Citation: Neubauer, M.; Genßler, J.;
Radmann, V.; Kohlenberg, F.; Pohl,
M.; Böhme, K.; Knobloch, K.; Sarradj,
E.; Höschler, K.; Modler, N.; et al.
Experimental and Numerical
Investigation of Novel Acoustic
Liners and Their Design for
Aero-Engine Applications. Aerospace
2023,10, 5. https://doi.org/10.3390/
aerospace10010005
Academic Editors: Peng Wei
and Rosario Pecora
Received: 2 November 2022
Revised: 2 December 2022
Accepted: 15 December 2022
Published: 21 December 2022
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
aerospace
Article
Experimental and Numerical Investigation of Novel Acoustic
Liners and Their Design for Aero-Engine Applications
Moritz Neubauer 1,* , Julia Genßler 2, Vincent Radmann 3,*, Fleming Kohlenberg 2, Michael Pohl 4,
Kurt Böhme 1, Karsten Knobloch 5, Ennes Sarradj 3, Klaus Höschler 4, Niels Modler 1and Lars Enghardt 2
1Institute of Lightweight Engineering and Polymer Technology (ILK), Technische Universität Dresden,
Holbeinstraße 3, 01307 Dresden, Germany
2Institute of Fluid Dynamics and Engineering Acoustics, Technische Universität Berlin, Müller-Breslau-Str. 8,
10623 Berlin, Germany
3Institute of Fluid Dynamics and Engineering Acoustics, Technische Universität Berlin, Einsteinufer 25,
10587 Berlin, Germany
4Chair of Aero Engine Design, Brandenburg University of Technology Cottbus-Senftenberg,
Siemens-Halske-Ring 14, 03046 Cottbus, Germany
5
German Aerospace Center (DLR), Institute of Propulsion Technology, Engine Acoustics, Müller-Breslau-Str. 8,
10623 Berlin, Germany
*Correspondence: moritz.neubauer@tu-dresden.de (M.N.); [email protected] (V.R.);
Tel.: +49-351-463-4026
Abstract:
This paper presents a combined experimental and numerical investigation on a novel liner
concept for enhanced low-frequency and broadband acoustic attenuation. In particular, two different
realizations, derived from conventional Helmholtz resonators (HR) and plate resonators (PR) are
investigated, which both deploy flexible materials with material inherent damping. In this context, a
comprehensive experimental investigation was carried out focusing the identification and evaluation of
various geometric parameters and material properties on the acoustics dissipation and related properties
of various materials in a simplified setup of a single Helmholtz resonator with flexible walls (FHR
concept). Furthermore, a parameter study based on analytical models was performed for both liner
concepts, taking into account material as well as geometric parameters and their effects on transmission
loss. In addition, design concepts that enable cylindrical or otherwise curved liner structures and the
corresponding manufacturing technologies are presented, while considering essential structural features
such as drainage. With respect to the potential application in jet engines, a structural–mechanical analysis
considering the relevant load cases to compare and discuss the mechanical performance of a classical
HR and the FHR concept liner is presented. Finally, both concepts are evaluated and possible challenges
and potentials for further implementation are described.
Keywords:
acoustic liner; plate resonator; Helmholtz resonator; broadband noise; honeycomb
structure; model; curved design
1. Introduction
Aviation generates various emissions (e.g., CO
2
, NO
X
and noise), which impact peo-
ple’s quality of life in the vicinity of airports and beyond. These emissions occur at all
phases of the flight, with highest nuisance during take-off and landing. One way to reduce
the noise emissions is to optimize the geometry of the fan, respectively the whole engine,
which may interfere with contrary optimization requirements for fuel efficiency or other
aircraft design criteria. Currently, an important part of the reduction of the emitted engine
noise is obtained by liners (usually an array of cells covered by a perforate) installed in the
nacelle intake and at other locations of the engine. To increase propulsive efficiency and
reduce the gaseous emissions as well as the noise emissions, the increase of engine bypass
ratios has proven to be very successful. While delivering the same thrust, larger fans rotate
Aerospace 2023,10, 5. https://doi.org/10.3390/aerospace10010005 https://www.mdpi.com/journal/aerospace
Aerospace 2023,10, 5 2 of 24
slower than the smaller ones which leads to lower rotor-stator interaction frequencies.
To reduce the emitted tonal and broadband noise, standard liners would require a larger
volume and increased depth to address the tonal components at lower frequency, which is
conflicting with the limited design space and aerodynamic requirements. Most standard
liners for aero-engine applications consist of a perforated face sheet, which is attached to a
lightweight core structure and a rigid back plate underneath. This type of liner is called a
single-degree-of-freedom liner, as each cell can be modeled individually as a simple spring-
and-mass system—usually considered as a Helmholtz resonator (HR). To extend their
relatively small first resonance bandwidth, several concepts for multi-degree-of-freedom
liners exist. These include multi-layer liners consisting of two cell layers with a septum
or “mesh cap” in between [
1
–
4
]. While these concepts offer a more broadband damping,
they cannot lower the system’s first resonance frequency. In contrast, different concepts,
such as folded cavities [
1
–
4
], active elements [
5
–
8
] or attached mass elements [
6
,
9
], offer the
possibility for low frequency damping, with certain drawbacks and limitations connected
to each of these concepts.
In the current study, two liner concepts, with improved noise attenuating character-
istics, which use flexible elements with material inherent damping properties to address
low-frequency noise, are investigated. Their acoustic performance is described by their
dissipation or transmission loss of acoustic energy. Note, that in contrast to the liner
impedance, these entities depend on the specific assembly situation. In Figure 1the holistic
approach of the investigation is shown, which includes the experimental and analytical
modeling of the acoustic concepts as well as the structural mechanical analysis of different
cell configurations. Additionally, feasibility studies on the design and manufacture of the
liner structures were presented in order to assess the potential and challenges of integrating
them into jet engines.
Aerospace 2022, 10, 5 2 of 25
fans rotate slower than the smaller ones which leads to lower rotor-stator interaction fre-
quencies. To reduce the emitted tonal and broadband noise, standard liners would require
a larger volume and increased depth to address the tonal components at lower frequency,
which is conflicting with the limited design space and aerodynamic requirements. Most
standard liners for aero-engine applications consist of a perforated face sheet, which is
attached to a lightweight core structure and a rigid back plate underneath. This type of
liner is called a single-degree-of-freedom liner, as each cell can be modeled individually
as a simple spring-and-mass system—usually considered as a Helmholtz resonator (HR).
To extend their relatively small first resonance bandwidth, several concepts for multi-de-
gree-of-freedom liners exist. These include multi-layer liners consisting of two cell layers
with a septum or “mesh cap” in between [1–4]. While these concepts offer a more broad-
band damping, they cannot lower the system’s first resonance frequency. In contrast, dif-
ferent concepts, such as folded cavities [1–4], active elements [5–8] or attached mass ele-
ments [6,9], offer the possibility for low frequency damping, with certain drawbacks and
limitations connected to each of these concepts.
In the current study, two liner concepts, with improved noise attenuating character-
istics, which use flexible elements with material inherent damping properties to address
low-frequency noise, are investigated. Their acoustic performance is described by their
dissipation or transmission loss of acoustic energy. Note, that in contrast to the liner im-
pedance, these entities depend on the specific assembly situation. In Figure 1 the holistic
approach of the investigation is shown, which includes the experimental and analytical
modeling of the acoustic concepts as well as the structural mechanical analysis of different
cell configurations. Additionally, feasibility studies on the design and manufacture of the
liner structures were presented in order to assess the potential and challenges of integrat-
ing them into jet engines.
Figure 1. Holistic approach of the presented research to analyze novel acoustic liners concepts con-
sidering experimental, analytical modeling, structural mechanical and manufacturing aspects.
For the first concept, the FHR concept, the aim is to combine the high acoustic dissi-
pation of the standard HR with the low frequency geometric resonance of a flexible plate
by the use of flexible walls and a back cavity. While the Helmholtz resonator has been
investigated widely, including analytical, experimental and numerical investigations, the
combination with one or more flexible walls changes the system drastically and requires
different analytical description or boundary conditions for numerical simulations.
The second concept deploys a plate resonator (PR) silencer that consists of an expan-
sion chamber fully covered by a plate [10,11]. In addition to the ability to attenuate low-
frequency noise with low depth cavities, plate silencers have the advantage over porous
Figure 1.
Holistic approach of the presented research to analyze novel acoustic liners concepts
considering experimental, analytical modeling, structural mechanical and manufacturing aspects.
For the first concept, the FHR concept, the aim is to combine the high acoustic dissi-
pation of the standard HR with the low frequency geometric resonance of a flexible plate
by the use of flexible walls and a back cavity. While the Helmholtz resonator has been
investigated widely, including analytical, experimental and numerical investigations, the
combination with one or more flexible walls changes the system drastically and requires
different analytical description or boundary conditions for numerical simulations.
The second concept deploys a plate resonator (PR) silencer that consists of an ex-
pansion chamber fully covered by a plate [
10
,
11
]. In addition to the ability to attenuate
low-frequency noise with low depth cavities, plate silencers have the advantage over
porous absorbers or HR structures with perforated surfaces that they can be exposed to
Aerospace 2023,10, 5 3 of 24
contaminated air without any agglomeration of contaminants in the cavity. Furthermore,
their flow resistance is very low due to the smooth surface [12]. Beside other applications,
plate silencers are used in air conditioning systems to reduce the noise emission through
the pipework or in industrial ventilation systems [
13
,
14
]. Currently, the most advanced
model to describe the acoustic behavior of a plate silencer was introduced by Huang and
Wang [
15
,
16
]. It describes the interaction of the system of cavity and plate with the duct
above. Thereby, the performance significantly depends on the plate material [
17
]. To adjust
a suitable frequency range and bandwidth, different materials and resonator dimensions are
under investigation, without a comprehensive and accurate design process being available
so far.
A well-designed aero-engine liner excels in damping acoustical pressure waves but
also withstands mechanical pressure and is safe and reliable. Due to their lightweight
structure, liners usually consist of sandwich honeycomb core structures. The research
dealing with their safety and reliability focuses on the mechanical behavior of these struc-
tures. The examined cores in those studies are usually made out of aramid paper [
18
–
21
].
Giglio et al. [
22
] applied a Finite Element Analysis (FEA) simulation to determine the crush
mechanics for a Nomex core and showed a high-fidelity simulation. Liu et al. [
23
] evaluated
the impact of bonding imperfections under flatwise core compression of layered cell walls.
They investigated that the de-bonding causes out-of-plane stresses inside the wall. The
behavior of hybrid honeycomb structures, consisting of flexible and rigid wall areas, under
axial compression was also analyzed using FEA [
24
]. The results indicate not a stability
failure of the entire structure but material failure on the micro and meso level. Besides
the honeycomb core, there are also other core structures, such as the folded core [
25
] or
the X-type lattice structure [
26
]. However, for the intended application, the design with
square honeycombs is more relevant. In this context, Cote et al. [
27
] investigated the
impact of sandwich walls in contrast to monolithic walls and got the result of improved
through-thickness compressive strength. In contrast to the previous studies, the present
work improves the understanding of the effects of the change in core geometry due to the
integration of flexible films.
Many applications of honeycomb cores in functional sandwich structures, such as
acoustic liners, require a curved shape, in particular for instance the geometry of the intake
of a jet engine. However, sandwich cores are mainly manufactured planar and subse-
quently formed into the desired shape, which potentially causes damage of the composite,
malfunction and geometric change of the cells [
28
–
31
]. In this context, alternative pro-
cesses are necessary for the manufacturing of the resonator configurations considered here
comprising flexible walls to enable also curved design applications. This process needs to
ensure the geometric integrity of the resonator and especially the film. For the manufactur-
ing of the strip slotted design of cell cores introduced by Dannemann et al. [
32
], built of
fiber-reinforced plastic, a productive cutting process as abrasive water jet or laser milling is
needed to efficiently manufacture the face sheets and cell walls from flat panels [
33
]. In
addition, the deep drawing process enables highly efficient forming of fiber-reinforced
thermoplastic woven and knitted fabrics for load-bearing cell chambers, which are well-
suited for the production of cavities, especially for the PR liner concept [
34
–
36
]. With
regard to the process of joining the cavity and the flexible films made of thermoplastic
materials, there is the potential to apply welding technologies, such as ultrasonic welding,
to realize high joint strengths at high speed and low cost even without energy direction
transmitters [
37
,
38
]. In this context, studies that specifically investigated the weld-ability
of the targeted material polyamide 6 with glass fiber reinforcement (PA6-GF) imply that
fiber-reinforced polyamide 6 (PA6) requires significantly less energy than unreinforced PA6
to achieve high joint strengths [39,40].
In the following sections, comprehensive experimental results for a modular mock-up
of the novel FHR are presented. Subsequently, the acoustic performance of the PR silencer
as well as the FHR was evaluated by using semi-analytical models for each concept. In
order to compare the mechanical performance of both designs, the structural–mechanical
Aerospace 2023,10, 5 4 of 24
analysis of a classical HR and the FHR liner are conducted and discussed. With regard
to the application of the two acoustic liner principles in aerospace, design concepts that
enable a curved design and the corresponding manufacturing technologies are presented.
Finally, a conclusion and an outlook for further investigations are drawn.
2. Acoustic Analysis of Helmholtz Resonator with Flexible Walls and Results
2.1. Experimental Setup for the HR
In order to investigate several design parameters and parameter dependencies of the
FHR concept, acoustic measurements were performed in the DUCT-R facility of the DLR in
Berlin. The facility consists of a rectangular duct with the liner test section in the middle and
microphone sections upstream and downstream of the test section (see Figure 2). For the
excitation of acoustic waves with and against the mean flow, a loud speaker is attached on
the upstream and downstream end of the tunnel, respectively. The sound waves are excited
either via speaker A or speaker B with a single tone and an amplitude of 110 dB, ensuring a
linear regime for the periodic in- and outflow at the considered perforate. The microphones
(five in the upstream and five in the downstream section) are non-equidistantly attached
to the duct wall to avoid singularities in the wave decomposition needed to calculate the
scattering coefficients. The measured frequency range is 204–1020 Hz in steps of 26 Hz
and from 1071 Hz to 2040 Hz in steps of 51 Hz. Since the main dissipation peaks of the
investigated liner are expected below 1000 Hz, smaller step sizes were selected in this
frequency range. The cut-on-frequency of the first higher mode in the hard wall section
is 2142 Hz, thus only plane waves are investigated in the present study. The anechoic
terminations at both ends of the DUCT-R reduce end reflections and improve the accuracy
of the measurements. For more information about the test rig and wave decomposition,
see [
41
]. The rectangular shape of the DUCT-R allows the attachment of planar resonators,
that are easier to manufacture than curved ones and therefore more suitable for basic
studies.
Aerospace 2022, 10, 5 4 of 25
In order to compare the mechanical performance of both designs, the structural–mechan-
ical analysis of a classical HR and the FHR liner are conducted and discussed. With regard
to the application of the two acoustic liner principles in aerospace, design concepts that
enable a curved design and the corresponding manufacturing technologies are presented.
Finally, a conclusion and an outlook for further investigations are drawn.
2. Acoustic Analysis of Helmholtz Resonator with Flexible Walls and Results
2.1. Experimental Setup for the HR
In order to investigate several design parameters and parameter dependencies of the
FHR concept, acoustic measurements were performed in the DUCT-R facility of the DLR
in Berlin. The facility consists of a rectangular duct with the liner test section in the middle
and microphone sections upstream and downstream of the test section (see Figure 2). For
the excitation of acoustic waves with and against the mean flow, a loud speaker is attached
on the upstream and downstream end of the tunnel, respectively. The sound waves are
excited either via speaker A or speaker B with a single tone and an amplitude of 110 dB,
ensuring a linear regime for the periodic in- and outflow at the considered perforate. The
microphones (five in the upstream and five in the downstream section) are non-equidis-
tantly attached to the duct wall to avoid singularities in the wave decomposition needed
to calculate the scattering coefficients. The measured frequency range is 204–1020 Hz in
steps of 26 Hz and from 1071 Hz to 2040 Hz in steps of 51 Hz. Since the main dissipation
peaks of the investigated liner are expected below 1000 Hz, smaller step sizes were se-
lected in this frequency range. The cut-on-frequency of the first higher mode in the hard
wall section is 2142 Hz, thus only plane waves are investigated in the present study.
The anechoic terminations at both ends of the DUCT-R reduce end reflections and im-
prove the accuracy of the measurements. For more information about the test rig and
wave decomposition, see [41]. The rectangular shape of the DUCT-R allows the attach-
ment of planar resonators, that are easier to manufacture than curved ones and therefore
more suitable for basic studies.
Figure 2. Schematic view of the DUCT−R test rig.
To investigate the interactions between an HR and a flexible wall, a small modular
resonator was developed consisting of a resonator body that allows various elements,
such as flexible walls, to be attached to its five remaining sides. The additional elements
are connected to the main body via threaded rods. The basic structure for this investiga-
tion consists of a main resonator with a flexible wall and a back cavity attached to it. The
flexible walls are made out of different materials with different thicknesses and are
clamped between aluminium metal plates with distinctive cut-outs. Ten screws ensure a
clamped boundary condition. The other six holes visible in the plate holder (Figure 3b)
are used for the mounting on the threaded rods. The shape of the flexible element between
resonator and back cavity is determined by the cut-out shape. Several basic shapes were
investigated: round (diameter: 15 mm), square (side length: 15 mm) and rectangular (side
length: 15 × 26 mm). A plate holder with a mounted flexible plate with a square cut-out is
shown in Figure 3b.
Figure 2. Schematic view of the DUCT−R test rig.
To investigate the interactions between an HR and a flexible wall, a small modular
resonator was developed consisting of a resonator body that allows various elements, such
as flexible walls, to be attached to its five remaining sides. The additional elements are con-
nected to the main body via threaded rods. The basic structure for this investigation consists
of a main resonator with a flexible wall and a back cavity attached to it. The flexible walls
are made out of different materials with different thicknesses and are clamped between
aluminium metal plates with distinctive cut-outs. Ten screws ensure a clamped boundary
condition. The other six holes visible in the plate holder (Figure 3b) are used for the mount-
ing on the threaded rods. The shape of the flexible element between resonator and back
cavity is determined by the cut-out shape. Several basic shapes were investigated: round
(diameter: 15 mm), square (side length: 15 mm) and rectangular
(side length: 15 ×26 mm)
.
A plate holder with a mounted flexible plate with a square cut-out is shown in Figure 3b.
Aerospace 2023,10, 5 5 of 24
Aerospace 2022, 10, 5 5 of 25
Figure 3. (a) ① Assembly of resonator, ② holder with film, ③ back cavity (here ~0.5 of resonator
volume) and ④ back plate at the ⑤ DUCT-R; (b) holder with square cut-out and (TPU) film.
Two different sizes of back cavities were built in order to vary its volume. One back
cavity is as large as one-quarter of the resonator volume, the other is about one-half of the
resonator volume. The parts can be combined to form back cavities with a volume of one-
quarter, one-half, three-quarters up to twice the resonator volume. The back cavity is
closed by another aluminium plate with a thickness of 3 mm. This back plate is assumed
rigid and fastened by wing nuts as shown in Figure 3a. The resonator is attached to the
test section of the DUCT by a perforated face sheet. In the area of the resonator, the face
sheet has 18 holes with a diameter of 1.5 mm each. The resonator has a square area of 35
× 35 mm2 and a depth of 50 mm when used as a normal Helmholtz resonator. This config-
uration of the resonator exhibits a Helmholtz resonance between 600–700 Hz. The one-
quarter wave resonance frequency due to the cavity depth would be 1715 Hz but is altered
by the presence of the face sheet yielding the above Helmholtz resonance frequency. The
walls and back cavities can be attached parallel or orthogonal to the DUCT-R main axis
and to each other due to the nearly cubical form. The presented modular setup therefore
offers the possibility to change the shape of the flexible wall; the material and thickness of
the flexible wall; the position of the flexible wall with respect to the resonator (and thereby
the main duct); the size of the back cavity; and the number of flexible walls and back cav-
ities attached to the main resonator. The investigated materials with their Young’s modu-
lus and different thicknesses are shown in Table 1.
Table 1. Measured film materials with their Young’s modulus and thicknesses.
Thickness
mm
Aluminum
(Alu)
70,000 MPa
Poly Propylene
(PP)
1600 MPa
Thermoplastic Polyu-
rethan (TPU)
16 MPa
Polyamide 6
(PA6)
800 MPa
Polyphenylene
Sulphide (PPS)
2400 MPa
Polyether Ether
Ketone (PEEK)
2800 MPa
0.001
x
0.01
x
x
x
x
x
0.02
x
0.03
x
0.04
x
2.2. Results of Experimental Investigations of the FHR Design
The measurement results clearly show that the integration of a flexible wall has an
impact on the resonance of the resonator system (see Figure 4a). With regard to the possi-
ble variations of the modular resonator, the flexible wall made of TPU material had the
greatest impact on the dissipation of the resonator system. Compared to a simple HR with
Figure 3.
(
a
)
1
Assembly of resonator,
2
holder with film,
3
back cavity (here ~0.5 of resonator
volume) and 4
back plate at the 5
DUCT-R; (b) holder with square cut-out and (TPU) film.
Two different sizes of back cavities were built in order to vary its volume. One back
cavity is as large as one-quarter of the resonator volume, the other is about one-half of
the resonator volume. The parts can be combined to form back cavities with a volume of
one-quarter, one-half, three-quarters up to twice the resonator volume. The back cavity is
closed by another aluminium plate with a thickness of 3 mm. This back plate is assumed
rigid and fastened by wing nuts as shown in Figure 3a. The resonator is attached to the
test section of the DUCT by a perforated face sheet. In the area of the resonator, the face
sheet has 18 holes with a diameter of 1.5 mm each. The resonator has a square area of
35 ×35 mm2
and a depth of 50 mm when used as a normal Helmholtz resonator. This
configuration of the resonator exhibits a Helmholtz resonance between 600–700 Hz. The
one-quarter wave resonance frequency due to the cavity depth would be 1715 Hz but is
altered by the presence of the face sheet yielding the above Helmholtz resonance frequency.
The walls and back cavities can be attached parallel or orthogonal to the DUCT-R main axis
and to each other due to the nearly cubical form. The presented modular setup therefore
offers the possibility to change the shape of the flexible wall; the material and thickness
of the flexible wall; the position of the flexible wall with respect to the resonator (and
thereby the main duct); the size of the back cavity; and the number of flexible walls and
back cavities attached to the main resonator. The investigated materials with their Young’s
modulus and different thicknesses are shown in Table 1.
Table 1. Measured film materials with their Young’s modulus and thicknesses.
Thickness
mm
Aluminum
(Alu)
70,000 MPa
Poly Propylene
(PP)
1600 MPa
Thermoplastic
Polyurethan (TPU)
16 MPa
Polyamide 6
(PA6)
800 MPa
Polyphenylene
Sulphide (PPS)
2400 MPa
Polyether Ether
Ketone (PEEK)
2800 MPa
0.001 x
0.01 x x x x x
0.02 x
0.03 x
0.04 x
2.2. Results of Experimental Investigations of the FHR Design
The measurement results clearly show that the integration of a flexible wall has an
impact on the resonance of the resonator system (see Figure 4a). With regard to the possible
variations of the modular resonator, the flexible wall made of TPU material had the greatest
impact on the dissipation of the resonator system. Compared to a simple HR with the same
overall volume (cavity + back cavity), the resonator with an additional flexible wall has
Aerospace 2023,10, 5 6 of 24
a higher resonance frequency as shown in Figure 4a. Adding a back cavity changes the
effect of the flexible wall in the dissipation. This means that, by adding a back cavity, the
main dissipation shifts slightly to higher frequencies, and an additional dissipation peak
at lower frequencies occurs. This additional peak is strongly dependent on the material
and thickness of the flexible wall (Figure 4a) as well as dependent of the back cavity size
(Figure 4b). Using a flexible wall of polypropylene (PP) the dissipation is slightly widened
around the Helmholtz frequency. All the other materials tested showed no effect on the
Helmholtz frequency. This may be due to their comparatively high Young’s modulus, as
the materials appear to be “acoustically stiff”.
Aerospace 2022, 10, 5 6 of 25
the same overall volume (cavity + back cavity), the resonator with an additional flexible
wall has a higher resonance frequency as shown in Figure 4a. Adding a back cavity
changes the effect of the flexible wall in the dissipation. This means that, by adding a back
cavity, the main dissipation shifts slightly to higher frequencies, and an additional dissi-
pation peak at lower frequencies occurs. This additional peak is strongly dependent on
the material and thickness of the flexible wall (Figure 4a) as well as dependent of the back
cavity size (Figure 4b). Using a flexible wall of polypropylene (PP) the dissipation is
slightly widened around the Helmholtz frequency. All the other materials tested showed
no effect on the Helmholtz frequency. This may be due to their comparatively high
Young’s modulus, as the materials appear to be “acoustically stiff”.
Figure 4. Comparisons of different aspects in the dissipation in dependence of (a) materials and
thicknesses (constant back cavity and circular shaped cut-out), (b) the size of the back cavity in re-
lation to the resonator volume (same material and rectangular shaped cut-out), (c) orientation of the
back cavity in relation to the Duct (same material and circular shaped cut-out) and (d) the shape of
the cut-out (TPU_03 and same back cavity size).
Besides the material, the film thickness also has a great impact on the acoustic per-
formance. This holds especially true for the flexible wall made out of TPU. While the thin
TPU film (0.1 mm) shows a high secondary dissipation peak but involves difficulties in
reproducible mounting, the thicker TPU film (0.3 mm) is easier to apply and has easier
reproduction of results. Furthermore, the tension of the mounted film affects the dissipa-
tion. Measurements conducted with the thicker TPU film still showed a dependency on
the applied tension during assembly. The film was bent prior to acoustic excitation, and
the dissipation was altered significantly, if a torque higher than 0.2 Nm was applied to
fasten the screws. In more than 50 repetitions of mounting, this sensitivity caused both
higher and lower frequencies for the material dependent dissipation peak. Therefore, the
Figure 4.
Comparisons of different aspects in the dissipation in dependence of (
a
) materials and
thicknesses (constant back cavity and circular shaped cut-out), (
b
) the size of the back cavity in
relation to the resonator volume (same material and rectangular shaped cut-out), (
c
) orientation of
the back cavity in relation to the Duct (same material and circular shaped cut-out) and (
d
) the shape
of the cut-out (TPU_03 and same back cavity size).
Besides the material, the film thickness also has a great impact on the acoustic perfor-
mance. This holds especially true for the flexible wall made out of TPU. While the thin
TPU film (0.1 mm) shows a high secondary dissipation peak but involves difficulties in
reproducible mounting, the thicker TPU film (0.3 mm) is easier to apply and has easier
reproduction of results. Furthermore, the tension of the mounted film affects the dissipa-
tion. Measurements conducted with the thicker TPU film still showed a dependency on
the applied tension during assembly. The film was bent prior to acoustic excitation, and
the dissipation was altered significantly, if a torque higher than 0.2 Nm was applied to
fasten the screws. In more than 50 repetitions of mounting, this sensitivity caused both
higher and lower frequencies for the material dependent dissipation peak. Therefore, the
Aerospace 2023,10, 5 7 of 24
reproducibility of the mounting process is important regarding the manufacturing process
of the liner.
The size of the back cavity has an impact on the additional dissipation peak, especially
when using the flexible wall made out of TPU. A linear trend is visible for the dissipation
peak around 400 Hz (see Figure 4b). The material dependent dissipation (see Figure 4b)
depends on the material itself as well as on the flexible walls shape (compare Figure 4d) and
the depth of the back cavity. This effect becomes evident in Figure 4b, where the first peak
of material dependent dissipation occurs at around 400 Hz. The lower frequency peaks
seem to be dependent on the depth of the back cavity and the shape as it also occurs with
the round and rectangular shape. However, there is a slight shift in both frequencies for the
curve of V
res
/V
cav
= 1, which does not correlate with the observed trend for other cavity
sizes. This shift can be explained by a different thickness distribution over the investigated
film area, which is caused by the manufacturing process.
The position of the flexible wall in relation to the DUCT main axis has no influence
on the dissipation (compare Figure 4c). Therefore, it can be concluded that the orientation
of back cavity and Helmholtz cavity is interchangeable. This fact is important for the
liner sample geometry for future investigations. The slight difference in the first peak in
Figure 4c could be due to a manufacturing-related variation in thickness of the used film
material specimens and does not limit the above conclusion.
The cut-out shape also has an influence on the dissipation. In this context, the rectan-
gular cut-out shows a distinct dissipation with two peaks while, for the circular or square
cut-out, there is only one peak (Figure 4d). Note that the width of the square cut-out
is equal to the diameter of the circular cut-outs. The rectangular cut-out, however, has
different lengths of 15
×
26 mm. Since the rectangular cut-out has two distinct dimensions,
compared to one for the circular and square cut-out, two distinct resonances are visible.
To gain a better understanding of the trends observed in the experiments, parameter
studies were performed for both the FHR and PR liner concepts. Their modeling and
results are presented in the following section.
3. Semi-Analytical Parameter Studies for FHR and PR Liner Concepts
Parameter studies are a reasonable way to correctly understand the behavior of FHR
and PR liners. However, only a limited number of cases can be investigated with measure-
ments. Therefore, semi-analytical approaches are used in the following to conduct several
parameter studies. Thus, it is possible to evaluate the influence of the most important
geometrical and material-specific parameters for the FHR and the PR liner concept. The
experimental investigations from the previous section showed that materials with a low
Young’s modulus are needed for resonances in the investigated frequency range between
200 and 1500 Hz. In light of these results, only thermoplastics and thermoplastic elastomers
were considered for the parameter studies in order to restrict the parameter range to one
material group. For these materials there exists a functional relationship between the
Young’s modulus Eand the loss factor ηas shown in [17]:
η=0.0355·E−0.633, with Ein GPa. (1)
This functional relationship effectively reduces the parameter space dimensions by
one. The baseline values for both resonator concepts are shown in Table 2. Based on these
values, one parameter after the other is varied to highlight the main trends.
Aerospace 2023,10, 5 8 of 24
Table 2. Values of geometry and material parameters.
Parameter Symbol Unit Value, Value Range Design Point
Common parameters for both concepts
Duct height hdmm 60 60
Duct width wdmm ∞ ∞
Young’s modulus EMPa E∈101;10414
Poisson ratio ν- 0.48 0.48
Loss factor η-η∈[0.65;0.008]0.53
Density ρkg/m31080 1080
Plate thickness hpmm hp∈[0.1;0.5]0.3
FHR specific parameters
Plate diameter dpmm hp∈[12;18]15
Cell cross Section Acell mm219 ×19 19 ×19
Face sheet porosity σ- 2.6% 2.6%
Face sheet thickness hfs mm 2 2
Main cavity height hmc mm 40 40
Second cavity height hsc mm hsc ∈[5;20]10
Liner length lliner mm 200 200
PR specific parameters
Cavity length lcmm lc∈[30;90]65
Cavity height hcmm hc∈[5;35]30
Cavity width wcmm ∞ ∞
The transmission loss (TL) is a commonly used parameter to characterize silencers and
is used in this work as the target variable to quantify the performance of both liner concepts.
The transmission loss describes the acoustic effectivity of a liner, and following [
42
], it is
calculated from the ratio of the transmitted sound power
Pt
and the incident sound power
Pi:
TL =−10 log10
Pt
Pi
. (2)
Note that the TL does not indicate whether the losses are due to reflection or dis-
sipation. Conversely, a very reflective and a very dissipative silencer both yield a high
transmission loss, while only the latter has a high dissipation (as energy is just reflected
back to the source but not converted into heat). The TL was chosen in our parameter studies
since it is a commonly used parameter to characterize silencers and offers the comparability
of the acoustic performance of both concepts. The following results for both liner concepts
are presented as color maps. These color maps can be read as topographic maps of the
transmission loss over frequency for each varied parameter (or in the case of the Young’s
Modulus and loss factor, parameter pair). Slicing the color map horizontally leads to the
frequency spectrum of transmission loss of a single value—respectively, a value pair—of the
varied parameter. The lighter areas depict the peaks of the transmission loss and therefore
areas where the liner performs best.
3.1. Result and Discussion of Parameter Studies for the FHR Concept
Following the experimental setup from the previous section, the configuration consists
of cells with a main cavity, which is connected to a second cavity by a flexible plate and
attached to the duct channel by a perforated face sheet. A sketch of the single cell is depicted
in Figure 5. Note that the single cell was extended to multiple cells with a total liner length
lliner
of 200 mm to better highlight the results. This is admissible as the single cell is locally
reacting.
Aerospace 2023,10, 5 9 of 24
Aerospace 2022, 10, 5 9 of 25
Figure 5. Schematic view of a single FHR cell.
The analytical modeling of the FHR concept is based on the works of Kohlenberg et
al. [9], where the modeling was introduced and verified using experimental data. It com-
bines one dimensional waveguide theory with lumped elements. The idea is to start at the
thermal boundary layer at the back of the resonator and use a waveguide model to
spatially transform that impedance through the resonator up to the channel. The flexible
plate is modeled as an equivalent impedance and integrated into the waveguide model.
The result is an overall impedance of the resonator system where the interaction of the
cavities and the flexible wall together form a Multi-Degree-Of-Freedom system. There-
fore, it is incorporated in the successive transformation of impedances. The flexible plate
is assumed to be round, clamped and only vibrating in its first mode. With these
assumptions, an equivalent impedance is calculated and integrated into the waveguide
model. The result is an impedance of the resonator system, which is used as a boundary
condition in a numerical simulation, which solves the Helmholtz equation to predict
scattering coefficients including the TL and the dissipation of the duct section with the
resonator system attached to one side. The results of the parameter studies of the Helm-
holtz resonator system with flexible walls are summarized in Figure 6.
Figure 5. Schematic view of a single FHR cell.
The analytical modeling of the FHR concept is based on the works of
Kohlenberg et al. [9],
where the modeling was introduced and verified using experimental data. It combines
one dimensional waveguide theory with lumped elements. The idea is to start at the
thermal boundary layer at the back of the resonator and use a waveguide model to spatially
transform that impedance through the resonator up to the channel. The flexible plate
is modeled as an equivalent impedance and integrated into the waveguide model. The
result is an overall impedance of the resonator system where the interaction of the cavities
and the flexible wall together form a Multi-Degree-Of-Freedom system. Therefore, it is
incorporated in the successive transformation of impedances. The flexible plate is assumed
to be round, clamped and only vibrating in its first mode. With these assumptions, an
equivalent impedance is calculated and integrated into the waveguide model. The result is
an impedance of the resonator system, which is used as a boundary condition in a numerical
simulation, which solves the Helmholtz equation to predict scattering coefficients including
the TL and the dissipation of the duct section with the resonator system attached to one
side. The results of the parameter studies of the Helmholtz resonator system with flexible
walls are summarized in Figure 6.
The parameter studies revealed that the frequency dependent TL of the liner is strongly
dependent on the Young’s modulus (and thereby also the loss factor) of the flexible plate
(see Figure 6a). Two peaks are visible in the low elastic region. The lower frequency peak
starting from around 550 Hz can be attributed to the plate resonance. The second resonance
frequency starting from around 900
Hz
is due to the Helmholtz resonance between the face
sheet and main cavity. With increasing Young’s modulus, the plate resonance increases as
well. This is expected since only the first clamped circular mode is taken into account with
a resonance frequency of
feig,plate ∼Re(h
d2·sE(1+iη)
ρ), (3)
with hthe plate thickness, dthe plate diameter and
ρ
the plate density. Note that the
resonance frequency of the system attributed to the plate resonance is not the same as the in
vacuo resonance frequency represented in Equation 3. This is because the overall resonance
behavior depends on the plate as well as on the cavities dimensions. In the modeling
they are linked through the combination of their respective impedances. The relationship
regarding the plate resonance inside the resonator system is not presentable in a satisfying
analytical form, hence we conducted parameter studies to show this behavior discretized.
In contrast to the resonance associated with the plate resonance, the Helmholtz resonance
hardly changes up to a transition zone around
E=
100 MPa. In this transition zone, the
transmission loss peak attributed to the plate’s resonance rises sharply with increasing
Young’s Modulus. For very stiff plates (
E=
10
3
MPa) only one transmission loss peak
Aerospace 2023,10, 5 10 of 24
is visible. In this configuration the flexible plate acts as a rigid back wall and only the
Helmholtz resonance is visible. To dampen low frequency noise, materials with a low
Young’s modulus are therefore preferred.
Aerospace 2022, 10, 5 10 of 25
Figure 6. Results of the parameter study of the Helmholtz resonator with flexible walls, (a) variation
of Young’s modulus 𝐸 and loss factor 𝜂, (b) variation of plate thickness ℎ𝑝, (c) variation of plate
diameter 𝑑𝑝, (d) variation of second cavity height ℎ𝑠𝑐.
The parameter studies revealed that the frequency dependent TL of the liner is
strongly dependent on the Young’s modulus (and thereby also the loss factor) of the flex-
ible plate (see Figure 6a). Two peaks are visible in the low elastic region. The lower fre-
quency peak starting from around 550 Hz can be attributed to the plate resonance. The
second resonance frequency starting from around 900 Hz is due to the Helmholtz reso-
nance between the face sheet and main cavity. With increasing Young’s modulus, the plate
resonance increases as well. This is expected since only the first clamped circular mode is
taken into account with a resonance frequency of
feig,plate∼Re{ℎ
𝑑2⋅√𝐸(1+i𝜂)
𝜌},
(3)
with h the plate thickness, d the plate diameter and 𝜌 the plate density. Note that the
resonance frequency of the system attributed to the plate resonance is not the same as the
in vacuo resonance frequency represented in Equation 3. This is because the overall reso-
nance behavior depends on the plate as well as on the cavities dimensions. In the model-
ing they are linked through the combination of their respective impedances. The relation-
ship regarding the plate resonance inside the resonator system is not presentable in a sat-
isfying analytical form, hence we conducted parameter studies to show this behavior dis-
cretized. In contrast to the resonance associated with the plate resonance, the Helmholtz
resonance hardly changes up to a transition zone around 𝐸 = 100 MPa. In this transition
zone, the transmission loss peak attributed to the plate’s resonance rises sharply with in-
creasing Young’s Modulus. For very stiff plates (𝐸=103 MPa) only one transmission loss
peak is visible. In this configuration the flexible plate acts as a rigid back wall and only
the Helmholtz resonance is visible. To dampen low frequency noise, materials with a low
Young’s modulus are therefore preferred.
Figure 6.
Results of the parameter study of the Helmholtz resonator with flexible walls, (
a
) variation
of Young’s modulus
E
and loss factor
η
, (
b
) variation of plate thickness
hp
, (
c
) variation of plate
diameter dp, (d) variation of second cavity height hsc.
The plate thickness has a strong impact on the TL as well (see Figure 6b). For very thin
plates, three effects are visible: First, the higher TL peak associated with the Helmholtz
resonance is altered towards higher frequencies. Second, the frequency of the TL peak due
to the plate resonance decreases up to a thickness of around 0.3 mm which is in contrast to
Equation 3, where the in-vacuo resonance increases linearly with the plate thickness. Thus,
the plate’s behavior with respect to the plate thickness inside the resonator system differs
from the in-vacuo case. For thicker plates, the resonator system tends to show only one
TL peak associated with the Helmholtz resonance. This can be explained by the fact that a
very thick plate approaches a rigid back wall. A thin plate is consequently preferable for a
strong attenuation of noise with low frequency components.
In contrast to the previous depicted parameters, the TL is altered in its amplitude
but not in its frequency with respect to a variable plate diameter (see Figure 6c). For
small flexible plates, the Helmholtz resonance seems to dominate the spectrum. For large
diameters, the flexible plate enables a higher TL at lower frequencies. The plate diameter
thus needs to be as big as possible to put the flexible plate effectively into use but is
limited by the dimensions of the cavity. However, as the plate resonance gets stronger, the
Helmholtz resonance is shifted towards higher frequencies. In comparison to the parameter
study regarding Young’s modulus (see Figure 6a), the system seems to be insensitive
regarding the plate diameter. However, it must be considered that the variation of the
elastic modulus includes several decades.
Finally, the influence of the second cavity depth regarding the TL was investigated (see
Figure 6d). The Helmholtz resonance seems to be largely independent of the second cavity
depth greater than 10 mm but is slightly altered to higher frequencies for very shallow
Aerospace 2023,10, 5 11 of 24
second cavities. The TL peaks associated with the plate-cavity sub-system is highest for
small second cavity depths, yet the resonance frequency is anti-proportional to the depth.
As nacelle space for aero-engine applications is very limited, a smaller second cavity is thus
advisable.
3.2. Result and Discussion of Parameter Studies for PR Liner Concept
Furthermore, parameter studies were carried out with the PR liner. The applied
semi-analytical model (see Figure 7) was initially developed by Huang and Wang [
15
,
16
].
It describes a two-dimensional PR liner with a simply supported plate. A simple PR
liner is composed of a duct and a wall mounted thin plate facing the duct and closing a
cavity behind it. The flexible plate is excited by the sound propagating along the duct,
which causes a pressure difference above and below the plate. Thus, the vibrating plate
interacting with the cavity dissipates one part of the incoming sound energy, and another
part is reflected back in direction of the sound source. The validity of the model has already
been demonstrated in former publications [
43
,
44
]. Furthermore, this model has already
been used to conduct parameter studies to investigate the acoustic performance of the plate
silencer. These researchers investigated, for example, the effects of the plate material on the
transmission loss and the approximation quality of the model [10,12,17,45].
Aerospace 2022, 10, 5 11 of 25
The plate thickness has a strong impact on the TL as well (see Figure 6b). For very
thin plates, three effects are visible: First, the higher TL peak associated with the Helm-
holtz resonance is altered towards higher frequencies. Second, the frequency of the TL
peak due to the plate resonance decreases up to a thickness of around 0.3 mm which is in
contrast to Equation 3, where the in-vacuo resonance increases linearly with the plate
thickness. Thus, the plate’s behavior with respect to the plate thickness inside the resona-
tor system differs from the in-vacuo case. For thicker plates, the resonator system tends to
show only one TL peak associated with the Helmholtz resonance. This can be explained
by the fact that a very thick plate approaches a rigid back wall. A thin plate is consequently
preferable for a strong attenuation of noise with low frequency components.
In contrast to the previous depicted parameters, the TL is altered in its amplitude but
not in its frequency with respect to a variable plate diameter (see Figure 6c). For small
flexible plates, the Helmholtz resonance seems to dominate the spectrum. For large diam-
eters, the flexible plate enables a higher TL at lower frequencies. The plate diameter thus
needs to be as big as possible to put the flexible plate effectively into use but is limited by
the dimensions of the cavity. However, as the plate resonance gets stronger, the Helm-
holtz resonance is shifted towards higher frequencies. In comparison to the parameter
study regarding Young’s modulus (see Figure 6a), the system seems to be insensitive re-
garding the plate diameter. However, it must be considered that the variation of the elastic
modulus includes several decades.
Finally, the influence of the second cavity depth regarding the TL was investigated
(see Figure 6d). The Helmholtz resonance seems to be largely independent of the second
cavity depth greater than 10 mm but is slightly altered to higher frequencies for very shal-
low second cavities. The TL peaks associated with the plate-cavity sub-system is highest
for small second cavity depths, yet the resonance frequency is anti-proportional to the
depth. As nacelle space for aero-engine applications is very limited, a smaller second cav-
ity is thus advisable.
3.2. Result and Discussion of Parameter Studies for PR Liner Concept
Furthermore, parameter studies were carried out with the PR liner. The applied semi-
analytical model (see Figure 7) was initially developed by Huang and Wang [15,16]. It
describes a two-dimensional PR liner with a simply supported plate. A simple PR liner is
composed of a duct and a wall mounted thin plate facing the duct and closing a cavity
behind it. The flexible plate is excited by the sound propagating along the duct, which
causes a pressure difference above and below the plate. Thus, the vibrating plate interact-
ing with the cavity dissipates one part of the incoming sound energy, and another part is
reflected back in direction of the sound source. The validity of the model has already been
demonstrated in former publications [43,44]. Furthermore, this model has already been
used to conduct parameter studies to investigate the acoustic performance of the plate
silencer. These researchers investigated, for example, the effects of the plate material on
the transmission loss and the approximation quality of the model [10,12,17,45].
Figure 7. Sketch of a simple plate silencer.
The parameter studies presented here are based on the geometric and material spe-
cific values in Table 2. The results show the frequency dependent TL for different param-
eter variations in form of a color map (Figure 8). Different from the FHR, the PR model
Figure 7. Sketch of a simple plate silencer.
The parameter studies presented here are based on the geometric and material specific
values in Table 2. The results show the frequency dependent TL for different parameter
variations in form of a color map (Figure 8). Different from the FHR, the PR model provides
the results for one chamber and not for an entire liner consisting of several chambers in
series. This must be taken into account when evaluating the absolute transmission loss
values. Varying Young’s modulus (and correlated the loss factor), the TL appears with
increasing Young’s modulus in clear s-shaped patterns, and between them more and more
distinctive discontinuities occur. This behavior corresponds to an eigen frequency shift
from higher to lower odd modes of the plate and is also discussed in [
17
]. However, in
addition to the direct relationship between Young’s modulus and plate resonances, there
is also an interaction with the cavity below, which can affect the frequency of the plate
resonance. Another effect, which can be observed, is the blurring of the s-shaped patterns
with increasing loss factor and more distinct and brighter shapes with increasing Young’s
modulus. This implies that the peaks of the TL become narrower and higher as the Young’s
modulus becomes higher. Otherwise, the peaks become wider and flatter as the loss factor
increases. Furthermore, it can be seen that the s-shaped patterns cause one or two peaks to
appear in the TL over the frequency spectrum. Thus, one or two TL peaks can be obtained
by the choice of material as well as the width of these peaks.
Aerospace 2023,10, 5 12 of 24
Aerospace 2022, 10, 5 12 of 25
provides the results for one chamber and not for an entire liner consisting of several cham-
bers in series. This must be taken into account when evaluating the absolute transmission
loss values. Varying Young’s modulus (and correlated the loss factor), the TL appears
with increasing Young’s modulus in clear s-shaped patterns, and between them more and
more distinctive discontinuities occur. This behavior corresponds to an eigen frequency
shift from higher to lower odd modes of the plate and is also discussed in [17]. However,
in addition to the direct relationship between Young’s modulus and plate resonances,
there is also an interaction with the cavity below, which can affect the frequency of the
plate resonance. Another effect, which can be observed, is the blurring of the s-shaped
patterns with increasing loss factor and more distinct and brighter shapes with increasing
Young’s modulus. This implies that the peaks of the TL become narrower and higher as
the Young’s modulus becomes higher. Otherwise, the peaks become wider and flatter as
the loss factor increases. Furthermore, it can be seen that the s-shaped patterns cause one
or two peaks to appear in the TL over the frequency spectrum. Thus, one or two TL peaks
can be obtained by the choice of material as well as the width of these peaks.
Figure 8. Results of the parameter study of the plate silencer, (a) variation of Young’s modulus 𝐸
and loss factor 𝜂, (b) variation of plate thickness ℎ𝑝, (c) variation of plate length 𝑙𝑝, (d) variation of
cavity height ℎ𝑐.
Furthermore, the results show that the plate thickness ℎ𝑝 has a very strong impact
on the location of the TL maximum (see Figure 8b). It can be seen that a thicker plate
results in attenuation at lower frequencies. Thereby, the maximum TL converges to ap-
proximately 500 Hz. Thus, it does not seem possible to attenuate even lower frequencies
with an even thicker plate. In addition, thicker plates result in lower absolute transmission
loss. In the extreme case, the duct wall and the flexible plate would approach each other,
resulting in the loss of the desired TL. However, the bandwidth of the TL is barely influ-
enced by the plate thickness. Moreover, the s-shaped patterns caused by the plate modes
cannot be observed here. This is due to the selection of the design point with a compara-
tive high loss factor.
Figure 8.
Results of the parameter study of the plate silencer, (
a
) variation of Young’s modulus
E
and
loss factor
η
, (
b
) variation of plate thickness
hp
, (
c
) variation of plate length
lp
, (
d
) variation of cavity
height hc.
Furthermore, the results show that the plate thickness
hp
has a very strong impact on
the location of the TL maximum (see Figure 8b). It can be seen that a thicker plate results in
attenuation at lower frequencies. Thereby, the maximum TL converges to approximately
500 Hz. Thus, it does not seem possible to attenuate even lower frequencies with an even
thicker plate. In addition, thicker plates result in lower absolute transmission loss. In the
extreme case, the duct wall and the flexible plate would approach each other, resulting
in the loss of the desired TL. However, the bandwidth of the TL is barely influenced by
the plate thickness. Moreover, the s-shaped patterns caused by the plate modes cannot be
observed here. This is due to the selection of the design point with a comparative high loss
factor.
The length of the plate and cavity
lc
has a much smaller impact on the frequency of
the maximum TL (see Figure 8c). There is only a minimal shift to higher frequencies with
increasing plate length observable. This parameter has a more obvious influence on the
absolute TL, which increases significantly with increasing plate length. Furthermore, it
leads to slightly more broadband attenuation.
To influence the frequency of the maximum TL, the cavity height
hc
has the biggest
impact (see Figure 8d). Thus, a cavity height between 5 and 35 mm covers a frequency
range of almost 1000 Hz. The frequency of maximum TL decreases with increasing cavity
height but approaches 500 Hz asymptotically for the considered PR liner configuration. A
higher cavity also broadens the TL peak slightly, but a significantly higher attenuation is
not achieved.
The application of the FHR or PR concept as a liner in jet engines requires not only
acoustics but also structural mechanics and manufacturing investigations, which are pre-
sented in the following chapters.
Aerospace 2023,10, 5 13 of 24
4. Structural Mechanics Analysis and Results
The application of an acoustic liner does not merely depend on the acoustical perfor-
mance but also on its ability to withstand the conditions during the operation inside a jet
engine. It is crucial to determine the maximum load capacity of each component to ensure
the reliability of the acoustic liner throughout its intended life cycle. In this context, a study
was conducted to compare the mechanical properties between a conventional HR liner and
a novel FHR liner with flexible films integrated in its side walls.
4.1. Structural Design
The conventional HR liners consist of a perforated face sheet, a back plate and a
bioinspired honeycomb core structure with a high specific modulus suiting the strict
requirements in aviation (Figure 9a) [
46
,
47
]. In the present study the conventional core
is compared to an alternative core structure comprising square cells (Figure 9b). Due to
the comparatively larger areas of the side walls and the less complex manufacturing and
joining process, square combs hold an advantage for the integration of flexible films. The
change in the geometry of the cell and the implemented cut-outs for the flexible films as
well as the selection of a new combination of materials leads to miscellaneous mechanical
properties that need to be considered for the application of maximum loads, which the
liner has to withstand.
Aerospace 2022, 10, 5 14 of 25
Figure 9. (a) Conventional HR liner and detailed honeycomb, (b) Resonator liner with square hon-
eycombs detail of the square cells with film (turquoise).
In the course of this study, three configurations of the core design of the FHR Liner
were compared. The first configuration (HR liner) represents the standard liner with a
honeycomb core structure, made out of Carbon Fiber Reinforced Polymer (CFRP), Glass
Fiber Reinforced Polymer (GFRP) and Nomex. The second and third configuration have
a different core structure with square cells. The second configuration has the same mate-
rials and stack ups as the standard liner. The components of the third type are completely
made out of PA6-GF. The components and the corresponding materials of the three design
configurations are listed in Table 3. In order to enable a more accurate comparison with
the HR liner, the chamber volume of the rectangular core was converted to hexagonal
shape for an initial preliminary investigation.
Table 3. Structure component, corresponding materials and thickness of the acoustic liner configu-
ration.
Component
Face Sheet
Core
Back Plate
Cell
Geometry
Mass
[kg]
HR liner
2/2 Twill
Weave * CFRP
(0.2 mm)
Aramid Paper
(Nomex)
(0.194 mm)
10 UD-plies CFRP
Orientation:
[0/0/45/90/−45/𝑠]
(1 mm)
2 UD-plies GFRP
Orientation: [0/90]
(0.2 mm)
Honeycomb
0.218
FHR-Type 1
Square Cells
0.240
FHR-Type 2
PA6-GF–2/2 Twill
Weave (1 mm)
PA6-GF–2/2 Twill
Weave (1 mm)
PA6-GF–2/2 Twill
Weave (1 mm)
PA6-GF–2/2 Twill
Weave (1 mm)
Square Cells
0.573
* diagonal appearance by a two-by-two weave where two warp yarns float over two weft yarns.
4.2. Materials
Apart from the geometry, a variation of different materials is considered for the com-
ponents of the three configurations. In this context, the core of the conventional acoustic
liner (HR and FHR-Type 1) consists of aramid paper (Nomex) and a face sheet and back
Figure 9.
(
a
) Conventional HR liner and detailed honeycomb, (
b
) Resonator liner with square
honeycombs detail of the square cells with film (turquoise).
In the course of this study, three configurations of the core design of the FHR Liner
were compared. The first configuration (HR liner) represents the standard liner with a
honeycomb core structure, made out of Carbon Fiber Reinforced Polymer (CFRP), Glass
Fiber Reinforced Polymer (GFRP) and Nomex. The second and third configuration have a
different core structure with square cells. The second configuration has the same materials
and stack ups as the standard liner. The components of the third type are completely
made out of PA6-GF. The components and the corresponding materials of the three design
configurations are listed in Table 3. In order to enable a more accurate comparison with the
Aerospace 2023,10, 5 14 of 24
HR liner, the chamber volume of the rectangular core was converted to hexagonal shape
for an initial preliminary investigation.
Table 3.
Structure component, corresponding materials and thickness of the acoustic liner configura-
tion.
Component Face Sheet Core Back Plate Cell
Geometry Mass [kg]
HR liner 2/2 Twill
Weave * CFRP
(0.2 mm)
Aramid Paper
(Nomex)
(0.194 mm)
10 UD-plies CFRP
Orientation:
[0/0/45/90/ −45/s]
(1 mm)
2 UD-plies GFRP
Orientation: [0/90]
(0.2 mm)
Honeycomb 0.218
FHR-Type 1 Square Cells 0.240
FHR-Type 2 PA6-GF–2/2 Twill
Weave (1 mm)
PA6-GF–2/2 Twill
Weave (1 mm)
PA6-GF–2/2 Twill Weave
(1 mm)
PA6-GF–2/2 Twill
Weave (1 mm) Square Cells 0.573
* diagonal appearance by a two-by-two weave where two warp yarns float over two weft yarns.
4.2. Materials
Apart from the geometry, a variation of different materials is considered for the
components of the three configurations. In this context, the core of the conventional
acoustic liner (HR and FHR-Type 1) consists of aramid paper (Nomex) and a face sheet and
back plate, which are made out of carbon fiber and glass fiber reinforced epoxy resin. In
contrast, the structure of the novel liner concept (FHR-Type 2) is made entirely of PA6-GF.
In Table 4, the properties for each material are listed, including the detailed listing of
the orthotropic material behavior and the consideration of different values in each load
direction of unidirectional plies and woven plies.
Table 4. Material properties of the acoustic liner components.
Material
Nomex with
Phenolic
Resin
PVC-Rigid
Foam Core
Carbon Fiber with
Epoxy Resin–
Unidirectional-
(Woven Fabric)
PA6-GF
E-Glass
Glass Fiber
with Epoxy
Resin
Youngs Modulus E1[MPa] 6034 70 129,000 (61,000) 18,000 29,700
Youngs Modulus E2[MPa] 5263 70 7380 (61,000) 18,000 29,700
Youngs Modulus E3[MPa] 4427 70 7380 (6900) 22,000 8600
Poisson’s ratio ν12 0.316 0.3 0.319 (0.04) 0.17 0.17
Poisson’s ratio ν13 0.327 0.3 0.319 (0.3) 0.17 0.17
Poisson’s ratio ν23 0.317 0.3 0.4 (0.3) 0.49 0.17
Shear Modulus G12 [MPa] 2142 27 4480 (3300) 7692 5300
Shear Modulus G13 [MPa] 1588 27 4480 (2700) 7692 3070
Shear Modulus G23 [MPa] 1865 27 2636 (2700) 7382 3070
Density ρ[kg/m3]1185 60 1560 (1420) 1800 2200
Fiber processing type - - Unidirectional
(Twill Weave 2/2) Twill 2/2 Twill 2/2
Stress limits
Tensile Strength R(+)
1[MPa] 62.3 1.5 2553 (805) 380 367
Tensile Strength R(+)
2[MPa] 48.2 1.5 42 (805) 380 367
Tensile Strength R(+)
3[MPa] 48.2 1.5 42 (50) - 128
Compression Strength R(−)
1[MPa] −85 0.96 1239 (509) - 549
Compression Strength R(−)
2[MPa] −78 0.96 199 (509) - 549
Compression Strength R(−)
3[MPa] −78 0.96 199 (170) - 39
Shear strength R12 [MPa] 71.8 0.93 138 (125) 64 97
Shear strength R13 [MPa] 71.8 0.93 138 (65) 64 97
Shear strength R23 [MPa] 71.8 0.93 138 (65) 64 97
Aerospace 2023,10, 5 15 of 24
4.3. Modeling and Numerical Implementation
In order to analyze and compare the behavior of the three different liner structures, an
FEA was carried out by using the simulation program (Ansys Workbench 2022 R.1., Ansys,
Canonsburg, PA, USA). For the definition of the woven and unidirectional plies, the Ansys
composite prepost (ACP) was used, allowing the specification of the fiber orientations
and the stack-ups for each component according to Table 3. Since the thickness of each
component is significantly lower than its length and width, shell elements of the type
SHELL 181 were used. The convergence of the results occurred with an element size of
0.7 mm with a quadratic basis function and 8 nodes (Quad8). The resulting models were
investigated in the course of a linear static–structural–mechanical analysis. Furthermore,
the Tsai-Wu criterion [
48
] was applied to investigate the failure behavior of the composite
structure for each component.
4.4. Constraints and Load Cases
In order to define the boundary conditions, a 3D Model was built for each core type
(Table 3) and provided with the prevailing restrictions based on the application of acoustic
liners in aero-engines. Typically, an acoustic liner is mounted on both sides in the axial
direction of the engine to the inner nacelle structure. Since the liners applied in the inlet
sections are rather short and the applications of screws lead to unfavorable aerodynamic
conditions, an adhesive bonding or a clamp connection is preferred. In the bypass duct, the
liners are additionally supported with screw connections due to their length. Therefore, the
displacements on both sides are assumed to be fixed in all directions (see Figure 10). The
green surfaces embody the fixed areas without displacement. To support the back plate, its
bottom face (blue) is connected to a stiffer structure underneath the liner. For the simulation
a friction free connection was chosen to prevent the liner from lifting off of the support
structure in
x3
-direction [
26
]. The common manufacturing process of acoustic liners leads
to an adhesive bonding between the core structure, foam [
47
] core, back plate and face
sheet. The sheets of each part were therefore implemented as a compound. Further, it
is assumed that the integrated films have no significant influence on the stiffness of the
FHR-Liner structure. Therefore, they are neglected in the CAD-Model and the simulation.
Aerospace 2022, 10, 5 16 of 25
4.4. Constraints and Load Cases
In order to define the boundary conditions, a 3D Model was built for each core type
(Table 3) and provided with the prevailing restrictions based on the application of acoustic
liners in aero-engines. Typically, an acoustic liner is mounted on both sides in the axial
direction of the engine to the inner nacelle structure. Since the liners applied in the inlet
sections are rather short and the applications of screws lead to unfavorable aerodynamic
conditions, an adhesive bonding or a clamp connection is preferred. In the bypass duct,
the liners are additionally supported with screw connections due to their length. There-
fore, the displacements on both sides are assumed to be fixed in all directions (see Figure
10). The green surfaces embody the fixed areas without displacement. To support the back
plate, its bottom face (blue) is connected to a stiffer structure underneath the liner. For the
simulation a friction free connection was chosen to prevent the liner from lifting off of the
support structure in 𝑥3-direction [26]. The common manufacturing process of acoustic
liners leads to an adhesive bonding between the core structure, foam [47] core, back plate
and face sheet. The sheets of each part were therefore implemented as a compound. Fur-
ther, it is assumed that the integrated films have no significant influence on the stiffness
of the FHR-Liner structure. Therefore, they are neglected in the CAD-Model and the sim-
ulation.
Figure 10. Fixed boundary condition (green), adhesive bonding (blue), applied forces (orange).
This study is limited to the two static load cases subjected to the acoustic liner during
the life of an engine:
• global pressure loads due to pressure differences between the face sheet and the back
side of the back sheet
• local loads due to maintenance
The maximal considered global pressure load during normal operation of the engine
is 0.07 MPa. Typical local loads depict for example the set of footsteps during maintenance
on the perforated face sheet. The load cases are applied normal to the face sheet along the
𝑥3-axis (see Figure 10). The global pressure induced higher stresses and was therefore ap-
plied in the FEA.
4.5. Results of the FEA
In order to assess the effect of the variation in the core structure and the application
of different materials, the three liner models were analyzed. The numerical analysis (Fig-
ure 11) shows the load influence of the face sheet. To determine the failure, a material
exposure indicator is used. The so-called inverse reserve factor is ranging from 0 to 1,
whereby 1 and above indicates the occurrence of failure and zero an unloaded condition.
Figure 10. Fixed boundary condition (green), adhesive bonding (blue), applied forces (orange).
This study is limited to the two static load cases subjected to the acoustic liner during
the life of an engine:
•
global pressure loads due to pressure differences between the face sheet and the back
side of the back sheet
•local loads due to maintenance
Aerospace 2023,10, 5 16 of 24
The maximal considered global pressure load during normal operation of the engine
is 0.07 MPa. Typical local loads depict for example the set of footsteps during maintenance
on the perforated face sheet. The load cases are applied normal to the face sheet along
the
x3
-axis (see Figure 10). The global pressure induced higher stresses and was therefore
applied in the FEA.
4.5. Results of the FEA
In order to assess the effect of the variation in the core structure and the application of
different materials, the three liner models were analyzed. The numerical analysis (Figure 11)
shows the load influence of the face sheet. To determine the failure, a material exposure
indicator is used. The so-called inverse reserve factor is ranging from 0 to 1, whereby 1 and
above indicates the occurrence of failure and zero an unloaded condition. The value in
the area of the face sheet for the HR-Liner (Figure 11a) is around 0.3. In contrast, for the
FHR-Type 1 (Figure 11b), the value exceeds 1 and the failure of the fiber can be expected
due to tensile stresses at the transition between face sheet and core wall in the area between
the passive and active cell. The maximal deformation occurs in the middle of the active
cell and nearly doubles between the honeycomb and square cell with the same material
properties. Still, the novel liner has an increase in mass of around 10% (Table 3). The change
in the core structure of an acoustic liner leads with the chosen material to a failure of the
perforated face sheet. The application of the PA6-GF for the face sheet and Nomex core
shows a much stiffer behavior (Figure 11c). However, this is associated with an increase of
the total mass by nearly 100% compared to the standard.
Aerospace 2022, 10, 5 17 of 25
The value in the area of the face sheet for the HR-Liner (Figure 11a) is around 0.3. In con-
trast, for the FHR-Type 1 (Figure 11b), the value exceeds 1 and the failure of the fiber can
be expected due to tensile stresses at the transition between face sheet and core wall in the
area between the passive and active cell. The maximal deformation occurs in the middle
of the active cell and nearly doubles between the honeycomb and square cell with the
same material properties. Still, the novel liner has an increase in mass of around 10% (Ta-
ble 3). The change in the core structure of an acoustic liner leads with the chosen material
to a failure of the perforated face sheet. The application of the PA6-GF for the face sheet
and Nomex core shows a much stiffer behavior (Figure 11c). However, this is associated
with an increase of the total mass by nearly 100% compared to the standard.
Figure 11. Workload of the perforated face sheets of the liner models (a) HR liner, (b) FHR liner with
carbon fiber, (c) FHR liner with PA6-GF.
The application of the novel liner concept requires a cut-out inside the supporting
core structure (Figure 9b). The influence of cut-out size and corner rounding on the me-
chanical properties was examined by Höschler et al. [49]. The investigations were carried
out on the assumption that there are only active cells. The concept revision consisting of
an active and passive cell leads, however, to a significant change for the load conditions
inside the core. The changing order of walls with cut-outs and walls without cut-outs af-
fect the force distribution and relieve the upper web of the frame. Depending on the dis-
tance lscP of the passive cell, a reduction of the occurring stresses is evident. Figure 12
shows the correlation of the cell size and the maximum principal stresses for the FHR-
Liner type 1. It is noticeable that the stress decreases with a decrease of the distance 𝑙𝑠𝑐𝑃,
while the size of the active cell remains the same. The deformation also decreases to the
same extent.
Figure 11.
Workload of the perforated face sheets of the liner models (
a
) HR liner, (
b
) FHR liner with
carbon fiber, (c) FHR liner with PA6-GF.
The application of the novel liner concept requires a cut-out inside the supporting core
structure (Figure 9b). The influence of cut-out size and corner rounding on the mechanical
properties was examined by Höschler et al. [
49
]. The investigations were carried out on
the assumption that there are only active cells. The concept revision consisting of an active
and passive cell leads, however, to a significant change for the load conditions inside the
core. The changing order of walls with cut-outs and walls without cut-outs affect the force
distribution and relieve the upper web of the frame. Depending on the distance
lscP
of the
passive cell, a reduction of the occurring stresses is evident. Figure 12 shows the correlation
of the cell size and the maximum principal stresses for the FHR-Liner type 1. It is noticeable
that the stress decreases with a decrease of the distance
lscP
, while the size of the active cell
remains the same. The deformation also decreases to the same extent.
Aerospace 2023,10, 5 17 of 24
Aerospace 2022, 10, 5 18 of 25
Figure 12. Change in stress and strain for different passive cell spacings.
Simultaneously, the weight of the liner increases as an increasing number of walls
are necessary to cover a certain axial length 𝑙𝑙𝑖𝑛𝑒𝑟. The maximum stresses and the largest
deformations occur in the upper region for both HR and FHR liner. However, due to the
cut-out, the stresses and deformations are higher for the FHR configuration. The combi-
nation of smaller spacing of the passive cell walls (see Figure 12) and the change of the
material to PA6-GF results in significantly lower stresses in the cut-out frame (Figure 13c).
Dependent on the chosen configuration, the thickness can be reduced and therefore the
total weight of the FHR-liner. Figure 13d shows an increase in stress for the HR-Liner type
2 while reducing the spacing, the material thickness and the weight by 40% compared to
the configuration of Figure 13c.
Figure 13. Distribution plot of the principal stresses of the core walls for the (a) HR-Liner; (b) FHR-
Liner type 1; (c) FHR-Liner type 2 with 𝑡𝑠𝑐=1 mm and 𝑙𝑠𝑐𝑃=5 mm; (d) FHR-Liner type 2 with
𝑡𝑠𝑐=0.25 mm and 𝑙𝑠𝑐𝑃=5 mm.
5. Design and Manufacturing Feasibility Study for Curved Acoustic Liners
To evaluate the potential and challenges associated with the realization of curved
acoustic liners for integration into jet engines, the following feasibility study was con-
ducted. Given the film material is a key component in the introduced FHR and PR liner
Figure 12. Change in stress and strain for different passive cell spacings.
Simultaneously, the weight of the liner increases as an increasing number of walls
are necessary to cover a certain axial length
lliner
. The maximum stresses and the largest
deformations occur in the upper region for both HR and FHR liner. However, due to the cut-
out, the stresses and deformations are higher for the FHR configuration. The combination
of smaller spacing of the passive cell walls (see Figure 12) and the change of the material to
PA6-GF results in significantly lower stresses in the cut-out frame (Figure 13c). Dependent
on the chosen configuration, the thickness can be reduced and therefore the total weight of
the FHR-liner. Figure 13d shows an increase in stress for the HR-Liner type 2 while reducing
the spacing, the material thickness and the weight by 40% compared to the configuration
of Figure 13c.
Aerospace 2022, 10, 5 18 of 25
Figure 12. Change in stress and strain for different passive cell spacings.
Simultaneously, the weight of the liner increases as an increasing number of walls
are necessary to cover a certain axial length 𝑙𝑙𝑖𝑛𝑒𝑟. The maximum stresses and the largest
deformations occur in the upper region for both HR and FHR liner. However, due to the
cut-out, the stresses and deformations are higher for the FHR configuration. The combi-
nation of smaller spacing of the passive cell walls (see Figure 12) and the change of the
material to PA6-GF results in significantly lower stresses in the cut-out frame (Figure 13c).
Dependent on the chosen configuration, the thickness can be reduced and therefore the
total weight of the FHR-liner. Figure 13d shows an increase in stress for the HR-Liner type
2 while reducing the spacing, the material thickness and the weight by 40% compared to
the configuration of Figure 13c.
Figure 13. Distribution plot of the principal stresses of the core walls for the (a) HR-Liner; (b) FHR-
Liner type 1; (c) FHR-Liner type 2 with 𝑡𝑠𝑐=1 mm and 𝑙𝑠𝑐𝑃=5 mm; (d) FHR-Liner type 2 with
𝑡𝑠𝑐=0.25 mm and 𝑙𝑠𝑐𝑃=5 mm.
5. Design and Manufacturing Feasibility Study for Curved Acoustic Liners
To evaluate the potential and challenges associated with the realization of curved
acoustic liners for integration into jet engines, the following feasibility study was con-
ducted. Given the film material is a key component in the introduced FHR and PR liner
Figure 13.
Distribution plot of the principal stresses of the core walls for the (
a
) HR-Liner; (
b
) FHR-
Liner type 1; (
c
) FHR-Liner type 2 with
tsc =
1
mm
and
lscP =
5
mm
; (
d
) FHR-Liner type 2 with
tsc =0.25 mm and lscP =5 mm.
5. Design and Manufacturing Feasibility Study for Curved Acoustic Liners
To evaluate the potential and challenges associated with the realization of curved
acoustic liners for integration into jet engines, the following feasibility study was conducted.
Given the film material is a key component in the introduced FHR and PR liner principles
Aerospace 2023,10, 5 18 of 24
in terms of acoustic performance, it is important to avoid compromising the geometry
and bearing conditions of the films by implementing the curved shapes for the intended
applications in jet engines. Since most of the currently used fabrication methods implement
the curvature of the general liner structure in a way that can cause severe damage to the
acoustic structure, a new design and corresponding fabrication methods are introduced in
the following.
5.1. Design and Manufacturing Concept HR-Liner
The targeted design of the curved HR-Liner is based on the design introduced by
Dannemann et al. [
32
]. The curved frame and rectangular stringer with cut-outs are
manufactured using a laser or water jet cutting process (see Figure 14). In order to enable
the necessary deflection of the film, an acoustically active cell, connected to the duct
via perforations in the face sheet, and a passive cell without perforations are arranged
alternately along the perimeter. This creates a pressure gradient between the cavities that
allows the film material to deflect. In this context, for the passive cells, the slots of the frame
should be closer together to decrease their volume and consequently increase the ratio of
the acoustically active cells to the overall area covered.
Aerospace 2022, 10, 5 19 of 25
principles in terms of acoustic performance, it is important to avoid compromising the
geometry and bearing conditions of the films by implementing the curved shapes for the
intended applications in jet engines. Since most of the currently used fabrication methods
implement the curvature of the general liner structure in a way that can cause severe dam-
age to the acoustic structure, a new design and corresponding fabrication methods are
introduced in the following.
5.1. Design and Manufacturing Concept HR-Liner
The targeted design of the curved HR-Liner is based on the design introduced by
Dannemann et al. [32]. The curved frame and rectangular stringer with cut-outs are man-
ufactured using a laser or water jet cutting process (see Figure 14). In order to enable the
necessary deflection of the film, an acoustically active cell, connected to the duct via per-
forations in the face sheet, and a passive cell without perforations are arranged alternately
along the perimeter. This creates a pressure gradient between the cavities that allows the
film material to deflect. In this context, for the passive cells, the slots of the frame should
be closer together to decrease their volume and consequently increase the ratio of the
acoustically active cells to the overall area covered.
Figure 14. (a) Process of cutting the components of the resonator cavity out of sheet material, i.e.,
water jet or laser cutting, (b) curved frame with slits, the stringer with and without cut-outs for the
flexible film.
According to previous studies and the experimental investigations presented before
in this work, the stress state of the film is a pivotal constrain due to its impact on the
damping characteristic of the liner [32]. In this context, the goal is to reproducibly pre-
tension the film in the form that a subsequent joining process with the support structure
without wrinkles but a defined stress state of the film is possible. For this purpose, the
film is cut in the form of a biaxial specimen, clamped at the edges of the tabs and is force-
controlled deflected by weights applied to the tabs. Subsequently, a fixing frame is used
to conserve the films pretension state. In order to utilize the thermoplastic material prop-
erties of the film and the support structure while saving additional adhesives, the ultra-
sonic welding process is proposed for joining the two components. As shown in Figure
15b, the fixing frame is positioned and mounted on top of a lower support carrying the
stringers with cut-outs. Then a windowed die, used to minimize the impact of the welding
process on the conserved stress state of film, is mounted within the frame. In the next step,
a rectangular sonotrode welds the film onto the stringers at a web width of 2 mm around
the cut-out.
Figure 14.
(
a
) Process of cutting the components of the resonator cavity out of sheet material, i.e.,
water jet or laser cutting, (
b
) curved frame with slits, the stringer with and without cut-outs for the
flexible film.
According to previous studies and the experimental investigations presented before in
this work, the stress state of the film is a pivotal constrain due to its impact on the damping
characteristic of the liner [
32
]. In this context, the goal is to reproducibly pre-tension the
film in the form that a subsequent joining process with the support structure without
wrinkles but a defined stress state of the film is possible. For this purpose, the film is cut
in the form of a biaxial specimen, clamped at the edges of the tabs and is force-controlled
deflected by weights applied to the tabs. Subsequently, a fixing frame is used to conserve
the films pretension state. In order to utilize the thermoplastic material properties of the
film and the support structure while saving additional adhesives, the ultrasonic welding
process is proposed for joining the two components. As shown in Figure 15b, the fixing
frame is positioned and mounted on top of a lower support carrying the stringers with
cut-outs. Then a windowed die, used to minimize the impact of the welding process on the
conserved stress state of film, is mounted within the frame. In the next step, a rectangular
sonotrode welds the film onto the stringers at a web width of 2 mm around the cut-out.
Aerospace 2023,10, 5 19 of 24
Aerospace 2022, 10, 5 20 of 25
Figure 15. (a) Process of pretension the film using a force-controlled set-up including clamps and
weights and the subsequent conservation of the resulting stress state by applying a fixing frame, (b)
necessary components for ultrasonic welding including welding die, lower support carrying the
stringers and the pre-tensioned film, (c) rectangular sonotrode with its cross-section as well as the
final setup for ultrasonic welding of the film and the stringer, (d) stringers with attached films.
After removing the excess film material, the curved frame and the stringers are as-
sembled. Finally, the cover layer and the perforated cover sheet are adhesively bonded to
the cavity structure (see Figure 16).
Figure 16. Design study of a curved FHR liner with the perforated face sheet including active and
passive cavities, the covering face sheet and the strip slotted cavity structure.
5.2. Design and Manufacturing Concept of Curved PR-Liner
Since the cavities of the PR liner do not have flexible side walls compared to the FHR
liner, their manufacturing process is less complex, allowing a reduction in manufacturing
steps and higher automation potential. Here, the low cost deep drawing process is a suit-
able choice for manufacturing the resonator cavities (see Figure 17a). This process enables
arbitrary shapes of the resonator cavity and mounting surfaces, e.g., a curved geometry
of the resonator bottom matching the targeted design space and the corresponding con-
tour of the top layer of the structure [35,49]. However, due to the curved shape, the process
of joining the curved film layer onto the cavity structure is more complex. Since the tar-
geted thermoplastic films have a low stiffness, a form-die is required that sets the shape
of the curved liner (see Figure 17b). In order to establish a homogeneous tension state,
irregular distribution of friction forces during the deflection process of the film, due to the
Figure 15.
(
a
) Process of pretension the film using a force-controlled set-up including clamps and
weights and the subsequent conservation of the resulting stress state by applying a fixing frame,
(
b
) necessary components for ultrasonic welding including welding die, lower support carrying the
stringers and the pre-tensioned film, (
c
) rectangular sonotrode with its cross-section as well as the
final setup for ultrasonic welding of the film and the stringer, (d) stringers with attached films.
After removing the excess film material, the curved frame and the stringers are assem-
bled. Finally, the cover layer and the perforated cover sheet are adhesively bonded to the
cavity structure (see Figure 16).
Aerospace 2022, 10, 5 20 of 25
Figure 15. (a) Process of pretension the film using a force-controlled set-up including clamps and
weights and the subsequent conservation of the resulting stress state by applying a fixing frame, (b)
necessary components for ultrasonic welding including welding die, lower support carrying the
stringers and the pre-tensioned film, (c) rectangular sonotrode with its cross-section as well as the
final setup for ultrasonic welding of the film and the stringer, (d) stringers with attached films.
After removing the excess film material, the curved frame and the stringers are as-
sembled. Finally, the cover layer and the perforated cover sheet are adhesively bonded to
the cavity structure (see Figure 16).
Figure 16. Design study of a curved FHR liner with the perforated face sheet including active and
passive cavities, the covering face sheet and the strip slotted cavity structure.
5.2. Design and Manufacturing Concept of Curved PR-Liner
Since the cavities of the PR liner do not have flexible side walls compared to the FHR
liner, their manufacturing process is less complex, allowing a reduction in manufacturing
steps and higher automation potential. Here, the low cost deep drawing process is a suit-
able choice for manufacturing the resonator cavities (see Figure 17a). This process enables
arbitrary shapes of the resonator cavity and mounting surfaces, e.g., a curved geometry
of the resonator bottom matching the targeted design space and the corresponding con-
tour of the top layer of the structure [35,49]. However, due to the curved shape, the process
of joining the curved film layer onto the cavity structure is more complex. Since the tar-
geted thermoplastic films have a low stiffness, a form-die is required that sets the shape
of the curved liner (see Figure 17b). In order to establish a homogeneous tension state,
irregular distribution of friction forces during the deflection process of the film, due to the
Figure 16.
Design study of a curved FHR liner with the perforated face sheet including active and
passive cavities, the covering face sheet and the strip slotted cavity structure.
5.2. Design and Manufacturing Concept of Curved PR-Liner
Since the cavities of the PR liner do not have flexible side walls compared to the FHR
liner, their manufacturing process is less complex, allowing a reduction in manufacturing
steps and higher automation potential. Here, the low cost deep drawing process is a suitable
choice for manufacturing the resonator cavities (see Figure 17a). This process enables
arbitrary shapes of the resonator cavity and mounting surfaces, e.g., a curved geometry of
the resonator bottom matching the targeted design space and the corresponding contour
of the top layer of the structure [
35
,
49
]. However, due to the curved shape, the process of
joining the curved film layer onto the cavity structure is more complex. Since the targeted
thermoplastic films have a low stiffness, a form-die is required that sets the shape of the
curved liner (see Figure 17b). In order to establish a homogeneous tension state, irregular
distribution of friction forces during the deflection process of the film, due to the parabolic
Aerospace 2023,10, 5 20 of 24
shape of the die, should be reduced to minimum by applying lubricants. The cavities
are then adhesively joined to the film, cut and finally attached on the cavity support (see
Figure 17c). It should be noted that the film does not adopt a curved shape in the area
where it is not connected to the cavity. The cross-section of the liner structure is therefore
not circular, but a polygon due to the film’s elastic properties. The effects on aerodynamic
and fluid mechanical conditions must therefore be considered. In order to incorporate
drainage channels, the guard panel and cavity-mounts, the injection molding process is
chosen for the manufacturing of the cavity support (see Figure 17). A design concept of the
barrel-shaped PR-liner with its main components is shown in Figure 17d. The guard plate
is installed on the in-cooperated mounts of the cavity support. Its perforations must be
evenly distributed to create homogeneous flow conditions for each resonator. Furthermore,
the size of the perforation should be small enough to prevent objects from passing through
and damaging the film layer and big enough to prevent blockage. To avoid a reduction
of the acoustic performance of the PR-liner, the guard plate should have a perforation
percentage of about 30% to achieve acoustical transparency [50,51].
Aerospace 2022, 10, 5 21 of 25
parabolic shape of the die, should be reduced to minimum by applying lubricants. The
cavities are then adhesively joined to the film, cut and finally attached on the cavity sup-
port (see Figure 17c). It should be noted that the film does not adopt a curved shape in the
area where it is not connected to the cavity. The cross-section of the liner structure is there-
fore not circular, but a polygon due to the film’s elastic properties. The effects on aerody-
namic and fluid mechanical conditions must therefore be considered. In order to incorpo-
rate drainage channels, the guard panel and cavity-mounts, the injection molding process
is chosen for the manufacturing of the cavity support (see Figure 17). A design concept of
the barrel-shaped PR-liner with its main components is shown in Figure 17d. The guard
plate is installed on the in-cooperated mounts of the cavity support. Its perforations must
be evenly distributed to create homogeneous flow conditions for each resonator. Further-
more, the size of the perforation should be small enough to prevent objects from passing
through and damaging the film layer and big enough to prevent blockage. To avoid a
reduction of the acoustic performance of the PR-liner, the guard plate should have a per-
foration percentage of about 30% to achieve acoustical transparency [50,51].
Figure 17. (a) Schematic thermoforming process of the resonator cavity, (b) joining process of the
curved and pre-tensioned film and the cavity, (c) cavity support with functional elements such as
the drainage channel and mounts for attaching the guard panel, (d) design concept of the barrel-
shaped PR-liner.
Due to described differential design approach, separating the cavity and the cavity
support increases the manual effort for the assembly of the entire liner. An alternative
approach to eliminate the assembly process is to combine the two parts in an integral de-
sign and manufacture them by injection molding or, for even greater cost efficiency, by
rotational thermoforming. However, this approach requires the joining process of the film
to be adapted. Since the supports and drainage channels have to be omitted, the film needs
to be joined individually for each circularly arranged cell row, requiring high manual ef-
fort.
6. Conclusions
Different aspects of two new liner concepts have been addressed in the current study.
Both concepts, the Helmholtz Resonator liner with flexible walls (FHR) and the plate res-
onator concept (PR) make use of material inherent damping for the flexible elements of
Figure 17.
(
a
) Schematic thermoforming process of the resonator cavity, (
b
) joining process of the
curved and pre-tensioned film and the cavity, (
c
) cavity support with functional elements such as the
drainage channel and mounts for attaching the guard panel, (
d
) design concept of the barrel-shaped
PR-liner.
Due to described differential design approach, separating the cavity and the cavity
support increases the manual effort for the assembly of the entire liner. An alternative
approach to eliminate the assembly process is to combine the two parts in an integral
design and manufacture them by injection molding or, for even greater cost efficiency, by
rotational thermoforming. However, this approach requires the joining process of the film
to be adapted. Since the supports and drainage channels have to be omitted, the film needs
to be joined individually for each circularly arranged cell row, requiring high manual effort.
6. Conclusions
Different aspects of two new liner concepts have been addressed in the current study.
Both concepts, the Helmholtz Resonator liner with flexible walls (FHR) and the plate
resonator concept (PR) make use of material inherent damping for the flexible elements of
Aerospace 2023,10, 5 21 of 24
the concepts. The following summarizes the conclusions of the four main thematic aspects
of the presented study.
6.1. Experimental Investigation
The experimental results show an additional effect in the dissipation of the FHR
compared to the established HR. Regarding the acoustical measurements at low frequencies,
the TPU films with a rectangular cut-out showed the highest dissipation. The presented
experimental results confirm the results of previous numerical studies [
17
], which indicated
that materials with Young’s modulus higher than 50 MPa seem to be less suitable for the
application in the targeted broadband silencers. The size and position of the back cavity
does not seem to have a big effect on the dissipation, implying that the back cavity can be
small compared to the resonator.
Further studies will investigate the optimal number of active and passive cells, as well
as the optimal position of the passive cells in relation to the active cells. In regards to the
dissipation, the relationship between the shape and the area of the flexible wall should be
analyzed as well. In further investigations the following topics will be answered, such as
the optimal number of active and passive cells. Also, the best position of the passive cells
in relation to the active ones will be investigated. In addition, the relationship between the
shape and the area of the flexible wall in relation to its dissipation will be analyzed.
6.2. Models and Parameter Studies of FHR/PR Liner
The parameter studies revealed that special care should be taken when selecting
adequate materials and geometries to tune the concepts for low-frequency damping. The
Young’s modulus in combination with the loss factor is a highly influential parameter for
both concepts. For the FHR, a low Young’s modulus shifts the TL to lower frequencies, and
for the PR, it is possible to adjust the attenuation to one or two peaks in the TL spectrum.
Additionally, a lower Young’s modulus (in combination with a high loss factor) leads to a
more broadband peak in the TL curve for the PR liner.
Plate thickness is a parameter that influences the frequency as well as the amplitude
of the attenuation for both concepts. For highest attenuation, the plate should be very thin
(< 0.2 mm). However, the resonance frequency of the PR liner is lowest with a thick plate.
Consequently, there exists a trade-off between highest attenuation and attenuation at the
lowest possible frequency for both concepts regarding plate thickness.
The plate dimensions (diameter for FHR, length for PR) alters the frequency of the TL
significantly less than the other varied parameters. Still, the results suggest that the plate
should be as large as possible for maximum attenuation for both the FHR and PR concept.
Thereby, the limiting factor is certainly the installation space.
The height of the cavity (PR), respectively, the second cavity (FHR) has a similar
influence as the plate thickness. A higher cavity leads to attenuation at lower frequencies
but is limited by the installation space as well. Besides, the concepts differ in the height of
the TL. A higher cavity leads to a slightly higher TL for the PR but to a lower TL for the
FHR.
These parameter studies revealed the main trends for selected parameters of the
Helmholtz resonator concept with flexible walls and the plate resonator. To find an optimal
design, however, these parameters need to be varied simultaneously. This is a subject of
future investigations.
6.3. Structural Mechanical Analysis
The change of the core structure leads to higher stresses, especially for the face sheet.
Therefore, an adjustment was made, using PA6-GF with promising structural–mechanical
properties to withstand the occurring static loads. The key issue for the application of the
novel acoustic liners in a jet engine is the relation between acoustic efficiency, structural
mechanics and total weight of the liner structure. The load relief of the core structure
through the application of additional walls with and without cut-outs must be further
Aerospace 2023,10, 5 22 of 24
optimized. As a result, depending on the distance between the cell walls, the tension in the
cut-out bars could be reduced. In this context, a reduction of the weight is possible using
thinner core walls made out of PA6-GF. On the contrary, the investigations show that the
acoustic behavior is strongly dependent on the tension state of the films. Therefore, the
deformation of the frame should be minimal, which stands in contrast to thinner walls and
weight reduction. Simultaneously, the aspired load reduction in the upper web leads to a
tighter arrangement of the square combs and to an increase of nonfunctional passive cells.
Further investigations are necessary to find the optimal parameter settings of the described
multidimensional optimization problem.
6.4. Design Concepts and Production
With regard to the manufacturing process of the FHR liner, the introduced process
of ultrasonic welding bears the potential to automatize the joining process of the flexible
thermoplastic films and the support structure. However, the assembly of the strip-slot
design of the cell core requires an excessive amount of manual effort. Here, the adaption of
the process introduced by Britzke [
52
] has the potential to resolve this issue. In contrast, the
presented concept of the PR liner allows the application of the cost-efficient deep drawing
process, rotational thermoforming or injection molding in dependence of an integral or
differential design of the cavities and support structure.
With regard to the design and introduced manufacturing concepts, the integration of
the film is the critical process step of both liner principles. Since the tension state of the
integrated films affects the performance of the acoustic liners, a concept for reproducible
pre-stressing and incorporating the film into the support structure was presented. However,
since the targeted material group of thermoplastics and thermoplastic elastomers tends
to relaxation, experiments must be carried out to determine the extent of relaxation as a
function of deflection force and time in order to predict which tension state the film will
attain in the state of operation.
Author Contributions:
Conceptualization, M.N.; methodology, M.N., J.G., F.K, V.R., M.P. and K.K.;
formal analysis, V.R., F.K., M.P. and M.N.; investigation, M.N., J.G., F.K, V.R., M.P., K.B. and K.K.;
writing—original draft preparation, M.N., J.G., F.K, V.R., M.P. and K.B.; writing—review and editing,
M.N., J.G., F.K, V.R., M.P., K.B., K.K. and E.S.; visualization, M.N., J.G., F.K, V.R. and M.P.; supervision,
N.M., L.E., E.S. and K.H.; project administration, N.M., L.E., E.S., K.K. and K.H.; funding acquisition,
N.M., L.E., E.S. and K.H. All authors have read and agreed to the published version of the manuscript.
Funding:
Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—
416814415, 416728326 and 416728553. The financial support of the work in the framework of the
LuFo VI-1 project “FLIER“ (Flexible wall structures for acoustic LINERs) by the Federal Ministry for
Economic Affairs and Climate Action (contract numbers: 20E1915A, 20E1915B and 20E1915C), based
on a decision of the German Bundestag, is gratefully acknowledged.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data presented in the current study are available on request from
the corresponding author.
Conflicts of Interest: The authors declare no conflict of interest.
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