fluids
Article
Design of a Fluidic Actuator with Independent Frequency and
Amplitude Modulation for Control of Swirl Flame Dynamics
Amrit Adhikari 1,2, Thorge Schweitzer 1,2, Finn Lückoff 1,* and Kilian Oberleithner 1,*
Citation: Adhikari, A.; Schweitzer, T.;
Lückoff, F.; Oberleithner, K. Design of
a Fluidic Actuator with Independent
Frequency and Amplitude
Modulation for Control of Swirl
Flame Dynamics. Fluids 2021,6, 128.
https://doi.org/10.3390/fluids6030128
Academic Editor: V’yacheslav
Akkerman
Received: 26 February 2021
Accepted: 17 March 2021
Published: 20 March 2021
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1Laboratory for Flow Instabilities and Dynamics, Technische Universität Berlin, Müller-Breslau-Straße 8,
2FDX Fluid Dynamix GmbH, Rohrdamm 88, 13629 Berlin, Germany
*Correspondence: finn.lueckof[email protected] (F.L.); [email protected] (K.O.);
Tel.: +49-30-314-73874 (F.L.)
Abstract:
Fluidic actuators are designed to control the oscillatory helical mode, called a precessing
vortex core (PVC), which is often observed in gas turbine combustors. The PVC induces large-
scale hydrodynamic coherent structures, which can considerably affect flow and flame dynamics.
Therefore, appropriate control of this structure can lead to a more stable and efficient combustion
process. Currently available flow control systems are designed to control the PVC in laboratory-scale
setups. To further develop these systems and find an approach applicable to the industrial scale, a
new actuator design based on fluidic oscillators is presented and studied in this paper. This actuator
allows for independently adjusting forcing frequency and amplitude, which is necessary to effectively
target the dynamics of the PVC. The functionality and flow control of this actuator design are studied
based on numerical simulations and experimental measurements. To verify the flow control authority,
the actuator is built into a prototype combustor test rig, which allows for investigating the impact
of the actuator’s forcing on the PVC at isothermal conditions. The studies conducted in this work
prove the desired functionality and flow control authority of the 3D-printed actuator. Accordingly, a
two-part stainless steel design is derived for future test conditions with flame.
Keywords: active flow control; fluidic oscillator; precessing vortex core; swirl flame dynamics
1. Introduction
Turbulent flows can be found in many technical applications. For example, the
operation of turbomachines relies primarily on the working fluid, which flows through the
machine in a turbulent manner. The inherent dynamics and instabilities of these flows can
severely impact the machine’s operation. These instabilities can lead to the formation of
large-scale coherent flow structures that produce oscillatory dynamics with high amplitude.
These oscillations compromise the overall flow field and, therefore, the operation of the
machine. To minimize this impact and to guarantee the safe and reliable operation of the
machine, efficient flow control methods are required.
In modern gas turbines, a turbulent swirling flow is generated inside the combustor
to allow for aerodynamic stabilization of the flame [
1
,
2
]. This is achieved by exploiting a
phenomenon known as vortex breakdown, which results in a central recirculation zone in
the vicinity of the nozzle outlet [
3
–
5
]. The swirling jet emanating from the burner nozzle
into the combustion chamber generates shear layers between the central recirculation zone
and the jet (inner shear layer) and between the jet and the surrounding fluid (outer shear
layer). These shear layers provide a gradient of flow velocities, which allows matching
with the flame’s burning velocity, leading to aerodynamic stabilization. However, these
shear layers are prone to hydrodynamic instabilities, leading to large-scale coherent flow
oscillations. Due to the vortex breakdown phenomenon, the flow inside the gas turbine
combustor is globally unstable and produces a helical-shaped large-scale coherent flow
structure, known as the precessing vortex core (PVC). The PVC generates alternating
Fluids 2021,6, 128. https://doi.org/10.3390/fluids6030128 https://www.mdpi.com/journal/fluids
Fluids 2021,6, 128 2 of 16
vortices meandering along the inner shear layer in the downstream direction that are
characterized by a certain oscillation frequency [
6
,
7
]. Under reacting conditions involving
a swirl-stabilized flame, a PVC arises depending on the flame shape and the associated
density field in the region of the upstream end of the central recirculation zone. Whereas
flames that are attached to the nozzle outlet typically suppress the PVC, detached flames
that are stabilized further downstream let a PVC arise in the shear layers around the burner
outlet [
8
,
9
]. If a PVC is present in the reacting flow configuration, the flame dynamics,
mixing of fuel and air, and flame stability can be considerably influenced by the PVC-
induced vortices [
10
–
16
]. These vortices can affect the generation of pollutant emissions
and the flame response to (thermo-)acoustic perturbations [
16
–
19
]. Therefore, the control of
the PVC allows for controlling thermoacoustic oscillations and pollutant emissions, which
are both key design parameters of premixed combustion systems.
To control the PVC in combustion systems, Lückoff et al. developed an active flow
control system [
20
–
23
]. that relies on a loudspeaker-based actuator, which works according
to the zero-net-mass-flux principle [
24
]. It combines the advantages of actuator designs that
were successfully developed for isothermal flows [
7
,
25
]. This active flow control system
may not only be used to suppress the instabilities driving the PVC, but also to excite it.
This allows the investigation of its exclusive impact on other flow and flame quantities, as
illustrated by an example in Figure 1.
Figure 1.
Precessing vortex core (PVC) mode and flame dynamics reconstructed from time-resolved particle image
velocimetry (PIV) and OH*-chemiluminescence snapshots revealing PVC-induced vortices (gray-scale) overlaid with heat
release rate indicating the corresponding variation in the flame. Top row: phase-averaged heat release rate fluctuations in
longitudinal section; bottom row: PVC-induced heat release rate fluctuations in cross-sectional view (x/D = 0.75). Heat
release rate is normalized to maximal values.
The shown phase-averaged flow and flame dynamics were measured in a gas turbine
combustor with active PVC flow control. They reveal the alternating (helical-shaped)
vortices induced by the excited PVC as they propagate along the inner shear layer before
they collide with the combustion chamber wall. In the cross-sectional view (bottom row in
Figure 1), the helical movement in the clockwise direction induced by the PVC is depicted.
The flame surface dynamics, indicated by the phase-averaged OH*-chemiluminescence
fluctuations, are clearly driven by the vortex dynamics, as they entrain a very inflammable
composition of fuel–air mixture and high-temperature burnt gas from the central recircu-
lation zone. The acquisition and post-processing of the required data needed to derive
Fluids 2021,6, 128 3 of 16
this illustration are documented in some of our previous publications [
26
,
27
]. Applying
different actuation amplitudes generates PVCs of different strengths which allows for
investigating the impact of the PVC on important design parameters of the premixed
combustion system such as thermoacoustic instabilities and pollutant emissions. Lückoff
et al. [
23
,
28
] showed that an excited PVC can damp the growth rate and amplitude of
thermoacoustic modes, which lead to a more stable combustion process. The loudspeaker-
based flow control system was applied to show that an excited PVC slightly increases the
NOx
emission level in partially and perfectly premixed flames due to increased vorticity [
27
].
The loudspeaker-based flow control design by Lückoff et al. is well-suited to academic
purposes on a laboratory scale to study PVCs. However, robustness and applicability
are lacking to implement this design as used in an industrial-scale machine. Therefore,
an alternative actuator concept needs to be derived that is more robust and preferably
maintenance-free. The obvious choice is fluidic oscillators, which are capable of generating
an oscillating synthetic jet without moving parts [26,29].
Fluidic devices were first developed in the early 1960s at Harry Diamond Labo-
ratories as logic elements for missile control systems [
30
]. These elements included
oscillators [
31
,
32
], amplifiers [
33
], and classic logic gates [
34
]. With the increase in the
use of electronic control systems and their increased reliability, fluidic control systems
were quickly replaced. In recent years, fluidic oscillators have seen a rise in interest for
addressing modern engineering problems. They are used in active flow control [
35
–
37
],
windshield wipers [
38
], future combustion processes [
39
,
40
], and the generation of mi-
crobubbles in bioreactors [
41
,
42
]. However, fluidic bistable amplifiers, sometimes called
fluidic switches, have not been used as much as oscillators. Bobusch and Tesaˇr [
43
,
44
]
demonstrated their use as high-speed gas valves in harsh environments. They can also
be used to create high-frequency fluidic oscillators [
45
]. In comparison with traditional
actuators, fluidic devices are virtually maintenance-free because they contain no moving
parts. Additionally, they are not affected by radiation, shock, or temperature changes, and
can be run from a pressure reservoir without any electronic parts. Further information
on the functioning and application of fluidic oscillators may be found in the works of
Gregory [46], Tesaˇr [47,48], Foster [49], Raghu [35], and Bobusch [43].
Common feedback-type fluidic oscillators have a linear relationship between mass
flow and frequency [
40
]. In this case, the mass flow governs the actuator’s forcing am-
plitude. Therefore, the independent control of actuation frequency and amplitude is
impossible, but is necessary for successful control of the PVC dynamics, as achieved
with the loudspeaker-based actuator [
20
]. Tesaˇr [
50
] offered a possibility, of replacing the
loudspeaker-based actuator with a more robust actuation system to facilitate the control of
the PVC in industrial-scale gas turbine combustors. Following the approach of Tesaˇr [
50
],
the combination of a fluidic oscillator and a fluidic amplifier, which allows for the de-
coupling of the actuation amplitude (proportional to the mass flow) and frequency, was
investigated in this study.
In the following section, the design of the newly developed fluidic actuator is described
and its functionality is illustrated using numerical simulations. Subsequently, a short
description of the flow control approach is provided, which includes an introduction
to the concept of lock-in serving as a proof-of-concept of the actuation principle. The
fourth section deals with the experimental validation and proof-of-concept of the new
fluidic actuator in two different experimental setups. Finally, conclusions are drawn and
an outlook for future studies are provided. This involves the presentation of a two-part
stainless steel design of the successfully tested actuator for experiments under reacting
flow conditions with flame.
2. Design and Functionality of the OsciAmp Fluidic Oscillator
The new actuator, named OsciAmp, was designed based on the master–slave concept.
It is a two-stage layout that generates a desirable frequency in an oscillator stage, whose
output switches a large mass flow downstream of an amplifier stage. In this context,
Fluids 2021,6, 128 4 of 16
the oscillator acts as a master providing frequency commands and the amplifier, as the
slave, obeys and switches accordingly. Although the working principle seems simple, the
practical implementation of this concept is demanding; hence, its industrial implementation
has not yet been achieved, most probably because the matching of the properties between
the oscillator and amplifier is a tedious task. This difficulty arises basically from the large
number of inlets and outlets consisting of different conditions, i.e., pressure and flow rate,
which have to be matched simultaneously [50].
Figure 2shows the implementation of the master–slave concept used in this work.
The oscillator (illustrated in red) acts as a master and the amplifier (illustrated in blue)
obeys as a slave, which results in well-defined alternating synthetic jets at the two output
ports. The oscillator contains an inlet and two outlets. The outlets of the oscillator are the
(frequency) control ports in the amplifier. The amplifier has its own inlet and two outlets.
The amplifier inlet flow is subjected to the control flows of the oscillator, which switches
between the two actuator outlet ports. In this configuration, the magnitude of the mass flow
through the actuator, and with the forcing amplitude, is mainly governed by the amplifier
inlet flow. The forcing frequency is determined by the oscillator inlet flow. Accordingly,
independent control of forcing amplitude and frequency can be achieved. The OsciAmp
is a combination of the fluidic oscillator investigated in a previous study [
51
] with the
fluidic amplifier described above. Instead of using an amplifier with a Spyropoulos-type
feedback as the master (used by Tesaˇr [
50
]), a sweeping-jet-type oscillator with an attached
splitter geometry is used. This allows the master stage to be entirely two-dimensional and
simplifies manufacturing down the line. The same sweeping oscillator was used in the
aforementioned study [
51
], allowing the master to operate in the same frequency band
without requiring several tuning iterations to match the two systems.
Figure 2.
Design of the actuator based on the master–slave concept. The high-frequency oscillator, as
the master, provides frequency information to the high-flow output of the amplifier, which acts as a
slave.
To test the functionality of the design and visualize the flow field inside the actuator,
2D-incompressible unsteady Reynolds-averaged Navier–Stokes (URANS) simulations
Fluids 2021,6, 128 5 of 16
were performed. The inlet flow rate for the oscillator and amplifier were set to 0.25 g/s and
a k-
ω
-SST model was selected for turbulence modeling. Figure 3shows different phase
angles of the combined system and the oscillator shows full control over the switching
action of the amplifier.
Figure 3.
Numerical results for a 2D unsteady Reynolds-averaged Navier–Stokes (URANS) simula-
tion of the actuator’s internal flow field (
a
–
d
) from top to bottom: (
a
) stable condition top output;
(
b
) the oscillator output is switching to the upper control channel, the amplifier flow is beginning
to detach from the top attachment wall; (
c
) the oscillator flow is fully switched to the upper control
channel and the amplifier flow is in the process of switching; (d) stable condition bottom output.
3. Flow Control Approach and Lock-In Investigation
In the present experimental setup, the developed fluidic oscillator was applied in an
open-loop control approach. Accordingly, no feedback-signal from some sort of sensor was
Fluids 2021,6, 128 6 of 16
used to control the performance of the actuator. The amplifier and oscillator mass flows
were chosen based on hot-wire measurements, which were performed to characterize the
amplitude and frequency range of the actuator (Section 4.1). Under reacting conditions, the
open-loop control approach was applied to excite the PVC in flow configurations where
the flame dampened the PVC.
In previous publications [
20
,
23
], a lock-in study was shown to serve as a proof-of-
concept for a newly developed actuator design targeting an oscillator such as the PVC.
If lock-in can be achieved by the actuator system, it can be concluded that the actuator
is capable of controlling the oscillator. The same strategy was followed in this study by
applying open-loop control to study the lock-in behavior of the isothermal combustor flow.
Terhaar et al. [
52
] showed that the PVC can be modeled well by a parametric nonlinear Van
der Pol oscillator. The synchronization behavior of such a model oscillator with a periodic
forcing is shown in the lock-in diagram in Figure 4[53].
Figure 4.
Sketch of a simplified lock-in diagram describing a periodically forced model oscillator.
The actuation amplitude
Af
is presented as a function of the normalized actuation frequency
ff/fn
.
Orange area: lock-in (phase and frequency fully synchronized).
This lock-in diagram typically relates the forcing amplitude
Af
to the ratio of forcing
frequency
ff
and natural frequency
fn
. In the present study, the natural frequency is equal
to the PVC frequency which naturally occurs in the swirling jet. The lock-in diagram
describes the state of synchronization of the naturally occurring oscillator (PVC) and the
forcing signal induced by the actuator. For a small value of
Af
and
ff
sufficiently far away
from
fn
(point a in Figure 4), the dynamic of the (forced) oscillator will not be considerably
compromised and the phases of oscillator and forcing are drifting (phase drifting). Keeping
ff
constant and increasing
Af
to moderate values leads to an effect called frequency pulling
(point b in Figure 4). This effect can be observed in the power spectral density, showing
that
fn
is pulled toward
ff
with increasing
Af
(compare Figure 9) [
53
,
54
]. Increasing
Af
even further and over a critical value (lock-in amplitude) causes a full synchronization of
frequency (
ff=fn
) and the phases of the forcing and oscillator (point c in
Figure 4
). In
this state, which is called lock-in, the dynamics of the oscillator are following the forcing
induced by the actuator. If lock-in reaches for
ff
far from
fn
, a higher value of
Af
is required,
meaning that the lock-in amplitude increases. More details on lock-in and synchronization
of forced hydrodynamically self-excited jets and flames are provided in [53–55].
Fluids 2021,6, 128 7 of 16
4. Experimental Validation
Firstly, this section describes the experimental validation of the functionality of the
OsciAmp, which allows for independent control of frequency and amplitude. Subsequently,
the flow control authority of the OsciAmp on the PVC is demonstrated inside a prototype
combustor test rig.
4.1. Validation of Functionality
The functionality of the actuator was verified based on hot-wire measurements at the
outlet ports of the actuator. The corresponding experimental setup for these measurements
is shown in Figure 5. A single-wire probe was used, which was connected to a constant
temperature anemometer to measure the velocity of the synthetic jets emanating from the
actuator outlets. An oscilloscope was used to observe the instantaneous effective value of
the measurement signal. The signal of the hot-wire probe was filtered and amplified with a
signal conditioner and digitally processed in an A/D converter (16 bit). The digital signals
were recorded and processed by a measurement computer (PC). The probe was directly
aligned at the actuator outlet at a distance of approximately
15
mm. A linear translation
stage was used to locate the probe at the position where the maximal magnitude of the
effective velocity could be measured. This position was estimated empirically by traversing
the probe around the actuator outlets. The air mass flows through the oscillator and the
amplifier of the actuator were controlled by a flow controller and a rotameter, respectively.
A measurement time of
30
s was taken with a sampling frequency of
20, 000
Hz to obtain a
quasi-stationary statistical moment of the fluctuating velocities.
Figure 5.
Hot-wire measurement setup for the measurement of the velocity of the flow at the outlet
of the actuator.
In the first experiment, the operational range of the actuator was estimated by varying
the amplifier and oscillator mass flows. Based on the measured velocity signals, the power
spectral density (PSD) spectra were generated, which served to characterize the oscillation
characteristics of the actuator for different combinations of amplifier and oscillator mass
flows. An amplifier mass flow range between approximately 0.775 and 2.327 kg/h, an
oscillator mass flow range between approximately 0.4 and 0.8 kg/h, and a frequency
range between approximately 100 and 190 Hz were determined based on this preliminary
evaluation.
Fluids 2021,6, 128 8 of 16
In a subsequent experiment, the total mass flow (sum of oscillator and actuator mass
flows) through the actuator was kept constant to generate a constant actuation amplitude
with varying frequency. Starting at a total mass flow of
1.37
kg/h, the following steps were
carried out:
1.
The total mass flow was kept constant at
1.37
kg/h. The oscillator flow was set to the
minimum and the amplifier flow was adjusted accordingly to maintain constant total
mass flow.
2.
For the same total mass flow, the oscillator flow was gradually increased in equivalent
to
10
Hz steps and the amplifier flow was adjusted accordingly to maintain a constant
total mass flow.
Goal:
Demonstrate the possibility of changing frequency without changing the actua-
tion amplitude.
3. The total mass flow was increased by 0.387 kg/h and step 2 was repeated.
Goal:
Demonstrate the possibility of changing frequency for a higher (constant)
actuation amplitude.
4.
Step 3 was repeated until maximum total mass flow in the estimated range was
achieved.
Goal:
Demonstrate applicability of the actuation concept over the entire operational
range of the actuator.
Figure 6summarizes the results of this experiment following the four steps described
above. The root mean square (RMS) velocity as a measure of the amplitude of the actuator
is plotted against the frequency of the oscillation. The figure demonstrates the possibility
of changing the frequency for the same constant amplitude within the operational range
of the actuator. The figure shows the actuation amplitude can be varied for a constant
frequency. These variations only require a change in the mass flow through the oscillator to
adjust the frequency or a change in the amplifier mass flow to vary the actuation amplitude.
Additionally, the figure depicts the operational range of the fluidic actuator developed in
this study. Finally, Figure 7shows that the measured RMS velocities are linearly related to
the supplied total mass flow. This linear relation holds for the whole actuation frequency
range, which underlines OsciAmp’s versatility and applicability as an actuator for targeted
control of the PVC’s dynamics.
100 110 120 130 140 150 160 170 180 190
Frequency Hz
10
15
20
25
30
35
RMS Velocity m/s
1.37 kg/h
1.76 kg/h
2.15 kg/h
2.53 kg/h
2.92 kg/h
3.31 kg/h
Total Mass Flow
Figure 6.
Independent control of frequency and amplitude. The diagram shows the root mean
square (RMS) values of the velocity signals at the outlet ports for different actuation frequencies. It
demarcates the operational range of the fluidic actuator.
Fluids 2021,6, 128 9 of 16
1.5 2 2.5 3 3.5
Total Mass Flow kg/h
10
15
20
25
30
35
40
RMS Velocity m/s
Data points
Approximation
100 Hz
110 Hz
120 Hz
130 Hz
140 Hz
150 Hz
160 Hz
170 Hz
180 Hz
Figure 7.
Linear fit between RMS velocity and total mass flow. The approximation was achieved by
fitting the linear function to the measured data points.
4.2. Validation of Flow Control Authority
After the validation of OsciAmp’s functionality, this actuator was built into a prototype
combustion chamber test rig where a PVC was generated in an isothermal swirling flow
without flame. In this setup, the flow control authority of OsciAmp was studied based
on a lock-in study. This section starts with a description of the experimental setup, the
post-processing of the recorded pressure signals, and the measurement procedure. In the
following results section, the capability of the actuator to achieve lock-in is discussed.
4.2.1. Experimental Setup
The experimental setup for the validation of the flow control authority is sketched in
Figure 8. A section through the generic swirl-stabilized combustor test rig is presented on
the left side. The main air flow enters the test rig at the bottom and propagates through a
swirler (shown in green), which transforms the non-swirling turbulent flow into swirling
flow. The swirl generator consists of movable blocks, with which swirl numbers between 0
and 1.5 can be set. In this work, a constant swirl number of
S=0.7
was used. The swirling
flow propagates through the mixing tube and around a centerbody before it enters the
quartz glass combustion chamber. The fluidic actuator is integrated in this centerbody.
The mixing tube and front plate are composed of plastic and contain various pressure
measurement ports. Further details about this test rig and the pressure measurement
system are provided in [
20
]. The present prototype test rig only allows for isothermal
experiments without flame.
The actuator inside the centerbody is supplied with air via a separate pressurized air
line. The incoming air is divided into two lines and connected to a rotameter and a flow
controller, which in turn are connected to the amplifier and oscillator, respectively. The
amplifier and oscillator are supplied with air flows at 2.5 and 3.5 bar of air, respectively.
The pressure is measured far upstream of the actuator, which explains the relatively
high pressure values required to compensate for the pressure loss in the flow controller,
rotameter, and the connecting channels. Accordingly, the pressures inside oscillator and
amplifier are considerably lower, allowing for stable and sub-critical flow conditions inside
the actuator.
The experimental setup allows for measuring the differential pressure at the front
plate and inside the mixing tube. For that, differential pressure sensors can be integrated at
the front plate and the walls of the mixing tube. The red points on the top right view of the
front plate, as shown in Figure 8, represent the locations at which the pressure is measured.
Fluids 2021,6, 128 10 of 16
The four pressure sensors are arranged circumferentially around the burner outlet. The
sensors have a measuring range of 1000 Pa and allow for measuring pressure fluctuations
up to 0.1 Pa. The analog signals of the sensors are amplified and digitally converted with a
sample frequency of 8192 Hz.
Figure 8. Measurement setup for validation of the flow control authority: prototype combustor test
rig on the left and pressure measurement chain on the right.
4.2.2. Post-Processing of the Pressure Signals
The pressure signals measured from four circumferentially arranged sensors were
decomposed into Fourier modes. The spatial Fourier mode decomposition in azimuthal
direction for the mth azimuthal mode is defined as
ˆ
pm(t) =
4
∑
k=1
pk(t)ei2πmk
4, (1)
where
pk
represents the pressure signal of the
k
th sensor and
m
represents the azimuthal
wavenumber. With the four equidistantly placed and circumferentially arranged sensors,
azimuthal modes of
m= [
0, 1, 2
]
can be determined. The estimated Fourier coefficient
ˆ
pm(t)
is a function of time and complex. For an azimuthal number of unity
m=
1, the
Fourier mode
ˆ
p1(t)
represents the PVC in its instantaneous amplitude and phase. These
coefficients were used to calculate the power spectral density, which is visualized in the
frequency spectra shown in Figure 9.
4.2.3. Measurement Procedure
For the case presented in this study, the PVC was actuated with different frequencies
ranging
±10%
around the natural PVC frequency
fPVC =137
Hz. The differential pressure
signal was measured for
40
s with a sampling rate of 8192 samples/s. The aim of the
pressure measurements was to determine the dynamic behavior of the PVC for different
forcing frequencies (ff) and amplitudes.
At first, the dynamic pressure was measured in the natural flow where no external
forcing was applied by the actuator. The corresponding natural PVC dynamics were
characterized by the frequency peak at
fPVC =137 Hz
, as shown in the spectra in Figure 9
Fluids 2021,6, 128 11 of 16
(grey solid line). Before the natural flow was forced by the actuator, the adjusted actuation
(amplifier and oscillator flow) was characterized by an individual pressure measurement
without main flow. The resulting forcing frequency was derived from the peak frequency
in the PSD spectrum of the corresponding pressure signal (blue dotted line in Figure 9).
Finally, the impact of the forcing, applied by the actuator, on the natural PVC was estimated
based on pressure measurements where main flow and forcing were active. The resulting
spectra are illustrated by the red solid lines in Figure 9.
Figure 9.
Validation of flow control authority. Lock-in diagram (bottom right) and surrounding example of spectra show
lock-in, damping, and shifting response of the PVC to the actuation.
4.2.4. Results
The impact of the forcing, induced by the fluidic actuator, on the natural PVC can
be differentiated into three categories, which are related to those explained in connection
with the simplified lock-in diagram shown in Figure 4. Category one involves all the
combinations of forcing amplitudes and frequencies where lock-in occurs, which means
that the PVC is fully synchronized with the forcing. In a PSD spectrum, the lock-in state
is characterized by a single distinct peak at the forcing frequency (compare the spectra
in the top row of Figure 9). Another category, which is referred to as damping, includes
all cases without a distinct frequency peak in the corresponding spectrum. In these cases,
the forcing is not strong enough to generate lock-in, such that the PVC is not oscillating
at a distinct frequency, but temporarily escapes from the induced forcing. As a result, a
very broad peak evolves in the PSD spectrum, covering primarily frequencies between
forcing and natural frequency (compare the top spectrum on the left of Figure 9). At even
smaller forcing amplitudes, the forcing shifts the frequency peak slightly toward the forcing
frequency due to the frequency-pulling effect described above. In the present study, this
shifting was accompanied by a reduction in the PVC amplitude and a broadening in the
frequency peak.
To classify the individual measurements into the three categories described above,
certain threshold values and criteria need to be defined, which was achieved in this study
as follows:
Fluids 2021,6, 128 12 of 16
Lock-In: |ff−fPVC&f|
|fPVC|≤0.01 |fPVC|&APVC&f≥0.5 APVC
Damping: |ff−fPVC&f|
|fPVC|≤0.01 |fPVC|&APVC&f<0.5 APVC
Shifting: |ff−fPVC&f|
|fPVC|>0.01 |fPVC|.
In these criteria, the variables
f
and
A
represent the frequency and the amplitude,
respectively; the subscripts
PVC
,
f
,and
PVC
&
f
represent the natural PVC signal (main
flow without forcing), the forcing signal (forcing without main flow), and the interaction of
forcing and natural PVC (main flow with forcing), respectively. The mentioned margins
are reasonable considering the associated systematic and averaging errors.
With these criteria, the impact of the forcing on the natural PVC was characterized
for different combinations of forcing frequency and amplitude, as presented in the lock-
in diagram in Figure 9. The ordinate shows the total actuation mass flow, representing
the amplitude of the forcing, and the abscissa shows the normalized forcing frequency
relative to the natural PVC frequency. The green full circles in the diagram represent
cases where lock-in occurred and the hollow green circles represent the damping cases.
A V-form distribution containing the lock-in and damping cases is demarcated in light
green (
Figure 9
) and agrees very well with the orange region in the lock-in diagram shown
in Figure 4. The hollow yellow circles represent the shifting cases of the natural PVC
frequency toward the forcing frequency.
The exemplary spectra arranged around the lock-in diagram illustrate the changes in
the PVC dynamics due to forcing with constant frequency and increasing amplitude, which
was induced by the newly designed fluidic oscillator, named OsciAmp. The impact of this
forcing on the PVC is similar to the effect of the actuation induced by the loudspeaker-
based actuator used in [
20
]. A small forcing amplitude broadens the characteristic spectral
peak, which decreases the amplitude in connection with a small shift toward the forcing
frequency (compare the bottom plot in the left column in Figure 9). By increasing the
amplitude slightly, the peak is pulled closer toward the forcing frequency, whereas the
amplitude remains low (compare the top plot in the left column in Figure 9). In this
state, the PVC frequency considerably alternates between the forced and the natural PVC
frequency. This dynamic changes distinctly when the actuation increases into the light
green lock-in area. For those combinations of forcing frequency and amplitude situated
inside this area, the corresponding spectra (see the top row in Figure 9) show a very distinct
peak at the forcing frequency. Increasing the actuation amplitude further increases the
amplitude of the forced PVC. The V-form of the lock-in diagram is in line with that in other
studies [20,55].
In summary, the lock-in diagram in connection with the spectra shown in
Figure 9
demonstrates that the newly designed fluidic actuator is capable of controlling the PVC
in an open-loop control approach. The spectra show that the amplitude of the PVC
can be damped considerably for low forcing amplitudes. For high amplitudes, the PVC
synchronizes with the forcing, which confirms the full control authority of the actuator.
5. Conclusions and Outlook
In this work, a new fluidic actuator design, named OsciAmp, for active flow control
of the PVC in a swirl-stabilized combustor was presented and analyzed regarding its
functionality and control authority. We showed that the combination of oscillator and
amplifier allows for independently adjusting the forcing amplitude and frequency. This
feature tremendously extends the range of application for active flow control purposes
compared with an actuator consisting of only a single fluidic oscillator. Therefore, the
OsciAmp actuator was predestined to control a large-scale coherent flow structure as the
PVC frequency grows linearly with the main flow rate. Based on a lock-in study, we found
that the OsciAmp is capable of synchronizing the natural PVC with the induced forcing.
The findings prove the flow control authority of the actuator and serve as a general proof
of concept. In the state of lock-in, distinct PVC dynamics are achieved, which allows for
Fluids 2021,6, 128 13 of 16
detuning resonating technical systems, such as hydro turbines or gas turbine combustors.
These damping and detuning capabilities are valuable control properties that can help to
stabilize turbomachines affected by hydrodynamic instabilities such as the PVC.
As shown in previous studies, the PVC has the potential to considerably damp ther-
moacoustic instabilities in premixed swirl-stabilized combustion systems. Open-loop flow
control, as conducted in this work, can lead to a damping of thermoacoustic instabilities,
which increases the stability and efficiency of the combustion system. In addition to swirl-
stabilized combustion chambers, other turbomachines such as hydro turbines have to deal
with helical flow instabilities similar to the PVC described in this study. Accordingly, the
fluidic actuator developed in this work may serve to improve the performance of different
types of turbomachines.
To include the new fluidic actuator design into a combustion chamber where a
swirl-stabilized flame is present, the manufacturing method and material properties
need to be modified to withstand high temperatures. Therefore, stainless steel was
chosen as the material, which is processed applying computerized numerical control
(CNC) milling technologies. The modified two-part design, containing the same oscil-
lator and amplifier geometries of the design discussed above, is shown in
Figure 10
.
Both halves are aligned with two center pins and assembled with four screws. The
centerbody is finally sealed with a circumferential weld seam. This stainless steel cen-
terbody can replace the one used in the loudspeaker-based actuator, which was ap-
plied in previous studies examining the active flow control of the PVC [
20
–
23
]. This
robust and versatile design of a maintenance-free actuator appears to be much more
applicable to industrial-scale applications and may pave the way to active PVC control
in turbomachinery.
Figure 10. Two-part design stainless steel actuator for application in a combustion chamber.
Author Contributions:
Conceptualization, K.O. and F.L.; software, T.S. and A.A.; validation, A.A.,
F.L., and T.S.; investigation, A.A. and F.L.; data curation, A.A. and F.L.; writing—original draft
preparation, A.A., F.L., and T.S.; writing—review and editing, K.O., F.L., A.A., and T.S.; visualization,
A.A., T.S. and F.L.; supervision, K.O.; project administration, F.L.; funding acquisition, K.O. All
authors have read and agreed to the published version of the manuscript.
Funding: German Reserach Foundation (DFG), grant number 247226395.
Data Availability Statement:
The data presented in this study are available on request from the
corresponding author.
Acknowledgments:
We would like to thank the German Research Foundation (DFG) for funding
this work within the project 247226395. Special thanks go out to Andy Göhrs for his technical support
Fluids 2021,6, 128 14 of 16
as well as Sara Schulz and Daniel Barkowski, who dedicated their Bachelor and Master thesis to the
development of the actuator studied in this paper.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
CNC Computerized Numerical Control
PSD Power Spectral Density
PVC Precessing Vortex Core
RMS Root mean square
URANS Unsteady Reynolds-averaged Navier–Stokes
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