Control effect on deep cavity noise by slanted walls at low Mach numbers

1. Article
Journal of Vibration and Control
2020, Vol. 0(0) 1–11
© The Author(s) 2020
Article reuse guidelines:
sagepub.com/journals-permissions
DOI: 10.1177/1077546320936510
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Control effect on deep cavity noise by
slanted walls at low Mach numbers
Zhifei Guo1,2
, Peiqing Liu1,2
and Hao Guo1,2
Abstract
Experimental and numerical studies on noise radiated by flow past a rectangular two-dimensional deep cavity with passive
control are conducted to research the mechanism of cavity noise reduction at low Mach numbers. The clean cavity has
a depth-to-length ratio of 1.5 and a width-to-length ratio of 3. The passive control method is used by slanting the front and
rear walls. Using acoustic microphones, both the surface noise and far-field noise are tested in an aeroacoustic wind tunnel.
It is observed that the slanted rear wall can suppress the noise effectively, but for the slanted front wall, the tones will be
enhanced at some velocities. Numerical simulation is conducted to reveal the mechanism. The results reveal that the
slanted rear wall can reflect the unsteadiness back to the shear layer and break up the vortices in it. These vortexes will
diffuse after impacting the rear wall and prevent the perturbation from moving deeper, which brings a stable flow field into
the cavity. As for the slanted front wall, the vortices will be enlarged and become accelerated in the shear layer, which makes
the impingement of it to the rear wall more intense, thus leading to an increase in the noise level.
Keywords
Aeroacoustic noise, cavity noise, passive control, wind tunnel experiment, numerical simulation
1. Introduction
When the flow passes the cavity, the shear layer will im-
pinge on the rear wall and produce intense oscillation and
noise radiation. Cavity noise has been extensively studied in
the last 50 years because of its geometrical simplicity and
engineering significance in aeronautic applications (Grace,
2001; Hüttl, 2007). Cavity structures, such as slat cove, pin
holes, landing gear bay, and hub (Pott-Pollenske et al.,
2002), are a major noise source during aircraft takeoff and
landing. The generation mechanism of tones in cavity noise
can be classified into two sorts (Rockwell and Naudascher,
1978). One is the flow-induced oscillation, which is caused
by flow instability, also called flow dynamic oscillation
or acoustic feedback. The empirical formula proposed
by Rossiter (1964) is still widely used to match the tonal
frequency, which depends on the freestream velocity. The
other is the acoustic resonance caused by enhanced oscil-
lation due to the standing wave inside the cavity. The tonal
frequency is linked to the geometry of the cavity and almost
independent of the flow velocity.
Generally, the control strategies proposed to suppress the
cavity noise in the literature can be divided into two types,
that is active and passive control. Active control provides
external energy (mechanical or electrical) input to the flow,
such as air mass injection, actuators, or oscillated leading-
edge devices. On the other hand, passive control just requires
simple geometric modifications without external energy
input (Cattafesta et al., 2008; Thangamani et al., 2013). It is
cheaper and easier to implement.
Much effort has been put into studying the effect of
slanted wall on cavity noise control. Most of these cavities
are shallow, whereby their lengths are greater than their
depths (Sarohia, 1977). Baysal et al. (1994) computation-
ally investigated two passive control methods to suppress
the acoustic noise in a shallow cavity at transonic flow. By
installing a 45-degree ramp on the rear wall of the cavity, the
tones were suppressed because of the pressure distributions
and the wave propagation pattern was altered. Perng and
Dolling (2001) experimentally explored the effectiveness of
a slanted downstream wall in controlling the pressure os-
cillations in different shallow cavities at Mach 5. The root
1
Key Laboratory of Aero-Acoustics, Ministry of Industry and Information
Technology, Beihang University, China
2
Key Laboratory of Fluid Mechanics, Ministry of Education, Beihang
University, China
Received: 21 October 2019; accepted: 19 May 2020
Corresponding author:
Hao Guo, Key Laboratory of Aero-Acoustics, Ministry of Industry and
Information technology, Beihang University, No. 37 Xueyuan Road, Haidian
District, Beijing 100083, China.
Email: guohao@buaa.edu.cn

2. mean square (RMS) pressure near the intersection between
the downstream wall and the floor was reduced by 40%, as
more air with high energy escapes the cavity. Nayyar et al.
(2005) studied the effect of slanted front and rear walls on
shallow cavity pressure oscillation in transonic flow through
numerical simulation. The slanted front wall showed less
effective suppression than the slanted rear one. Lawson and
Barakos (2009) investigated transonic flow over a shallow
cavity with a slanted rear wall by computational fluid dy-
namics (CFD) prediction. As the flow hit the rear wall at an
angle, more flow was deflected out of the cavity. Moreover,
the oscillation in the shear layer appeared to be weakened,
leading to the energy feedback between the shear layer and
the reflected waves from the rear wall being reduced.
Saddington et al. (2016) studied different passive control
techniques on a shallow cavity, including leading-edge and
trailing-edge ramps in a transonic wind tunnel. The trailing-
edge ramp decreased the tone intensity slightly and the
leading-edge ramp increased it by a similar amount. Luo
et al. (2018) found that the slanted rear wall could shorten
the effective cavity length and will shift some tones of
Rossiter to higher frequencies. In addition, it could also
suppress the upstream-traveling perturbation.
Relatively less attention has been paid to deep cavities.
The mechanisms of noise reduction by flow past shallow
and deep cavities are different. Flows over shallow cavities
are strongly influenced by the characteristics of the shear
layer and so, oscillation is dominated by longitudinal
modes. On the other hand, deep cavities are characterized
by standing wave–vortex interaction and acoustic depth
modes. The standing wave is excited by the instability of the
shear layer separating the exterior flow from the cavity flow
(Komerath et al., 1987; McGrath and Olinger, 1996). Block
and Heller (1975) elicited the depth modes of deep cavities
as being more efficient radiating sources than the longi-
tudinal modes of shallow cavities. Knotts and Selamet
(2003) experimentally investigated the suppression effect
of suppressor blocks with various shapes mounted upstream
and downstream of the side branch in a duct. These blocks
could redirect and stabilize the shear layer, thus preventing
it from forming large-scale vortices.
Generally speaking, investigations on the cavity noise
mechanism or the control methods mainly focus on acoustic
oscillation inside the cavity. As the Mach number of the
flow is fairly high (transonic or even supersonic), damage to
the structure inside the cavity is the key issue of concern.
However, when the air flows past the cavity at a low Mach
number, intense noise especially discrete tone radiating to
the far field is also a problem that needs to be addressed.
Moreover, a deep cavity structure, such as a slot, pin hole, or
gear bay, is a major source of airframe noise. So, measuring
the far-field noise radiated from a cavity with passive
control is significant in evaluating noise reduction strategies
on an aircraft. In this article, far-field and surface noises
from a two-dimensional deep rectangular cavity at various
locations are tested in an acoustic wind tunnel. Passive
control devices are applied by reshaping the geometry in-
side the cavity. The effect of these devices is compared and
analyzed further by CFD simulation.
2. Experimental setup
Experiments were conducted in the D5 aeroacoustic wind
tunnel at Beihang University, which is a newly commis-
sioned closed-circuit wind tunnel. Regarding the open
section, the size is 2.5 m in length, 1 m in height, and 1 m in
width. The wind speed can be continuously controlled from
0 to 80 m/s, with a turbulence intensity less than 0.08% in
the core of the jet. An anechoic chamber of 7.0 m in length,
6.0 m in width, and 6.0 m in height was built surrounding
the test section to provide the nonreflecting condition (Liu
et al., 2017). For the experiments presented here, the tunnel
working section Mach number ranged from 0.1 to 0.18.
Figure 1 shows the photograph of the clean rectangular
cavity, which is mounted on a plate parallel to the flow
direction, with its leading edge attached to the wind tunnel’s
nozzle. The dimensions of the cavity are L × W × D =
200 mm × 600 mm × 300 mm. Here, L, W, and D represent
the length, width, and depth of cavity, respectively. This
cavity is a two-dimensional deep cavity because the length
is less than either depth or width, as defined by Ahuja and
Mendoza (1995). The leading edge of the cavity is located
1.4 m downstream of the nozzle. The coordinate axis is
presented in Figure 2, with its origin beginning at the center
of the cavity’s leading edge. The x axis is along the flow
Figure 1. Photograph of the test section with the clean cavity
studied and the far-field microphones.
2 Journal of Vibration and Control 0(0)

3. direction, whereas the z axis is normal to the plate and
reverse to the depth direction of the cavity. Six Brüel &
Kjær Type 4189 1/2” free-field microphones are mounted
above the cavity to measure the far-field noise, and among
them, F1 to F5 are in the flyover direction (x–z plane),
whereas F6 is in the sideline one. The distance from the
origin to every microphone is fixed to 2 m, which is equal to
10 times the cavity length. The coordinates of each far-field
microphones are exhibited in Table 1. The near-field noise is
measured by G.R.A.S. 1/4” surface microphone, which is
flush mounted on the wall of the cavity. Four microphones
are measured at the same time in total, which are located at
the center of the side wall, front wall, floor, and rear wall of
cavity, as shown in Figure 3. The sampling frequency of the
acoustic signal is 65,536 Hz, and the whole recording time
is about 50 s. The signal is divided into a number of blocks
with an overlapping ratio of 66.7%. Each block contains
16384 samples and is treated by a Hanning window before
a fast Fourier transform. Then, the final spectrum is aver-
aged over these blocks to smooth the spectrum curve, and
the frequency resolution is 4 Hz.
Two different passive control devices have been tested.
The rectangular cavity is reshaped by slanting the rear and
front walls of cavity, as shown in Figure 4. The slanted
angle is β = 20°. It has been noted that the positions of some
surface microphones should be adjusted to keep them at the
center of the wall.
Figure 2. Plane sketch of the experimental clean cavity and the far-field microphones at the: (a) symmetric plane of cavity, and (b) plane
parallel to the nozzle of the wind tunnel and passing microphones F1 and F6.
Table 1. Positions of far-field microphones shown in a spherical
coordinate system defined as: r ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
x2 þ y2 þ z2
p
; θ ¼ arccos
ðx=rÞ; and f ¼ arctanðy=zÞ.
Number r (m) θ (°) Φ (°)
F1 2 135 0
F2 2 120 0
F3 2 105 0
F4 2 90 0
F5 2 75 0
F6 2 135 À45
Figure 3. Locations of four surface microphones.
Guo et al. 3

4. 3. Experimental results
3.1. Clean cavity
Figure 5 illustrates the near-field noise spectra measured
from S3 inside the clean cavity at different Mach numbers.
Various distinct peaks can be observed at different fre-
quency ranges. Notably, the peaks beyond 350 Hz are in-
dependent of the Mach number, and they are characterized
by acoustic resonant tones. The frequencies of these tones
can be determined by (Ahuja and Mendoza, 1995)
fjmn ¼
c0
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j
2D
2
þ
m
L
2
þ
n
W
2
s
(1)
where j = 1, 3, 5,… and m and n = 0, 1, 2,… are the mode
numbers for the depth-wise, length-wise, and span-wise,
respectively. However, Dalmont et al. (2001) declared that
the depth D should be corrected as the “effective” acoustical
depth D0
= D + δ. For a cavity with infinite flange, δ is
valued as
δ ¼
1 þ 0:77ka
1 þ 0:77ka þ ð0:77kaÞ
2 Á 0:82159a (2)
where k = 2πf/a is the wave number and a is the radius of the
cavity, if it is cylindrical in shape. For a rectangular cavity, it
can be replaced as L=
ffiffiffi
π
p
. For the cavity in this study, it can
be regarded as one with an infinite flange. To verify that the
tones beyond 300 Hz belong to acoustic resonance, Figure 6
compares the frequencies predicted by equation (1) and the
noise spectra from different microphones in the clean cavity.
Consistency is achieved with an error of less than 3%,
which may be due to the influence of the thickness of the
surface microphones. Tones with effective depth D0
valued
as D + δ and D are all presented. When the frequency
is beyond 800 Hz, they are combined together as their
frequencies are very close. Moreover, it seems that the
peaks in S4 are less distinct due to intense broadband
noise produced by the strong impingement of the shear
layer to the rear wall drowning them out.
As for the tones below 350 Hz, their frequencies vary
with the Mach number, corresponding to the mechanism of
flow-induced oscillation. The frequencies of them can be
predicted by Rossiter (1964)
fN ¼
U∞ðN À γÞ
Lðð1=κÞ þ MaÞ
(3)
where N is the modal number, whereas κ = 0.57 and γ = 0.25
are two constants. It is found that the peaks become sharp
when the frequency is around 230 Hz. According to the
view proposed by Verdugo et al. (2012), the coupling be-
tween a hydrodynamic and an acoustic mode could amplify
the pressure oscillations. To validate this, tonal frequencies
acquired from different surface microphones are compared
with Rossiter’s formula and the first-order depth mode f100,
as shown in Figure 7. The tonal frequencies correspond to
Rossiter’s formula very well only when N = 2. When N = 1
Figure 4. Profile of passive control devices with: (a) slanted rear wall and (b) slanted front wall.
Figure 5. Surface noise spectra from the clean cavity measured
by S3 at different Mach numbers.
4 Journal of Vibration and Control 0(0)

5. or 3, the tonal frequencies measured in the experiment fall
between those of the depth and Rossiter modes.
The amplitudes of dominant tones and overall sound
pressure level (OASPL) from different far-field micro-
phones are illustrated in Figure 8. For Ma = 0.1, the fre-
quency of the dominant tone corresponds to the 3rd-order
Rossiter mode. For other Mach numbers, the frequencies of
dominant tones correspond to the 2nd order. The OASPL is
calculated by integrating the power spectral density ranging
from 160 Hz to the maximum. It seems that the tone radiated
in the flyover direction (F1–F5) is stronger than that in the
sideline one (F6). In the flyover direction, the noise level
increases as the polar angle θ of the microphone increases.
It is suggested that the rectangular cavity noise spreads
mainly in the forward direction of the symmetric plane, as
the main noise source is concentrated on the rear wall.
3.2. Slanted wall control
Figure 9 shows a comparison between noise from a clean
cavity and slanted wall cavity measured by different surface
Figure 7. Comparison of the tonal frequencies between ex-
perimental data and theoretical values. Scatter: experimental
surface noise, dashed line: acoustic resonance of first-order depth
mode, and solid line: Rossiter’s formula.
Figure 6. Surface noise spectra measured by different micro-
phones in clean cavity at Ma = 0.16. Dashed line represents the
frequencies predicted by equation (1).
Figure 8. Amplitudes of dominant tones and overall sound
pressure level comparison from different far-field microphones
radiated by clean cavity.
Guo et al. 5

6. microphones at various Mach number. As the shape changes,
the peaks induced by acoustic resonance are suppressed
because of the wavelength of the standing wave varying
with the depth. Tones excited by the Rossiter mode move to
higher frequencies because the slanted wall decreases the
effective length of the cavity, which agrees with Luo et al.
(2018). The slanted rear wall can weaken or even eliminate
the discrete peaks effectively and broad noise received from
the surface microphones can also be reduced slightly.
However, broadband noise in S4 is not reduced, suggesting
that the slanted rear wall could not suppress the impact of
the shear layer. Nevertheless, it may destroy the acoustic
feedback such that the tones are not as sharp as that from
the clean cavity. On the other hand, the slanted front wall
increases the broadband noise in the near-field appreciably,
and the peak of the Rossiter mode at Ma = 0.18 is enhanced
considerably, while additional peaks are raised somewhere
around 350 Hz. This agrees with results in a shallow cavity
at transonic flow (Nayyar et al., 2005; Saddington et al.,
2016) that a slanted front wall shows less effective sup-
pression than a slanted rear one.
A comparison of the reduction in the OASPL of far-field
noise between two control devices is illustrated in Figure 10.
In the case of the slanted rear wall, the maximum reduction
is acquired at Ma = 0.14, exactly where the Rossiter mode
is coupling to the acoustic resonance in the clean cavity.
The breaking down of this coupling effect leads to the
suppression of the sharp peak dominating the spectra in the
clean cavity. The reduction received in F5 is not as obvious
as others, as the tones of the clean cavity are the weakest
here. As for the slanted front wall, the OASPL is increased
in all the microphones at Ma = 0.18 because the very in-
tense tone comes out, as shown in Figure 9. When the Mach
number is between 0.12 and 0.16, an increment of the
OASPL can also be observed in most of the microphones,
except F6.
Figure 9. Surface noise spectra comparison for different cavity configurations.
6 Journal of Vibration and Control 0(0)

7. 4. CFD simulation
To reveal the mechanism of noise control, a commercial
CFD solver ANSYS FLUENT 18.2 was used to simulate
the flow field.
4.1. Computational setup
The computational domain and surface mesh of the cavity
are shown in Figure 11. No-slipping boundary condition is
applied on the wall inside and surrounding the cavity. Other
plates are all considered as the pressure far-field boundary
condition. A freestream Mach number of 0.16 is specified at
these plates, with the temperature and pressure equal to
those in the experimental environment: T∞ = 303 K and
P∞ = 101325 Pa. The total number of cells is about
1.79 million. There are about 0.36 million cells (Nx × Ny ×
Nz = 50 × 75 × 95) within the cavity and 1.43 million cells
(Nx × Ny × Nz = 144 × 113 × 88) above it. The grid is highly
clustered toward the wall surrounding the cavity and the
opening of cavity to resolve the viscous boundary and shear
layers. The first cell height is Δy = 8 × 10À4
D. The detached
eddy simulation model, also named as hybrid LES/RANSs
(large eddy simulation/Reynolds-averaged Navier–Stokes
equations) model, is applied in this simulation. The RANS
model of it is the Spalart–Allmaras model, whereas the
subgrid-scale model of LES is wall-adapting local eddy-
viscosity. The time step is set to Δt = 5 × 10À5
s to ensure
the Courant–Friedrichs–Lewy number is less than one,
corresponding to the Nyquist frequency of 10 kHz. After
initialization, 4000 steps are performed first to acquire
a fully developed flow field, and then, another 22,000 time
steps are implemented.
4.2. Computational result
Validation of the numerical simulation is very essential.
Figure 12 illustrates the comparison of the pressure fluc-
tuation spectra between CFD and the experimental result
measured in S3. Broadband noise below 800 Hz can be well
predicted, whereas the tone of flow-induced oscillation at
240 Hz is overpredicted. Another tone around 150 Hz is due
to the second-order standing wave occurring in the z di-
rection in the CFD simulation: f0 = 2 × c/2/H0 = 166 Hz.
Here, H0 represents the distance between the cavity bottom
and the top bound of the domain. The underestimation of
the broadband noise beyond 800 Hz may be due to the
background noise of the high frequency in the experiment
and the numerical dissipation of the high-frequency signal
in the CFD simulation. The background noise does not
affect the low frequency because the tone of the flow-
induced oscillation is in the low-frequency range, which
makes the cavity noise greater than the wind tunnel
background noise in this range.
As the main noise source is concentrated on the rear wall,
it is important to make observations of the pressure fluc-
tuation at this wall for three cavities, as shown in Figure 13.
The unit is presented in “dB” so the pressure fluctuation is
equal to the OASPL. A fairly symmetric and width-
independent phenomenon is observed, which proves that
the time-averaging flow field is similar to the two-
dimensional one. Only the OASPL value in the center
region is a little greater than the two sides, owing to the re-
stricting of the flow by the two side walls inside the cavity.
The maximum level of OASPL in each cavity appears in
top of the rear wall because of the impingement of the shear
layer to it. For the clean cavity and slanted rear wall,
magnitudes of OASPL in this region are almost the same.
This is different from a shallow cavity in supersonic flow
(Perng and Dolling, 2001), in which the RMS in this region
was reduced by 40%. However, the OASPL in a clean
cavity reaches its minimum at the depth of Z/D = 0.2 and
will rise again in deeper region, not as slanted rear wall in
which it decreases rapidly with the depth. It is demonstrated
that this device is not able to decrease the impact of the shear
layer, but it can effectively prevent the propagation of the
pressure fluctuation in depth direction. This is similar to Luo
et al. (2018), who found that a slanted rear wall would
suppress the upstream-traveling perturbation in a shallow
Figure 10. Effect of two passive control devices on far-field noise.
Guo et al. 7

8. cavity. However, the cavity studied here is deep, so the
perturbation traveling direction that has been suppressed is
the depth direction. In the case of a slanted front wall, the
amplitude of OASPL at the top of the rear wall is obviously
higher than for the other two configurations, thus revealing
a more violent impingement. The OASPL value will fall at
Z/D = 0.2 and rise again in deeper region as clean cavity.
Hence, it can reasonably be concluded that the slanted front
wall can amplify the impingement of the shear layer on the
rear wall.
Figure 14 shows the turbulent kinetic energy (TKE) on
the symmetric plane of a spanwise direction for three
cavities, which is acquired by averaging the turbulence
normal stresses 0:5u2
i . The TKE at the mouth of the clean
cavity is relatively low, indicating a more stable flow
compared with the other two types. It seems that reshaping
the rectangular cavity could bring more perturbation into the
shear layer, as the length varies in depth direction. Although
the TKE at this region in the cavity with the slanted rear
wall is the highest, its velocity fluctuation inside the cavity is
lower than with other configurations, especially at the front
part of space inside the cavity. It can be demonstrated that if
the shear layer impacts the rear wall at an angle, the un-
steadiness will be reflected back into the shear layer rather
than entering into the cavity. This may help in stabilizing the
flow field inside the cavity, leading to a damping effect of
flow-induced oscillation. It is a little different from a shal-
low cavity in transonic flow, in that oscillation in the shear
layer will be weakened with the use of a slanted rear wall
(Barakos et al., 2009). As the cavity is shallow, the deflected
oscillation will escape from the cavity rather than back into
the shear layer. The high-level region of the TKE in the
cavity with a slanted front wall is not restricted to the shear
layer, for it stretches to the wall after the cavity’s trailing
edge. Its distribution also indicates a thicker shear layer, all
of which may lead to an increase in the surface noise at the
rear wall.
To get further information of the shear layer, Figure 15
shows the instantaneous isosurface of Q criteria colored by
the Mach number. The isovalue is defined by
QD2
U2
∞
¼ 10 (4)
At the front part, the flow field is very similar in the three
cavities. The shear layers are all characterized by spanwise
coherent structures, presenting the behavior of vortex
shedding from the leading edge of the cavity. In the clean
cavity, this coherence is kept until the shear layer hits the
rear wall. However, for the cavity with slanted rear wall, the
coherence is destroyed after half of the cavity length, and
the vortex structure has already broken into pieces before
hitting the rear wall. This could disrupt the feedback
mechanism and suppress the flow-induced tones further. No
vortex structure can be found inside this cavity as other two,
which verifies that the flow field inside the cavity with the
Figure 12. Spectra comparison of the pressure fluctuation be-
tween computational fluid dynamics simulation and the experi-
mental result measured in S3 (floor of cavity).
Figure 11. Computational domain and surface mesh of the cavity.
8 Journal of Vibration and Control 0(0)

9. slanted rear wall is very stable. As for the cavity with the
slanted front wall, the vortices are enlarged violently in the
shear layer and they do not completely impact the rear wall
as in other two cases. Some of these vortices even fly over
the trailing edge of cavity and travel downstream along the
plate. The rest of them do not diffuse as that in slanted rear
wall, but rather, break into large numbers of discrete smaller
structures, which fill the whole cavity. The Mach number of
the upper part of shear layer is even higher than the free-
stream. It seems that the slanted front wall has the effect of
accelerating and thickening the shear layer. This will also
extend the vortices inside it and intensify the impacting
strength.
Figure 13. Overall sound pressure level distribution on the rear
wall.
Figure 14. Turbulent kinetic energy (m2
/s2
) at the symmetric
plane (y/D = 0) in : (a) clean cavity, (b) cavity with slanted rear wall,
and (c) cavity with slanted front wall.
Guo et al. 9

10. 5. Conclusion
In this article, the controlling effect on aeroacoustic noise in
a deep cavity by slanting the rear and front walls has been
investigated. Both the wind tunnel test and CFD simulation
have been conducted, with the results showing fairly good
agreement. Through measuring the aeroacoustic noise at
different Mach numbers, it has been found that the Rossiter
tone will be enforced, if its frequency is overlapped with
acoustic resonance, because of the coupling effect. Both the
broadband noise and Rossiter tones could be reduced by the
slanted rear wall effectively. On the other hand, the slanted
front wall will increase the tonal and broadband noise. The
CFD results show that if the shear layer impacts the rear
wall at an angle, the unsteadiness will be reflected back into
the shear layer, rather than entering into the cavity, while the
strength of this impact will not be reduced. This will damage
the spanwise coherent structures in the shear layer and lead
to the breaking up of the vortices in it. These pieces of
vortexes will diffuse soon after impacting the rear wall. So,
the perturbation cannot move deeper, which gives a more
stable flow field in the cavity. The feedback mechanism is
then destroyed, thus leading to the suppression of noise. The
slanted front wall will enlarge and accelerate the vortices in
the shear layer. This will make the impingement of the shear
layer to the rear wall more intense and increase its noise
level.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with re-
spect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support
for the research, authorship, and/or publication of this article:
This work was supported by the National Natural Science
Foundation of China, under grant No. 11850410440, 11772033,
and 117221202.
ORCID iD
Zhifei Guo  https://orcid.org/0000-0002-8183-5303
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Figure 15. Instantaneous isosurface of Q criteria colored by the Mach number for: (a) clean cavity, (b) slanted rear wall, and (c) slanted
front wall.
10 Journal of Vibration and Control 0(0)

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