# Experimental Tests and Aeroacoustic Simulations of the Control of Cavity Tone by Plasma Actuators

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## Abstract

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## Featured Application

**Noise reduction in high-speed transport vehicles.**

## Abstract

## 1. Introduction

## 2. Methodologies

#### 2.1. Experimental Tests

#### 2.1.1. Wind Tunnel and Test Section

#### 2.1.2. Measurement of Sound and Flow Fields

_{0}= 10–45 m/s. The measurement time required for data acquisition was 30 s, and the sampling frequency was 40 kHz.

#### 2.2. Test Case Descriptions

_{0}= 10–45 m/s, while the simulations were performed at U

_{0}= 30 m/s. The actuators are shown in Figure 3. The Reynolds number based on the cavity length was Re ≡ U

_{0}L/ν = 1.3 × 10

^{4}–6.0 × 10

^{4}, and the Mach number was M ≡ U

_{0}/a = 0.029–0.131, where ν and a are the dynamic viscosity and the speed of sound in air, respectively. In addition, to clarify the nature of the flow induced by the actuators, flow visualizations and simulations were performed in the absence of a freestream flow.

_{0}= 15–45 m/s at the location x/L = 6.75 and y/L = 21.5 without control. The frequency resolution of the spectral analysis was 4.88 Hz. As shown in this figure, the tonal sound at the fundamental frequency f = 1500 Hz becomes most intense at a velocity of 30 m/s, where the existence of an acoustic resonance was confirmed by the phase distributions of the pressure in the cavity [8].

_{0}= 30 m/s at the upstream edge of the cavity, where this value was measured and found to be consistent with that predicted for flow over a flat plate without a cavity.

#### 2.3. Plasma Actuator Control

#### 2.3.1. Control by Streamwise Plasma Actuators

_{pa}= 4.2 kHz was applied to the electrodes. To clarify the effects of the applied voltage on the control, it was changed in the range from E

_{pa}= 4 kV

_{p-p}to 5.5 kV

_{p-p}in the experiments. Addtionally, the effects of the pitch of the actuators, s = 4, 10 mm, and the spanwise width of the lower electrode, d

_{l}= 1, 3, 5, 7 mm, on the control were investigated. Moreover, to clarify the nature of the control on the cavity flow and tone, aeroacoustic simulations were performed, as well as flow measurements, both with and without control. An actuator with E

_{pa}= 5 kV

_{p-p}, s = 10 mm (s/L = 0.5, s/θ = 71), and d

_{l}= 3 mm was utilized at U

_{0}= 30 m/s, where substantial reduction of the intense sound was achieved.

#### 2.3.2. Flush-Mounted Plasma Actuators

#### 2.4. Numerical Simulations

#### 2.4.1. Governing Equations and Finite-Difference Schemes

**Q**is the vector of the conserved variables,

**E**,

**F**,

**G**are the inviscid flux vectors, and

**E**

_{v},

**F**

_{v},

**G**

_{v}are the viscous flux vectors. To reproduce the body force produced by the actuator, the term

**D**representing the body force and the power added by it to the unit volume are included on the right-hand side of the equation [9]. Details of the body forces are described in next subsection.

_{n}, the same values as Gaitonde and Visbal [15] were utilized, and the value of the parameter α

_{f}was set to be 0.45. Cavity flows with incoming laminar and turbulent boundary layers can be predicted with high accuracy using the methods described above [16].

#### 2.4.2. Body Force Exerted by Plasma Actuators

_{x}, s

_{y}, s

_{z}and us

_{x}+ vs

_{y}+ ws

_{z}in the Navier-Stokes equations. For the body-force vector, the expression as follows was used:

_{c}is the plasma density, and

**φ**is the electric field. The square of the sine function in Equation (4) means that the plasma discharge occurs twice in one period, as in the body-force model of [9].

_{pa}), which is non-dimensionalized using the pitch of the actuators. As shown in the figure, the predicted distributions agree well with those determined in the experiments.

_{c}= ρ

_{c,max}E

_{pa}/(ρ

_{0}U

_{0}

^{2}/L) = 2.8 × 10

^{−6}so that control effects on the mean velocity profile in the cavity were in good agreement with those measured in the experiments discussed in Section 3.1.

#### 2.4.3. Computational Grid

_{c}/L = 3.0 of the computational domain was sufficiently wide to reproduce the effects of control by an actuator with pitch s/L = 0.5, with six sets of electrodes included in the computation. The spanwise grid resolution was Δz/L = 1/80. The streamwise resolution in the cavity was Δx/L = 1/100, and the normal resolution near the wall in the incoming boundary layer and in the shear layer in the cavity was Δy

_{min}/L = 1/400. The grid was stretched into the far field in both the normal and streamwise directions. The grid resolution in the x-y cross-section in the cavity was the same as that in our past research [8], where the predicted flow and sound fields were found to be in good agreement with those measured. The total number of grid points was 55 million.

#### 2.4.4. Boundary Conditions

#### 2.4.5. Prediction of the Far Acoustic Field

_{c}= 3L, which was chosen to be smaller than that of the experiment, W = 7.5L, was utilized in order to reduce computational resources. To take the effects of this difference into account, the sound-pressure levels, SPL (f), were corrected by using the equivalent coherence length, L

_{c}(f), which was computed based on the coherence of the velocity along the center of the cavity (x/L = 0.5, y = 0) in the spanwise direction. The detailed method is described in [5].

## 3. Comparison and Validation

#### 3.1. Flow Fields

_{pa}for U

_{0}= 30 m/s, both with and without control are compared with those measured. The time-series velocity, measured by the hot-wire anemometer in our experiment, was given by u

_{h}= (u

^{2}+ [0.5v]

^{2})

^{0.5}in the computation, in the same way as in our previous research [26], and the time-averaged values, U

_{h}, were computed. Figure 12 shows that the predicted profile agrees well with that measured for cases both with and without control. The free shear layer is moved in the upward direction by the control. This is because the incoming boundary is moved upward due to the streamwise vortices induced by the control.

#### 3.2. Sound-Pressure Spectra

## 4. Results and Discussions

#### 4.1. Measured Geometric Effects of Actuators on Control

_{pa}applied to the actuators was measured, where the spanwise pitch of the lower electrode was either s = 4 mm or s = 10 mm, and the fixed width of the lower electrode was d

_{l}= 3 mm. Figure 14a shows the measured variation. The frequency resolution of spectral analysis was Δf = 4.88 Hz and it should be noted that the reduction level was different from that in the previous section due to the difference of the frequency resolution.

_{pa}= 4 kV

_{p-p}to 5.5 kV

_{p-p}. The sound level drops sharply at lower voltages for the narrower pitch s = 4 mm, as compared to the case with s = 10 mm. For s = 4 mm, the sound reduction level of 31 dB was achieved at E

_{pa}= 5 kV

_{p-p}. However, for a fixed cavity width, more actuators and greater power consumption are necessary for narrower pitches. In the next subsection, the sound-reduction mechanism is discussed for s = 10 mm and E

_{pa}= 5.0 kV

_{p-p}.

_{j}/U

_{0}= 0.07, which roughly corresponds to the jet velocity (2 m/s) induced by the present plasma actuators, show that the control effects became smaller for finer spanwise displacement of the jets, such as s/L = 0.1 and 0.25. The maximum reduction level was achieved at s/L = 0.5. This was because the induced longitudinal vortices were weakened for the finer displacement.

_{l}= 1, 3, 5, and 7 mm, at a constant pitch of s = 10 mm, as shown in Figure 14b. The results show that sound reduction was obtained and that the influence of the lower-electrode width on sound reduction was small, except for the narrowest width, d

_{l}= 1 mm. Streamwise vortices are not induced at this narrow width, possibly because the body force is not sufficiently large, due to too narrow a width for expansion of the plasma between the exposed electrodes [27].

#### 4.2. Control Effects on Flow Structures and Pressure Fields

#### 4.2.1. Vortical Structures

^{2}− ||S||

^{2}, where Ω and S are the anti-symmetric parts and symmetric parts, respectively, of the velocity gradient tensor for the phase-averaged flow fields at the phase where the vortex collides with the downstream edge of the cavity. The iso-surfaces are color-coded by the values of the streamwise vorticity.

_{z}, which was computed from Equation (6):

_{z}is the spanwise vorticity and S

_{xx}, S

_{xy}, and S

_{yy}are the elements of the symmetric parts of the velocity gradient tensor. This quantity is related to vortices with spanwise axes and is color-coded by the spanwise vorticity in the figure. Figure 16 also shows the contours of streamwise vorticity in the shear layer (y/θ = 2.9).

#### 4.2.2. Power Spectra of Velocity Fluctuations

_{pa}at the peak of maximum power for y/θ = 6.4 and 3.6, respectively, with and without control, along with the measured data. The figure shows that the power at the fundamental frequency is weakened by the control in both computations and experiments. This corresponds to the weakening of the above-mentioned large-scale vortices with spanwise axes that produce the cavity tone.

#### 4.2.3. Spanwise Coherence

## 5. Conclusions

_{l}= 3, 5, and 7 mm, while the control effects on the cavity tone were negligible for d

_{l}= 1 mm. The predicted and measured flow fields show that streamwise vortices are induced by the actuators for d

_{l}= 3 mm in the absence of a freestream.

_{l}= 3 mm at the applied voltage of E

_{pa}= 5 kV

_{p-p}, even though they can only induce flows with a maximum velocity of 2 m/s. In comparison with the control by blowing jets, the plasma actuators can more effectively reduce the cavity tone by introducing streamwise vortices with the fine displacement.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Measured sound-pressure spectra without control at U

_{0}= 15, 25, 30, 35, 45 m/s. SPL is the sound-pressure level in decibels

**Figure 5.**Configuration of the streamwise plasma actuators: (

**a**) top view; and (

**b**) view in a cross-section perpendicular to the streamwise direction.

**Figure 6.**Comparison of the sound-pressure level SPL of the cavity flow both with and without a flush-mounted actuator.

**Figure 7.**Plasma distributions. Photograph of the plasma luminescence (

**left**). Predicted distributions of plasma density near the wall (y = 0.05 mm), compared with those determined from the plasma luminescence in the photograph (

**right**).

**Figure 11.**Vortices induced by actuators in the absence of a freestream flow: (

**a**) visualized flow in the experiment; and (

**b**) the predicted velocity vectors color-coded by values of the vertical velocity.

**Figure 12.**Predicted and measured mean velocity profiles with and without control (x/L = 0.05, z = z

_{pa}).

**Figure 14.**(

**a**) The variation of the sound-reduction level, in decibels, at the fundamental frequency of 1500 Hz as a function of the applied voltage; and (

**b**) the variation of the sound-reduction level for different lower-electrode widths as a function of the freestream velocity U

_{0}.

**Figure 15.**Iso-surfaces of the second invariant of q/(U

_{0}/L)

^{2}= 0.45 color-coded by values of the streamwise vorticity for phase-averaged flow fields at U

_{0}= 30 m/s at the phase where the vortex collides with the downstream edge of the cavity: (

**a**) baseline flow; and (

**b**) controlled flow.

**Figure 16.**Iso-surfaces of the component of the second invariant related to vortices with a spanwise axis q

_{z}/(U

_{0}/L)

^{2}= −20 color-coded by the spanwise vorticity, together with contours of the streamwise vorticity in the shear layer (y/θ = 2.9) at the phase where the vortex collides with the downstream edge of the cavity: (

**a**) baseline flow; and (

**b**) controlled flow.

**Figure 17.**Predicted power spectra of velocity, u

_{h}, with and without control at the peak of maximum power for y/θ = 6.4 and 3.6 at x/L = 0.5 and z = z

_{pa}, with and without control, respectively. The measured spectra at the peak of maximum power for y/θ = 5.7 and 2.8 at the same streamwise and spanwise positions of x/L = 0.5 and z = z

_{pa}with and without control, respectively, are also shown.

**Figure 18.**Spanwise coherence of streamwise velocity, u, at x/L = 0.5 and y = 0 for baseline and controlled flows.

**Figure 19.**Contours of the fluctuation pressure at U

_{0}= 30 m/s for phase-averaged flow fields at the phase where the vortex collides with the downstream edge of the cavity: (

**a**) baseline flow; and (

**b**) controlled flow.

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**MDPI and ACS Style**

Yokoyama, H.; Tanimoto, I.; Iida, A.
Experimental Tests and Aeroacoustic Simulations of the Control of Cavity Tone by Plasma Actuators. *Appl. Sci.* **2017**, *7*, 790.
https://doi.org/10.3390/app7080790

**AMA Style**

Yokoyama H, Tanimoto I, Iida A.
Experimental Tests and Aeroacoustic Simulations of the Control of Cavity Tone by Plasma Actuators. *Applied Sciences*. 2017; 7(8):790.
https://doi.org/10.3390/app7080790

**Chicago/Turabian Style**

Yokoyama, Hiroshi, Isamu Tanimoto, and Akiyoshi Iida.
2017. "Experimental Tests and Aeroacoustic Simulations of the Control of Cavity Tone by Plasma Actuators" *Applied Sciences* 7, no. 8: 790.
https://doi.org/10.3390/app7080790