Investigation of cavity flow noise attenuation using acoustic liners in the locked-on state

Abstract

The focus of this study is on utilizing acoustic liner technology to control the aerodynamic noise generated by cavities. The primary objective is to investigate the impact of these passive control measures on the coupled noise of low-speed cavity flows and shear layer turbulence. The design of the acoustic liner incorporates the characteristics of cavity-coupled noise, and experimental measurements are conducted to assess the configurations of the lining at different installation positions. The near-field and far-field noise were measured to evaluate the noise reduction performance of the liner, and the flow characteristics of the shear layer were measured to assess the effect of the acoustic liner on the cavity flow. It was found that the acoustic liner was effective in reducing cavity noise. Furthermore, the study reveals that the effectiveness of the acoustic liner is influenced by its different installation positions. In this study, the noise reduction mechanism of the acoustic liner was also investigated to effectively suppress the coupling of cavity self- sustained oscillations and acoustic resonance. Finally, the influence of acoustic liner on the flow characteristics in the shear layer of the cavity was explored. This study guides the application of acoustic liner in cavity noise control.

Keywords

Cavity noise passive control acoustic liner dominant mode aeroacoustics

Introduction

The interaction between self-sustained oscillations and acoustic resonance in cavities is a significant area of research in engineering due to its wide range of applications.^1–3 In many practical applications, it results in negative consequences such as excessive noise, vibration, and structural damage. In the context of automotive engineering, significant research has focused on mitigating the undesirable noise effects caused by acoustic resonance in components like sunroofs^4,5 and gas transmission pipes with closed branches.⁶ Similarly, in aerospace engineering, the noise and vibrations caused by self-sustained oscillations in landing gears and weapons bays have been extensively studied.^7,8 These oscillations, when coupled with acoustic resonance, can produce high amplitude noises that not only create serious noise pollution but also lead to structural damage over time.

Many studies have utilized active and passive control measures to control cavity self-sustained oscillatory noise. Active control methods involve adding external energy to the system.^9–12 These include the use of plasma actuators,¹¹ periodic excitation,¹⁰ upstream mass-injection,¹³ three-dimensional steady blowing.⁹ On the other hand, passive control methods do not require additional energy, involving placing the cylinder upstream,¹⁴ changing the shape of the trailing edge,¹⁵ high-frequency vortex generators,¹⁶ porous media, spanwise array of leading-edge tabs and incorporating sub cavities.¹⁷

Passive control measures for reducing noise in cavities have been widely researched due to their simplicity and effectiveness. Ali¹⁸ performed experiments on aft-wall ramp cavities, showing that smaller ramp angles were effective in suppressing oscillations and controlling entrainment. Abderrahmane et al.¹⁹ studied the effect of leading edge waviness on cavity noise at low Mach numbers. Their findings indicated that such surface modifications significantly decreased both self-sustained oscillations and overall sound pressure levels. Liu et al.¹⁵ explored the influence of trailing edge geometry on cavity noise, testing three different shapes. Their experiments demonstrated that modifying the shape near the trailing edge can disrupt the feedback mechanism, thus reducing self-sustained oscillations. Zhao et al.²⁰ investigated the impact of serrated and rounded leading edges on cavity flow. The control measure of the rounded trailing edge is more effective than the sawtooth structure flow control method.

Acoustic liners function by dissipating sound energy through viscous and thermal losses within their porous structure. When sound waves enter the liner, part of the acoustic energy is converted into heat due to the friction between air particles and the porous material, effectively attenuating the noise. One of the primary applications of acoustic liners is in aerospace engineering, particularly in reducing noise in aircraft engines and cavities such as landing gears and weapons bays. The high-speed flow over these cavities can lead to strong self-sustained oscillations and resonance, generating significant noise. Techniques involving acoustic liners have proven effective in mitigating these effects. Ma²¹ explores the effectiveness of acoustic liners in reducing noise generated by slats in aerodynamic applications. The research utilizes numerical simulations to analyze how different configurations and materials of acoustic liners impact noise levels. Results indicate that properly designed acoustic liners can significantly attenuate slat noise, enhancing the overall acoustic performance of the system. The study by Roberts et al.²² investigated the use of acoustic liners to reduce pressure fluctuations in cavity flows. Experimental results show that these liners can achieve attenuation levels up to 26 dB under supersonic conditions (Mach number M = 1.5). Bauerheim et al.²³ used Large Eddy Simulation (LES) to examine the interactions between airflow and acoustic liners with multiple cavities. The findings highlight that the design and arrangement of the cavities significantly influence the aero-acoustic coupling and effectiveness of noise reduction in practical applications.

Experimental research on controlling low-speed cavity self-sustained oscillations and acoustic resonance coupled noise has been limited. Most studies have focused on self-sustained oscillatory noise or the coupling noise under high-speed flow, and the coupling noise under low-speed condition is less studied. This study aims to address this gap by conducting experiments to control coupled noise in low-speed cavity flows using acoustic liners. The effectiveness of acoustic liners in mitigating the coupled noise between self-sustained oscillations and acoustic resonance will be evaluated, providing new insights into passive noise control strategies for low-speed applications. Specifically, this study investigates the suppression of the dominant mode and the overall sound pressure level of cavity coupling noise using an acoustic liner. Additionally, it examines the impact of the acoustic liner on the flow characteristics of the cavity shear layer.

This paper investigates the acoustic properties of various acoustic liner configurations in the D7 aeroacoustics wind tunnel at Beihang University. The primary focus is on examining how the acoustic liner affects the dominant mode of cavity coupled noise and comparing the noise reduction effects at different locations. The paper is structured as follows. Experimental setup describes the experimental methodology, including the experimental setup. The next section outlines the design method of the acoustic liner. The following section describes the characteristics of the noise and shear layers of the acoustic lining configuration. The final section summarizes the conclusions.

Experimental setup

Measurements of aerodynamic noise and shear layer velocities of cavities were carried out in the D7 wind tunnel at Beihang University. The D7 wind tunnel²⁴ is an open jet closed circuit wind tunnel, which is an aeroacoustic testing wind tunnel. The experimental nozzle’s cross-section measures 200 mm × 200 mm, with a test section length of 500 mm. The test section can measure the maximum wind speed of 40 m/s. The test section is surrounded by small anechoic chambers, measuring 1.4 m in length, 1.6 m in width, and 1.9 m in height, to ensure non-reflective measurement conditions. The low-frequency cutoff of the wind tunnel for far-field noise measurements is 200 Hz.

An aluminum alloy plate cavity was mounted on a plate with its leading edge positioned 100 mm from the nozzle. The experiment utilized two microphones and two hot wire probes to capture acoustic and flow field signals, respectively. Mic 1 was located on the front surface of the inner wall of the cavity and is a G.R.A.S. 1/4″ surface microphone as shown in Figure 1. Mic 2, a Brüel & Kjær Type 4189 1/2″ free-field microphone, was located above the center of the cavity’s rear edge. Flow field data were acquired using a StreamLine CTA (Constant Temperature Anemometer) from DANTEC. One-dimensional hot-wire probes 55P11 and 55P14 were used for flow field data collection; 55P11 was fixed 13 mm above the cavity’s rear wall, while 55P14, an L-shaped probe, moved within the cavity’s shear layer. Velocities ranged from 10 m/s to 35 m/s, measured in 1 m/s intervals, with the microphone sampling frequency set at 25,600 Hz.

Design of the acoustic liner

The acoustic liner absorber used in the experiments was designed using Maa’s theoretical analysis of MPP absorber.²⁵ When the sound wave enters the small hole to let the air in the cavity vibrate, if the frequency of the sound wave is the same as the resonance frequency of the structure, the air in the cavity will resonate and the energy contained in the sound wave will be converted from friction to heat loss, which will cause the sound absorption effect. There are four main parameters affecting the acoustic performance of the microperforated plate absorber as shown in Figure 2(a), which are the diameter of the micro perforation d, the thickness of the microperforated plate t, the perforation rate $σ$ and the depth of the microperforated plate absorber cavity D.

A micro-perforated plate (MPP) can be viewed as a parallel connection of multiple tubes, and its acoustic impedance can be expressed as:

Z_{M P P} = \frac{32 ρ μ t}{σ d^{2}} (\sqrt{1 + \frac{k^{2}}{32}} + \frac{\sqrt{2} k}{8} \frac{d}{t} + j ω ρ t (1 + \frac{1}{\sqrt{9 + \frac{k^{2}}{2}}} + 0.85 \frac{d}{t})

(1)

where

= d \sqrt{\frac{ω ρ}{4 η}}

, is the perforation constant,

ω = 2 π f

is the angular frequency of the sound wave,

ρ

is the air density, and

η

is the air viscosity coefficient. When the depth of the MPP acoustic absorber cavity is D, the acoustic impedance equation of the cavity can be expressed as:

Z_{D} = - j ρ c \cdot \cot (ω D / c)

(2)

The acoustic impedance of the whole structure is:

Z_{t o t a l} = Z_{M P P} + Z_{D}

(3)

The relative acoustic impedance ratio is

\frac{Z_{t o t a l}}{ρ c} = r + j ω m - j ρ c \cdot \cot (\frac{ω D}{c})

(4)

c is the speed of sound. r is the normalized specific acoustic resistance of MPP, m is the normalized acoustic mass of MPP.

r = \frac{32 ρ μ t}{σ d^{2}} (\sqrt{1 + \frac{k^{2}}{32}} + \frac{\sqrt{2} k}{8} \frac{d}{t})

(5)

m = \frac{t}{σ c} (1 + \frac{1}{\sqrt{9 + \frac{k^{2}}{2}}} + 0.85 \frac{d}{t})

(6)

where

σ

is the perforation rate. When the perforations are arranged in a square arrangement, the relationship between the perforation rate

σ

and the perforation spacing b is as follows:

σ = \frac{π d^{2}}{4 b^{2}}

(7)

The absorption coefficient for a sound wave incident vertically is given by

α = \frac{4 r}{{(1 + r)}^{2} + {(ω m - \cot (ω D / c))}^{2}}

(8)

The maximum absorption coefficient is

α = \frac{4 r}{{(1 + r)}^{2}}

(9)

In this paper, it is necessary to consider the requirements of sound absorption characteristics and the dimensions of the structural parameters. Five control parameters are considered in the design, which are the lower frequency limit of noise reduction $f_{1}$ , the upper frequency limit of noise reduction $f_{2}$ , the minimum absorption coefficient $a_{1}$ at frequency $f_{1}$ , the minimum absorption coefficient $a_{2}$ at frequency $f_{2}$ , and the material parameter B of the microperforated plate. The material chosen in this paper is metal due to its ease of processing. The material parameter $B = 2 μ / π$ , for the metal plate or the micro perforated plate with a large heat transfer coefficient B = 22.3. All possible structural parameters are given according to the actual processing capability and experimental conditions, where the perforation diameter d ranges from 0.2 mm to 1 mm, plate thickness t ranges from 0.5 mm to 1 mm, cavity depth D ranges from 1 mm to 50 mm, the perforation distance b ranges from 4 mm to 10 mm, and the percentage open area (porosity) varies within the range of 0.03% to 4.91% (calculated based on perforation diameter and spacing). And the accuracy of variation of the d and t parameters is taken as 0.1 mm, and the accuracy of variation of the D and b parameters is taken as 1 mm. The sound absorption coefficients a( $f_{1}$ ), a( $f_{2}$ ) at frequencies under different structural parameter conditions are obtained by iterating between different structural parameters through equation (9).Then judge $a (f_{1})$ $>$ $a_{1}$ and $a (f_{2})$ $>$ $a_{2}$ , when the calculation result meets the given conditions, output the structural parameters, and select a parameter with better noise reduction effect among the final multiple structural parameters obtained, and the multi-parameter design of the acoustic liner is completed.

According to the characteristics of the cavity baseline configuration noise, the input parameters

f_{1}

= 400 Hz,

f_{2}

= 760 Hz,

a_{1}

= 0.75,

a_{2}

= 0.75. Table 1 shows the structural parameters of the acoustic liner obtained by multi-parameter design and Figure 2(b) shows the acoustic liner model. The red dashed line in Figure 3 shows the sound absorption coefficient of the designed acoustic liner, compared with the acoustic resonance. The design of the acoustic liner is intended to eliminate the locking of self-sustained oscillation noise near acoustic resonance. The figure compares the sound absorption coefficient with the first-order acoustic resonance frequency, where

f (0, 0, 1)

represents the acoustic resonance mode most likely to occur within the frequency range of self-sustained oscillations.²⁴ Near this frequency point, the absorption coefficient reaches its peak, showing optimal absorption performance, with the absorption coefficient approaching 1, indicating that most of the sound energy is absorbed at this frequency.

Table 1.

Structural parameters of the acoustic lining obtained from the multi-parameter design.

Perforated plate material	d (mm)	t (mm)	D (mm)	b (mm)	σ (%)
Metal	0.6	0.8	48	6	0.8

Effect of acoustic liner on cavity noise

Noise reduction with acoustic liner in different positions

Acoustic liners were installed at different locations in the cavity to test the effect of the sound absorbing structures on cavity noise at different locations and velocities as shown in Figure 4. The experimental acoustic liners are installed in the form of bottom area only ( $L_{B}$ ), the front area only ( $L_{F}$ ), the rear area only ( $L_{R}$ ), the front and rear areas ( $L_{F R}$ ), and all three areas ( $L_{F R B}$ ).

To quantify the noise characteristics, Power Spectral Density (PSD), Overall Sound Pressure Level (OASPL), and ΔOASPL are calculated as follows:

• The PSD is estimated using the Fast Fourier Transform (FFT) with a Hanning window and 50% overlap to minimize spectral leakage. The sampling frequency is 25,600 Hz, and the frequency resolution is 8 Hz, ensuring sufficient resolution for analyzing noise components. The PSD is calculated as: $P S D (f) = \frac{p^{2} (f)}{∆ f}$ , where $p^{2} (f)$ represents the mean-square pressure and $∆ f$ is the frequency resolution. The PSD is commonly expressed in dB as: $P S D_{d B} = 10 \log_{10} \frac{P S D (f)}{p_{r e f}^{2}})$ , where $p_{r e f} = 20 µ P a$ is the reference sound pressure.

• The OASPL is computed as $O A S P L = 10 \log_{10} (\sum_{f} \frac{p^{2} (f)}{p_{r e f}^{2}})$ , integrating the PSD over the frequency range.

• The $∆ O A S P L$ is defined as $∆ O A S P L = O A S P L_{b a s e l i n e} - O A S P L_{l i n e r c o n f i g u r a t i o n}$ indicating noise reduction due to the liner.

As shown in Figure 5, the far-field noise spectra of the five installation methods are compared with the baseline configuration. The acoustic liner significantly reduces discrete noise, with variations depending on its position. The liner design targets cavity noise, particularly the coupled noise of acoustic resonance and self-sustained oscillations, which can intensify near resonance.²⁴ The acoustic liner absorption coefficient is higher at the acoustic resonance $f (0, 0, 1)$ . The discrete noise near 571 Hz is significantly reduced at different speeds, however the intensity of the lower Rossiter mode increases. The $L_{F R B}$ configuration has the least effect on the intensity increase of the lower modes except when the speeds are 10 m/s and 15 m/s, so the noise reduction effect is better.

At 25 m/s, all lining methods effectively reduce primary discrete noise but slightly raise the sound pressure level of the 2nd mode noise. At 30 m/s, several methods continue to reduce prominent baseline peaks. At the velocity of 35 m/s, the three-sided lining of the cavity emerges as superior to other installation methods in both attenuating high SPL modal noise and minimizing excitation of 2nd modal noise.

The frequency of multiple modals of self -sustaining oscillating noise can be predicted with the semi -experience formula proposed by Rossiter.

f_{n} = \frac{U_{\infty}}{L} \frac{n - γ}{M a + 1 / κ}

(10)

where, L is the length of the cavity, n is the order of the shear layer mode, κ is the convection velocity of the shear layer normalized by the free stream velocity

U_{\infty}

, γ is the phase delay coefficient and Ma is the flow Mach number.

According to Stephens’s research,²⁶ when the convection speed is much less than the speed of sound, the phase lag term can be ignored. Therefore, at the low speed in this study, the phase delay parameter $γ = 0$ . Delprat²⁷ analyzed the relationship between the self-sustained oscillation frequency measured by the experiment and Rossiter’s formula. From the point of view of signal processing, the modulation characteristics of self-sustaining oscillations can be studied through the distribution of spectrum. The main feature of self-sustained oscillations is that there are multiple modes between these discrete frequencies, with a uniform interval $∆ f$ equal to the fundamental frequency $f_{a}$ of the self-sustained oscillation mechanism.

f_{a} = \frac{U_{\infty}}{L} \frac{1}{M a + 1 / κ}

(11)

Therefore, the frequency of self-sustaining oscillation is:

f_{n} = n * f_{a}

(12)

As shown in Figure 6, the contour of the near-field noise spectrograms measured by several acoustic liner installation methods with velocity changes are shown for incoming flow velocities of 10–35 m/s. The figure reveals that all the acoustic liner configurations significantly reduce noise in the frequency band above 0.75 of the designed absorption coefficients. They effectively reduce the original discrete peak noise with high sound pressure levels but somewhat excite the original low-frequency noise with weaker sound pressure levels (the second mode). This suggests that after the high-frequency noise is absorbed, some energy is transferred to the low frequency. For incoming velocities below 17 m/s, the $L_{B}$ configuration has the least excitation on the third mode noise, and provides the best noise reduction in this velocity range. When the incoming velocity is in the range of 17-28 m/s, the $L_{F}$ configuration has the smallest excitation to the 2nd mode, offering the best noise reduction effect. When the incoming flow velocity is greater than 28 m/s, the $L_{F R B}$ configuration shows a clear advantage over other configurations in reducing the 2nd mode noise level. Additionally, the noise-reduced configurations significantly improve the modal deviation from the predicted value caused by the coupling of self-excited oscillatory noise of the cavity and the acoustic resonance in the baseline configuration. This improvement is especially notable in the third mode noise, where the baseline configuration shows modal deviation. For instance, at a velocity of 35 m/s, normalizing the noise spectrum according to the fundamental frequency in equation (11) (as shown in Figure 7), where $κ = 0.57$ and $γ = 0$ . The figure shows that there is a significant deviation in the third mode noise in the baseline configuration, but it is significantly improved in the acoustic liner configurations.

To evaluate the noise reduction effect of the acoustic liner, it is necessary to compare the overall sound pressure levels of cavities with different configurations. Figure 8(a) illustrates the variation in overall sound pressure level with velocity and noise reduction effect for different configurations, considering a cutoff frequency of 200 Hz. The figure indicates that there is a local maximum of the overall sound pressure level of the baseline configuration, caused by self-sustaining oscillation and resonant coupling. The undulation in OASPL with increasing velocity is primarily due to the interaction between different orders of Rossiter modes and the acoustic resonance frequency of the cavity. While the acoustic resonance modes remain constant, changes in velocity cause different Rossiter modes to successively align with these resonance frequencies, leading to periodic increases in OASPL. As illustrated in Figure 6(a), at velocities of 21 m/s and 29 m/s, the 4th-order and 3rd-order Rossiter modes, respectively, coincide with the acoustic resonance mode. This frequency matching amplifies self-sustaining oscillations, resulting in local maxima in OASPL at these velocities, as observed in Figure 8. These findings demonstrate the strong coupling between flow-induced oscillations and cavity resonance, which influences the noise characteristics at specific velocity ranges. Previous analyses have shown that the acoustic liner design achieves the highest sound absorption coefficient near acoustic resonance, thereby significantly weakening the coupling of sound resonance and self-sustaining oscillation. Figure 8(b) shows that the acoustic liner configuration effectively eliminates the local maximum value of the overall sound pressure level. All acoustic liner configurations show no significant local peaks, except for the maximum intensity near 15 m/s. Additionally, from the perspective of noise reduction effect, since coupling noise has a greater impact at higher speeds, the acoustic liner configuration achieves the best noise reduction effect at 30 m/s, with the $L_{F R B}$ configuration reducing noise by up to 20 dB.

Flow characteristics of a shear layer under the influence of an acoustic liner

The acoustic liner can effectively reduce the noise of the cavity’s self- sustained oscillation. The relationship between velocity field and pressure field in cavity noise can be better studied. The baseline configuration and the $L_{F R B}$ configuration with good noise reduction effect were selected for flow field measurement.

Compare the hot wire data of the shear layer at a speed of 25 m/s. Figure 9 shows the comparison of mean velocities measured by a hot wire probe at four positions x = 10 mm, 30 mm, 50 mm, and 70 mm. From the perspective of the mean velocity in the cavity shear layer, the velocity values of the two configurations are almost identical. The velocity variation of the acoustic liner configuration in the shear layer is relatively small compared to the baseline configuration. Therefore, the influence of the installation of the acoustic liner on the mean velocity characteristics of the cavity shear layer can be almost ignored. From the root mean square (RMS) of velocity fluctuation in the cavity shear layer, it can be seen that adding the acoustic liner also has a small impact on the thickness of the cavity shear, while the cavity shear layer of the acoustic liner configuration at the flow direction positions x = 50 mm and x = 70 mm has a slight increase compared to the baseline configuration. Overall, the changes in acoustic behavior caused by the installation of acoustic liners do not result in significant changes in the mean value and RMS of the velocity in the cavity shear layer.

Compare the spectral characteristics measured at fixed probes (x = 80 mm, y = 13 mm) in different configurations. Figure 10 shows a comparison of the velocity spectra of different configurations at 25 m/s. The installation of an acoustic liner significantly impacts the fluctuation characteristics within the shear layer of the cavity. Figure 11 shows the spectral comparison of flow characteristics and acoustic signals in different configurations. The results indicate that the discrete modes of velocity signals in the shear layer are consistent with the excitation modes of microphone sound pressure signals. Combining Figures 10 and 11, it is concluded that the acoustic phenomenon in the cavity is affected by the change of the acoustic liner configuration, thereby affecting the coupling effect of vortices and sound waves during the self- sustained oscillation process. The acoustic liner configuration reduces the noise of the coupled modes of acoustic resonance and self-sustaining oscillation, while increasing the intensity of low mode discrete noise. This is because the acoustic liner reduces the locking behavior of self- sustained oscillation near acoustic resonance, so that the vortex shedding frequency in the cavity is not locked near the frequency of acoustic resonance. The frequency of vortex shedding changes to the low-frequency mode where the absorption coefficient of the acoustic liner is lower, which causes the acoustic liner to excite more energy in the low-frequency mode noise spectrum. Under the influence of the acoustic liner, the interaction between the flow field and the acoustic modes within the cavity is effectively suppressed,²⁸ interrupting the feedback mechanism and leading to a reduction in the efficiency of sound-flow energy transfer, thereby weakening the formation and development of vortices. This suppression reduces the coupling between the vortices and acoustic feedback, significantly lowering noise levels.

In order to reveal the influence mechanism of the acoustic liner on the self-sustained oscillation noise in the cavity, it is necessary to conduct a joint time-frequency analysis of the hot-wire signals of the two configurations to reveal the impact of the acoustic lining on the self-sustained oscillation noise in the cavity. As shown in Figure 12, it is the wavelet transform contour of the signal in Figure 10 within 5 s. The figure shows that in the baseline configuration, mode 3 is the dominant mode. Due to the acoustic feedback and locking effect of self-sustained oscillation noise, the velocity fluctuations at this frequency almost always appears with a higher wavelet coefficient. The dominant mode occasionally switches to the frequency of Mode 2, but this occurs for a shorter period of time and with lower wavelet coefficients. However, in the acoustic liner configuration, the velocity fluctuation frequency of Mode 3 is almost completely eliminated, lower wavelet coefficient fluctuation values appearing near this frequency. The velocity fluctuation in Mode 2 is significantly enhanced. And in the time domain this mode occurs more frequently and for a significantly longer total time, but is not locked for as long as Mode 3 in the baseline configuration. In terms of intensity, the intensity peaks in this mode are significantly stronger, even exceeding the intensity of Mode 2 in the base configuration.

The onset of the narrowband tone at $f / f_{a} = 2$ in Figure 12 can be attributed to the absorption characteristics of the acoustic liner. The liner is designed to absorb sound effectively near the cavity’s acoustic resonance frequency, which leads to the suppression of the coupling between the self-sustained oscillation third mode and the acoustic resonance mode. This suppression reduces the energy contribution of the third mode, thereby weakening its influence in the spectral response. As a result, with the attenuation of the third mode, the second mode becomes the dominant oscillation mode, leading to the emergence of a distinct narrowband tone at $f / f_{a} = 2$ . This shift in mode prominence is a direct consequence of the frequency-dependent absorption characteristics of the liner, which selectively attenuate higher-order modes while allowing lower-order modes to remain significant.

Overall, these findings indicate that the acoustic liner not only affects the acoustic behavior but also has a profound impact on the vortex shedding characteristics of the shear layer. This suggests that the self-sustained oscillation process in cavity noise is a wave-vortex coupling phenomenon, where the suppression of acoustic feedback leads to a redistribution of energy among oscillation modes.

Spectrum analysis was performed on the velocity signals of the cavity shear layer at the four flow direction positions in Figure 9. Figures 13 and 14 show the spectral contour at different flow direction positions in the shear layer of the baseline configuration and acoustic lining configuration respectively. There are differences in velocity fluctuation intensity at different heights at the same flow direction position in the cavity shear layer, which is mainly related to the vortex structure in the shear layer. The discrete peaks of the velocity fluctuation in the baseline configuration cavity shear layer are all in mode 3. The discrete peaks of the velocity fluctuation in the shear layer of the acoustic lining cavity are all in mode 2, which is consistent with the results of the acoustic phenomenon. The position with the maximum intensity of the discrete peak occurs at X = 50 mm. A higher intensity of discrete peaks in the baseline configuration than in the acoustic liner configuration indicates that more energy is contained. The broadband fluctuations at different positions in the acoustic liner configuration are stronger than those in the baseline configuration, which is why the root mean square values of the velocity fluctuations of the two configurations are not much different in Figure 9(b). That is, although installing the acoustic liner to the cavity can change the velocity fluctuation frequency in the cavity shear layer, the total energy at different locations in the cavity shear layer always remains at a certain level and will not change significantly.

Conclusion

This paper investigates the effect of acoustic liners on cavity noise. The study finds that all acoustic liner configurations effectively reduce noise at target frequencies. However, they tend to excite lower modes with relatively small liner absorption coefficients. Different liner installation positions influence the excitation of these lower modes, leading to varying noise reduction effects in the overall sound pressure level diagram. In addition, the variation of the overall sound pressure level with velocity for different configurations shows that when the velocity is less than 18 m/s, the noise reduction effect of the acoustic liner is not good due to the low excitation frequency of the self- sustained oscillatory noise in the cavity. When the velocity is greater than 18 m/s, the self- sustained oscillation modes of the cavity of the baseline configuration are locked in the frequency band of the high absorption coefficients of the liner design, and thus the noise reduction effect is better.

Hot wire measurements indicate that the acoustic liner configuration has minimal impact on the time-averaged velocity characteristics and the root mean square value of the pulsation velocity of the cavity shear layer. However, it significantly affects the frequency of velocity pulsations in the shear layer. The spectral characteristics of the cavity shear layer with the acoustic liner configuration remain consistent with the far-field acoustic characteristics. When the acoustic liner reduces the pulsation energy at a particular frequency in the shear layer, it increases the energy value of another mode to maintain the overall energy balance. Time-frequency analysis results show that the dominant mode rarely occurs after the addition of the acoustic liner, while the occurrence and intensity of lower modes increase. Taking into account the influence of the acoustic liner on both velocity and sound pressure, it is evident that the addition of the acoustic liner impacts the acoustic resonance of the first depth mode. This, in turn, affects the wave-vortex coupling effect within the cavity, altering the self-oscillating feedback loop. As a result, the self-oscillation noise of the cavity is prevented from being locked into the original acoustic resonance band, thereby achieving a better noise reduction effect.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect 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 research was funded by the National Natural Science Foundation of China (No. 12072016), National Key R&D Program of China (No. 2022YFB2602000) and the Fundamental Research Funds for the Central Universities.

ORCID iDs

Yuan Liu

Hao Guo

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