# Numerical Study on Flow-Induced Noise of Deflector Jet Servo Valve Based on LES/Lighthill Hybrid Method

Authors: Yukai Ren; Hao Yan; Cunkun Cai
Journal: Shock and Vibration
 (2022)

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## Abstract

The flow-induced noise occurring in the prestage of the deflector jet servo valve (DJV) significantly affects the performance of DJV, which is a critical issue for electrohydraulic servo valves. To capture the root causes of flow-induced noise, DJV is numerically studied using computational aeroacoustics (CAA) methods in this paper. The acoustic field is investigated with Lighthill’s acoustic analogy based on the pulsation data from a large eddy simulation (LES). The flow-induced noise generation mechanism in DJV is revealed by analyzing the sound pressure level and vorticity distribution at different moments. Moreover, a kind of oscillation cavity model based on the Helmholtz oscillator is built, which reveals that the flow-induced noise is caused by self-excited oscillation and vortex. In addition, the result shows that continuous broadband dipole noise with medium- and high-frequency components of 1100 Hz and 2501 Hz dominates the DJV flow field. In order to avoid unexpected resonance, the natural frequency of the prestage should not coincide with the frequency of the flow oscillation frequency. Thus, this work can benefit the design and optimization of the prestage structure.


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## Body

## 1. Introduction

Deflector servo valves are the key basic elements in major aerospace equipment. The deflector jet servo valve (DJV) is becoming a popular topic in servo valve research because of its excellent dynamic characteristics and strong resistance to contamination [1]. However, the servo valve will produce high-frequency noise or even scream in high-pressure work conditions. It will seriously affect the control precision and service life of the servo valve. The high frequency belongs to a kind of self-excited noise induced by the fluid-solid interaction. Consequently, the most terrible self-excited noise will appear when the flow oscillation frequency is consistent with the mechanical vibration frequency. To the best of our knowledge, the mode of the mechanical components of the DJV is easy to obtain [2], However, the complex flow noise is unpredictable.In the most recent research into the flow-induced noise of servo valves, cavitation is considered to be the main cause of the noise. Because of the complexity of the inner structure of the servo valve, cavitation occurs easily in the flow field. It will cause undesired effects of noise and vibration during oil bubble collapse. Zou et al. [3] studied the characteristics of cavitation and acoustic noise in a spool valve numerically and experimentally. The transparent model of the spool valve is built to observe the cavitation phenomena under different structural parameters, and the results revealed that the cavitation is affected by the pressure distribution, besides the flow structure. Li et al. [4] found that pressure oscillations increase with increasing inlet velocity. Yin et al. [5] proved that reducing the inlet pressure of the DJV can suppress the cavitation effectively. Wu et al. [6] analyzed the cavitation phenomena using the large eddy simulation (LES) method, drawing a similar conclusion. Otherwise, the instability of the shear layer instability is regarded as the cause of the flow-induced noise in hydraulic counterbalance valves through numerical and experimental studies [7]. Baines and Mitsudera [8] pointed out that the shear layer instability is mainly caused by the wave interaction mechanism rather than the Kelvin–Helmholtz instability in the inviscid shear flows. Li et al. [9] measured self-excited high-frequency pressure oscillations and noise in a hydraulic jet pipe servo valve. Their results showed that the high-frequency pressure oscillations are generated by the shear layer instability, and the higher supply pressure will increase the pressure oscillations. Lu et al. [10] noted that the vortex street flow in the nozzle flapper channel will produce pressure oscillations, and the frequency of oscillation decreases with the increase of inlet velocity and increases with the distance between the nozzle flapper. Smith and Luloff [11] indicated that the noise is caused by vortex shedding over the valve seat cavity, coupled with an acoustic resonance across the throat of the valve. Janzen et al. [12] confirmed that the noise in the gate valves is caused by the vortex shedding that is related to the angle of the chamfer next to the cavity. Liu and Tan [13] pointed out that the oscillation of the tip leakage vortex in the pump will cause flow instability in the primary tip leakage vortex trajectory. Zhang et al. [14] researched the noise generation mechanism of the ball valve by analyzing the contours of pressure, velocity, and sound pressure level. The numerical and experimental results indicated that the flow noise is caused by Reynolds stress in the jet transition region and the eddy current. Furthermore, the experimental results showed that the noise in the ball valve can be suppressed by installing transverse spool plates and orifice plates. Yi et al. [15] put forward that the high-frequency noise in hydraulic poppet valves is produced by Helmholtz resonance. Ma et al. [16] made a detailed study of a flow-excited Helmholtz resonator. The Helmholtz resonator has its own natural frequency, and some studies have given theoretical and experimental solutions [17, 18]. In our study, we mainly focus on the flow-induced noise in the prestage of DJV based on the Helmholtz resonator.As mentioned above, different types of noise sources cause flow-induced noise in the flow field, including cavitation, shear layer instability, pressure oscillation, vortex, and Helmholtz resonance. With the rapid development of computing technology, numerical simulation has become a reliable and efficient method to study the flow field characteristics of the DJV and the acoustic field. Compared with the direct numerical simulation (DNS) and Reynolds-averaged Navier-Stokes (RANS) model, the LES is considered to be the most promising numerical method to study the flow characteristics [19]. Using the LES method, we can obtain the velocity contours evolution [10] and the development of cavitation [6, 20]. Especially, the pressure pulsation at key points in the flow field can be used to analyze the vibration and noise characteristics. However, it is not comprehensive to obtain the acoustic noise through the frequencies of the pressure pulsations. The computational aeroacoustics (CAA) theories are helpful for further study of the flow field noise. Liu et al. [21] proposed a hybrid method that combined the detached eddy simulation (DES) with Lighthill’s acoustic analogy to simulate flow-induced noise in pipes and found that the noise source is near the opening of the cavity. Nie et al. [22] used LES and Lighthill’s acoustic analogy to study the flow noise characteristics of a control valve with different openings. As the valve opening decreases, the whole SPL of the valve becomes strong and exhibits dipole characteristics. Zhang et al. [14] built a cavity model to verify LES and Lighthill’s acoustic analogy hybrid method before computing the flow-induced noise of a three-dimensional pipeline. Wang et al. [23] also used the LES and Lighthill acoustic analogy to investigate the hydrodynamic noise of an underwater vehicle. They also paid attention to the distribution of the main energy of the flow-induced noise in the shell. Wei et al. [24] used the Ffowcs Williams and Hawkings model based on Lighthill’s acoustic analogy to compute the flow-induced noise in high-pressure-reducing valves. To date, the LES and Lighthill’s acoustic analogy method has not been used to analyze the flow-induced noise in DJV.In this paper, the structure and work principle of DJV are explained. Then, a numerical simulation of three-dimensional flow characteristics and flow-induced noise is presented. A method is introduced to combine LES and Lighthill’s acoustic analogy theory to study flow-induced noise. The pressure characteristic experiment is used to verify the CFD method, and the results of the simulation agree well with the experimental results. Following this, the numerical study was carried out to obtain the flow characteristics and analyze the flow-induced noise in DJV. Finally, the oscillation characteristics of the prestage flow field are studied to reveal its acoustic mechanism.The major contributions of this paper are summarized as follows:(1)
A three-dimensional numerical model of DJV is carried out to analyze the distribution of pressure, velocity, and vorticity, as well as sound pressure distribution.(2)
The source of flow-induced noise in DJV is studied numerically based on LES and Lighthill’s acoustic theory. According to the frequency spectrums and radiation analysis, the basis of flow-induced noise is dipole noise with wide middle-high frequency characteristics.(3)
An oscillation cavity model of DJV based on the Helmholtz oscillator is built to analyze the jet oscillation characteristics. It is found that the flow-induced noise is caused by self-excited oscillation and vortex with the frequencies of 1100 Hz and 2501 Hz.


## 2. Structure and Work Principle of DJV

As one of the most important power-control components in the hydraulic system, DJV can convert electrical signals to high-power hydraulic signals, which has excellent performance, such as fast dynamic response, high control accuracy, small hysteresis, good linearity of physical gain, and so on. DJV is a two-stage magnified electrohydraulic servo valve, and its structure is mainly composed of torque motor component, prestage, and spool valve, as shown in Figure1. Among them, the prestage is the key component of the DJV, which is composed of the jet pan and the deflector [25]. Two receivers are connected to both sides of the spool valve to realize its motion control.Figure 1
Structure of the DJV.As shown in Figure2, hydraulic oil is diverted from the deflector to the two receivers by the pressure inlet jet. When the deflector is in the middle, the spool valve is in the static position and the recovery pressure on both sides of the spool valve is equal. But when the deflector starts to move following the action of the torque motor assembly, the pressure in the receivers will no longer be equal, resulting in a differential pressure on both sides of the spool valve and triggering its movement. The movement will produce a feedback torque on the armature assembly. When the feedback torque is equal to the electromagnetic torque generated by the input control current, the spool valve will stay in a static position again, resulting in a constant output flow. It can be seen that adjusting the control current can achieve proportional control of the output flow rate of the servo valve [26, 27].Figure 2
Work principle of the DJV.


## 3. Numerical Simulation Model

### 3.1. LES Model

Solving the pulsation is the basis for calculating the flow-induced noise, so the oil flow characteristics in DJV are numerically studied, firstly. We did a large eddy two-phase flow simulation to get the pulsation and sound source information in the flow field of DJV. The governing equations of LES are obtained by filtering out the eddies whose scales are smaller than the filter width or grid spacing used in the computations. Thus, the governing equations can capture the evolution of large-scale vortices.The filter function is defined as(1)Gx,x′=1V,x∈v,0,x′∉v,where V is the volume of a computational cell. The flow belongs to incompressible flow, and the filtered Navier–Stokes equations can be expressed as follows:(2)∂ρ∂t+∂∂xiρu¯i=0.Also,(3)∂∂tρu¯i+∂∂xjρu¯iu¯j=∂∂xjσij−∂p¯∂xi−∂τij∂xj,where ρ is the destiny of the oil, σij is the stress tensor because of molecular viscosity, and τij is the subgrid-scale stress (SGS) described as follows:(4)τij=ρuiuj¯−ρu¯iu¯j=13τkkδij−2μts¯ij,where μt is the subgrid-scale turbulent viscosity. s¯ij is the rate of strain tensor for the resolved scale defined by the following:(5)s¯ij=12∂u¯i∂xj+∂u¯j∂xi.In our numerical model, we use the Smagorinsky–Lilly model to simulate the subgrid-scale stress. In the Smagorinsky–Lilly model, the eddy-viscosity is modelled by the following:(6)μt=ρLs2s¯,where Ls is the mixing length of the subgrid scales and S¯=2s¯ijs¯ij. Ls can be expressed as follows:(7)Ls=minkd,CsΔ,where k is the von Karman constant, d is the distance to the closest wall, Δ is the local grid scale. Cs is the Smagorinsky constant, and its default value is 0.1 in ANSYS FLUENT.


### 3.2. Lighthill’s Acoustic Analogy Theory

The flow-induced noise in DJV can be solved by computational aeroacoustics based on Lighthill’s acoustic analogy. Lighthill’s acoustic analogy comes from the Navier–Stokes equations. The continuity and momentum equations can be written as follows:(8)∂ρ∂t+∂ρui∂xi=0,(9)ρ∂ui∂t+∂uiuj∂xj=−∂p∂xi+∂τij∂xi,where τij is the viscous stress tensor. Upon combining (8) and (9), we obtain the following:(10)∂ρui∂t=−∂∂xjρuiuj+δijp−τij.Upon adding and subtracting the termc02∂ρ/∂xi, (10) can be expressed as follows:(11)∂ρui∂t+c02∂ρ∂xi=−∂Tij∂xj,where C0 is the sound speed and Tij is Lighthill’s turbulence stress tensor, which can be written as follows:(12)Tij=ρuiuj+δijp−p0−c02ρ−ρ0−τij,where ρ0 and p0 are the atmospheric density and pressure, respectively. Differentiating the continuity (8) with respect to time, taking the divergence of (11), and subtracting the results lead to Lighthill’s acoustic analogy equation, which is as follows:(13)∂2ρ′∂t2−c02∂ρ′∂xi∂xi=−∂2Tij∂xi∂xj,where ρ′ is the acoustic density fluctuation, and ρ′=ρ−ρ0.


## 3.1. LES Model

Solving the pulsation is the basis for calculating the flow-induced noise, so the oil flow characteristics in DJV are numerically studied, firstly. We did a large eddy two-phase flow simulation to get the pulsation and sound source information in the flow field of DJV. The governing equations of LES are obtained by filtering out the eddies whose scales are smaller than the filter width or grid spacing used in the computations. Thus, the governing equations can capture the evolution of large-scale vortices.The filter function is defined as(1)Gx,x′=1V,x∈v,0,x′∉v,where V is the volume of a computational cell. The flow belongs to incompressible flow, and the filtered Navier–Stokes equations can be expressed as follows:(2)∂ρ∂t+∂∂xiρu¯i=0.Also,(3)∂∂tρu¯i+∂∂xjρu¯iu¯j=∂∂xjσij−∂p¯∂xi−∂τij∂xj,where ρ is the destiny of the oil, σij is the stress tensor because of molecular viscosity, and τij is the subgrid-scale stress (SGS) described as follows:(4)τij=ρuiuj¯−ρu¯iu¯j=13τkkδij−2μts¯ij,where μt is the subgrid-scale turbulent viscosity. s¯ij is the rate of strain tensor for the resolved scale defined by the following:(5)s¯ij=12∂u¯i∂xj+∂u¯j∂xi.In our numerical model, we use the Smagorinsky–Lilly model to simulate the subgrid-scale stress. In the Smagorinsky–Lilly model, the eddy-viscosity is modelled by the following:(6)μt=ρLs2s¯,where Ls is the mixing length of the subgrid scales and S¯=2s¯ijs¯ij. Ls can be expressed as follows:(7)Ls=minkd,CsΔ,where k is the von Karman constant, d is the distance to the closest wall, Δ is the local grid scale. Cs is the Smagorinsky constant, and its default value is 0.1 in ANSYS FLUENT.


## 3.2. Lighthill’s Acoustic Analogy Theory

The flow-induced noise in DJV can be solved by computational aeroacoustics based on Lighthill’s acoustic analogy. Lighthill’s acoustic analogy comes from the Navier–Stokes equations. The continuity and momentum equations can be written as follows:(8)∂ρ∂t+∂ρui∂xi=0,(9)ρ∂ui∂t+∂uiuj∂xj=−∂p∂xi+∂τij∂xi,where τij is the viscous stress tensor. Upon combining (8) and (9), we obtain the following:(10)∂ρui∂t=−∂∂xjρuiuj+δijp−τij.Upon adding and subtracting the termc02∂ρ/∂xi, (10) can be expressed as follows:(11)∂ρui∂t+c02∂ρ∂xi=−∂Tij∂xj,where C0 is the sound speed and Tij is Lighthill’s turbulence stress tensor, which can be written as follows:(12)Tij=ρuiuj+δijp−p0−c02ρ−ρ0−τij,where ρ0 and p0 are the atmospheric density and pressure, respectively. Differentiating the continuity (8) with respect to time, taking the divergence of (11), and subtracting the results lead to Lighthill’s acoustic analogy equation, which is as follows:(13)∂2ρ′∂t2−c02∂ρ′∂xi∂xi=−∂2Tij∂xi∂xj,where ρ′ is the acoustic density fluctuation, and ρ′=ρ−ρ0.


## 4. Coupling of Flow and Acoustic Simulations

The acoustic mechanism of the prestage is investigated using a hybrid simulation method combining CFD and CAA theories. The RNG k-ɛ model and LES in ANSYS FLUENT are used to perform steady and unsteady simulations. The acoustic simulation software ACTRAN is used to compute the flow-induced noise in DJV based on Lighthill’s acoustic analogy. The transient solution results in CFD are set as CAA sources in the acoustic simulation to analyze the flow-induced noise of DJV.


### 4.1. Numerical Model

The DJV numerical model is built based on the channel structure, as shown in Figure3, and the boundary conditions mainly include pressure inlet, pressure outlet, and walls. The pressures of the inlet and outlet are set as 21 MPa and 3.1 MPa, respectively, and the rest of the boundary conditions are nonslip walls. The effect of gravity is neglected along with the energy exchange in the flow field. Aircraft hydraulic oil is used with a density of 850 kg/m3 and viscosity of 0.01026 Pa·s. The RNG k-ɛ model is adopted to perform the steady-state numerical simulation with a number of time steps of 800, and the LES model is used to perform the transient simulation with a time step size of 0.00001 s and time steps of 2000. Meanwhile, the mixture model is selected to do the two-phase flow simulation. The liquid phase is hydraulic oil, the vapor phase is oil-vapor with a density of 3 kg/m3, and the vaporization pressure is 3540 Pa. Then, the convergence of simulation results is verified by monitoring the mass flow rate of the inlet and outlet.Figure 3
Numerical calculation model of the prestage.Because of the complex and tiny structure of the prestage, the front processor of ANSYS Fluent Meshing is employed for meshing. Meanwhile, the mesh refinement method is used in the jet core area to guarantee the accuracy of the calculation, as shown in Figure4. In addition, polyhedral meshing technology is adopted to accelerate the simulation speed.Figure 4
Mesh of the prestage.


### 4.2. Mesh Independence and Numerical Model Validation

It is necessary to perform the mesh independence validation before the numerical simulation. It can help us to select the proper mesh to get the simulation results efficiently. Table1 shows the detailed information of four mesh schemes.Table 1
Information of the mesh scheme.
Mesh modelMesh size (mm)Number of cellsMinimum orthogonal massMaximum orthogonal slopeMesh 1(0.006, 0.1)4613190.070.89Mesh 2(0.005, 0.1)14086670.060.79Mesh 3(0.005, 0.08)16968690.070.79Mesh 4(0.005, 0.06)22402910.060.79Mesh scheme 1 directly meshes the model with a small number of grids, and the pressure simulation result of the two receivers is small, which is quite different from the actual measured value of 6.2 MPa. Mesh scheme 2 densifies the deflector grid in the jet core area, and the receiver’s pressure increases close to the actual measured value. Mesh scheme 3 further refines the flow field grid, and the receiver pressure is consistent with the actual measured value. Mesh scheme 4 continues to densify the flow field grid in the core area, and it is found that the simulation results remain unchanged as shown in Figure5. Therefore, further increasing the mesh density will not affect the simulation results, however, it only increases the simulation calculation time. Considering the time and cost of simulation calculation, mesh scheme 3 is selected to complete the subsequent numerical calculation.Figure 5
Receiver pressure at different mesh sizes.To verify the effectiveness and accuracy of numerical simulation, an experiment is designed to measure the pressure of the prestage specially used for research. Figure6 is the schematic diagram of the test system. The pressure sensor is installed at the inlet and the bottom of the two receivers. The inlet pressure is set to 21 MPa, and the input current of the servo valve is set to zero. The pressure characteristics of the prestage under different deflector offsets are obtained by detecting the pressures of the inlet and the two receivers. The experimental device of the jet deflector mechanism is shown in Figure 7.Figure 6
Schematic diagram of the test system.Figure 7
Experimental device of the jet deflector mechanism.The electric actuator is used to drive the mechanical feedback device at the upper end of the armature, and the small displacement is measured by a laser sensor. The displacement of the deflector can be calculated based on the parameters of the deflector jet mechanism. In the process of offsetting, the pressures of the two receivers are measured. The pressures of two receivers under different deflector offsets are shown in Table2.Table 2
Receiver pressures under different deflector offsets.
Displacement (mm)Numerical resultsExperimental resultsLeft receiver (MPa)Right receiver (MPa)Left receiver (MPa)Right receiver (MPa)0.062.369.872.59.60.053.009.313.09.10.043.398.683.58.50.033.938.034.17.90.024.717.594.97.50.015.336.825.56.706.176.176.26.2−0.016.885.366.85.5−0.027.624.747.54.9−0.038.103.997.84.1−0.048.753.418.53.5−0.059.433.139.33.1−0.069.962.449.62.40.062.369.872.59.6The curves in Figure8 depict the load pressure-offset relationship, which are plotted using these pressure data. The simulation results are shown to be in agreement with the experimental results.Figure 8
Load pressure-offset curves.


### 4.3. ACC Numerical Model

The acoustic simulation model with three domains is built for acoustic computation: acoustic source domain, propagation domain, and infinite element surface (see Figure9). The Lighthill volume boundary condition is used for an aeroacoustic source of the DJV model and the source extraction comes from the LES results. Then, ICFD in ACTRAN is used to extract the acoustic sources by fast Fourier transform (FFT). Finally, the acoustic source is interpolated into the acoustic mesh to solve the acoustic domains by the integral method. To reduce the frequency leakage, the Hanning window is adopted to do the frequency domain conversion of the pressure fluctuation coefficient. The infinite element surface and propagation domain can be used to calculate the acoustic propagation and radiation from the acoustic source to the far-field. The infinite element surface and the propagation domain are defined as air, while the acoustic source domain is oil. In addition, three groups of polar points are, respectively, located in three coordinate planes, and the number of observation points in each group is 360. The distance from the observation points to the center of the DJV model is 200 mm.Figure 9
Computational acoustic model.


## 4.1. Numerical Model

The DJV numerical model is built based on the channel structure, as shown in Figure3, and the boundary conditions mainly include pressure inlet, pressure outlet, and walls. The pressures of the inlet and outlet are set as 21 MPa and 3.1 MPa, respectively, and the rest of the boundary conditions are nonslip walls. The effect of gravity is neglected along with the energy exchange in the flow field. Aircraft hydraulic oil is used with a density of 850 kg/m3 and viscosity of 0.01026 Pa·s. The RNG k-ɛ model is adopted to perform the steady-state numerical simulation with a number of time steps of 800, and the LES model is used to perform the transient simulation with a time step size of 0.00001 s and time steps of 2000. Meanwhile, the mixture model is selected to do the two-phase flow simulation. The liquid phase is hydraulic oil, the vapor phase is oil-vapor with a density of 3 kg/m3, and the vaporization pressure is 3540 Pa. Then, the convergence of simulation results is verified by monitoring the mass flow rate of the inlet and outlet.Figure 3
Numerical calculation model of the prestage.Because of the complex and tiny structure of the prestage, the front processor of ANSYS Fluent Meshing is employed for meshing. Meanwhile, the mesh refinement method is used in the jet core area to guarantee the accuracy of the calculation, as shown in Figure4. In addition, polyhedral meshing technology is adopted to accelerate the simulation speed.Figure 4
Mesh of the prestage.


## 4.2. Mesh Independence and Numerical Model Validation

It is necessary to perform the mesh independence validation before the numerical simulation. It can help us to select the proper mesh to get the simulation results efficiently. Table1 shows the detailed information of four mesh schemes.Table 1
Information of the mesh scheme.
Mesh modelMesh size (mm)Number of cellsMinimum orthogonal massMaximum orthogonal slopeMesh 1(0.006, 0.1)4613190.070.89Mesh 2(0.005, 0.1)14086670.060.79Mesh 3(0.005, 0.08)16968690.070.79Mesh 4(0.005, 0.06)22402910.060.79Mesh scheme 1 directly meshes the model with a small number of grids, and the pressure simulation result of the two receivers is small, which is quite different from the actual measured value of 6.2 MPa. Mesh scheme 2 densifies the deflector grid in the jet core area, and the receiver’s pressure increases close to the actual measured value. Mesh scheme 3 further refines the flow field grid, and the receiver pressure is consistent with the actual measured value. Mesh scheme 4 continues to densify the flow field grid in the core area, and it is found that the simulation results remain unchanged as shown in Figure5. Therefore, further increasing the mesh density will not affect the simulation results, however, it only increases the simulation calculation time. Considering the time and cost of simulation calculation, mesh scheme 3 is selected to complete the subsequent numerical calculation.Figure 5
Receiver pressure at different mesh sizes.To verify the effectiveness and accuracy of numerical simulation, an experiment is designed to measure the pressure of the prestage specially used for research. Figure6 is the schematic diagram of the test system. The pressure sensor is installed at the inlet and the bottom of the two receivers. The inlet pressure is set to 21 MPa, and the input current of the servo valve is set to zero. The pressure characteristics of the prestage under different deflector offsets are obtained by detecting the pressures of the inlet and the two receivers. The experimental device of the jet deflector mechanism is shown in Figure 7.Figure 6
Schematic diagram of the test system.Figure 7
Experimental device of the jet deflector mechanism.The electric actuator is used to drive the mechanical feedback device at the upper end of the armature, and the small displacement is measured by a laser sensor. The displacement of the deflector can be calculated based on the parameters of the deflector jet mechanism. In the process of offsetting, the pressures of the two receivers are measured. The pressures of two receivers under different deflector offsets are shown in Table2.Table 2
Receiver pressures under different deflector offsets.
Displacement (mm)Numerical resultsExperimental resultsLeft receiver (MPa)Right receiver (MPa)Left receiver (MPa)Right receiver (MPa)0.062.369.872.59.60.053.009.313.09.10.043.398.683.58.50.033.938.034.17.90.024.717.594.97.50.015.336.825.56.706.176.176.26.2−0.016.885.366.85.5−0.027.624.747.54.9−0.038.103.997.84.1−0.048.753.418.53.5−0.059.433.139.33.1−0.069.962.449.62.40.062.369.872.59.6The curves in Figure8 depict the load pressure-offset relationship, which are plotted using these pressure data. The simulation results are shown to be in agreement with the experimental results.Figure 8
Load pressure-offset curves.


## 4.3. ACC Numerical Model

The acoustic simulation model with three domains is built for acoustic computation: acoustic source domain, propagation domain, and infinite element surface (see Figure9). The Lighthill volume boundary condition is used for an aeroacoustic source of the DJV model and the source extraction comes from the LES results. Then, ICFD in ACTRAN is used to extract the acoustic sources by fast Fourier transform (FFT). Finally, the acoustic source is interpolated into the acoustic mesh to solve the acoustic domains by the integral method. To reduce the frequency leakage, the Hanning window is adopted to do the frequency domain conversion of the pressure fluctuation coefficient. The infinite element surface and propagation domain can be used to calculate the acoustic propagation and radiation from the acoustic source to the far-field. The infinite element surface and the propagation domain are defined as air, while the acoustic source domain is oil. In addition, three groups of polar points are, respectively, located in three coordinate planes, and the number of observation points in each group is 360. The distance from the observation points to the center of the DJV model is 200 mm.Figure 9
Computational acoustic model.


## 5. Results and Discussion

### 5.1. Flow Characteristics Analysis

Oil flows into the prestage from the pressure inlet, forming two jet processes [28]. The pressure and velocity distributions are shown in Figure 10. The inlet pressure energy is converted into kinetic energy, forming a high-speed jet with a velocity up to 190 m/s at the initial jet port. Low-pressure areas are formed in three symmetrical regions (see Figure 10(a)). When the oil flows out of the initial jet port at a high speed, low pressure occurs because of the boundary layer separation [29]. The jet shear layer continuously extends outward when the oil flows downstream along the axis. The oil impacts on the sidewalls of the deflector, and the phenomenon of oil reflux appears because of the jet reattaching effect. In the reflux region, two symmetric vortices are formed. Then, part of the oil continues to flow downstream along the V-shaped groove, forming a high-pressure area above the secondary jet port. Subsequently, the oil pressure energy is converted into kinetic energy at the secondary jet port, and the oil impacts on the wedge, forming an impact jet. The oil flows to both sides of the outlet after impacting on the wedge, forming two vortices on both sides of the secondary jet port.Figure 10
Pressure and velocity distributions. (a) Internal pressure contours. (b) Internal velocity contours.
(a)(b)Analyzing the vortex structure inside the prestage contributes to understanding the flow characteristics and the oscillation mechanism. The Q criterion [30] is used to obtain the characteristics of the vortex. Figure 11 shows the vorticity (Q = 2.0048e + 6 s−1) in the prestage at different moments, and t0 is the steady-state calculation time.Figure 11
Vortex evolution process in the prestage. (a)t = t0 + 0.1 ms, (b) t = t0 + 0.4 ms, (c) t = t0 + 0.7 ms, (d) t = t0 + 1 ms, (e) t = t0 + 1.3 ms, and (f) t = t0 + 1.6 ms.
(a)(b)(c)(d)(e)(f)The vorticity distribution inside the prestage is similar, and the vortices are mainly distributed in the impact area and the outlet of the secondary jet port. Meanwhile, the vortex ring generated in the initial jet shear layer is continuously developed along the jet direction and combined with the vortex generated after the impact. Thus, the main vortices are formed in the impact area and move up and down along the sidewall of the V-shaped groove. The vortices will converge and increase in the impact area with time. When approaching the downstream secondary jet port, the vortices are formed again at the secondary jet port. The main reason is that the boundary layer separation appears at the corner of the secondary jet port [31]. The disordered vortices generated in the two-jet process will excite the pressure oscillation.The unsteady flow in the prestage caused the pressure pulsation, and the pressure pulsation coefficient is used to describe the pressure pulsation degree. The pressure pulsation coefficient is defined as follows:(14)Cp=p−p¯0.5ρu2,where p is static pressure, p¯ is static pressure mean, and u is jet velocity.To analyze the frequency of the flow field oscillation, thex-z plane of the prestage is intercepted, and four monitoring points are set in the prestage (see Figure 12). According to the jet characteristics and vortices distribution, the points are arranged at two jet ports and vortices. Figure 13 is a time-domain curve of the pressure pulsation of each monitoring point. As shown in Figure 13, points 1 and 3 are both at the outlet of the jet port. Because of the higher jet velocity at the jet port, the effect of vortices and perturbations in the flow field is small, which results in small pressure pulsation. At monitoring point 2, the violent vortex is formed with the large pressure pulsation. Compared with point 2, the pressure pulsation of point 4 is small. It means that the vortex caused by boundary layer separation is weak. Thus, pressure pulsation occurs mainly in the impact area, and it acts as one of the predominant sources of flow-induced noise.Figure 12
Monitoring points located in the prestage.Figure 13
Pressure fluctuation coefficient at different monitoring points. (a) Initial jet port. (b) Vortex 1. (c) Secondary jet port. (d) Vortex 2.
(a)(b)(c)(d)


### 5.2. Flow-Induced Noise Analysis

According to spectrum characteristics, aerodynamic noise can be divided into low-frequency noise (20 Hz∼200 Hz), medium frequency noise (200 Hz∼2000 Hz), and high-frequency noise (above 2000 Hz). Figure14 shows the sound pressure contours of the x-z section of the prestage at different frequencies.Figure 14
Sound pressure contours at different frequencies. (a) 100 Hz. (b) 500 Hz. (c) 1000 Hz. (d) 2000 Hz. (e) 3000 Hz. (f) 4000 Hz.
(a)(b)(c)(d)(e)(f)The maximum sound pressures corresponding to 100 Hz, 500 Hz, 1000 Hz, 2000 Hz, 3000 Hz, and 4000 Hz are 188.6 dB, 186.8 dB, 186.3 dB, 184.8 dB, 171.1 dB, and 176.8 dB, respectively. The flow-induced noise is mainly distributed in the two jet areas. Low-frequency noise with a frequency of 100 Hz is mainly concentrated at the sidewall of the V-shaped groove. Similarly, the noise with the frequency of 500 Hz is also distributed near the sidewall, however, the sound pressure level decreases. The medium frequency noise of 1000 Hz is distributed widely not only inside the deflector but also on both sides of the secondary jet port. The high-frequency noise of 2000 Hz and the frequency above 2000 Hz are concentrated inside the V-shaped groove. Thus, the flow-induced noise of the prestage is mainly concentrated inside the V-shaped groove, and there is also medium frequency noise appears near the secondary jet port. Otherwise, we analyze the frequency spectrum of the four monitoring points, and the results are shown in Figure15.Figure 15
Frequency spectrums of P1, P2, P3, and P4.Figure15 shows the frequency spectrums of the four monitoring points in the flow field of the prestage. Compared with monitoring points 1, 3, and 4, monitoring point 2 at vortex 1 has higher amplitude sound pressure in high, medium, and low-frequency components. Combined with the contours of the sound pressure distribution, it is found that the low-frequency noise at point 2 comes from the wall voice caused by the impact between the oil and the sidewall of the V-shaped groove. The high-frequency noise that occurs only at point 2 is mainly concentrated in the V-shaped groove, which belongs to the vortex noise. Obvious medium frequency noise appears at the monitoring points 1, 2, and 4, and it is related to the two jet process, which is caused by self-excited oscillation from the jet instability.The 1/3-octave band curves of the four monitoring points were obtained using the Fourier transform method, as shown in Figure16. At points 1, 3, and 4, the variation trend of sound pressure at these monitoring points is basically consistent. The sound pressure distribution of monitoring point 2 in the V-shaped groove of DJV is the largest, mainly including broadband medium and high-frequency noise. Also, it can be seen that the frequency band gradually widens after the frequency of 500 Hz. Therefore, the flow-induced noise in DJV is mainly the continuous broadband noise with medium and high-frequency components.Figure 16
1/3 octave band curve of P1, P2, P3, and P4.Figure17 shows the directivity distribution of radiated noise in the flow field of the prestage. In the x-y plane of the sound field, the 100 Hz noise shows the dipole noise characteristics with double slots, and the 1000 Hz noise has the same dipole characteristics in the x-z and y-z planes. The noise radiation range and sound pressure of 1000 Hz and 3000 Hz in three plane directions are significantly higher than that of 100 Hz. Therefore, the noise radiated from the flow field is mainly medium and high-frequency noise with dipole characteristics, which is consistent with the main noise source in the flow field.Figure 17
Directional distribution of noise at three frequencies: 100 Hz, 1000 Hz, and 3000 Hz. (a)x-y plane. (b) x-z plane. (c) y-z plane.
(a)(b)(c)The experimental setup of the vibration and noise test is shown in Figure18. The prestage transparent model is an enlarged model based on similarity criterion, and the model is made of transparent plexiglass. Thus, it is convenient to observe the internal flow pattern of the flow field. The acceleration sensor that is used to measure the vibration is connected to the shell of the presatge transparent model. The noise analyzer is used to monitor the radiated noise. The relief valve is used to adjust the outlet pressure.Figure 18
Experimental setup of the vibration and noise test.The oscillation frequency of the prestage model is collected within 30 s. Then, the time domain data of the oscillation is converted into frequency domain data by FFT. As shown in Figure19, the prestage oscillation is mainly concentrated at a medium frequency of 1100 Hz and a high frequency of 2097 Hz.Figure 19
Oscillation characteristics of the prestage. (a) 0∼30 s frequency domain. (b) 0∼10 s frequency domain. (c) 10∼20 s frequency domain. (d) 20∼30 s frequency domain.
(a)(b)(c)(d)Three groups of experiments were carried out by the noise analyzer to monitor the radiated noise of the prestage flow field. Then, the average value of these tests is calculated. As shown in Figure20, the main radiated noise is the medium frequency noise with the frequency of 1000 Hz and the sound pressure of 76 dB.Figure 20
Sound pressure level by experiments.Acoustic simulation results were compared with the experimental results. Both simulation and experimental results show the oscillation frequency of the prestage are dominated by medium and high-frequency, and the radiated noise at the frequency of 1000 Hz has the highest sound pressure level. The simulation results agree well with the experimental results. However, the high-frequency components in the simulation are higher than those of the experiments. The difference is most likely because the experimental prestage model is enlarged, and the oscillation in the flow field cannot be measured directly by the experiment.


### 5.3. Acoustic Mechanism

To further study the sound generation mechanism in the prestage, we build the oscillation cavity model of the prestage based on the Helmholtz oscillator. The flow field in the prestage is divided into three cavities: acceleration cavity, oscillation cavity 1, and oscillation cavity 2 (see Figure21). The oil flows into the oscillation cavity1 at a high speed after acceleration in the acceleration cavity, forming a turbulent jet. When the oil flows out of the secondary jet port, the high-speed jet will appear again. Then, the oil impacts on the wedge, forming a kind of impact jet. After the oil impacts on the wedge, it flows out of the oscillation cavity 2 from the outlets on both sides.Figure 21
Prestage oscillation cavity based on the Helmholtz oscillator model.Monitoring points are set in different areas of the cavity to analyze oscillation characteristics (see Figure21). P5 is located at the center of the acceleration cavity, P6 and P8 are located at the inlet and outlet of oscillation cavity 1, respectively, and P7 is located in the symmetrical vortex center of the jet core area in oscillation cavity 1. P9 is located at the secondary jet axis, P10 in the oscillation cavity 2 is located at the wedge, P11 is located at vortex 2, P12 is located at the arc corner of the receiver, and P13 is located at the outlet direction. Frequency spectrum analysis is carried out for the monitoring points in each area, and the results are shown in Figures 22 and 23. Figure 22 is the frequency spectrum diagram of each monitoring point in the acceleration cavity and oscillation cavity 1, and Figure 23 is the frequency spectrum diagram of each monitoring point in oscillation cavity 2.Figure 22
Frequency spectrums of P5, P6, P7, and P8.Figure 23
Frequency spectrums of P9, P10, P11, P12, and P13.When the oil enters the prestage flow field from the pressure inlet, the oil itself has an internal perturbation. It can be seen that the perturbation is weak in P5 with small oscillation amplitude in the acceleration cavity. Then, jet oil emerges from the initial jet port with a sudden area enlargement at the port as a result of the sudden changes of pressure and stress distribution in the jet, and the perturbation will be generated at the initial jet port. In oscillation cavity 1, the velocity of the jet core area is higher than that of the environmental fluid, forming a typical shear jet [32]. The interaction of the jet and fluid in the cavity combined with the perturbation will lead to the formation of small continuous vorticities in the jet shear layer (see Figure 11). These vortices interact with the surrounding fluid and move downstream at a velocity smaller than that of the jet. Then, the jet shear layer containing small vorticities collides on the V-shaped groove and forms acoustic waves and pressure pulsation (see Figure 13(b)). Because of the influence of the V-shaped groove, these disturbance waves will be reflected and move upstream to the initial jet port, where the initial perturbations formed. The resonance is formed in oscillation cavity 1, if the reflection wave frequency matches the initial perturbations’ frequency, resulting in a self-excited oscillation and the formation of a large number of vortices [33]. Thus, these vortices merge into large-scale coherent structures, causing stronger disturbance waves. Therewith, the generation, growth, motion, and collapse of these large-scale vortices will lead to a strong pulsating pressure acting on the jet periodically. Coupled with the jet instability and interactions of the jet and the environmental fluid, the self-excited oscillation jet will be formed, and the oscillation phenomenon will form a closed loop in the oscillation cavity [34–36].It can be seen from Figure22 that the pressure oscillation amplitude of the oil entering the flow field is low in the acceleration cavity (P5) as the flow is steady and has not formed a jet yet. When the oil flows out of the initial jet port, there will be an initial vorticity disturbance. The amplitude of these disturbances will gradually increase as the jet flows downstream. Then, the jet impacts the sidewalls of the V-shaped groove and the sound frequency, and the disturbance wave propagates upstream in the impact area, inducing new vorticity disturbance. Monitoring point 7 has large amplitude oscillation in the medium frequency and high-frequency components, respectively. The medium frequency is about 1100 Hz, which is consistent with the disturbance frequency at the initial jet port, and it belongs to the noise caused by the self-excited disturbance. Compared with other monitoring points, the large amplitude, which is only generated at monitoring point 7, belongs to vortex noise. When the oil enters the outlet of oscillation cavity 1, a high-pressure area is formed without violent self-excited oscillation. In oscillation cavity 2 (see Figure 23), the impact time between the oil and the wedge is short, and the pressure energy generated after the impact will be consumed by the fluid flowing to the outlet direction on both sides of the wedge without forming a high-amplitude oscillation. However, the higher amplitude oscillations are generated in vortex 2 (P10) and at the corner of the receivers (P11), caused by boundary layer separation. Finally, the oil flows out of the outlet with a small oscillation amplitude because the flow tends to be stable with a lower velocity at the outlet. Therefore, the flow field noise is mainly from the medium frequency jet noise near 1100 Hz caused by self-excited oscillation and the 2501 Hz high-frequency noise caused by vortices.By monitoring the sound pressure amplitudes in different regions of the prestage, it can be found that there is medium frequency noise with an amplitude of 1100 Hz in the oscillation cavities 1 and 2 because the jet process in oscillation cavities 1 and 2 is similar to the same size of the two jet nozzles (d0≈d1), and the two jet processes have the similar initial velocity according to the Bernoulli energy equation. Therefore, the 1100 Hz intermediate frequency noise in the flow field is mainly caused by jet instability, while the 2501 Hz high-frequency noise that only appears at P7 is caused by the vortices generated upstream after a jet impact belongs to eddy current noise. Furthermore, it is found that the noise amplitude decreases obviously in the low-speed areas (P8, P10, and P13). Thus, we can conclude that the jet velocity is the key factor affecting the flow-induced noise amplitude under the condition of consistent jet flow.


## 5.1. Flow Characteristics Analysis

Oil flows into the prestage from the pressure inlet, forming two jet processes [28]. The pressure and velocity distributions are shown in Figure 10. The inlet pressure energy is converted into kinetic energy, forming a high-speed jet with a velocity up to 190 m/s at the initial jet port. Low-pressure areas are formed in three symmetrical regions (see Figure 10(a)). When the oil flows out of the initial jet port at a high speed, low pressure occurs because of the boundary layer separation [29]. The jet shear layer continuously extends outward when the oil flows downstream along the axis. The oil impacts on the sidewalls of the deflector, and the phenomenon of oil reflux appears because of the jet reattaching effect. In the reflux region, two symmetric vortices are formed. Then, part of the oil continues to flow downstream along the V-shaped groove, forming a high-pressure area above the secondary jet port. Subsequently, the oil pressure energy is converted into kinetic energy at the secondary jet port, and the oil impacts on the wedge, forming an impact jet. The oil flows to both sides of the outlet after impacting on the wedge, forming two vortices on both sides of the secondary jet port.Figure 10
Pressure and velocity distributions. (a) Internal pressure contours. (b) Internal velocity contours.
(a)(b)Analyzing the vortex structure inside the prestage contributes to understanding the flow characteristics and the oscillation mechanism. The Q criterion [30] is used to obtain the characteristics of the vortex. Figure 11 shows the vorticity (Q = 2.0048e + 6 s−1) in the prestage at different moments, and t0 is the steady-state calculation time.Figure 11
Vortex evolution process in the prestage. (a)t = t0 + 0.1 ms, (b) t = t0 + 0.4 ms, (c) t = t0 + 0.7 ms, (d) t = t0 + 1 ms, (e) t = t0 + 1.3 ms, and (f) t = t0 + 1.6 ms.
(a)(b)(c)(d)(e)(f)The vorticity distribution inside the prestage is similar, and the vortices are mainly distributed in the impact area and the outlet of the secondary jet port. Meanwhile, the vortex ring generated in the initial jet shear layer is continuously developed along the jet direction and combined with the vortex generated after the impact. Thus, the main vortices are formed in the impact area and move up and down along the sidewall of the V-shaped groove. The vortices will converge and increase in the impact area with time. When approaching the downstream secondary jet port, the vortices are formed again at the secondary jet port. The main reason is that the boundary layer separation appears at the corner of the secondary jet port [31]. The disordered vortices generated in the two-jet process will excite the pressure oscillation.The unsteady flow in the prestage caused the pressure pulsation, and the pressure pulsation coefficient is used to describe the pressure pulsation degree. The pressure pulsation coefficient is defined as follows:(14)Cp=p−p¯0.5ρu2,where p is static pressure, p¯ is static pressure mean, and u is jet velocity.To analyze the frequency of the flow field oscillation, thex-z plane of the prestage is intercepted, and four monitoring points are set in the prestage (see Figure 12). According to the jet characteristics and vortices distribution, the points are arranged at two jet ports and vortices. Figure 13 is a time-domain curve of the pressure pulsation of each monitoring point. As shown in Figure 13, points 1 and 3 are both at the outlet of the jet port. Because of the higher jet velocity at the jet port, the effect of vortices and perturbations in the flow field is small, which results in small pressure pulsation. At monitoring point 2, the violent vortex is formed with the large pressure pulsation. Compared with point 2, the pressure pulsation of point 4 is small. It means that the vortex caused by boundary layer separation is weak. Thus, pressure pulsation occurs mainly in the impact area, and it acts as one of the predominant sources of flow-induced noise.Figure 12
Monitoring points located in the prestage.Figure 13
Pressure fluctuation coefficient at different monitoring points. (a) Initial jet port. (b) Vortex 1. (c) Secondary jet port. (d) Vortex 2.
(a)(b)(c)(d)


## 5.2. Flow-Induced Noise Analysis

According to spectrum characteristics, aerodynamic noise can be divided into low-frequency noise (20 Hz∼200 Hz), medium frequency noise (200 Hz∼2000 Hz), and high-frequency noise (above 2000 Hz). Figure14 shows the sound pressure contours of the x-z section of the prestage at different frequencies.Figure 14
Sound pressure contours at different frequencies. (a) 100 Hz. (b) 500 Hz. (c) 1000 Hz. (d) 2000 Hz. (e) 3000 Hz. (f) 4000 Hz.
(a)(b)(c)(d)(e)(f)The maximum sound pressures corresponding to 100 Hz, 500 Hz, 1000 Hz, 2000 Hz, 3000 Hz, and 4000 Hz are 188.6 dB, 186.8 dB, 186.3 dB, 184.8 dB, 171.1 dB, and 176.8 dB, respectively. The flow-induced noise is mainly distributed in the two jet areas. Low-frequency noise with a frequency of 100 Hz is mainly concentrated at the sidewall of the V-shaped groove. Similarly, the noise with the frequency of 500 Hz is also distributed near the sidewall, however, the sound pressure level decreases. The medium frequency noise of 1000 Hz is distributed widely not only inside the deflector but also on both sides of the secondary jet port. The high-frequency noise of 2000 Hz and the frequency above 2000 Hz are concentrated inside the V-shaped groove. Thus, the flow-induced noise of the prestage is mainly concentrated inside the V-shaped groove, and there is also medium frequency noise appears near the secondary jet port. Otherwise, we analyze the frequency spectrum of the four monitoring points, and the results are shown in Figure15.Figure 15
Frequency spectrums of P1, P2, P3, and P4.Figure15 shows the frequency spectrums of the four monitoring points in the flow field of the prestage. Compared with monitoring points 1, 3, and 4, monitoring point 2 at vortex 1 has higher amplitude sound pressure in high, medium, and low-frequency components. Combined with the contours of the sound pressure distribution, it is found that the low-frequency noise at point 2 comes from the wall voice caused by the impact between the oil and the sidewall of the V-shaped groove. The high-frequency noise that occurs only at point 2 is mainly concentrated in the V-shaped groove, which belongs to the vortex noise. Obvious medium frequency noise appears at the monitoring points 1, 2, and 4, and it is related to the two jet process, which is caused by self-excited oscillation from the jet instability.The 1/3-octave band curves of the four monitoring points were obtained using the Fourier transform method, as shown in Figure16. At points 1, 3, and 4, the variation trend of sound pressure at these monitoring points is basically consistent. The sound pressure distribution of monitoring point 2 in the V-shaped groove of DJV is the largest, mainly including broadband medium and high-frequency noise. Also, it can be seen that the frequency band gradually widens after the frequency of 500 Hz. Therefore, the flow-induced noise in DJV is mainly the continuous broadband noise with medium and high-frequency components.Figure 16
1/3 octave band curve of P1, P2, P3, and P4.Figure17 shows the directivity distribution of radiated noise in the flow field of the prestage. In the x-y plane of the sound field, the 100 Hz noise shows the dipole noise characteristics with double slots, and the 1000 Hz noise has the same dipole characteristics in the x-z and y-z planes. The noise radiation range and sound pressure of 1000 Hz and 3000 Hz in three plane directions are significantly higher than that of 100 Hz. Therefore, the noise radiated from the flow field is mainly medium and high-frequency noise with dipole characteristics, which is consistent with the main noise source in the flow field.Figure 17
Directional distribution of noise at three frequencies: 100 Hz, 1000 Hz, and 3000 Hz. (a)x-y plane. (b) x-z plane. (c) y-z plane.
(a)(b)(c)The experimental setup of the vibration and noise test is shown in Figure18. The prestage transparent model is an enlarged model based on similarity criterion, and the model is made of transparent plexiglass. Thus, it is convenient to observe the internal flow pattern of the flow field. The acceleration sensor that is used to measure the vibration is connected to the shell of the presatge transparent model. The noise analyzer is used to monitor the radiated noise. The relief valve is used to adjust the outlet pressure.Figure 18
Experimental setup of the vibration and noise test.The oscillation frequency of the prestage model is collected within 30 s. Then, the time domain data of the oscillation is converted into frequency domain data by FFT. As shown in Figure19, the prestage oscillation is mainly concentrated at a medium frequency of 1100 Hz and a high frequency of 2097 Hz.Figure 19
Oscillation characteristics of the prestage. (a) 0∼30 s frequency domain. (b) 0∼10 s frequency domain. (c) 10∼20 s frequency domain. (d) 20∼30 s frequency domain.
(a)(b)(c)(d)Three groups of experiments were carried out by the noise analyzer to monitor the radiated noise of the prestage flow field. Then, the average value of these tests is calculated. As shown in Figure20, the main radiated noise is the medium frequency noise with the frequency of 1000 Hz and the sound pressure of 76 dB.Figure 20
Sound pressure level by experiments.Acoustic simulation results were compared with the experimental results. Both simulation and experimental results show the oscillation frequency of the prestage are dominated by medium and high-frequency, and the radiated noise at the frequency of 1000 Hz has the highest sound pressure level. The simulation results agree well with the experimental results. However, the high-frequency components in the simulation are higher than those of the experiments. The difference is most likely because the experimental prestage model is enlarged, and the oscillation in the flow field cannot be measured directly by the experiment.


## 5.3. Acoustic Mechanism

To further study the sound generation mechanism in the prestage, we build the oscillation cavity model of the prestage based on the Helmholtz oscillator. The flow field in the prestage is divided into three cavities: acceleration cavity, oscillation cavity 1, and oscillation cavity 2 (see Figure21). The oil flows into the oscillation cavity1 at a high speed after acceleration in the acceleration cavity, forming a turbulent jet. When the oil flows out of the secondary jet port, the high-speed jet will appear again. Then, the oil impacts on the wedge, forming a kind of impact jet. After the oil impacts on the wedge, it flows out of the oscillation cavity 2 from the outlets on both sides.Figure 21
Prestage oscillation cavity based on the Helmholtz oscillator model.Monitoring points are set in different areas of the cavity to analyze oscillation characteristics (see Figure21). P5 is located at the center of the acceleration cavity, P6 and P8 are located at the inlet and outlet of oscillation cavity 1, respectively, and P7 is located in the symmetrical vortex center of the jet core area in oscillation cavity 1. P9 is located at the secondary jet axis, P10 in the oscillation cavity 2 is located at the wedge, P11 is located at vortex 2, P12 is located at the arc corner of the receiver, and P13 is located at the outlet direction. Frequency spectrum analysis is carried out for the monitoring points in each area, and the results are shown in Figures 22 and 23. Figure 22 is the frequency spectrum diagram of each monitoring point in the acceleration cavity and oscillation cavity 1, and Figure 23 is the frequency spectrum diagram of each monitoring point in oscillation cavity 2.Figure 22
Frequency spectrums of P5, P6, P7, and P8.Figure 23
Frequency spectrums of P9, P10, P11, P12, and P13.When the oil enters the prestage flow field from the pressure inlet, the oil itself has an internal perturbation. It can be seen that the perturbation is weak in P5 with small oscillation amplitude in the acceleration cavity. Then, jet oil emerges from the initial jet port with a sudden area enlargement at the port as a result of the sudden changes of pressure and stress distribution in the jet, and the perturbation will be generated at the initial jet port. In oscillation cavity 1, the velocity of the jet core area is higher than that of the environmental fluid, forming a typical shear jet [32]. The interaction of the jet and fluid in the cavity combined with the perturbation will lead to the formation of small continuous vorticities in the jet shear layer (see Figure 11). These vortices interact with the surrounding fluid and move downstream at a velocity smaller than that of the jet. Then, the jet shear layer containing small vorticities collides on the V-shaped groove and forms acoustic waves and pressure pulsation (see Figure 13(b)). Because of the influence of the V-shaped groove, these disturbance waves will be reflected and move upstream to the initial jet port, where the initial perturbations formed. The resonance is formed in oscillation cavity 1, if the reflection wave frequency matches the initial perturbations’ frequency, resulting in a self-excited oscillation and the formation of a large number of vortices [33]. Thus, these vortices merge into large-scale coherent structures, causing stronger disturbance waves. Therewith, the generation, growth, motion, and collapse of these large-scale vortices will lead to a strong pulsating pressure acting on the jet periodically. Coupled with the jet instability and interactions of the jet and the environmental fluid, the self-excited oscillation jet will be formed, and the oscillation phenomenon will form a closed loop in the oscillation cavity [34–36].It can be seen from Figure22 that the pressure oscillation amplitude of the oil entering the flow field is low in the acceleration cavity (P5) as the flow is steady and has not formed a jet yet. When the oil flows out of the initial jet port, there will be an initial vorticity disturbance. The amplitude of these disturbances will gradually increase as the jet flows downstream. Then, the jet impacts the sidewalls of the V-shaped groove and the sound frequency, and the disturbance wave propagates upstream in the impact area, inducing new vorticity disturbance. Monitoring point 7 has large amplitude oscillation in the medium frequency and high-frequency components, respectively. The medium frequency is about 1100 Hz, which is consistent with the disturbance frequency at the initial jet port, and it belongs to the noise caused by the self-excited disturbance. Compared with other monitoring points, the large amplitude, which is only generated at monitoring point 7, belongs to vortex noise. When the oil enters the outlet of oscillation cavity 1, a high-pressure area is formed without violent self-excited oscillation. In oscillation cavity 2 (see Figure 23), the impact time between the oil and the wedge is short, and the pressure energy generated after the impact will be consumed by the fluid flowing to the outlet direction on both sides of the wedge without forming a high-amplitude oscillation. However, the higher amplitude oscillations are generated in vortex 2 (P10) and at the corner of the receivers (P11), caused by boundary layer separation. Finally, the oil flows out of the outlet with a small oscillation amplitude because the flow tends to be stable with a lower velocity at the outlet. Therefore, the flow field noise is mainly from the medium frequency jet noise near 1100 Hz caused by self-excited oscillation and the 2501 Hz high-frequency noise caused by vortices.By monitoring the sound pressure amplitudes in different regions of the prestage, it can be found that there is medium frequency noise with an amplitude of 1100 Hz in the oscillation cavities 1 and 2 because the jet process in oscillation cavities 1 and 2 is similar to the same size of the two jet nozzles (d0≈d1), and the two jet processes have the similar initial velocity according to the Bernoulli energy equation. Therefore, the 1100 Hz intermediate frequency noise in the flow field is mainly caused by jet instability, while the 2501 Hz high-frequency noise that only appears at P7 is caused by the vortices generated upstream after a jet impact belongs to eddy current noise. Furthermore, it is found that the noise amplitude decreases obviously in the low-speed areas (P8, P10, and P13). Thus, we can conclude that the jet velocity is the key factor affecting the flow-induced noise amplitude under the condition of consistent jet flow.


## 6. Conclusions

In this paper, we numerically studied flow-induced noise in the prestage of DJV using LES and Lighthill’s acoustic analogy hybrid method to reveal the acoustic mechanism. Conclusions were drawn as follows:(1)
Unlike the common cavitation noise in the electrohydraulic servo valve, the noise of the prestage flow field of DJV is mainly composed of 1100 Hz jet noise and 2501 Hz high-frequency vortex noise. Meanwhile, the noise radiated from the prestage is a continuous dipole noise dominated by medium frequency components.(2)
The jet noise is caused by the combination of the initial jet perturbations and the interactions of the jet and fluids in the cavity, while the high-frequency and large-amplitude vortex noise is caused by the large-scale vortex, which is a collection of vortices after the impact between initial jet and deflector.(3)
To avoid the intense self-excited oscillating noise generated by the prestage cavity resonance induced by the prestage flow field oscillation, the analysis of the flow field noise provides a theoretical basis for the suppression of the self-excited noise, and the natural frequency of the prestage feedback rod should not be consistent with that of the flow field oscillation during the design process.



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*Source: 8379245-2022-03-22.xml*