the applicability of the proposed method for different setups, the distance

between the laser and the specimen, as well as between the transducer and the laser, were

varied using a semi-contact setup with an accelerometer as back wall sensor. It has been

shown that a certain minimum distance between the laser and the specimen, here 20 mm,

is needed so that the overlap between the direct and reflected signal does not influence

the correlation result too much. For the measurement of the time of entrance into the

specimen at larger distances, the results show an error per step in the order of 0.4

s or 3.5%

of the signal wavelength when the specimen is moved away from the laser. The overall

ranging error of the distance between the laser beam and the specimen is below 1.5%.

When calculating the time-of-flight through the specimen itself, the results agree well with

the literature and deviate from the reference values by a maximum of 0.8

s except for a

small number of outliers. In the case of the polyamide specimen used in this study, this

equates to a maximum offset of 1%. The error approximation due to misalignment of

the vibrometer appears to not fully explain this offset. In addition to employing a non-

contact back wall sensor, future research should investigate more detailed error models

to increase the accuracy of this method even further. Since in this paper it is assumed

that some of the inaccuracies are caused by the periodic waveform of the ultrasonic pulse,

the accuracy obtained by using coded waveforms is expected to be even higher and should

be investigated in the future alongside applications in other fluids.

Author Contributions:

Conceptualization, B.B., S.M., C.S.; methodology, B.B., S.K.; software, B.B.;

validation, B.B., S.K.; formal analysis, B.B., S.K; investigation, B.B.; data curation, B.B.; writing—

original draft preparation, B.B.; writing—review and editing, S.K., S.M., C.S.; visualization, B.B.;

supervision, S.M., C.S..; project administration, C.S.; funding acquisition, S.M., C.S. All authors have

read and agreed to the published version of the manuscript.

Funding:

This research was funded by the German Federal Ministry for Economic Affairs and Climate

Action (BMWK) under the ZIM (Zentrales Innovationsprogramm Mittelstand) grant ZF4044222WM7.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement:

The data presented in this study are available on request from the

corresponding author.

Conflicts of Interest: The authors declare no conflict of interest.

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2 Publications

2.5 Publication V: Fluidic Ultrasound Generation for

Non-Destructive Testing

Bibliographic Data:

B. B¨uhling, S. Maack, and C. Strangfeld. “Fluidic Ultrasound Generation for Non-Destructive

Testing”. Advanced Materials (2024), 2311724. doi:10.1002/adma.202311724.

Version:

Preprint. The authors own their preprints. After submission of this thesis, the article has been

published under a Creative Commons Attribution (CC BY) license (http://creativecommons.

org/licenses/by/4.0/) as cited above.

1 INTRODUCTION

Fluidic Ultrasound Generation for Non-Destructive Testing1

Benjamin B¨uhling* Stefan Maack Christoph Strangfeld2

B. B¨uhling, Dr. S. Maack, Dr. C. Strangfeld3

Department 8 ”Non-Destructive Testing”4

Bundesanstalt f¨ur Materialforschung und -pr¨ufung5

Unter den Eichen 876

12205 Berlin, Germany7

Email: b[email protected] (B.B.), stefan.maac[email protected] (S.M.),8

c[email protected] (C.S.)9

Keywords: air-coupled ultrasound, non-destructive testing, fluidics, laser Doppler vibrometer, aeroa-10

coustics, harsh environment11

Air-coupled ultrasonic testing (ACU) is a pioneering technique in non-destructive testing (NDT). While contact testing and12

fluid immersion testing are standard methods in many applications, the adoption of ACU is progressing slowly, especially in13

the low ultrasonic frequency range. A main reason for this development is the difficulty of generating high amplitude ultra-14

sonic bursts with equipment that is robust enough to be applied outside a laboratory environment. This paper presents the15

fluidic ultrasonic transducer as a solution to this challenge. This novel aeroacoustic source uses the flow instability of a sonic16

jet in a bistable fluidic switch to generate ultrasonic bursts up to 60 kHz with a mean peak pressure of 320 Pa. The robust17

design allows operation in adverse environments, independent of the operating fluid. Non-contact through-transmission ex-18

periments are conducted on four materials and compared with the results of conventional transducers. Accordingly, the novel19

fluidic ultrasonic transducer provides a suitable acoustic signal for NDT tasks and is capable of furthering the implementation20

of ACU in industrial applications.21

1 Introduction22

Ultrasonic testing is a widely used tool to gain structural information about various materials. Ap-23

plications range from medical investigations [1] and trees health determination [2] to production24

monitoring of composites [3] and reassessment of bridges [4]. If the acoustic propagation velocity25

of the material is known, measuring the time-of-flight (ToF) of an ultrasonic signal through a spec-26

imen enables the detection of embedded objects, cracks or phase boundaries acting as reflectors.27

Depending on the measurement task, different wave types, such as longitudinal, transverse, plate28

or surface waves, can be used. For known specimen dimensions, ToF measurements are used to de-29

termine the acoustic propagation velocity of different waves and to infer further properties of the30

specimen. For example, the propagation velocity of longitudinal waves has been found to be re-31

lated to fat depositions in rat livers [5], particle content in two-phase suspensions [6], food prop-32

erties [7, 8], load [9] and residual stress in polymers [10], the curing process of resins [11, 3], the hy-33

dration of mortar [12], and the aggregate content of concrete [13].34

Most commonly, the sending and receiving ultrasonic transducers are coupled directly to the spec-35

imen surface [14, 15] or a liquid coupling medium is used [16, 17]. This procedure minimizes the36

loss of acoustic energy due to a mismatch of the characteristic acoustic impedance at the interface37

between transducers and specimen. Direct coupling at each measurement point is time consuming,38

so that immersing the transducers and specimen into the coupling agent can be used to increase39

flexibility and measurement speed [18, 19, 20]. However, liquid immersion may be restricted, e.g.40

for very large specimens such as concrete infrastructures [21], air immersed particles [22], sensi-41

tive specimens such as art works [23] and liquid foams [24], or when monitoring processes in harsh42

ambient conditions [11, 25]. In these cases, it is preferable to use the ambient fluid, i.e., air, as a43

couplant. While air-coupled ultrasonic (ACU) methods are considered the optimal choice in terms44

of time efficiency and of coupling feasibility [26], impedance mismatch losses at the interfaces be-45

tween transducer, air and specimen are high, amounting to −110 dB for materials with high acous-46

tic impedance such as concrete [27]. Several approaches have been pursued to minimize these losses.47

2 Publications

2 RESULTS AND DISCUSSION

Thus, matching layers have been applied at the interface of the common piezoelectric and capac-48

itive transducers to air [28, 29], or alternative ultrasound generation methods have been used to49

completely cut out this interface. The methods include ultrasound generation by thermoacoustic50

[30, 31] and plasma transducers [32, 33], as well as wave generation inside the specimen by X-rays51

[34, 35], microwaves [36, 37], or laser heating [38, 39].52

In this work, a novel approach to ultrasound generation based on fluidic transducers [40, 41] and53

its practical application for non-destructive testing (NDT) tasks is described. The signal itself is54

generated by an instationary air flow inside a fluidic switch, in contrast to approaches that use flu-55

ids as waveguides [18, 42] or as intermediaries to determine the strength of materials [43]. Enabling56

the generation of acoustic pulses is a significant development from previous approaches for aeroa-57

coustic ultrasonic sensing devices, that were only able to generate continuous tones [44, 45]. Since58

the acoustic signal is generated by the same medium that is emitted to, the characteristic impedance59

losses disappear when the pulse leaves the transducer into the ambience. The fluidic ultrasound60

generating part of the transducer is a purely static set of channels through which the flow is guided.61

Thus, the material can be chosen according to both working fluid and environmental properties,62

making it resistant to harsh environments while retaining their functionality as previous fluidics re-63

search has shown. These environments may include high [46, 47] temperature, radiation [48, 49] or64

corrosive atmospheres [50, 51]. Additionally, the sound generating part of the transducer requires65

no moving parts, making it maintenance-free, provided the working fluid is clean enough to avoid66

particle aggregation on inside the channels [52]. The transducer was developed for use in NDT in67

civil engineering, where transmitter robustness and low ultrasonic frequencies are specific require-68

ments. However, its principle resilience to harsh environmental conditions make it a suitable option69

for other ultrasonic generation applications. For the first time, the applicability of a fluidic ultra-70

sound setup for NDT tasks is demonstrated here in a laboratory setting and compared with con-71

ventional methods.72

2 Results and Discussion73

2.1 Fluidic Transducer74

The operating principle of the fluidic transducer is equivalent to a bistable fluidic switch [53, 47]75

and is outlined in Figure 1a. In the initial state, a pressurized fluid is connected to the main in-76

let of the device and leaves it through one of the outlet channels (O1 or O2). The active outlet77

channel can be controlled by allowing an additional pressurized fluid to enter the device through78

one of the control ports (C1 or C2). When O2 is the active outlet and C1 is opened, the main flow79

switches to O1. The main flow is switched back to O2 by closing C1 and opening C2. Once the80

switching of the outlet channels is complete, the flow in this configuration remains stable until the81

opposite control port is activated. During this switching process, strong sound pressures can be at-82

tained which originate from the supersonic flow inside the device, the exiting free jet and the flow83

instabilities during the switching process. The latter causes significantly higher acoustic pressure84

amplitudes than the other sources over a wide frequency range. In this study, only the sound emit-85

ted from O1 is used. Therefore, the device is described as on when the flow exits O1 and off when86

it exits O2. The ultrasonic signal generated by the fluidic transducer is shown in Figure 1b. The87

four parts of the fluidic switching cycle are reflected in the time signal (Figure 1b). Their average88

frequency content at location (x, y) = (110,0) mm is shown in Figure 1c. During the process of89

switching on, three distinct frequency peaks can be seen at 30.5 kHz, 43.5 kHz, 56.5 kHz. During90

switch-off, the first of these peaks is absent. In stable on and off states, the transducer shows none91

of these peaks.92

Comparing the ultrasonic signal of the fluidic transducer to that of a piezoelectric transducer (see93

2.5 Publication V

2.1 Fluidic Transducer 2 RESULTS AND DISCUSSION

Supporting Information S.2) or other recent ACU transducers shows a number of unexpected fea-94

tures. First, the signal is significantly longer than the low number of periods generated by the ring-95

ing of a piezoelectric transducer or than the single spike burst generated by a thermo-acoustic trans-96

ducer [30]. While Figure 1b shows a time frame of 35 ms, the characteristic ultrasonic frequen-97

cies generated by the transducer were found solely at the time of switching on the flow, when the98

sound pressure peaked. Thus, this part of the signal, which is still in the range of a few hundred99

milliseconds , can be considered as the main signal and will be referred to as the pulse in the fol-100

lowing. While Figure 1c shows the mean frequency content of 40 pulses, the frequency content101

of each individual pulse varies. The multiple peaks are a feature that is distinguishes the pulse of102

this transducer from those of common piezoelectric or capacitive transducers [26]. The variations103

of the frequency content of the individual pulses can be considered as inherent random phase and104

frequency modulation [54]. Analyzing fluidic pulses in this framework allows comparison of signal105

length with other pulse compression techniques, such as chirps [55]. Although the random mod-106

ulation technique is inferior to current pulse compression techniques, it has the advantage of not107

requiring additional modulation control when operating the fluidic transducer. Furthermore, this108

modulation is not restricted to the 1 to 2 ms pulse range of the time signal. As proposed in pre-109

vious publications on modulation in ultrasound [56, 57], it is possible to extend the time window110

used for correlation to the flow noise following the initial pulse in the transducer on state. While111

it does not contain all the frequency peaks of the pulse range, it still contains considerable acoustic112

energy that contributes to effective pulse compression, even if not to the same extent as the pulse113

itself. Analysis of the usability of fluidic signals for NDT is based on a 2 ms time window contain-114

ing the first pulse of the fluidic transducer. This signal duration is comparable to the time windows115

Figure 1: (a) Flow switching process inside the fluidic transducer. S – supply port, C1 – control port 1, C2 – control

port 2, O1 – outlet 1, O2 – outlet 2. (b) Exemplary microphone time signal in which the stages of the flow switching

process are highlighted. (c) Frequency domain of the highlighted regions showing the distinct frequency content of

the sound generated during the process of switching on.

2 Publications

2.2 Procedure 2 RESULTS AND DISCUSSION

used in previous pulse compression studies with chirped signals [58, 59, 60]. Extending the corre-116

lation time window further into the lower amplitude flow noise regime results in slightly improved117

cross-correlation results in terms of signal-to-noise ratio, but increases both measurement time and118

computational effort.119

The directivity of the transducer is shown in Figure 2 for the switch-on process. Close to the horn120

mouth, a mean ultrasonic pressure amplitude of 320 Pa is reached when the fluidic transducer is121

switched on and 140 Pa when it is switched off. At a distance of 110 mm, where the subsequent122

measurements were conducted, the mean centerline amplitude at switching on is 140 Pa. At this123

position, the ultrasonic field has a width of 90 mm at half maximum amplitude, ensuring a high124

directivity of the refracto-vibrometric measurements (see Supporting Information S.1). The ultra-125

sonic field given in Figure 2, shows a more directive sound field with a higher maximum sound126

pressure compared to the almost spherical radiation of the baseline transducer [40]. This can be at-127

tributed to the horn at the outlet, which reduces radiation impedance mismatch at the transducer128

outlet and increases the directivity through an increased outlet diameter. The resulting acoustic129

power of the transducer amounts to 0.23 W, which is about four times the power of the piezoelec-130

tric ACU reference transducer (see Supporting Information S.3). The ultrasonic field of the sec-131

ondary pulse generated when the flow is switched off has a lower peak sound pressure and is briefly132

discussed in Supporting Information S.4. Additionally, the horn acts as a diffuser for the high-velocity133

flow exiting the device. As a secondary effect, the horn therefore enables the application of the flu-134

idic transducer to sensitive specimens as it prohibits a high velocity mass flow to impinge on the135

specimen surface [61].136

Figure 2: (a) Ultrasonic field of the fluidic transducer, where ˆpis the mean peak pressure. (b) Radial distribution of

ˆpat various axial positions y. (c) ˆpdistribution along the acoustic axis.

2.5 Publication V

2.2 Procedure 2 RESULTS AND DISCUSSION

2.2 Procedure137

Due to the pressure amplitude generated by the fluidic transducer, it is expected that the signal138

can penetrate specimens at considerable depth. Since the longitudinal acoustic velocity can be re-139

lated to various material parameters of the specimen, this property was chosen as the quantity to140

be measured. For this purpose, the ToF of the signal was measured in a fully optical through-transmission141

setup (see Figure 3a) that was recently introduced [62]. By using two laser Doppler vibrometers142

(LDVs), this approach allows contact-free ToF measurements without requiring prior knowledge143

about the ambient speed of sound and has been shown to achieve an accuracy of less than 1 µs144

for transducer working distances larger than 40 mm. The use of LDVs for sensing requires opti-145

cal access to the specimen and a vibration-free mount of the devices. While these conditions are146

met in a laboratory environment, they may restrict the use of this approach for in-situ measure-147

ments. The longitudinal velocity was then calculated from the ToF with knowledge of the speci-148

men thickness. In order to assess the applicability of the fluidic transducer to a broad range of ap-149

plications, four materials with various thicknesses were investigated. Two of these were the build-150

ing materials concrete and wood, since the transducer was originally designed for testing applica-151

tion in civil engineering. Contrary to the other materials investigated, wood and wood-based ma-152

terials are anisotropic. To limit the scope of the investigation, only the transverse propagation di-153

rection [63] was chosen. To investigate the applicability to biological specimens, a block of ballistic154

Figure 3: (a) Measurement setup used in this study. After the acoustic pulse exits the transducer, it propagates

through air before entering the specimen. To obtain the ToF through the specimen, the delay resulting from the

travel time through the air has to be subtracted from the overall ToF. (b)-(i) Exemplary cross-correlation outputs

obtained using the fluidic transducer. The gray lines are the first five individual cross-correlation outputs, the ma-

genta lines are the mean cross-correlation outputs from 100 measurements. (j) Measurements needed for the maxi-

mum of the cross-correlation to converge. The whiskers refer to the 5th and 95th percentiles of the respective distri-

butions. The annotated numbers refer to the 95th percentiles. Specimens are abbreviated using the initial letter of

their material followed by their thickness in mm, e.g. C160 is the concrete specimen with thickness of 160 mm. All

specimens used in this study are tabulated in the experimental section.

2 Publications

2.3 Time-of-Flight Measurements 2 RESULTS AND DISCUSSION

gel was tested. The sound velocity of this material is comparable to that in various tissues [64] and155

has been used for the fabrication of ultrasound phantoms [65, 66, 67]. The fourth material is cast156

polyamide PA6, a polymer that is often used as a reference case for ultrasonic testing [68, 69, 70].157

Table 1 provides a summary of the specimens investigated. The results were compared with those158

of a commercial piezoelectric ACU transducer, using the same all-optical measurement setup as for159

the fluidic transducer, and with those of a commercial piezoelectric contact transducer. In general,160

the longitudinal acoustic velocity of a material is independent of the transducer used, so besides161

demonstrating the applicability of the fluidic transducer for NDT tasks, comparing the results will162

give insight into the performance of the optical sensing approach compared to contact measure-163

ments. Also expected are conclusions about the performance of the fluidic ACU transducer com-164

pared to the piezoelectric ACU transducer.165

For each specimen, 100 individual pulses were recorded and evaluated using the matched filter ap-166

proach outlined in the experimental section. The correlation results were then averaged to find the167

resulting ToF. Five individual examples for the resulting correlation outputs and the averages from168

all 100 outputs are given in Figure 3b-i for a subset of the specimens tested. Results obtained169

for all specimen using the piezoelectric and fluidic transducers are given in Figures S6 and S7 in170

the Supporting Information, respectively. The results show that there is some variation in the indi-171

vidual correlation results, which is greater for the concrete specimen than for the other specimens.172

When the multiple correlation results are averaged, the correlation result converges. This raises the173

question of how many individual measurements must be averaged until the correlation output con-174

verges. Without considering the corresponding sound velocities, the number of measurements was175

evaluated that was required for the ToF to lie consistently within ±2.5 % of the final ToF, which176

was obtained using the total number of 100 pulses. To account for the stochastic variations in the177

individual correlation outputs, this convergence analysis was executed on 100 permutations of the178

correlation data from each specimen and ACU transducer combination. Figure 3j shows the re-179

sults from this analysis, while the underlying distributions are shown in Figures S4 and S5 in180

the Supporting Information.181

For most specimens, the fluidic transducer requires more individual pulses to be averaged than the182

piezoelectric transducer. In general, the most repetitions were required for the concrete specimens,183

both using the fluidic and the piezoelectric transducer. Except for specimen C80 with fluidic ac-184

tuation, the numbers of required repetitions increase with specimen thickness, attributed to in-185

creasing scattering noise and attenuation. For fluidic measurements at two specimens, C240 and186

P312, the results converge late, requiring almost all of the measured pulses. This indicates that187

either more pulses are required to faithfully measure the ToF or that the SNR in these measure-188

ments is so low that no stable ToF can be determined. For most other non-concrete specimens, a189

single digit number of measurements was needed to achieve convergence. The piezoelectric trans-190

ducer converged immediately for all non-concrete specimens. Concrete and polyamide have the191

highest specific acoustic impedance of the materials tested in this study, which results in the lowest192

transmitted acoustic energy. Thus, the influence of noise on the correlation result is greater. The193

convergence results show that the high acoustic pressure generated by the fluidic transducer can-194

not fully compensate for the influence of its diverging ultrasonic field, reducing the usable acoustic195

energy arriving at the receiver. However, in the lower acoustic impedance materials, the radiation196

characteristics of the proposed transducer are sufficient to obtain results with a small number of197

repetitions.198

2.3 Time-of-Flight Measurements199

The measured ToFs and velocities obtained by applying the described method are shown in Fig-200

ure 4a and 4b, respectively, and detailed in Table S1 in the Supporting Information. Qualita-201

tively, the velocities measured by the different transducers agree well for most specimens. However,202

2.5 Publication V

2.3 Time-of-Flight Measurements 2 RESULTS AND DISCUSSION

Figure 4: Measurement results of the fluidic transducer compared to the piezoelectric and contact transducer. The

specimens are abbreviated using the initial letter of their material followed by their thickness in mm, e.g. C160 is

the concrete specimen with a thickness of 160 mm. All specimens used in this study are tabulated in the Experi-

mental section. (a) Time of flight. (b) Longitudinal velocity cL. The bar referring to the fluidic transducer results

for specimen P312 (∗) is cropped. The actual velocity is calculated to be 156000 m/s. (c) Peak-to-peak ratio (P2P)

of the cross-correlation output. The ∞sign for the P2P of the fluidic transducer transmitting through the first three

concrete specimens indicates that no second peak was found, so the P2P would approach infinity. Data from the

contact transducer is not included as the P2P measure is applicable only to the ACU measurements.

there are a number of notable exceptions. For the concrete specimens and two of the spruce spec-203

imens, the ACU measurements consistently show lower velocities than the contact measurements,204

which corresponds to longer ToFs. For heterogeneous materials, two effects have been described to205

cause ToF deviations. First, the ToF overestimation can be caused by different paths taken by the206

signal through the materials, as argued by Purnell et al. [71] and Berriman et al. [72] who encoun-207

tered significant TOF deviations when comparing ACU and contact ultrasound measurements on208

concrete. When the signal is transmitted from the air to the specimen, it tends to couple into the209

portion of the material with lower specific acoustic impedance. In concrete, this is the cement in-210

stead of the aggregates. This results in a path of propagation that is longer than the direct path to211

the receiver. Second, both concrete [13, 73] and wood [74, 75] exhibit dispersive behavior, charac-212

terized by reduced acoustic velocity for lower frequency signals generated by the ACU transducers.213

A third error source is not limited to heterogeneous materials, but to specimens that are slim in214

the off-axis direction, such as the long side of the ballistic gel specimen. The directivity of the trans-215

ducer influences the cross-correlation result by reflections inside the specimen. The ultrasonic waves216

generated by the fluidic transducer presented in this study, contrary to those from the piezoelectric217

ACU transducer, cannot be considered as plane waves. Thus, reflections on the boundaries of the218

2 Publications

2.4 Output Quality 2 RESULTS AND DISCUSSION

specimen arriving later at the receiving sensor than the direct wave may cause a higher correlation219

result than the direct wave, leading to an erroneous ToF pick. However, these error sources do not220

explain the large velocity measured with the fluidic transducer through the thickest dimension of221

the PA6 specimen (P312), the cause of which remains unclear. The non-convergence of the ToF222

(Section 2.3) can be interpreted as an early indicator of these faulty results. This is also the only223

significant negative ToF deviation of the fluidic transducer from the contact measurements.224

The ToF deviation of the fluidic measurements compared to the contact measurements was within225

5µs for all specimens except the thinnest spruce specimen (S58) and the thickest side of the bal-226

listic gel (B412). For these two exceptions, the deviation was still within one period of the domi-227

nant 30 kHz wavelength. The resulting deviations of the measured longitudinal velocity depended228

strongly on the specimen thickness. Thus, the measured velocity deviations were high for the thinnest229

concrete specimens (21.8 %) and for the thickest side of the ballistic gel block (9.7 %), although230

the ToF deviation by the latter was seven times higher. Generally, the measured longitudinal ve-231

locities shown in Figure 4b were comparable for all transducer types, except for the aforemen-232

tioned P312 specimen. In detail, there were cases where one transducer deviates moderately from233

the others. Apart from the fact that deviations were more frequent for heterogeneous materials,234

these outliers showed no discernable trend.235

The results presented in Figures 4a and 4b show that this signal is suitable for measurement of236

longitudinal acoustic velocity in transmission mode. The identified ToFs of the fluidic transducer237

agreed well with the reference measurements except for two specimens. Except for the largest prop-238

agation distances in polyamide and the ballistic gel (P312 and B412), the ToF difference between239

the fluidic measurements and the reference measurements was smaller in homogeneous materials240

than in heterogeneous ones.241

2.4 Output Quality242

The peak-to-peak ratio (P2P) of the cross-correlation output, given as the ratio of the cross-correlation243

maximum to the secondary positive peak in the observed time interval, was chosen as the measure244

of output quality. The P2P is based on the peak sidelobe ratio (PSLR), which is often used as a245

quality measure in radar technology [76]. While the PSLR is a measure calculated from the auto-246

correlation of the transmitted signal, the P2P of the cross-correlation result indicates how clearly247

the correlation maximum can be distinguished from later peaks. These peaks can be caused by248

multiple reflections or alternative sound propagation paths in the actual specimens. Figure 4c249

shows that the P2P of the correlation results from the fluidic transducer measurements is in all250

cases equal or superior to the results with the piezoelectric transducer. Only for the specimens that251

exhibit large ToF deviations and thus seem to be already faulty, differences in the results can be252

seen. For the thinnest portions of the concrete specimen, no P2P values could be calculated be-253

cause there was only one correlation peak in the time frame investigated, leading to a theoretical254

P2P of infinity.255

The generally higher P2P value of the fluidic transducer compared to the piezoelectric transducer256

is caused by the inherent pulse compression of the transducer [54]. Since the piezoelectric trans-257

ducer produced a very reproducible narrowband signal, the correlation result appears as a short258

narrowband wave packet containing multiple local maxima (see Figure S4 in the Supporting In-259

formation). The amplitudes of the maxima are close to each other, resulting in a low P2P. The sig-260

nal of the fluidic transducer did not produce a packet-like result, but a single prominent peak. De-261

pending on the investigated time frame of the correlation output, this peak can even be singular,262

as in the case of the thin concrete specimens. Since the emitted acoustic wave cannot be consid-263

ered as a plane wave, most of the acoustic energy entering the specimen is refracted off the direct264

sound path to the backwall vibrometer. Thus, the sensed particle velocity has a low signal-to-noise265

ratio, requiring averaging of the correlation results. While this averaging aids the convergence of266

2.5 Publication V

4 EXPERIMENTAL SECTION

the calculated ToF, i.e., the time shift at the cross-correlation maximum, it does not significantly267

increase the piezo transducer’s P2P, which is limited by the waveform. However, the P2P of the268

fluidic transducer is additionally increased, as random noise terms are canceled out. The P2P of269

the fluidic transducer then converges like the ToF, as only systematic sources of correlation max-270

ima remain.271

3 Conclusions272

A novel air-coupled ultrasound transducer for non-destructive testing based on the design of a bistable273

fluidic switch is presented. This fluidic transducer uses pressurized air to generate an ultrasonic274

pressure signal in the ambient air without the impedance mismatch losses common to conventional275

transducers. Due to its simple and rugged design, it can theoretically withstand harsh environ-276

ments that are outside the operating conditions of conventional ultrasonic transducers. The signal277

has an average peak acoustic pressure of 320 Pa and a frequency range of up to 60 kHz. Trans-278

ducer performance for time-of-flight measurements in through-transmission was investigated for279

various homogeneous and inhomogeneous materials and compared to a conventional piezoelectric280

air-coupled transducer and a conventional contact transducer with comparable center frequency.281

While the results showed deviations between all transducers, the measured acoustic velocities fell282

largely within the expected range. Due to the inherent random modulation of the fluidic pulses283

and the high acoustic pressure, the peak-to-peak ratio of the cross-correlation results was generally284

higher and the time-of-flight results converged as well or faster than the piezoelectric air-coupled285

transducer. The results show that the fluidic transducer is suitable for through-transmission mea-286

surements of various technically relevant materials. This first proof of usabilitity and competitive-287

ness enables the exploration of further use cases that require robust ultrasound generation. Beside288

determining the environmental limits of this transducer, further research will be directed at opti-289

mizing the generated waveform in terms of length and frequency content to broaden the range of290

realizable measurement tasks. Developing alternative receiver strategies will alleviate the depen-291

dence on optical access vibrational sensitivity of the currently employed LDVs and reduce the bar-292

rier to adaption in industrial settings by lowering the cost of equipment.293

4 Experimental Section294

Fluidic transducer operation: The fluidic transducer was operated in the mode described in a pre-295

vious study [77] and shown in Figure 3a. A constant pressure of 1.8 bar was applied to the main296

inlet. The control valves (MHJ10 by Festo, Germany) were operated for 15 ms each to initiate the297

switching process and subsequently reset the fluidic state, at a pulse repetition rate of 4 Hz. The298

control flow tube has a length of 250 mm. An additively manufactured exponential horn (length299

ℓ= 86.6 mm and exponent ε= 36.6) was mounted on its main outlet O1, while the secondary300

outlet O2 was equipped with an AMTE brass silencer (Festo, Germany).301

Microphone averages: The ultrasonic field of the fluidic transducer was investigated with a cal-302

ibrated microphone (MK301 measurement microphone capsule with MV302 preamplifier by Mi-303

crotech Gefell, Germany). These data were recorded using a USB-6361 DAQ (National Instruments,304

USA). The average peak sound pressure was determined using 40 individual pulses at each mea-305

surement point. The accuracy of these averaged maximum pressure values was estimated to be306

about ±5% [77].307

Materials: The materials used in this study are listed in Table 1 together with the dimensions308

of the specimens and the literature values for the respective sound velocities. The time window309

2 Publications

4 EXPERIMENTAL SECTION

Table 1: Materials tested in this study and a selection of literature values for their longitudinal sound propagation

velocity cLand mean longitudinal sound propagation velocity ¯cLused to determine the time interval in which the

cross-correlation is evaluated.

Material Through thickness [mm] Specimen shape cL[m/s] ¯cL[m/s]

Concrete 80, 120, 160, 200, 240 Step-shaped block, with 5

steps of 400 mm ×400 mm

width

4200 . . . 5000 [13, 78] 4600

Spruce 58, 78, 98 3 timber beams each of

200 mm ×400 mm width

1146 . . . 1850 [79, 80, 81] 1500

Polyamide 6 206, 262, 312 Single block with

the dimensions

206 mm ×262 mm ×312 mm

2635 . . . 2653 [68, 82] 2645

Ballistic gel 145, 415 Single block with the dimen-

sions 145 mm ×145 mm

×415 mm

1424 . . . 1470 [66, 83, 67] 1450

[τl, τu] in which the cross-correlation maximum occurs was limited to both reduce the computation310

time and exclude cross-correlation maxima caused by the airborne sound interacting with the back-311

surface vibrometer. The lower limit of this time windows was set to τl= 0 µs, which would corre-312

spond to an infinite longitudinal velocity or an infinitely thin specimen. The upper limit was set to313

τu= 1.5d/¯cL, where dis the specimen thickness and ¯cLis the center velocity of the material un-314

der investigation (see Table 1). This upper limit allows an underestimation of longitudinal velocity315

by 33 % and an underestimation of the material thickness by 50 %. In practical applications where316

more precise a priori knowledge is included in the process, the time window for maximum search317

may be reduced significantly.318

Contact measurements: Contact ToF measurements were conducted with two single 100 kHz S0208319

piezoelectric transducers (ACS, Russia) for sending and receiving. They were coupled to the spec-320

imen using a thin layer of petroleum jelly. The contact transducers were excited using a A1220321

Monolith ultrasonic tester (ACS, Russia) and sensed with the same device at a sampling rate of322

1 MSs-1. The first maximum of the signal was chosen to determine the ToF.323

Air-coupled measurements: ACU ToF measurements were conducted using two laser Doppler vi-324

brometers (Nova Sense by Optomet, Germany, and OFV 3001 vibrometer controller with OFV 303325

laser head from Polytec, Germany) and a M2p5966-x4 measurement card (Spectrum Instrumenta-326

tion, Germany) with a sampling rate of 20 MSs-1 for recording. The measurement setup was based327

on a previous study [62]. While one vibrometer (LDV1) was used in refracto-vibrometry (RV) mode,328

the other (LDV2) was aimed at the back surface of the specimen. When an LDV laser beam is329

used as an acoustic sensor in RV mode, it is sensitive to all acoustic signals that pass the laser beam330

perpendicularly. Therefore, the LDV records the incoming signal from the transducer and the sig-331

nal reflected from the specimen surface. Autocorrelation of the signal from LDV1 resulted in a sec-332

ondary peak corresponding to twice the time delay between the acoustic signal passing the laser333

beam and entering the specimen. The ToF through the specimen can then be determined by cross-334

correlating the two LDV signals and subtracting the in-air time delay and a separately determined335

hardware delay.336

Contrary to the study that introduced this measurement technique [62], the LDVs in the current337

investigation did not measure the same physical quantities. LDV1 in RV operation sensed the tem-338

poral change in refractive index n(t) so that the signal s1(t) = s1(∂n/∂t). In the pressure range339

considered here, n(t) can be considered as a linear function of the acoustic pressure p[84], so that340

s1(t) = s1(∂p/∂t). The second vibrometer measured the particle velocity at the specimen surface.341

This is in phase with p(t) in far-field condition. Thus, s1(t) was integrated before correlation to342

correct for the π/2 phase shift between sound pressure and particle velocity.343

2.5 Publication V

REFERENCES REFERENCES

The hardware delay for the settings used in this experiment was determined to be td= 160 µs by344

focusing the vibrometers on the same spot of a rigid surface and vibrating them with a small ham-345

mer. The in-air time delay was calculated individually for each measured ultrasonic pulse so that346

small changes in cL,air were corrected for each instant.347

A piezoelectric ACU transducer NCG100-S63 (Ultran Group, USA) with a center frequency of 80 kHz348

[40, 62] was used for comparison with commercial systems. The same measurement setup was used.349

All signals were band-pass filtered using a Butterworth filter in the [20,100] kHz range. The dis-350

tances from the surface to the transducers and the RV laser beam were 110 mm and 50 mm, re-351

spectively. Although the transducer positioning influences the achievable sound pressure of the ul-352

trasonic pulse entering the specimen, depending on the transducer directivity, the same transducer353

positions were chosen to obtain comparability for practical applications.354

Supporting Information355

Supporting Information is available from the Wiley Online Library or from the author.356

Acknowledgements357

This research was funded by the German Federal Ministry for Economic Affairs and Climate Ac-358

tion (BMWK) under the Zentrales Innovationsprogramm Mittelstand (ZIM) grant number ZF4044222WM7.359

Conflict of Interest360

The authors declare no conflict of interest.361

Data Availability362

The data that support the findings of this study are available from the corresponding author upon363

reasonable request.364

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[63] T. Ehrhart, R. Steiger, A. Frangi, Eur. J. Wood Wood Prod. 2018,76, 3 925.452

[64] M. O. Culjat, D. Goldenberg, P. Tewari, R. S. Singh, Ultrasound Med. Biol. 2010,36, 6 861.453

2 Publications

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[67] L. Al-Zogbi, B. Bock, S. Schaffer, T. Fleiter, A. Krieger, Ultrasound Med. Biol. 2021,47, 3458

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[68] S. Maack, Doctoral thesis, Technische Universit¨at Berlin, Germany, 2012.460

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Berlin, Germany, 2018 1–10.463

[71] P. Purnell, T. H. Gan, D. A. Hutchins, J. Berriman, Cem. Concr. Res. 2004,34, 7 1185.464

[72] J. Berriman, P. Purnell, D. A. Hutchins, A. Neild, Ultrasonics 2005,43, 4 211.465

[73] M. Schickert, M. Krause, In Non-Destructive Evaluation of Reinforced Concrete Structures,466

volume 2, book section 22, 490–530. Woodhead Publishing, Cambridge, UK, 2010.467

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mark, 2014.483

2.5 Publication V

S.1 Directivity of refracto-vibrometry

Supporting Information1

Benjamin B¨uhling* Stefan Maack Christoph Strangfeld2

S.1 Directivity of refracto-vibrometry3

Transmission measurements were conducted using a recently introduced non-invasive technique [1]4

based on the use of a laser Doppler vibrometer in refracto-vibrometry mode to measure an in-air5

reference signal before the acoustic pulse enters the specimen (see Experimental Section). The sig-6

nal obtained by refracto-vibrometry is not a point, but a line measurement along the laser beam7

intersecting the sound field. The obtained signal sRV is described by [2, 3]:8

sRV (t) = α1

n0 ∂n

∂p!d

dtZLp(t) dl(1)

where p(t) is the sound pressure, n0is the refractive index of air, Lis the length of the laser beam9

intersecting the sound field, and (∂n/∂p) is the piezo-optic coefficient. The directivity factor αde-10

pends on the wave number of the signal K, the intersection length Land the angle of incidence θ11

of the sound wave passing through the laser beam:12

α=|sinc(KL sin θ)|.(2)

Thus, if the aperture expressed by KL is large, refracto-vibrometry has a very high directivity,13

where waves passing the laser beam non-perpendicularly have little effect on the output signal.14

To evaluate the directivity of the refracto-vibrometry approach in the setup used in this study,15

Lwas approximated by the full width at half maximum (FWHM) of the peak sound pressure of16

the transducers. The intersection length was Lp= 45 mm for the piezoelectric transducer and17

Lf= 87 mm for the fluidic transducer at a distance of y= 110 mm from the respective transducer18

surface. For a peak frequency of 80 kHz of the piezoelectric transducer and 30 kHz of the fluidic19

transducer, the respective apertures were KLp= 67 and KLf= 48. From the resulting refracto-20

vibrometric directivities shown in Figure S1, it can be concluded that the aperture is high enough21

to allow only a small angular range of acoustic waves to affect sRV , allowing precise ToF measure-22

ments [1].23

Figure S1: Directivity of the laser Doppler vibrometer in refracto-vibrometry mode as a function of the angle of inci-

dence of the wave fronts relative to the laser beam. As this directivity depends on the sound field characteristics of

the employed transducer, the directivity factor αis plotted for both the piezoelectric and fluidic transducers.

2 Publications

S.2 Acoustic signal of the piezoelectric ultrasonic transducer

Figure S2: Acoustic characteristics of the piezoelectric ACU transducer: (a) time signal at 110 mm distance, (b) fre-

quency domain of this signal, (c) sound field of the maximum absolute sound pressure ˆp. The data were taken from

a public data set [7].

S.2 Acoustic signal of the piezoelectric ultrasonic transducer24

The NCG100-S63 piezoelectric transducer is a commercially available device for air-coupled ultra-25

sound (ACU) non-destructive testing (NDT). It was used in a previous study as comparison to the26

fluid ultrasonic transducer [4], and its sound field was discussed in detail. Its usability for NDT has27

been discussed in previous PhD theses [5, 6]. The time signal and frequency content of a pulse, as28

well as the acoustic field, were reproduced from a public data set [7] to provide a reference to the29

fluidic transducer characteristics presented in Section 2.1.30

The pulse was excited using a 12.5µs square pulse, resulting in an ultrasonic burst with a duration31

of about 300 µs (Figure S2a). Although the nominal center frequency of the transducer is speci-32

fied by the manufacturer to be 100 kHz, Figure S2 shows that the actual peak frequency is around33

80 kHz [1], independent of the excitation pulse frequency [5]. The acoustic field of the transducer34

shown in Figure S2c has a high directivity and a peak pressure maximum of 160 Pa at 235 mm35

from the transducer surface.36

S.3 Acoustic power calculation37

The power of the fluidic transducer was calculated assuming rotational symmetry of the sound field38

shown in Figure 2. Using a characteristic acoustic impedance of Zair = 407 Rayl [8], the acoustic39

power of the transducer was calculated using40

2.5 Publication V

S.4 Sound field of the secondary fluidic pulse

Figure S3: Sound field of fluidic transducer pulses generated while transducer was (a) switched on and (b) was

switched off, where ˆpis the average maximum sound pressure at each measurement point. The dashed line indicates

the distance from the specimen (110 mm) used in this study.

P=ZφZz| |ˆ

Id dφ, φ = [0, π], = [−0.1,0.1] m (3)

where ˆ

I= ˆp2/Zair is the acoustic intensity of the average peak acoustic pressure of the fluidic ul-41

trasound pulses. The result can be interpreted as a lower bound estimate since the angle of inci-42

dence of the acoustic waves is not necessarily perpendicular to the microphone axis. Due to the43

microphone directivity, the off-axis acoustic pressure and thus the total acoustic power is under-44

estimated. The acoustic intensity was calculated using the radial sound pressure distribution at45

a distance of y= 20 mm from the transducer outlet (Figure 2b). The acoustic power amounted46

to 0.23 W, which is about four times the power of the piezoelectric transducer similarly calculated47

from the data presented in Supplementary Information S.2.48

S.4 Sound field of the secondary fluidic pulse49

The secondary pulse generated when the fluidic transducer had been switched off was produced50

by the same fluidic mechanism as the primary pulse. However, a previous study [9] has shown that51

the sound pressure generated by a fluidic transducer is reduced when the static pressure in the in-52

active control port has not reached a steady state, i.e., when there is still an outflow from the in-53

active control port. This is the case in this experiment, where the switching-off mechanism is trig-54

gered immediately after the transducer reaches a stable on-state. If only the fluidic transducer is55

used without a horn to reduce the flow velocity downstream of the device, the sound field of the56

2 Publications

S.5 Detailed results of the time-of-flight measurements

secondary pulse diverges as the pulse is emitted into the decaying jet flow of the on-state [4]. Due57

to the diffuser property of the horn, this flow field was highly attenuated, so that no significant off-58

axis divergence was observed when comparing the sound fields of primary (Figure S3a) and sec-59

ondary pulses (Figure S3b).60

S.5 Detailed results of the time-of-flight measurements61

The complete results of the time-of-flight (ToF) measurements of the different materials using a62

piezoelectric and a fluidic transducer are given in Table S1. The corresponding histograms of the63

convergence tests of the piezoelectric and fluidic transducers are given in Figures S4 and S5, re-64

spectively. The cross-correlation outputs of the piezoelectric and fluidic transducers are given in65

Figures S6 and S7, respectively.66

Table S1: Measurement results of the fluidic transducer compared to the piezoelectric air-coupled transducer. The

columns refer to the material, the specimen thickness d, the according label, the calculated longitudinal velocity cL,

the percentage deviation of cLfrom the air-coupled measurements compared to the contact measurements ϵc, the

ToF t, the absolute divergence of tfrom the air-coupled measurements compared to the contact measurements, the

peak-to-peak ratio of the correlation output ϵt, and the pulses needed until the correlation output converges.

Convergence [-]

Material d[mm] Label ACU Transducer cL[ms−1]ϵc[%] t[µs] ϵt[µs] P2P [-] (Percentile 5/50/95)

Concrete 80 C80 Fluidic 3912 -21.8 20.45 4.45 ∞21/61/84

Piezoelectric 4908 -1.8 16.30 0.30 1.37 2/7/28

Concrete 120 C120 Fluidic 4404 -8.3 27.25 2.25 ∞5/21/49

Piezoelectric 4580 -4.6 26.20 1.20 1.04 1/14/57

Concrete 160 C160 Fluidic 4463 -2.4 35.85 0.85 ∞12/37/67

Piezoelectric 4571 0.0 35.00 0.00 1.12 2/17/50

Concrete 200 C200 Fluidic 4400 -5.4 45.45 2.45 1.38 14/50/80

Piezoelectric 3568 -23.3 56.05 13.05 1.06 1/22/78

Concrete 240 C240 Fluidic 4585 -0.7 52.35 0.35 1.68 76/99/100

Piezoelectric 4520 -2.1 53.10 1.10 1.08 11/46/84

Spruce 58 S58 Fluidic 1015 -35.3 57.15 20.15 1.74 1/1/1

Piezoelectric 1079 -31.2 53.75 16.75 1.84 1/1/1

Spruce 78 S78 Fluidic 1711 0.9 45.60 -0.40 3.08 1/1/1

Piezoelectric 2308 36.1 33.80 -12.20 1.20 1/1/1

Spruce 98 S98 Fluidic 1750 -1.8 56.00 1.00 2.43 1/1/3

Piezoelectric 1390 -22.0 70.50 15.50 1.04 1/9/45

Polyamide 6 206 P206 Fluidic 2663 0.8 77.35 -0.65 1.28 1/1/4

Piezoelectric 2631 -0.4 78.30 0.30 1.13 1/1/3

Polyamide 6 262 P262 Fluidic 2684 1.4 97.6 -1.40 1.16 1/6/31

Piezoelectric 2628 -0.7 99.70 0.70 1.14 1/1/3

Polyamide 6 312 P312 Fluidic 156000 5800 2.00 -116 1.01 93/99/100

Piezoelectric 2616 -1.0 119.25 1.25 1.12 1/2/6

Ballistic gel 145 B145 Fluidic 1435 -2.0 101.05 2.05 1.37 1/1/2

Piezoelectric 1415 -3.4 102.50 3.50 1.19 1/1/1

Ballistic gel 412 B412 Fluidic 1319 -9.7 312.4 30.4 1.11 1/1/4

Piezoelectric 1464 0.2 281.40 -0.60 1.12 1/1/1

2.5 Publication V

S.5 Detailed results of the time-of-flight measurements

Figure S4: Histogram of averages required to obtain a converged ToF result with samples drawn from the acquired

sample of 100 pulses, using the piezoelectric air-coupled transducer: (a) 80 mm concrete; (b) 120 mm concrete; (c)

160 mm concrete; (d) 200 mm concrete; (e) 240 mm concrete; (f) 58 mm spruce wood; (g) 78 mm spruce wood;

(h) 98 mm spruce wood; (i) 206 mm polyamide 6; (j) 262 mm polyamide 6; (k) 312 mm polyamide 6; (l) 145 mm

ballistic gel; (m) 412 mm ballistic gel. The gray lines are the first five individual cross-correlation results, and the

magenta lines are the mean cross-correlation results.

2 Publications

S.5 Detailed results of the time-of-flight measurements

Figure S5: Histogram of averages required to obtain a converged ToF result with samples drawn from the ac-

quired sample of 100 pulses, using the fluidic air-coupled transducer: (a) 80 mm concrete; (b) 120 mm concrete;

(h) 98 mm spruce wood; (i) 206 mm polyamide 6; (j) 262 mm polyamide 6; (k) 312 mm polyamide 6; (l) 145 mm

ballistic gel; (m) 412 mm ballistic gel. The gray lines are the first five individual cross-correlation results, and the

magenta lines are the mean cross-correlation results.

2.5 Publication V

S.5 Detailed results of the time-of-flight measurements

Figure S6: Cross-correlation results obtained using the piezoelectric air-coupled transducer: (a) 80 mm concrete;

(b) 120 mm concrete; (c) 160 mm concrete; (d) 200 mm concrete; (e) 240 mm concrete; (f) 58 mm spruce wood;

(g) 78 mm spruce wood; (h) 98 mm spruce wood; (i) 206 mm polyamide 6; (j) 262 mm polyamide 6; (k) 312 mm

polyamide 6; (l) 145 mm ballistic gel; (m) 412 mm ballistic gel. The gray lines are the first five individual cross-

correlation results, and the magenta lines are the mean cross-correlation results.

2 Publications

S.5 Detailed results of the time-of-flight measurements

Figure S7: Cross-correlation results obtained using the fluidic air-coupled transducer: (a) 80 mm concrete; (b)

120 mm concrete; (c) 160 mm concrete; (d) 200 mm concrete; (e) 240 mm concrete; (f) 58 mm spruce wood; (g)

78 mm spruce wood; (h) 98 mm spruce wood; (i) 206 mm polyamide 6; (j) 262 mm polyamide 6; (k) 312 mm

polyamide 6; (l) 145 mm ballistic gel; (m) 412 mm ballistic gel. The gray lines are the first five individual cross-

correlation results, the magenta lines are the mean cross-correlation results.

2.5 Publication V

REFERENCES REFERENCES

References67

[1] B. B¨uhling, S. K¨uttenbaum, S. Maack, C. Strangfeld, Sensors 2022,22, 6.68

[2] A. Torras-Rosell, Doctoral thesis, Technical University of Denmark, Kongens Lyngby, Denmark,69

2014.70

[3] A. Torras-Rosell, S. Barrera-Figueroa, F. Jacobsen, J. Acoust. Soc. Am. 2012,131, 5 3786.71

[4] B. B¨uhling, C. Strangfeld, S. Maack, T. Schweitzer, J. Acoust. Soc. Am. 2021,149, 4 2150.72

[5] B. Gr¨afe, Doctoral thesis, Technische Universit¨at Berlin, Germany, 2009.73

[6] S. Maack, Doctoral thesis, Technische Universit¨at Berlin, Germany, 2012.74

[7] B. B¨uhling, S. Maack, E. Sch¨onsee, T. Schweitzer, C. Strangfeld, Data in Brief 2021,3875

107280.76

[8] L. L. Beranek, T. J. Mellow, Acoustics: Sound Fields and Transducers, Academic Press, Ox-77

ford, UK, 2012.78

[9] B. B¨uhling, T. Schweitzer, S. Maack, C. Strangfeld, In Fortschritte der Akustik – DAGA 2021.79

DEGA, Berlin, Germany, 2021 48–51.80

2 Publications

3 Results and Discussion

The goal of this dissertation was to improve air-coupled ultrasonic testing by using a novel aeroa-

coustic ultrasonic transducer based on a bistable fluidic wall-attachment amplifier. To achieve

this, five research questions were formulated in Section 1.6. The research conducted to answer

these questions was published as Publications I – V and reproduced in the previous chapter.

Figure 3.1 shows schematically how the publications relate to the final through-transmission

ToF setup as a whole. Publication I discusses the flow field and acoustic signal characteristics

of the transducer and their interactions. In doing so, it provides the baseline data for subsequent

publications. Publication II explores the possibility to manipulate the sound field in order

to separate it from the from field using sonic crystals. Although these structures were shown

to be capable of performing this function, an exponential horn was used instead in the final

through-transmission setup. In Publication III, it is shown that the characteristics inherent

in the signal can be interpreted as random phase modulation. A signal processing approach is

proposed that utilizes this modulation to enable multi-input multi-output measurements. Pub-

lication IV presents a novel contact-free ToF measurement method based on the use of a laser

Doppler vibrometer in refracto-vibrometry mode, which does not require any prior information

about the transducer characteristics or the exact setup. This setup is applied to the fluidic

transducer in Publication V to test various specimens of different materials and thicknesses.

In an all-optical setup, it is shown that the fluidic transducer compares well with conventional

transducers and provides high-quality results in through-transmission ToF measurements.

In this chapter, the results of the publications and the overarching methodology are summa-

rized and discussed with respect to the research questions formulated in Section 1.6. By placing

this discussion in an overall context, the opportunities and limitations of the approaches to using

a fluidic transducer pursued in this work are examined.

Figure 3.1: Schematic contextualization of the publications in relation to the final measurement setup.

3 Results and Discussion

3.1 Transducer and Operation

The fluidic transducers investigated in this work are based on a bistable fluidic amplifier geometry

developed by Bobusch [181], with the final design developed in cooperation with FDX Fluid

Dynamix GmbH (Berlin, Germany). The fluidic transducers were milled from brass and eroded

in BAM’s precision workshop. The first version of the transducer used in Publications I

and II, is shown in Figure 3.2a. It has the same functional geometry as the fluidic amplifier

shown in Figure 1.3, except that the outlets are not symmetric. The primary outlet, through

which the acoustic pulse is supposed to leave the device, defines the binary on-state and its

channel intersects the outlet plane perpendicularly. The secondary outlet channel, defining the

off -state, is led to the side of the device and is equipped with a deflection plate. The exact

internal dimensions of the transducer were presented by Schweitzer et al. [216].

To meet the later requirement to mount peripheral equipment, the design of the transducer

was changed (see Fig. 3.2b). All inlets and outlets were elongated to allow for threads, while

the functional design remained unchanged. The primary outlet was fitted with an exponential

horn and the secondary outlet with a muffler. This design was used in Publications III – V.

The operation procedure of the fluidic transducer was also different in Publications I and

II compared to the following papers. In Publications III – V, the transducer was operated

similarly to the regular operation procedure of a bistable amplifier (see Section 1.5). In a

parallel connection with an input pressure of 1.8−2 bar, two solenoid valves were opened and

closed successively to bring the transducer into either the on- or off -state (see Fig. 3.3b). In

Publications I and II, only one solenoid valve was used to switch on the device, while the

opposite control port was constantly fed with lower pressure air. In this monostable operation,

the main flow automatically switches off as soon as the solenoid valve is turned off (see Fig. 3.3a).

The implications of this change in procedure are discussed in Section 3.2.

3.2 Signal Characteristics and Flow-Sound Interactions

As pointed out in Sections 1.4 and 1.5.3, there is little research on the use of aeroacoustic

devices as ultrasonic transducers. Moreover, no precedent exists in which they have been used

Figure 3.2: Versions of the fluidic transducer incorporating all the elements of a bistable amplifier, as shown

in Fig. 1.3a. (a) Initial version used in Publications I and II, (b) final version used in Publi-

cations III – V, allowing attachment of peripheral equipment, here an exponential horn and a

muffler.

3.2 Signal Characteristics and Flow-Sound Interactions

Figure 3.3: Operating procedure of the fluidic transducer: (a) monostable operating mode, used in Publica-

tions I and II; (b) bistable operating mode, used in Publications III – V.

to generate transient ultrasonic signals, let alone in which a fluidic amplifier has been used for

this purpose. Thus, as a first step in assessing the applicability of the fluidic transducer for

NDT tasks, the acoustic characteristics of the device were investigated. The main part of this

investigation was published in Publication I and provides the basis for all subsequent research

papers.

The focus of the presented investigation is on the interaction between acoustics and flow.

Although the exact aeroacoustic sound generation mechanism inside the device is not subject of

this study, the flow field outside the device needs to be considered as part of the UT setup. In

order to evaluate both flow and sound characteristics, the operation of the fluidic transducer was

divided into four distinct time segments: the stable on and off states and the transient processes

of switching on and switching off. Other detailed stages during the switching process, outlined

in Section 1.5.2, are omitted due to the lack of knowledge about the time-resolved internal flow

dynamics of the device. Flow velocity measurements were performed only at stable state, since

the response of the Pitot tube used was slower than the time scale of the flow fluctuations

predicted by numerical simulations [216].

The velocity measurements during on state show a high velocity free jet exiting the main

outlet, extending over a length scale relevant for practical ACU measurements. The jet exhibits

a maximum velocity of uj= 293 m/s at a downstream position of 5 mm. This near sonic

velocity is to be expected due to the high pressure at the main inlet of the transducer and has

been confirmed by numerical simulations which also show supersonic flow inside the device [216].

While the non-contact measurement concept of the device still holds, non-destructive measure-

ments may not be possible if the high velocity jet impinges on sensitive surfaces. This issue

is addressed in Publication II, but also affects the results presented in Publication I, since

the microphone measurements could only be obtained off the main flow axis to avoid damaging

the microphone. In the off state, an omnidirectional low velocity suction flow was measured.

The existence of this suction flow is confirmed by previous research on fluidic amplifiers (see

Section 1.5.2). Given the low velocity and undirected flow, the influence of this suction flow

on sound propagation is considered negligible. However, its occurrence indicates probable chal-

lenges concerning the longevity of the fluidic transducer. In a dusty environment, particles may

be entrained and enter the fluidic device. Although the presumed supersonic flow in channels of

several millimeters width suggests a certain self-cleaning behavior, it cannot be ruled out that

particles adhere to the inner walls and change the switching behavior of the main flow [172].

3 Results and Discussion

In the microphone measurements, the four distinct time segments of the fluidic transducer

switching cycle are clearly visible (Figs. 3.4a and 3.4b). When the device is in the off state,

only low-amplitude noise is measured. This is the flow noise of the jet exiting the secondary

outlet channel. When the device is switched on, a short peak in sound pressure is observed,

followed by a period of higher amplitude noise from the jet exiting through the main outlet at

switch-on. The higher sound pressure is attributed to the closeness of the microphone to the

air jet rather than to significant changes in the jet properties downstream of the primary and

secondary outlets. When the transducer is switched off, the sound pressure peaks again before

returning to the off -state with a lower amplitude. Given this sound generation behavior, the

acoustic signal generated during switching is of most interest for further investigations into the

applicability of the fluidic transducer for NDT.

The average peak sound pressure in the ultrasonic range generated at switch-on shows roughly

a point source behavior (see Fig. 3.4e) with only a slightly elliptical spreading. The reason for this

is that the outlet acts similar to a small piston in a rigid baffle due to its low outlet to wavelength

ratio. The ultrasonic pulse emanating from the device propagates into an environment with

omnidirectionally equal sound propagation velocity. The condition of this propagation velocity

field is not met when the second ultrasonic pulse is generated during switch-off of the device.

Since this signal is generated immediately after the airflow inside the fluidic transducer is directed

away from the primary outlet, it propagates into an ambient flow field dominated by the decaying

high velocity free jet that previously existed in the stable on-state. Close to the outlet, this

self-similar flow deceleration has a time scale of 10−4s and takes even longer further downstream

Figure 3.4: Sound characteristics of the fluidic transducer. (a) and (b) representative signals generated by the

fluidic transducers used in Publication I and V, respectively. The stages of the switching cycle

are shaded in colors. (c) and (d) averaged spectra during the stages of the switching process of the

transducers used in Publication I and V, respectively. (e) and (f) average absolute peak sound

pressure pˆ of bandpass filtered ([20,100] kHz) signals of the transducers used in Publication I and

V, respectively.

3.2 Signal Characteristics and Flow-Sound Interactions

[217]. Thus, the ultrasonic pulse propagates into a velocity field that is close to a steady free

jet and therefore encounters an anisotropic sound propagation velocity field. Resulting from

the radially decreasing total propagation velocity, the sound waves diverge from the jet axis,

where the sound pressure then exhibits a local minimum. The corresponding hollow cone-

shaped directivity is known as cone of silence and has been discussed for aeroacoustic sources

inside jets [218] and for ultrasonic signals propagating into a fluid jet waveguide [219], which

conceptually resembles the case at hand. The ultrasonic average peak sound pressure shows

maxima of pˆon = 162 Pa and pˆoff = 121 Pa at switch-on and switch-off, respectively. Thus,

the sound pressure close to the transducer outlet is approximately equal to that of the reference

piezoelectric transducer. In stable states, the effective sound pressure of the steady jet noise

does not exceed 16 Pa and also features a cone of silence while in the on-state.

The four segments of the switching cycle are also clearly distinguishable in the frequency

domain (Figs. 3.4c and 3.4d). In the stable on- and off -states, a jet noise with lower amplitude

is measured in both the audible and ultrasonic frequency ranges. In both pulses generated during

the switching process, additional frequency peaks occur at approximately 35 kHz, 42 kHz, and

56 kHz. These signals therefore contain frequencies that are clearly in the ultrasonic range

that is useful for NDT-CE applications. Notably, the waveforms exhibit stochastic features in

both stable and transient states, which may be caused by control valve jitter and the stochastic

nature of aeroacoustic sound generation due to turbulence. Frequency content, signal onset,

and amplitude are therefore not exactly reproducible, so the given sound fields and spectra are

averaged values. The implications for signal processing and the measurement procedure are

elaborated in Sections 3.4 and 3.6. The main effort of the subsequent research is focused on

using the first pulse for NDT applications, which is generated when the transducer is switching

on, given its higher sound pressure and negligible impact by the steady suction flow field.

Publication I demonstrated that a transducer based on a fluidic amplifier is capable of

producing high-pressure ultrasonic signals and that the interactions between sound and flow

field can be identified. To the knowledge of the author, this was the first description of an

aeroacoustic device for generating a triggered transient acoustic signal that can be used for

ultrasound applications. Based on this knowledge and further parameter studies, the operating

regime and outlet of the transducer were modified in Publication III and V (see Section 3.1).

The almost point source like behavior of the transducer design used in Publication I and II

is unfavorable for UT applications, especially in NDT-CE, because a large part of the emitted

acoustic energy is reflected from the specimen surface. Due to the generally large mismatch

between the longitudinal wave propagation velocities, the permissible entrance angle of the

waves, which prevents total reflection (see Section 1.3), is small. Therefore, most of the acoustic

energy is unused, while the small portion of the wave fronts incident at an angles below θcr is

additionally affected by reflection due to acoustic impedance mismatch (see Sections 1.2). An

increase in directivity would allow more acoustic energy to be incident below the critical angle.

Therefore, in the latest design of the transducer, an exponential horn was mounted downstream

of the main outlet. The horn increases the radiated sound pressure by matching the radiation

impedance of the transducer outlet to the ambience. By increasing the outlet area, the horn

also increases the transducer directivity, acting on the reflection mechanisms described above.

The resulting sound field is shown in Figure 3.4f and features an average peak sound pressure of

pˆon = 320 Pa, which is higher than that of the piezoelectric reference transducer. Changing the

solenoid valve operation from monostable to bistable (see Fig. 3.3) allowed another dominant

frequency in the first pulse at 30.5 kHz, which has twice the amplitude of the remaining higher

frequency peaks.

It is assumed that the constant outflow from the passive control port in the monostable

operation mode of Publication I and II (see Section 3.1) suppresses an internal aeroacoustic

3 Results and Discussion

Figure 3.5: Supply pressure dependence of the pulse characteristics of the initial transducer version using bistable

operation: (a) spectrum as a function of inlet pressure and (b) average absolute peak sound pressure,

both relative to the maximum value.

feedback loop causing this high-amplitude frequency component and, furthermore, reduces the

overall pulse sound pressure [220]. Looking at the fluidic pulse spectrum as a function of inlet

pressure (see Fig. 3.5a), a staging behavior can be observed. A dominant 40 kHz component

is generated for inlet pressures of 1.0 bar ≲pin ≲1.4 bar, whereas the 30.5 kHz component

appears only for inlet pressures 1.3 bar ≲pin ≲2.2 bar. This staging behavior is a typical

behavior of supersonic screech and impingement sound generation (see Section 1.4), which should

be considered as the main sound generation mechanism in further studies. The relative peak

pulse pressure increases with inlet pressure until pin ≈1.8 bar (see Fig. 3.5b) and largely

stagnates beyond that as the sound is increasingly dominated by the broadband higher-frequency

components.

Analysis of the sound and flow fields generated by the fluidic transducer and their interaction

has shown a complex and stochastic behavior. Nonetheless, the sound pressure generated by

the unmodified device compares well to the reference piezoelectric transducer and was modified

to outperform it. It was shown that the simple design of the fluidic amplifier can be adapted

to generate high amplitude transient ultrasonic signals that can be used for NDT applications.

This is the first aeroacoustic or fluidic device for this purpose.

3.3 Separation of Flow and Sound Fields

In Publication I, the fluidic transducer was found to generate a slightly ellipsoidal, almost

spherical sound field accompanied by a high velocity air jet. In applications involving gener-

ally thick and rigid specimens, such as NDT-CE, an impinging jet may cause unwanted high-

frequency noise (see Sec. 1.4). For thin specimens, such as membranes, filters [68] or textiles

[221], it could cause unwanted flexural oscillations. In sensitive specimens, such as artworks [69]

or the human cornea [222], it can even alter surface properties or even cause permanent damage.

Publication II investigates a passive method of redirecting the sound field away from the jet

axis to both improve the directivity of the transducer and prevent the air jet from acting on a

specimen.

A simple and established method to redirect sound in air is the use of a continuous acoustic

3.3 Separation of Flow and Sound Fields

mirror [223]. However, such a device would also redirect the air jet. Publication II presents a

proof-of-concept study on the use of two-dimensional sonic crystals (SCs) to divert the sound field

without altering the main flow direction. SCs are artificial periodic structures used to manipulate

longitudinal waves in fluids [224]. Depending on their geometry, these periodic structures can

cause constructive and destructive interference for certain frequency ranges, allowing waves of

the respective frequencies to pass through the crystal or be blocked [225]. In Publication II,

circular steel rods are arranged in a rectangular grid to create two-dimensional crystals that are

placed in the ambient air at the outlet of the fluidic transducer. These SCs have been calculated

to have a band gap between 45 kHz and 66 kHz, which means that sound transmission is blocked

in the frequency range in which most acoustic energy is radiated by the fluidic transducer. Thus,

for these frequencies, they act similarly to a sound barrier, while allowing the other frequencies

and airflow to pass.

While the spectral bandgap properties of SCs are well understood [224], few studies have

investigated their interaction with flow [226, 227]. Addressing subsonic channels and uniform

flows, rather than free jets at near supersonic speed, they suggest that the main flow direction

through SCs remains unchanged. However, SCs can induce aeroacoustic noise that can annihilate

the effect of the sound barrier initially created by SCs. This effect has been termed bandgap

quenching. The noise induced by the interaction between steady free jet and an SC wall was

assessed. This sound pressure was found to decrease linearly up to a distance of about 5 unit

cell size, from there on the decrease slows down. The number of SC rows had no significant

impact on the bandgap quenching. The addition of SC rows ,e.g., to increase the sound blocking

behavior of the SC, should therefore be restricted only by installation space and not by noise

considerations.

Aiming to deflect the sound perpendicular to the flow field, two different SC arrangements

were tested against the reference cases of a free jet and a jet bounded by one lateral SC wall

Figure 3.6: Effect of the sonic crystal on the transducer sound field: average absolute peak sound pressure

amplitudes in the ultrasonic range for (a) baseline measurement without SC, (b) lateral SC wall,

a= 3.5 mm. The Figure was taken from Publication II.

3 Results and Discussion

(see Figure 3.6). After using a lateral SC wall to verify that the SC indeed blocks ultrasonic

frequencies (see Fig. 3.6b), two different SC arrangements aimed at a perpendicular redirection

of the sound field relative to the jet axis were tested: a waveguide and a mirror concept (see

Figures 3.6c and 3.6d). Both SC arrangements have been shown to be effective in redirecting

sound fields [228]. The baseline measurements were conducted without a SC (see Fig. 3.6a). The

measurements show that the waveguide and mirror geometries are indeed appropriate to change

directivity of the transducer. The waveguide configuration caused an inclination of the main

sound propagation axis by 55◦, but also featured a secondary axis of sound propagation, the

cause of which remains unclear. As a result of this leakage and dissipation inside the waveguide,

the sound pressure of the redirected main lobe was slightly below that of the reference case. The

mirror SC configuration caused a redirection by 60◦and an additional sound pressure increase

compared to the reference case, due to the superposition of the undisturbed parts of the waves

with the redirected ones.

Flow velocity measurements during the stable on- and off -states of the transducers have shown

that the waveguide configuration has a negligible influence on the main flow direction, but slows

the flow to 20 % of its original axial velocity. The axial flow downstream of the mirror SCs

was to slow to be measured with the Pitot tube employed. Measurements of the flow velocity

perpendicular to jet main axis revealed that SCs do not deflect the main flow when slowing it

down. However, they may induce a slight entrainment flow toward the jet axis at locations of

missing SC cells, such as the waveguide outlet or the end of the single-sided SC wall.

In Publication II, it was shown that SCs can be successfully employed to separate the main

sound propagation direction from the main flow axis. Despite the fact that fully perpendicular

deflection was not achieved with the SC configurations used, they were able to increase the

directivity and deflect the main acoustic axis by up to 60◦. Furthermore, it was shown that

bandgap quenching a few millimeters from the jet outlet rapidly loses its significance, adding to

the sparse research on the topic of the interaction of flow with SCs. Additionally, the results

indicate that the entrainment flow enhanced by the SCs has low speed and is thus unlikely to

damage sensitive specimens. Despite this successful proof-of-concept, still requiring a trans-

fer from a two-dimensional study to a three-dimensional crystal design, the SC approach was

dropped in subsequent publications. Instead, the exponential horn was used (see Section 3.2),

which not only increases directivity and sound pressure, but also acts as a diffuser for the flow

exiting the fluidic transducer, reducing the flow velocity downstream of the horn to negligible

values.

3.4 Utilizing the Inherent Signal Characteristics

ToF measurements using transducers that use electromagnetic mechanisms for sound generation

(e.g. piezoelectric and capacitive transducers as well as laser and thermoacoustic transducers)

profit from the repeatability of the sound production process. Triggering with nanosecond accu-

racy and stable impulse response allow easy comparison of distinct signal features to determine

ToF and also enable pulse compression (PuC) techniques to improve signal quality (see Sec-

tion 1.2). However, these properties do not apply to the fluidic transducer investigated here.

Given the valve opening time variation of ±120 µs [229] and the stochastic, turbulence-based

sound generation mechanism of the fluidic amplifier, the system response time, the impulse re-

sponse following the electronic triggering of valve opening, and the pulse length are unknown

a priori. To deal with these unknowns, a method is presented in Publication III to derive

utility for ToF measurements from stochastic pulse properties. Following previous ultrasonic

PuC research that used continuous random signals (in phase and amplitude) [53, 54, 230] or

random frequency modulation [231], the fluidic ultrasonic signal is interpreted as randomly am-

3.4 Utilizing the Inherent Signal Characteristics

plitude and angle modulated. Leveraging this randomness would allow multi-input multi-output

(MIMO) measurement arrangements, which could decrease the overall measurement time for

surface scanning of large specimens.

Based on the signal formulation in Eq. (1.6), redundant envelope information, i.e., amplitude

modulation, between all pulses is removed using Hilbert demodulation. Only its unique spectral

signature remains, which is contained in the angular modulation component and is termed unit

envelope signal (UES). Bedrosian’s theorem states that envelope and the UES need to be fully

band-separated in order separate them without distortion using the Hilbert transform. From

microphone measurements, it is found that the fluidic ultrasound pulses violate this requirement,

as do most real-world signals. However, since there is a large spectral match before and after

decomposition, Hilbert demodulation was considered a suitable method for envelope removal.

After Publication III had been published, a study by Khyam et al. [232] came to the author’s

attention that proposes an approach essentially similar to the one used in Publication III

for detecting multiple echoes in ultrasonic ranging applications. Envelope removal is performed

directly during cross-correlation by exploiting the fact that cross-correlation is usually computed

via Fourier transforms. While not discussing the restrictions posed by Bedrosian’s theorem and

MIMO applications, the presented algorithm is more elegant than the one presented in this

section, since no extra Hilbert transform needs to be performed.

The performance of the Hilbert envelope removal method is evaluated in terms of the mu-

tual interference of the individual signals and their self-interference. The mutual interference is

characterized by the cross-correlation amplitude of the individual pulses related to their auto-

correlation amplitude and therefore determines whether multiple signals in a MIMO setup can

be distinguished. Self-interference describes the peak-to-peak ratio of the pulse autocorrelation

output. Using a series of microphone measurements for mutual interference assessment, it is

shown that Hilbert envelope removal reduces the mean mutual interference by about 3 dB and

its standard deviation by 1.4 dB compared to the original signals. These results show that

the uniqueness of the individual pulses is indeed contained in its random UES. However, in

removing the envelope, signal information is discarded, resulting in increased noise floor in the

cross-correlation result. Compared to the mutual interference results, the envelope removal had

little effect on the self-interference by reducing the autocorrelation peak-to-peak ratio by 1.6 dB.

Departing from this purely in-air assessment of this method to a multi-sensor NDT setup, the

microphone signals were correlated to accelerometer recordings of the same signals after passing

through an aluminum plate. It was found that the average mutual interference advantage of

the UES was reduced to 1 dB, while the difference in standard deviations stayed constant.

The self-interference performance was found to be unaffected by the envelope removal in this

setup, aside from reduction of far sidelobes in the autocorrelation output. These results show

that even in a more realistic setup involving a more complex signal path, the proposed method

results in reduced mutual interference between pulses, thus increasing the MIMO capability of

the transducer. Especially, the decrease in the standard deviation shows that the proposed

method enables a reliable means to distinguish the individual fluidic pulses.

To create a MIMO experiment synthetically, the signals acquired in this experiment were

superimposed at varying amplitudes and relative delays to simulate variations in signal atten-

uation and sensor positioning. The results in Figure 3.7 for two and four superimposed signals

show that the correct correlation maximum, i.e. the ToF of the pulse under inspection, was

more likely to be found using envelope removal when the time delays are short and attenuation

is low. As the delay increases, the individual pulses cease to overlap and are therefore easier to

distinguish. When the pulse under inspection has a much larger amplitude than the interfering

pulses, the information contained in the former dominates the cross-correlation result, making

correct ToF selection more likely. In these cases, the removal of the information associated with

3 Results and Discussion

Figure 3.7: Accuracy in semi-synthetic MIMO experiments: (a) with two subsequent pulses and (b) with four

subsequent pulses. The original signal is compared to the envelope-removed UES, with the interfering

pulses scaled by a factor α. The figure is adapted from Publication III.

the envelope removal reduces the ToF picking efficiency compared to using all the information

in the original signal. The time delay errors of misidentified ToF picks in synthetic experiments

containing two pulses are lower for UES cross-correlation picks than for the original signals, with

both values averaging in the single-digit microsecond range. When four pulses are superimposed,

these values increase to the order of milliseconds. Given the high error in misidentified ToFs

combined with a worst case success rate of roughly 50 %, the use of more than four transducers

of the current design under similar operating conditions does not seem desirable. Although the

fluidic pulses contain an individual spectral signature, only a limited number of them can be dis-

tinguished when recorded simultaneously. Their MIMO capability is therefore more comparable

to chirped pulses, which allow a maximum of two simultaneous pulses, than to more complex

PuC sequences, which allow more simultaneous pulses [231].

The results presented in Publication III show that while the stochastic characteristics of the

fluidic transducer may limit the ToF processing methodology and possible array functionality

requiring controllable phase relations, the inherent spectral signature can be used to facilitate

and enhance MIMO measurements, e.g., in production facilities [108]. This property has been

shown to be usable without additional pulse generation equipment, but it results from the pulse

properties themselves only exploited at the signal processing stage. However, the synthetic

MIMO experiments indicate that the parallel use of a high number of transducers in the given

setup can lead to highly spurious results. Measures such as using a variety of transducers

with different spectral properties or operating multiple transducers at different inlet conditions

(see Fig. 3.5) should improve the detectability of individual pulses and further increase MIMO

capability of fluidic transducers.

3.5 Development of a Fully Non-Contact ToF Measurement Setup

One challenge that the fluidic transducer shares with several other non-contact ultrasound gener-

ators is its inability to sense ultrasound. This makes ToF setups infeasible where two transducers

of the same type are used as band-matched transmitters and receivers, as is frequently the case

with piezoelectric transducers, for example [91]. Fluidic ultrasonic sensors based on laminar

to turbulent flow transition upon ultrasound actuation have been presented (see Section 1.5),

but these were designed for binary ultrasound detection only, and no information is given on

temporal resolution. Furthermore, the ultrasonic pressure exiting the specimen is assumed to

be too low to cause a laminar-turbulent transition. Thus, a non-fluidic receiver setup for use

100

3.5 Development of a Fully Non-Contact ToF Measurement Setup

with a fluidic ultrasonic transducer is required in order to conduct ToF measurements. Com-

mon sensing devices in UT include conventional microphones [234], optical microphones [89],

contact accelerometers [235], and laser Doppler vibrometers [236]. ACU additionally presents

the challenge for ToF measurements that the propagation time of the acoustic signal through

the coupling air is not negligible compared to the searched ToF through the specimen. The

common approach of conducting a reference measurement without a specimen and subsequently

subtracting it from the total ToF [237, 238] are prone to errors due to mispositioning, since an

in-air path length error of only 1 mm causes a ToF error of 2.9µs (see Eq. (1.5)). To allow ToF

measurements without knowledge of ambient conditions or in-air acoustic path length, a novel

measurement technique was developed in Publication IV.

Instead of assuming a fixed sound propagation length and speed through air, a laser Doppler

vibrometer (LDV) is employed using the acousto-optic effect in a refracto-vibrometry (RV)

arrangement [239, 240] to non-invasively record every single ultrasonic pulse before and after

reflection from the specimen surface. This approach leverages both the reflection coefficient at

the air-specimen interface (see Eq. (1.3)) and the ring-shaped directivity of an RV-LDV when

it is used as an acoustic sensor. By autocorrelating the so acquired signal, the time of entry

(ToE), i.e., the sound propagation time from the first pass of the laser beam to its entry into

the specimen, is found. In a through-transmission setup, as shown in Figure 3.8a, the same

RV signal then serves as a reference signal that is cross-correlated with a receiver signal at the

backwall of the specimen. The ToF is then found by subtracting the ToE from the total time

delay obtained by cross-correlation. This measurement concept is verified using a piezoelectric

ACU transducer instead of the fluidic transducer to facilitate repeatable waveforms. In order to

enable high SNR at the backwall, an accelerometer was used as a receiver in Publication IV.

Besides the measurement delay between the measurement devices, the largest source of sys-

tematic error is the mispositioning of the RV laser. The upper bound for a resulting time delay

error was calculated using a geometrical analysis of the sound paths and was found to be below

1µs for reasonable mispositioning distances.

The key concept behind the proposed through-transmission ToF setup is the use of RV-LDV

Figure 3.8: Schematic representation and performance of the novel through-transmission ToF setup: (a) Setup

containing the sound propagation velocities cand the specific acoustic impedance Zof air and

specimen, respectively; distances dT L (between transducer and laser beam), dLS (between laser beam

and specimen) and specimen thickness dS. In Publication IV, a piezoelectric ACU transducer and

an accelerometer were used as the transducer and backwall sensor, respectively. In Publication V,

the fluidic transducer and a second LDV were used as transducer and backwall sensor, respectively;

(b) measured values and literature values for the polyamide specimens. The literature values of

Maack (2012) and Zhu et al. (2014) refer to references [29] and [233], respectively. The figure was

adapted from Publication IV.

101

3 Results and Discussion

to measure the ToE, which is essentially an ultrasonic ranging measurement. Measurements

show that a ToE accuracy of less than 0.4µs, which is equal to 3.5 % of the signal wavelength,

could be reliably achieved with sufficient laser-specimen distance. A comparable approach was

recently proposed by Jia et al. [238] who used a custom made laser diffraction device to leverage

the acousto-optic effect for distance measurements in water. The measurement accuracy as a

fraction of wavelength is of the same order as the results presented in Publication IV. Finally,

the novel measurement concept was applied to a homogeneous polyamide specimen. Comparing

the measured ToF through the material with literature values, Figure 3.8b shows that at a

sufficient laser-specimen distance, the resulting ToF error is below 0.8µs or 1.1 % of the total

ToF.

These results from Publication IV demonstrate that the method provides accurate mea-

surements that require no prior knowledge about the ambient conditions or the measurement

setup, given a certain minimum distance between laser and specimen. It requires only optical

access and can be applied in any immersion fluid at any temperature. Thus, it can also be used

to correct for distance misalignments and changes in couplant propagation velocity, which have

been shown to severely reduce reconstruction accuracy in automated immersion tank measure-

ments [241]. Since a reference signal is always recorded for cross-correlation, this measurement

approach requires no prior knowledge about the exact signal trigger time or the waveform char-

acteristics. Thereby, the challenges posed by the stochastic signal characteristics of the fluidic

transducer are also alleviated. Accordingly, this setup was adapted in Publication V to use the

fluidic transducer for ultrasound generation and a second LDV as the backwall receiver instead.

By doing so, the measurement setup has been further developed to be fully contact-free. While

acoustic impedance losses at the transducer-air interface are avoided by the use of the fluidic

transducer, the use of an LDV additionally prevents impedance losses at the backwall-specimen-

air interface that usually occur with an air-coupled through-transmission setup.

While this setup is easily assembled from commercially available measurement equipment,

using two LDVs for in-situ NDT-CE measurements is not practical because they are large,

sensitive to ambient vibration, and their optics must be kept clean from dust. However, it is

well suited for ToF measurements in a controlled environment where the lasers remain at a fixed

position and the specimen is moved, such as laboratory or production facilities.

3.6 Application to ToF Measurements

In a final step toward investigating its applicability in NDT, in Publication V the fluidic

transducer has been used to conduct ToF measurements in through-transmission. To this end,

a fully non-contact setup was used, based on Publication IV described in the previous section.

The results were compared to a conventional piezoelectric ACU transducer operated in exactly

the same setup and to contact piezoelectric transducers in a through-transmission arrangement,

coupled to the specimens using vaseline. The measurements were conducted on various mate-

rials of varying thicknesses. While the concrete and spruce wood specimens represent common

building materials [242] and are heterogeneous (the anisotropy of wood is not addressed, as all

wood specimens are tested tangential to the fiber orientation), polyamide serves as an example

for polymeric materials [243] and ballistic gel shares its properties with human tissue [244].

Since the ACU results were obtained using the correlation-based method presented previously,

all results are assessed based on their cross-correlation output. Due to the sometimes low SNR

and the stochastic nature of the fluidic transducer signal, the correlation output of multiple

pulses needed to be averaged to obtain a stable result. The convergence behavior of the ACU

methods (see Fig. 3.9a) shows the general trend that the fluidic transducer requires a higher

number of averaged pulse cross-correlation results than the piezoelectric transducer. These

102

3.6 Application to ToF Measurements

numbers are highest for concrete and increase with thickness. It is this material that has the

highest characteristic acoustic impedance, reducing the received SNR significantly. In all other

specimens, the required pulses to convergence are in the single digit, with an exception for the

thickest plane of the polyamide specimen (P312), where the fluidic transducer results do not

converge at all. For reasons that remain unclear, the results from this particular specimen plane

were erroneous throughout the study when the fluidic transducer was used.

Qualitatively, the ToF results of the ACU transducers are generally in good agreement to

the results from the contact transducer, as shown in Figure 3.9b. For the heterogeneous ma-

terial specimens, the ACU ToF are consistently slower than the contact measurements, which

is attributed to coupling effects described in earlier studies [105, 245] and dispersive material

behavior. Furthermore, later pulse arrivals at the backwall caused by sidewall reflections in slim

Figure 3.9: Measurement results of the fluidic transducer compared to the piezoelectric ACU and contact trans-

ducers: (a) measurements required to convergence; whiskers refer to the 5th and 95th percentiles of

the respective distributions. Numbers in the annotations refer to the 95th percentiles. (b) Time of

flight; (c) longitudinal propagation velocity cL; The bar referring to the fluidic transducer results for

specimen P312 (∗) is cropped. The actual speed is calculated to be 156000 m/s. (d) peak-to-peak

ratio (P2P) of the cross-correlation output; The ∞sign for the P2P of the fluidic transducer trans-

mitting through the first three concrete specimens indicates that no second peak was found in the

investigated time frame, so the P2P would approach infinity. In (a) and (d), the contact transducer

data are not included as the respective measures are applicable only to the ACU measurements. The

specimens are abbreviated using the initial letter of their material (concrete, spruce, polyamide, and

ballistic gel) followed by their thickness in mm, e.g., C160 is the concrete specimen with a thickness

of 160 mm. The figure was adapted from Publication V.

103

3 Results and Discussion

specimens may result in higher correlation outputs than for the direct wave. Given the varying

material thickness, ToF deviations have varying impacts on the calculated longitudinal propaga-

tion velocities cL(see Fig. 3.9c). Similar to the ToF results, cLis generally comparable across all

transducers, where moderate deviations from the contact transducer results were observed for

both ACU transducers. The deviations were found to be smaller in the homogeneous materials

tested. This is unsurprising, as the different propagation paths of the signals from the different

transducers should have less influence under homogeneous conditions.

In addition to their convergence, the peak-to-peak ratio of the correlation output maxima

(P2P) was also investigated as a quality measure of the results. Here, the stochastic nature of

the fluidic ultrasonic pulses come as an advantage over the piezoelectric signal. The inherent

random pulse compression of the signal, also used in Publication III, caused a bigger distance

between the main correlation peaks and their surrounding maxima than the largely monofrequent

pulse generated by the piezoelectric transducer. As a result, the P2P of the fluidic transducer

is equal to or higher than the piezoelectric ACU P2P for almost all studied specimens (see

Fig. 3.9d). Generally, the P2P advantage of the fluidic transducer was shown to be larger for

the heterogeneous building materials.

The results presented in Publication V demonstrate for the first time that the fluidic trans-

ducer is suitable for through-transmission measurements of various technically relevant materials.

Although the correlation outputs must be averaged, especially for heterogeneous materials, the

results are comparable to those of conventional transducers. Furthermore, the signal quality of

the converged results is superior to those obtained with a piezoelectric ACU transducer. These

results are based on the findings in Publications I to IV and demonstrate the competitiveness

of the fluidic transducer for longitudinal wave ToF measurements. The stable results for the

polyamide and ballistic gel specimens demonstrate not only the applicability of the transducer

for characterization of construction materials, but also the applicability in domains beyond

NDT-CE.

3.7 Limitations and Future Research

The results presented in the previous sections of this chapter justify the novel concept of fluidic

ultrasound generation for ultrasonic nondestructive testing. In this section, limitations of the

presented methods and results are discussed and possible future directions of research are shown.

The proposed fluidic transducer was designed specifically to meet the requirements of NDT-

CE, which are a high pressure amplitude at low ultrasonic frequencies, robustness and the ability

to generate triggered transient signals for ToF measurements. The fluidic transducer presented

in this work meets all of these requirements and improves upon the characteristics of the refer-

ence piezoelectric transducer. However, further research is needed on the receiver side. In the

presented measurement arrangement, two laser Doppler vibrometers are used for measurement.

In addition to being bulky, which can hamper manual measurements, they are sensitive to am-

bient vibration and the lenses need to be kept free of dust, which makes them suboptimal for

in-situ measurements on construction sites. As discussed in Section 1.5, a common blind spot in

assessing the robustness of fluidic devices is that the peripheral equipment required for operation

is often excluded from the assessment. An alternative for ACU sensing is the use of microphones,

which do not suffer from the above restrictions. The impedance losses caused by the additional

air-solid interfaces may be reduced by using microphone arrays in conjunction with beamforming

processing [95]. As an alternative to conventional measurement microphones, these arrays could

be equipped with low-cost MEMS microphones [246] or more expensive but highly sensitive

optical microphones [89]. Since conventional transducers can usually both transmit and receive,

there is little literature on beamforming in ACU at the time of writing. Thus, further research

104

3.7 Limitations and Future Research

concerning the use of this sensing method in conjunction with the fluidic transducer will likely

need to include additional research in its applicability in ACU testing in general.

Given its predominant use in NDT-CE, the applicability of the novel fluidic transducer in

NDT was validated using longitudinal wave ToF measurements. These measurements were

conducted in a through-transmission arrangement, which is usually not feasible for in-situ NDT-

CE measurements, since it would require an enormous effort to enable two-sided access to a

specimen. However, in a laboratory or production setting, through-transmission is a common

setup. Given the performance in ToF measurements on defect-free specimens, it is expected

that further measurements on specimens with inclusions will perform comparably well. After

validation this hypothesis, the setup presented in Publication V could then be used to test the

environmental robustness of the fluidic transducer. In particular, high temperature scenarios,

such as those encountered in composite production [247] and pyrometry [248], could be use

cases for the fluidic transducer outside of NDT-CE, especially since these applications do not

necessarily violate the requirement of optical access during sensing that is imposed by the use

of LDVs. Directing further research efforts to the application of the fluidic transducer for high-

temperature applications could reduce the reliance on the highly complex existing transducers.

The use of an ACU pitch-catch setup instead of through-transmission in this work has been

deemed infeasible as the plane wave assumptions required for an established ACU pitch-catch

setup [99] are not satisfied. The sound field of the fluidic transducer with a horn attached (see

Fig. 3.4f) agrees less with the model of an ultrasonic beam than that of the reference piezoelectric

transducer (see Publication I) that has been used for a pitch-catch setup before. Accordingly,

the sound field inside the specimen is expected to undergo almost omnidirectional refraction (see

Eq. (1.7)) instead of being reflected at a distinct angle, as required by the method. Additionally,

on the sensor side a pitch-catch setup would have required sophisticated shielding of the LDV

laser along its whole laser path so that the acousto-optic effect, which is used intentionally in

the presented setup (see Publication IV), does not mask the received echo pulse. Further

improvements are needed with respect to the directivity of the transducer and the signal sensing

so that longitudinal wave pitch-catch measurements can be realized using the fluidic transducer.

As mentioned in Sections 1.2 and 1.3, a number of additional measurement techniques exist,

such as attenuation measurements and amplitude scans. Additionally, these methods, like ToF

measurements, can be based on different wave types, which may furthermore allow for pitch-

catch setups. While it is conceivable that the stochastic nature of fluidic ultrasound pulses, as

with the measurements presented, may present challenges, investigating the applicability of the

fluidic transducer to those alternative configurations will certainly expand its utility to NDT in

the future.

To enable further NDT applications, it is generally not sufficient to improve only peripherals

such as the attached horn or the receiver setup. A deeper understanding of the internal aeroa-

coustic mechanisms is required to increase the attainable frequency of the transducer and to

improve the repeatability of the generated pulses by reducing their stochastic behavior. Initial

steps toward understanding the fluid mechanic processes have already been made numerically

[216], but need to be extended to capture the accompanying acoustic effects. It is expected

that not only the presumably turbulence-based aeroacoustic generation mechanisms lead to a

spectral and temporal variance of the ultrasonic pulse, but also the variance in opening times

of the control valves. The sub-microsecond accuracy of the triggering system is offset by valve

opening time tolerances of several milliseconds. Solutions for alternative and more predictable

methods of triggering flow switching include the use of ultrasound [201, 202], ionic wind, [249]

or, most suitable for high-speed flows, Lorentz force [250].

Another challenge for the practical application of the proposed fluidic transducer is its air

consumption, which certainly leaves room for improvement in the current operating procedure,

105

3 Results and Discussion

Figure 3.10: Preliminary tests of a down-scaled oscillator-based fluidic transducer: (a) photograph of the down-

scaled transducer; (b) and (c) spectrogram as function of supply pressure, relative to their maximum

values, for the original and down-scaled transducers, respectively; (d) and (e) average absolute peak

sound pressure as a function of supply pressure at an on-axis distance of 200 mm for the original

and down-scaled transducers, respectively.

which involves a constant air flow through one of the outlets. While in laboratory or production

environments it can be assumed that compressed air supply is no issue, it may be a limited

resource if the device is to be used in the field. One of the advantages of the fluidic transducer

over alternative ACU transducers is that it does not require high voltages to generate high

pressure ultrasound. Given a hand-held transducer, a hypothetical operator would only need

a sufficient supply of pressurized air, such as a breathing air cylinder used by firefighters [251].

In such a scenario, it would be beneficial to use the available air economically. Therefore, a

mechanism that supplies air only during the process of switching on would be desirable.

In this thesis, a fluidic transducer based on a bistable fluidic amplifier was investigated. How-

ever, based on the fluidics literature review given in Section 1.5, the fluidic oscillator can also

be considered as a promising ultrasound generator. As part of the research, an oscillator-based

ultrasonic transducer was also investigated as an alternative to the amplifier-based one. As

discussed in Section 1.5, the fluidic oscillator can be used to generate sound at distinct frequen-

cies and can be considered a fluidic siren. Its frequency depends on the internal fluid velocity

and the path length that a fluid parcel needs to travel as part of the internal feedback loop

[252]. Assuming a rigid fluidic oscillator, only the latter parameter may be used to control

the generated signal frequency. Recent studies [253, 254] suggest that a fluidic oscillator could

also be used for NDT. In these studies, a bistable single-jet diverter oscillator (see Fig. 3.10a)

based on Bobusch’s design [181] was used, which had a maximum frequency of about 11 kHz

(see Fig. 3.10b). To achieve ultrasonic frequencies, the transducer was downsized by a factor

of 2, leading to an increase of the base frequency to a value of 27 kHz. Additionally, multiple

higher harmonics with significant relative amplitude were produced, which may also be used

for ultrasonic testing (see Fig. 3.10c). The pressure-dependent behavior can easily be used to

generate chirped pulses, i.e. by quickly opening a valve. However, similar to conventional sirens,

the sound pressure generated depends on the ejected fluid volume. Downsizing the oscillator

also reduces the sound pressure (see Figs. 3.10d and 3.10e), reaching only 1 Pa at a distance

of 200 mm. Thus, further research is required to design an oscillator that features both an

adequate sound pressure and a bandwidth suitable for NDT applications.

106

4 Conclusions

This dissertation presents a novel aeroacoustic ultrasound generator for use in nondestructive

testing based on a bistable fluidic amplifier. In this novel approach, the flow-generated acoustic

waves are considered as a useful signal instead of being neglected as noise. Based on the hypoth-

esis that this fluidic ultrasonic transducer meets the requirements posed by civil engineering,

the acoustic characteristics of the device were investigated to exploit their distinct signal char-

acteristics and establish a time-of-flight measurement technique in which the transducer can be

employed. Comparison with conventional ultrasonic measurement equipment has shown that

the fluidic transducer is a suitable alternative for materials characterization.

It was shown that the principle flow switching process of the fluidic transducer is represented in

the sound output behavior. Especially, it was shown that the switching process generates a sound

pulse with dominant frequency components in the lower ultrasonic regime, which is required for

many applications of NDT-CE. Due to the large wavelength compared to the transducer outlet,

a sound field of almost spherical directivity is generated when the transducer is switched on.

However, the sound field generated during switch-off is shaped conically due to interaction with

the high-velocity air jet, which is considered a by-product of transducer operation. The addition

of an exponential horn resulted in a more directed sound field with an average peak sound

pressure twice that of the reference piezoelectric transducer. Moreover, the outflow velocity was

significantly reduced, lowering the risk of mechanical damage to sensitive surfaces. Since it was

shown that the dominant frequencies are a function of the pressure of the supplied air, a deeper

understanding of the flow generation mechanism is required. This is expected to yield improved

control of the generated frequencies and result in an expansion of the application domains for

the fluidic transducer.

As an alternative to using a horn for directivity control and reduction of jet impact on surfaces,

the use of space-saving sonic crystals was investigated. Using a two-dimensional arrangement, it

was shown that the generated sound can be redirected while maintaining the main jet direction.

Although the aspired perpendicular sound redirection could not be achieved using sonic crystals

with only single-digit numbers of rows, the proof-of-concept study showed that the sonic crystals

are an elegant measure to tackle the concurrence of flow and sound. Given the complexity of

employing a three-dimensional sonic crystal compared to attaching a horn to the transducer,

the latter was used in this work.

While the stochastic character of the generated pulses restricts the use of phased arrays, they

have been shown to produce a characteristic spectral signature of each pulse. Extraction of

this signature results in better distinguishability between pulses and allows measurement time

reduction by using MIMO methods. Using synthetic MIMO experiments in a realistic ToF setup,

it was shown that two pulses close in time could be distinguished reliably. While the performance

was improved compared to the original signal, the amount of successful ToF picks decreased with

the processed signal as four pulses arrived in quick succession. This makes the MIMO capability

of the fluidic transducer comparable to that of chirped pulses. To further increase the number

of simultaneously operable transducers, their design and operating conditions should be varied.

Exploiting the peculiarities of the signal allowed to improve the measurement results and possibly

decrease the measurement time.

Given the uniqueness and unpredictable trigger time of every pulse generated by the fluidic

transducer, it is necessary to use a ToF measurement strategy in which a pulse received after

107

4 Conclusions

interaction with a specimen is always compared to a reference measurement of the same pulse

before the interaction. Furthermore, the acquisition of this reference pulse needs to be performed

in a non-intrusive manner. To meet these requirements, a novel through-transmission ToF

measurement setup based on the use of an LDV in refracto-vibrometry mode was developed. This

method does not require any information about the trigger time or even the distance between

the transducer and the specimen. After validation using an accelerometer on the specimen

backwall and the predictable characteristics of a piezoelectric ACU transducer, the method

was employed using the fluidic transducer and a second LDV as backwall sensor to form a

fully non-contact through-transmission ToF setup. By measuring the ToF and longitudinal

sound propagation velocity in four materials of various thicknesses, it was shown that the fluidic

transducer can be used to perform NDT tasks. Although the fluidic transducer allowed higher

output quality, more individual pulses needed to be averaged to reach a converged ToF result

than with the piezoelectric transducer. By requiring multiple fluidic pulses to retrieve a valid

ToF measurement, the measurement time achievable with the transducer is reduced. These

measurements show that the fluidic transducer can be successfully used to measure the sound

velocity of a material, allowing conclusions to be drawn about a wide range of structural and

material properties. Based on these promising results, it is expected that a similar setup may

be used to detect subsurface structures.

The methods developed in this thesis allow the fluidic transducer to be employed in a controlled

setting, such as a laboratory or a production facility. Measurements at a construction site are

currently not realistic due to the need to use bulky and delicate LDVs and the need to access the

specimen from both sides to set up the through-transmission. Besides addressing these major

limitations, further research should identify more use cases for the fluidic transducer. This should

include the use in additional measurement concepts, the environmental operation boundaries of

the transducer, and its use in research fields outside NDT-CE. However, to achieve this, further

research is required to better understand and subsequently control the pulse characteristics of

the fluidic transducer. Furthermore, additional fluidic transducer concepts should be assessed.

By redefining the aeroacoustic sound as a usable signal instead of noise, a novel and robust

type of fluidic ultrasound generator has been developed. In assessing the sound and flow char-

acteristics of this fluidic transducer and using these characteristics for NDT measurements, this

thesis has laid the groundwork for further development of this novel transducer principle.

The use of fluidic ultrasound sources in civil engineering and beyond could increase the us-

ability and range of use cases of air-coupled ultrasound. Fluidic transducers are expected to

be vital tools for increasing security of structures and reducing their ecological footprint. Their

simplicity and robustness allow for mass deployment and use in a multitude of adverse scenarios

that reach far beyond civil structures.

108

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thinger. “Low frequency ultrasonic pulse-echo datasets for object detection and thickness

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125

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doi:10.1016/j.dib.2021.107280.

126

Associated Publications

In addition to the publications that have been included in this dissertation as Chapter 2, a

number of additional research papers were published over the course of this research project.

These papers include peer-reviewed articles as well as contributions to conference proceedings

and are concerned with both the fluidic transducer and further acoustic NDT methods. These

associated publications are listed below:

B. B¨uhling and S. Maack. “Improving onset picking in ultrasonic testing by using a spectral

entropy criterion”. The Journal of the Acoustical Society of America 155.1 (2024), 544–554.

doi:10.1121/10.0024337

S. Maack, S. K¨uttenbaum, B. B¨uhling, K. Borchardt-Giers, N. Aßmann, and E. Niederlei-

thinger. “Low frequency ultrasonic pulse-echo datasets for object detection and thickness

measurement in concrete specimens as testing tasks in civil engineering”. Data in Brief 48

(2023), 109233. doi:https://doi.org/10.1016/j.dib.2023.109233

J. F. Scherr, J. Kollofrath, J. S. Popovics, B. B¨uhling, and C. U. Grosse. “Detection of

Delaminations in Concrete Plates Using a Laser Ablation Impact Echo Technique”. Journal

of Nondestructive Evaluation 42.1 (2023), 11. doi:10.1007/s10921-022-00921-x

B. B¨uhling, S. Maack, and C. Strangfeld. “OsciCheck: A Novel Fluidic Transducer for Air-

Coupled Ultrasonic Measurements. International Symposium on Non-Destructive Testing

in Civil Engineering (NDT-CE 2022), 16-18 August 2022, Zurich, Switzerland”. e-Journal

of Nondestructive Testing 27.9 (2022), 1–9. doi:10.58286/27319

C. Strangfeld, B. B¨uhling, M. Hauke, T. Schweitzer, and S. Maack. “Frequency modulated,

air-coupled ultrasound generated by fluidic oscillators”. 2022 IEEE International Ultrason-

ics Symposium (IUS). 2022, 1–4. doi:10.1109/IUS54386.2022.9958740

S. Maack, S. K¨uttenbaum, B. B¨uhling, and E. Niederleithinger. “Low frequency ultrasonic

dataset for pulse echo object detection in an isotropic homogeneous medium as reference

for heterogeneous materials in civil engineering”. Data in Brief 42 (2022), 108235. doi:

10.1016/j.dib.2022.108235

B. B¨uhling, T. Schweitzer, S. Maack, and C. Strangfeld. “Influence of Operating Condi-

tions on the Fluidic Ultrasonic Transducer Signal”. Fortschritte der Akustik – DAGA 2021.

Berlin, Germany: DEGA, 2021, 48–51. isbn: 9783939296188

B. B¨uhling, S. Maack, E. Sch¨onsee, T. Schweitzer, and C. Strangfeld. “Acoustic and flow

data of fluidic and piezoelectric ultrasonic transducers”. Data in Brief 38 (2021), 107280.

doi:10.1016/j.dib.2021.107280

T. Schweitzer, M. H¨ormann, B. B¨uhling, and B. Bobusch. “Switching Action of a Bistable

Fluidic Amplifier for Ultrasonic Testing”. Fluids 6.5 (2021), 171. doi:10.3390/fluids6050171

127

References

B. B¨uhling, C. Strangfeld, and S. Maack. “Entwicklung eines luftgekoppelten Ultraschall-

Echo-Pr¨ufverfahrens mittels fluidischer Anregung [in German]”. DGZfP Jahrestagung 2019.

Deutsche Gesellschaft f¨ur Zerst¨orungsfreie Pr¨ufung, 2019, 1–8. url:https://opus4.kobv.

de/opus4-bam/frontdoor/index/index/docId/48120

128