A prediction method for the background noise of a low-speed open wind tunnel

Abstract

The present invention discloses a method for predicting the background noise of a low-speed open wind tunnel, which relates to the field of aerodynamic noise research. The method includes: Step 1: Obtain the spectral characteristics and frequencies of the turbulent pulsations in the wind tunnel inflow, and obtain the intensity and frequencies of the vortex waves based on the spectral characteristics and frequencies of the turbulent pulsations in the wind tunnel inflow; Step 2: Obtain the shear layer thickness of the core test section of the wind tunnel, and obtain the vortex core radius of the vortices based on the shear layer thickness of the core test section of the wind tunnel; Step 3: Calculate the vortex wave propagation speed, vortex convection speed and vortex intensity based on the wind tunnel inflow velocity; Step 4: Perform numerical calculations based on the data obtained in Steps 1 to 3 to obtain the prediction result of the background noise of the low-speed open wind tunnel; wherein, the governing equation used in the numerical calculation in Step 4 is the improved governing equation with the velocity gradient term ignored. This method can accurately predict the aerodynamic noise in the complex flow dominated by vortices in engineering practice.

Description

Technical Field

[0001] The present invention relates to the field of aerodynamic noise research, and in particular to a method for predicting background noise of a low-speed open wind tunnel. Background Art

[0002] The regions where aerodynamic noise is generated and propagated can be divided into the near field and the far field. The far field is where sound waves propagate linearly. In this region, the flow and acoustic fields are decoupled, and linear propagation characteristics such as sound wave refraction and scattering can be directly obtained by solving the linearized Euler equations, provided the background flow field is known in advance. The near field is where aerodynamic noise is generated nonlinearly. In this region, the acoustic field and the flow field are strongly coupled. As part of the flow, the generation of sound waves, along with the strongly nonlinear and unsteady flow field motion, is governed by the compressible Navier-Stokes equations. Nonlinear processes in the near field generate not only sound waves but also vortex waves. In the far field, the only disturbing component in the flow is sound waves. For most aeroacoustic problems, there is a transition region between the near and far fields where vortices dominate. In this region, the physical process of vortex wave scattering and sound generation occurs, which is widely present in aerospace engineering. For example, in a turbofan engine, vortex waves generated in the upstream fan wake scatter in the downstream shear layer; in counter-rotating propeller flow, vortex waves in the upstream blade wake interact with the downstream blade tip vortex, generating scattering sound. The physical process of vortex wave scattering is coupled with the nonlinear generation of near-field noise and the far-field sound propagation process, serving as a bridge between the generation and propagation of noise. To further understand the mechanical mechanisms of noise generation and propagation, it is necessary to deeply study the physical process of vortex wave scattering in the vortex-dominated region between the near and far fields.

[0003] However, the existing numerical models of aerodynamic self-noise only explain the mechanism by which the vortex's own motion in low Mach number flow generates noise, but do not clearly give the process by which vortex waves scatter and generate sound in vortex flow, which hinders further quantitative research on the vortex wave scattering and generating sound process using numerical models. As a result, it is impossible to accurately predict the aerodynamic noise in complex flows dominated by vortices in actual engineering. For example, the traditional low-speed open wind tunnel background noise prediction method only explains the mechanism by which the vortex's own motion in low Mach number flow generates noise, but does not clearly give the process by which vortex waves scatter and generate sound in vortex flow. As a result, the current low-speed open wind tunnel background noise prediction method has the problem of insufficient prediction accuracy. Summary of the Invention

[0004] The purpose of the present invention is to accurately predict the aerodynamic noise in complex flows dominated by vortices in engineering practice and to achieve accurate prediction of the background noise of low-speed open wind tunnels.

[0005] To achieve the above object, the present invention provides a method for predicting the background noise of a low-speed open wind tunnel, the method comprising:

[0006] Step 1: Obtain the spectral characteristics and frequencies of the turbulent pulsations in the wind tunnel inflow, and obtain the intensity and frequencies of the vortex waves based on the spectral characteristics and frequencies of the turbulent pulsations in the wind tunnel inflow;

[0007] Step 2: Obtain the shear layer thickness of the core test section of the wind tunnel, and obtain the vortex core radius of the vortices based on the shear layer thickness of the core test section of the wind tunnel;

[0008] Step 3: Calculate and obtain the vortex wave propagation speed, the vortex convection speed, and the vortex intensity based on the wind tunnel inflow velocity;

[0009] Step 4: Perform numerical calculations based on the data obtained in Steps 1 to 3 to obtain the prediction result of the background noise of the low-speed open wind tunnel;

[0010] Among them, the control equation used in the numerical calculation in Step 4 is the improved control equation that ignores the velocity gradient term.

[0011] Among them, the applicant's research found that in the problem of acoustic scattering in globally unstable flows, the incident vortex waves can further excite exponentially growing unstable waves, generating strong non-physical perturbations in the flow field and contaminating the physical information of the scattering field. That is, it is found that the velocity gradient will generate unstable waves. In view of this situation, in the present invention, the velocity gradient in the linearized equation is ignored, and the control equation is corrected to ensure the stability of the solution, so as to accurately obtain the scattering field, and then accurately characterize the complex non-linear dynamic system of the spatio-temporal evolution of the vortex waves scattering and generating sound in typical vortex flows, and can accurately predict the aerodynamic noise in complex flows dominated by vortices in engineering practice, realizing the ability to accurately predict the background noise of low-speed open wind tunnels.

[0012] Preferably, Step 4 specifically includes:

[0013] Step 4.1: Perform non-dimensionalization processing on all the parameters used in the numerical calculation;

[0014] Step 4.2: Assign values to the parameters used in the numerical calculation based on the data obtained in Steps 1 to 3;

[0015] Step 4.3: Set a sponge layer around the physical domain, and obtain the damping term based on the sponge layer;

[0016] Step 4.4: Construct and obtain the improved control equation that ignores the velocity gradient term and adds the damping term, and obtain the background flow expression;

[0017] Step 4.5: Set the computational domain and the physical domain, and perform mesh division;

[0018] Step 4.6: Set the initial perturbation field;

[0019] Step 4.7: Set the boundary conditions;

[0020] Step 4.8: Set the spatial discretization;

[0021] Step 4.9: Set the time advancement;

[0022] Step 4.10: Set the numerical filtering;

[0023] Step 4.11: Set the calculation duration;

[0024] Step 4.12: Calculate to obtain the prediction result of the background noise of the low-speed open wind tunnel.

[0025] Among them, the prediction result of the background noise of the low-speed open wind tunnel can be accurately obtained through the above method.

[0026] Preferably, the said Step 4.12 specifically includes:

[0027] Start the calculation to obtain the calculation result;

[0028] Subtract the perturbation amount corresponding to the vortex wave at the current moment from the calculation result to obtain the prediction result of the background noise of the low-speed open wind tunnel.

[0029] Preferably, the improved control equation after ignoring the velocity gradient term and adding the said damping term is:

[0030] ;

[0031] ; ; ; ;

[0032] Among them, ρ ′, u ′, v ′ and p ′ are respectively the density of the perturbation in the flow, x direction velocity, y direction velocity and pressure; γ represents the adiabatic index, U c is the vortex convection velocity, is the damping term, σ ( x , y ) is the sponge layer strength, is the reference solution, ρ 0, u 0, v 0 and p0 are the density of the background flow, x the velocity in the direction, y the velocity in the direction and the pressure, u ∞ is the vortex wave propagation velocity, x is the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction.

[0033] Preferably, the spatial discretization adopts a sixth-order enhanced optimization format, the time advancement adopts a fourth-order Runge-Kutta method for time advancement, and a tenth-order central compact filtering method is used for numerical filtering.

[0034] Preferably, the calculation domain set in step 4.5 specifically includes: calculating in a rectangular coordinate system ( x, y ), the calculation adopts a rectangular calculation domain. At the initial moment, the vortex center is located at the geometric center of the rectangular calculation domain, and a plane vortex wave propagating along the x positive direction is introduced through the calculation boundary from infinity.

[0035] Preferably, the expression of the plane vortex wave propagating along the x positive direction from infinity is:

[0036] ;

[0037] where, are respectively the density of the vortex wave perturbation, x the velocity in the direction, y the velocity in the direction and the pressure; ε is the vortex wave intensity, c ∞ is the sound speed at infinity, f 0 is the vortex wave frequency, u ∞ is the vortex wave propagation velocity, and the vortex wave wavelength λ = u ∞ / f 0, t is the time, x is the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction.

[0038] Preferably, the expression of the background flow in step 4.4 is:

[0039] ;

[0040] where, ρ 0, u 0, v 0 and p 0 are respectively the density of the background flow, xDirectional velocity, y Directional velocity and pressure, u ∞ is the vorticity wave propagation velocity, U v is the maximum tangential velocity, x is the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction, R is the vorticity core radius, M v is the vorticity intensity, γ represents the adiabatic index, ρ ∞ and c ∞ are the density and sound speed at infinity respectively, , U c is the vorticity convection velocity, t is time, and r represents the distance from the spatial coordinate (x, y) to the vorticity center of the vortex.

[0041] Preferably, the calculation method for obtaining the low-speed open wind tunnel background noise prediction result by subtracting the disturbance amount corresponding to the vorticity wave at the current moment from the calculation result is:

[0042] ;

[0043] wherein, is the density of the acoustic wave disturbance, x directional velocity, y directional velocity and pressure; ρ ′, u ′, v ′ and p ′ are the density, x directional velocity, y directional velocity and pressure of the disturbance in the flow respectively; is the density of the vorticity wave disturbance, x directional velocity, y directional velocity and pressure, x is the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction.

[0044] Preferably, the physical domain for calculation is X 1⩽ x ⩽ X 2, Y 1⩽ y ⩽ Y 2, and a sponge layer with a thickness of 2.5 λ is set around the physical domain, λis the wavelength of the vortex wave. X1 and X2 represent the left and right boundaries of the computational domain respectively, and Y1 and Y2 represent the lower and upper boundaries of the computational domain respectively.

[0045] One or more technical solutions provided by the present invention have at least the following technical effects or advantages:

[0046] The present invention adopts a numerical calculation method of spatio-temporal analysis based on a high-order accurate and high-resolution method, which can simulate the physical process of vortex wave scattering and sound generation, and study the influence law of key physical parameters on the scattered sound field.

[0047] Combined with the classical theory of aeroacoustics, this method can accurately characterize the complex non-linear dynamic system of the spatio-temporal evolution of vortex wave scattering and sound generation in typical vortex flows, can accurately predict the aeroacoustic noise in complex flows dominated by vortices in engineering practice, realize the accurate prediction of the background noise of a low-speed open wind tunnel. The background noise results of the wind tunnel obtained by the method proposed by the present invention are less than 3 dB compared with the measured results, and are equivalent to the direct aeroacoustic noise calculation results to achieve accurate prediction, and the calculation efficiency is increased by more than 90% compared with the direct calculation results, realizing efficient prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, and constitute a part of the present invention, but do not limit the embodiments of the present invention;

[0049] Figure 1 is a schematic flow chart of a method for predicting the background noise of a low-speed open wind tunnel;

[0050] Figure 2 Schematic diagram of the numerical model in the present invention;

[0051] Figure 3 is a schematic diagram of the sound pressure result. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] In order to more clearly understand the above objects, features and advantages of the present invention, the present invention will be further described in detail below with reference to the drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0053] Many specific details are set forth in the following description in order to provide a thorough understanding of the present invention. However, the present invention may be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0054] Embodiment 1;

[0055] Please refer to Figure 1 , Figure 1It is a schematic flow chart of a method for predicting the background noise of a low-speed open wind tunnel. Embodiment 1 of the present invention provides a method for predicting the background noise of a low-speed open wind tunnel, and the method includes:

[0056] Step 1: Obtain the spectral characteristics and frequencies of the turbulent fluctuations in the wind tunnel inflow, and obtain the intensity and frequency of the vortex waves based on the spectral characteristics and frequencies of the turbulent fluctuations in the wind tunnel inflow;

[0057] Among them, the intensity of the turbulent fluctuations in the wind tunnel inflow is the intensity of the vortex waves. Perform one-third octave analysis on the spectral characteristics of the turbulent fluctuations, and the center frequency of the dominant frequency band of the frequency is the frequency of the vortex waves.

[0058] Step 2: Obtain the shear layer thickness of the wind tunnel core test section, and obtain the vortex core radius of the vortex based on the shear layer thickness of the wind tunnel core test section;

[0059] Among them, the vortex core radius is equal to half of the shear layer thickness of the core test section.

[0060] Step 3: Calculate and obtain the vortex wave propagation speed, vortex convection speed, and vortex intensity based on the wind tunnel inflow velocity;

[0061] Among them, the wind tunnel inflow velocity is the vortex wave propagation speed; the vortex convection speed is 60% of the wind tunnel inflow velocity; the vortex intensity is the ratio of the wind tunnel inflow velocity to the sound speed at infinity.

[0062] Step 4: Perform numerical calculations based on the data obtained in Steps 1 to 3 to obtain the prediction result of the background noise of the low-speed open wind tunnel;

[0063] Step 5: Perform three-dimensional correction on the prediction result of the background noise of the low-speed open wind tunnel to obtain the actual background noise result of the low-speed open wind tunnel.

[0064] Among them, the control equation used in the numerical calculation in Step 4 is the improved control equation that ignores the velocity gradient term.

[0065] The following is a detailed introduction to this method:

[0066] The numerical model in the present invention can be applied to the prediction of aerodynamic noise in low Mach number (Mach number less than 0.3) flows dominated by large-scale vortex structures. Taking the prediction of the background noise of a low-speed open wind tunnel as an example, the application of the present invention in actual engineering noise prediction will be described below.

[0067] The background noise of a low-speed open wind tunnel is mainly generated by the interaction between the turbulent fluctuations in the upstream that appear as vortex waves and the large-scale vortex structures in the downstream shear layer. The specific prediction steps using the present invention are as follows:

[0068] Obtain the spectral characteristics and intensity of the turbulent fluctuations in the wind tunnel inflow through experimental measurement or theoretical analysis, and the intensity of the vortex waves can be obtainedε With frequency f 0;

[0069] Then, the shear layer thickness is obtained through experimental measurement or numerical simulation, and the vortex core radius of the vortex can be obtained R ;

[0070] The vortex wave propagation speed is obtained from the oncoming flow velocity of the wind tunnel u ∞ , the vortex convection velocity U c and the vortex intensity M v ;

[0071] Directly adopt the numerical calculation method proposed by the present invention to carry out numerical calculation to obtain the far-field noise;

[0072] Perform three-dimensional correction on the calculation results to obtain the actual far-field noise results

[0073] Among them, the three-dimensional correction method can be: perform Fourier transform on the calculation results is the frequency f corresponding sound pressure, and the corrected sound pressure can be expressed as:

[0074] ;

[0075] The wind tunnel background noise results obtained by using the numerical model proposed by the present invention are less than 3 dB compared with the measured results, and are comparable to the direct aerodynamic noise calculation results, and the calculation efficiency is improved by more than 90% compared with the direct calculation results

[0076] The numerical calculation of a vortex wave scattering sound generation process proposed by the present invention includes a physical model and a calculation method, and the physical model includes:

[0077] The physical models used in the present invention mainly include a vortex wave model and a convective isentropic vortex model. The specific derivation processes of the two models are given below

[0078] Vortex wave model:

[0079] The vortex wave model adopted by the present invention is a form of perturbation propagating with a uniform background flow. Without loss of generality, the two-dimensional uniform background flow adopted in the present invention satisfies the density ρ ∞ , x the velocity in the u ∞ , y the velocity in the v ∞ and the pressure p ∞ are all constants, andv ∞ = 0. In this case, the specific form of the linearized Euler equations is as follows:

[0080] ; (1)

[0081] where ρ ′, u ′, v ′ and p ′ are respectively the density of the perturbation in the flow, x the velocity in the y direction, the velocity in the γ direction and the pressure; t denotes the adiabatic index, which is generally 1.4 in air, x is the time, y is the spatial coordinate in the mainstream direction,

[0082] Assume that the above system of equations (1) has a traveling wave solution in the following form:

[0083] ; (2)

[0084] where q 1, q 2, q 3 and q 4 are dimensionless constants, ω is the frequency, i is the imaginary unit, k 1 and k 2 are respectively the wave numbers in the x direction and the y direction, c ∞ is the speed of sound. Substituting the above equation (2) into the system of equations (1), a homogeneous linear system of equations about q 1, q 2, q 3 and q 4 can be obtained:

[0085] ; (3)

[0086] It should be noted that the relation of the ideal gas is used here. The condition for the homogeneous linear system of equations (3) to have a non - zero solution is that the coefficient determinant is equal to 0, that is:

[0087] ; (4)

[0088] Solving the above equation (4) gives:

[0089] ; (5)

[0090] That is or At this time, there are the following three traveling wave solutions for the system of equations (1), where corresponds to the sound wave, corresponds to the entropy wave and the vorticity wave, and the specific discussion is as follows.

[0091] The propagation speed of the sound wave is , where θ is the angle between the propagation direction of the sound wave and the flow direction, is the dispersion relation of the sound wave propagating in a uniform background flow with velocity u 0. At this time, the acoustic perturbation quantity is:[[]]

[0092] ; (6)

[0093] where ε is an infinitesimal quantity.

[0094] The vorticity wave and the entropy wave propagate with the background flow, and the propagation speed is u 0. The expression of the vorticity wave is:[[]]

[0095] ; (7)

[0096] The expression of the entropy wave is:[[]]

[0097] ; (8)

[0098] The sound wave and the entropy wave are longitudinal waves, the vorticity wave is a transverse wave. The sound wave propagates at the speed of sound, and the entropy wave and the vorticity wave propagate at the speed of the background flow.

[0099] The specific vorticity wave model used in the present invention is the vorticity wave propagating along the x direction, and the specific expression is as follows:[[]]

[0100] ; (9)

[0101] where are respectively the density of the vorticity wave perturbation, x the velocity in the y direction, the velocity in the c ∞ is the speed of sound at infinity, f 0 is the vorticity wave frequency, u ∞ is the vorticity wave propagation speed, the vorticity wave wavelength λ = u ∞ / f 0, t is the time, xis the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction; ε is the vorticity wave intensity, , indicating that the vorticity wave perturbation quantity is much smaller than the hydrodynamic quantity of the background flow.

[0102] Convective isentropic vortex model:

[0103] The expression of the classical Taylor vortex in polar coordinates ( r , θ ) is:

[0104] ; (10)

[0105] where, r represents the distance from the spatial coordinate (x, y) to the vortex core of the vortex, θ is the angle between the sound wave propagation direction and the flow direction, u rv is the normal velocity of the vortex, u θv is the tangential velocity of the vortex, ρ v is the density of the vortex, p v is the pressure of the vortex; The Taylor vortex is a compact vortex, and the velocity decays exponentially in the far field. Therefore, the far field can be regarded as a uniform field. ρ ∞ and c ∞ are the density and sound speed at infinity, respectively; R is the vortex core radius. At r = R , the tangential velocity reaches the maximum, denoted as U v , M v is the vortex strength, defined as .

[0106] From the above expression (10), it is not difficult to see that the classical Taylor vortex is a steady vortex. On this basis, by superimposing a uniform flow with a velocity of x in the u ∞ direction, the convective isentropic vortex, that is, the background flow, can be obtained. Its expression in the rectangular coordinate system ( x , y ) is:

[0107] ; (11)

[0108] where, ρ 0, u 0, v0 and p 0 are the density, x directional velocity, y directional velocity and pressure of the background flow respectively; , ( x c , y c ) is the vorticity center position coordinate of the Taylor vortex at t moment, x c = x c0 + U c t , y c = y c0 , U c is the vortex convection velocity, ( x c0 , y c0 ) is the initial vorticity center position coordinate, x is the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction.

[0109] When U c = u ∞ , the expression (11) of the convective isentropic vortex is the exact solution of the Euler equation, which is the most classical convective isentropic vortex model. However, considering the interaction between vortices in the actual vortex flow, the convective velocity of any vortex should include two parts of contributions: the background flow at this vortex (mostly simple flows such as uniform flow and potential flow) and the flow induced by other vortices at this vortex. For each isolated vortex in the actual flow, its convective velocity is not consistent with the velocity of the local background flow (this has been verified in the wind tunnel jet shear layer: the convective velocity of the vortex in the wind tunnel jet shear layer is about 65% of the incoming flow velocity). Therefore, in the present invention, a vortex convective velocity different from the uniform background flow is set, that is, U c ≠ u ∞ case. At this time, the equation satisfied by the expression (11) is:

[0110] ; (12)

[0111] Compared with the Euler equation, there are some source terms added to the right - hand side of the above system of equations (12), that is, density, x directional velocity, yThe derivatives of the direction velocity and pressure in the x direction, multiplied by the convective velocity difference between the uniform background flow and the vortex, are characterized as the net flux of the primitive variables in the convective direction. The above system of equations (12) is written in conservation form:

[0112] ; (13)

[0113] where U is the conserved variable, , F and G are respectively x , y the circulation vectors in the direction, , , ρ , u , v , p are respectively density, x and y the velocity in the direction, pressure; the total energy density . S is the source term circulation vector, representing the additional circulation vector brought to the selected isolated vortex structure in the present invention due to the interaction between vortices. The specific expression is:

[0114] ; (14)

[0115] respectively represent the additional mass flux, x the momentum flux in the direction, y the momentum flux in the direction and the energy flux. This is due to the action of other vortices, generating a mass flow rate along the convective direction with a velocity of the convective velocity difference between the uniform background flow and the vortex u ∞ - U c for the selected isolated vortex, and the inflowing mass brings x the momentum in the direction, y the momentum in the direction and energy.

[0116] In addition, for the convenience of solving the above system of equations (14), it can also be written in the following form:

[0117] ; (15)

[0118] Calculation method:

[0119] The following introduces the high-precision finite-difference time-domain method for calculating the scattering of convective isentropic vortices by vortex waves used in the invention, including the governing equations, spatial discretization format, time marching format, numerical filtering format, grid stretching function, sponge layer technology, and non-reflecting boundary conditions, etc.

[0120] Control equations:

[0121] Considering that the vortex waves and acoustic waves involved in the present invention are both small perturbation waves, the control equations for calculation are selected as the linearized equation systems obtained by linearizing the nonlinear equation systems (12), (13), or (15).

[0122] In the physical process of vortex wave scattering by convective isentropic vortices, the original physical variables ( ρ , u , v , p ) are composed of the background hydrodynamic quantities ( ρ 0, u 0, v 0, p 0) and the perturbation quantities in the flow ( ρ ′, u ′, v ′, p ′), that is:

[0123] ; (16)

[0124] wherein, both the flow field and the background flow field satisfy the nonlinear equation systems (12), (13), or (15) obtained previously.

[0125] Substituting (16) into (12), (13), or (15) and neglecting the high-order small terms, the linearized equations for the small perturbation quantities of vortex waves and acoustic waves can be obtained, and their conservation form is:

[0126] ; (17)

[0127] where:

[0128] ; ; ; ; (18)

[0129] Here, ρ 0, u 0, v 0, and p 0 satisfy the expression (11) of the convective isentropic vortex.

[0130] Compared with the standard linearized Euler equations (LEEs for short), the linearized equation (17) obtained for the vortex wave scattering by convective isentropic vortices has an additional term . Here characterizes the influence of the interaction between vortices on the vortex wave scattering.

[0131] The linearized equation (17) is an ideal governing equation for the vortex-wave scattering of convective isentropic vortices in the present invention, but it has its applicable conditions. From the above derivation process, it can be seen that the incident vortex wave must satisfy the small perturbation condition, that is, the amplitude of the perturbation is much smaller than the magnitude of the corresponding hydrodynamic quantity. In addition, the linearized equation only supports the propagation of various different waves such as vortex waves, sound waves, and entropy waves at the same time. These different types of waves are coupled together in a strongly non-uniform flow and are extremely difficult to separate. Even worse, in the acoustic scattering problem of globally unstable flows, the incident vortex wave can further excite exponentially growing unstable waves, generating strong non-physical perturbations in the flow field and contaminating the physical information of the scattering field. In view of this situation, in the present invention, the method of neglecting the velocity gradient term correction H term in the linearized equation (17) is adopted to ensure the stability of the solution, so as to accurately obtain the scattering field. The corrected H term is in the following form:

[0132] ; (19)

[0133] Numerical method:

[0134] In order to better analyze the various perturbation components in the scattering field, when numerically solving the two-dimensional linearized equation (17), the spatial discretization adopts the sixth-order enhanced optimized (Enhanced Optimized, abbreviated as EnhOpt) format, and the classical fourth-order Runge-Kutta (Runge-Kutta, abbreviated as R-K) method is used for time advancement. In order to maintain the stability of the calculation, the tenth-order central compact filtering technique is adopted to suppress the non-physical high-frequency oscillations generated in the calculation.

[0135] The calculation is carried out in the rectangular coordinate system ( x, y ), and a rectangular calculation domain is adopted. At the initial moment, the vortex center of the vortex is located at the geometric center of the calculation domain. A plane vortex wave propagating in the positive direction along x from infinity is introduced through the calculation boundary, and the specific form is shown in expression (9).

[0136] The physical domain of the calculation is X 1⩽ x ⩽ X 2, Y 1⩽ y ⩽ Y 2. X1 and X2 represent the left and right boundaries of the calculation domain respectively, and Y1 and Y2 represent the lower and upper boundaries of the calculation domain respectively. A sponge layer with a thickness of δ =2.5 λ is set around the physical domain. λ is the wavelength of the incident vortex wave, that is, in this region, a damping term is added to the governing equation (17). σ (x , y ) is the strength of the sponge layer. Among them, the strength of the sponge layer can be obtained by converting the thickness of the sponge layer. U ref is the reference solution. Specifically, at the left boundary, σ ( x ) = 0.5[( x − X 1) / δ ) 2.5 , x ⩽ X 1; at the right boundary, σ ( x ) = 0.5[( x − X 2) / δ ) 2.5 , x ⩾ X 2; at the upper boundary, σ ( y ) = 0.5[( y − Y 2) / δ ) 2.5 , y ⩾ Y 2; at the lower boundary, σ ( y ) = 0.5[( y − Y 1) / δ ) 2.5 , y ⩽ Y 1. U ref It includes the background flow and the plane vortex wave at the current moment, so that the sponge layer only absorbs the scattered wave without affecting the incident wave from entering the calculation area. At the boundary, the physical quantities are divided into the vortex background flow, the incident vortex wave, and the scattered wave. Among them, the background flow is given by the expression (11) of the convective isentropic vortex, the incident wave is given by the plane vortex wave expression (9), and the scattered wave part is determined by the radiation boundary condition in the x direction and y direction by the radiation boundary condition.

[0137] In the calculation, a uniform Cartesian grid is adopted. The grid spacing meets the requirements of being able to resolve both the vortex dynamic quantities and the acoustic small perturbation quantities simultaneously. Take ∆ x = ∆ y = min{ λ / 20, R / 10}. Y 1 = −max{4 λc ∞ / u∞ , 8 R},Y2 = max{4 λc ∞ / u ∞ , 8 R}, X 1 = Y 1 - 10 λU c / u ∞ , X 2 = Y 2 + 10 λU c / u ∞ 。Courant number c ∞ ∆ t / ∆ x = 0.2。After the calculation has been in progress for a period of time ([( X 2 - X 1 + ([( Y 2 - Y 1) + 4 δ ) / u ∞ ), it enters a quasi - steady - state scattering process with a definite period. At this time, record the data of 10 incident - wave periods 10 λ / u ∞ duration. At the beginning of the calculation, first freeze the flow field to keep it in a steady state. After entering the quasi - periodic state, start the normal calculation, that is, when the calculation time t < [( X 2 - X 1 + ([( Y 2 - Y 1) + 4 δ ) / u ∞ , let U c = 0.

[0138] Subtract the perturbation corresponding to the vortex wave at the current time from the calculation result, which is the acoustic quantity. The specific calculation method is:

[0139] ; (29)

[0140] where is the density of the acoustic wave perturbation, x the velocity in the y direction, the velocity in the ρ ′, u ′, v ′ and p′ are the density, x directional velocity, y directional velocity, and pressure of the disturbance in the flow; are the density, x directional velocity, y directional velocity, and pressure of the vortex-wave disturbance.

[0141] The present method will be introduced and illustrated below with specific examples and data:

[0142] Non-dimensionalization:

[0143] First, all the parameters used in the numerical calculation are non-dimensionalized to facilitate numerical calculation programming. Using the vortex core radius R of the vortex as the reference quantity for the spatial scale, and the sound speed c ∞ at infinity as the reference quantity for the velocity scale, and the density ρ ∞ at infinity as the reference quantity for the density scale, the time t is non-dimensionalized with and the pressure p is non-dimensionalized with

[0144] Parameter assignment:

[0145] The numerical model is as shown in Figure 2 Figure 2 and can be understood as a closed space formed by wrapping with a sponge layer, and there is a sound source inside the space. After non-dimensionalization, the parameters of the given numerical model are as follows:

[0146] Vortex intensity M v = 0.25, the intensity of the vortex wave is 0.00001, the frequency of the vortex wave is 0.125, the wavelength λ of the vortex wave = 2, the vortex wave propagates in the x direction with a propagation speed u ∞ = 0.25, the convection direction of the vortex is x direction and the velocity U c = 0.15.

[0147] Control equations:

[0148] First, the in the vortex reference frame can be expressed as:

[0149] ; (20)

[0150] The non-dimensional control equation is:

[0151] ; (21)

[0152] Among them,

[0153] ; (22)

[0154] ( ρ 0, u 0, v 0, p 0) is the background flow, and the specific form is as follows:

[0155] ; (23)

[0156] H The specific form of item

[0157] ; (24)

[0158] Sponge layer strength σ ( x , y ) has the specific form of:

[0159] ; (25)

[0160] Reference solution U ref has the specific form of:

[0161] ; (26)

[0162] Computational domain and mesh generation:

[0163] The calculation is carried out in the rectangular coordinate system ( x, y ), using a rectangular computational domain. The size of the physical domain for calculation is X 1, X 2] × Y 1, Y 2], X 1 = -38, X 2 = 38, Y 1 = -32, Y 2 = 32. A sponge layer with a strength of δ = 10 is set around the physical domain. Cartesian uniform grids are used, and the number of grids in the x and y directions are 481 and 421 respectively.

[0164] Initial perturbation field setting:

[0165] ; (27)

[0166] Boundary condition setting:

[0167] At the boundary, the physical quantity is divided into incident vortex waves and scattered waves, where the expression of the incident vortex wave is:

[0168] ; (28)

[0169] The scattered wave part is determined by the radiation boundary condition in the x direction and in the y direction by the radiation boundary condition.

[0170] Spatial discretization:

[0171] The sixth-order enhanced optimization format is adopted for spatial discretization.

[0172] Time marching:

[0173] The fourth-order Runge-Kutta method is used for time marching, and the time step is 0.02.

[0174] Numerical filtering:

[0175] The tenth-order central compact filtering technique is adopted to suppress the non-physical high-frequency oscillations generated in the calculation.

[0176] Calculation duration and data saving:

[0177] The total calculation duration is 800. When t > 720, data recording starts.

[0178] Result output:

[0179] Subtracting the perturbation quantity corresponding to the vortex wave at the current moment from the calculation result gives the acoustic quantity. The specific calculation method is

[0180] ; (29)

[0181] Where is the density of the acoustic wave perturbation, x the velocity in the y direction, the velocity in the ρ ′, u ′, v ′ and p ′ are respectively the density of the perturbation in the flow, x the velocity in the y direction, the velocity in the Figure 3 direction and the pressure. The sound pressure result is as shown in Figure 3 where E in

[0182] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made to these embodiments by those skilled in the art once they learn the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0183] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A prediction method for the background noise of a low-speed open wind tunnel, characterized in that, The method includes: Step 1: Obtain the spectral characteristics and frequency of the turbulent pulsation in the wind tunnel inflow, and obtain the intensity and frequency of the vortex wave based on the spectral characteristics and frequency of the turbulent pulsation in the wind tunnel inflow; Step 2: Obtain the shear layer thickness of the wind tunnel core test section, and obtain the vortex core radius of the vortex based on the shear layer thickness of the wind tunnel core test section; Step 3: Calculate and obtain the vortex wave propagation speed, vortex convection speed and vortex intensity based on the wind tunnel inflow velocity; Step 4: Perform numerical calculations based on the data obtained in Steps 1 to 3 to obtain the prediction result of the background noise of the low-speed open wind tunnel; Among them, the governing equation used in the numerical calculation in Step 4 is the improved governing equation that ignores the velocity gradient term; The specific content of Step 4 includes: Step 4.1: Nondimensionalize all the parameters used in the numerical calculation; Step 4.2: Assign values to the parameters used in the numerical calculation based on the data obtained in Steps 1 to 3; Step 4.3: Set a sponge layer around the physical domain and obtain the damping term based on the sponge layer; Step 4.4: Construct and obtain the improved governing equation that ignores the velocity gradient term and adds the damping term, and obtain the background flow expression; Step 4.5: Set the computational domain and physical domain, and perform grid division; Step 4.6: Set the initial perturbation field; Step 4.7: Set the boundary conditions; Step 4.8: Set the spatial discretization; Step 4.9: Set the time advancement; Step 4.10: Set the numerical filtering; Step 4.11: Set the calculation duration; Step 4.12: Calculate and obtain the prediction result of the background noise of the low-speed open wind tunnel; The specific content of Step 4.12 includes: Start the calculation to obtain the calculation result; Subtract the perturbation amount corresponding to the vortex wave at the current moment from the calculation result to obtain the prediction result of the background noise of the low-speed open wind tunnel; The improved governing equation that ignores the velocity gradient term and adds the damping term is: ； ； ； ； ； Among them, ρ ′, u ′, v ′ and p ′ are respectively the density, x directional velocity, y directional velocity and pressure of the perturbation in the flow; γ represents the adiabatic index, U c is the vortex convection velocity, is the damping term, σ ( x , y ) is the sponge layer strength, is the reference solution, ρ 0, u 0, v 0 and p 0 are respectively the density, x directional velocity, y directional velocity and pressure of the background flow, u ∞ is the vorticity wave propagation velocity, x is the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction; The spatial discretization adopts a sixth-order enhanced optimization format, the time advancement adopts a fourth-order Runge-Kutta method for time advancement, and a tenth-order central compact filtering method is used for numerical filtering; The specific settings of the computational domain in Step 4.5 include: performing calculations in a rectangular coordinate system ( x,y ), using a rectangular computational domain for the calculations. At the initial moment, the vortex center is located at the geometric center of the rectangular computational domain. A plane vortex wave propagating in the x positive direction from infinity is introduced through the computational boundary, x is the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction; The expression of the plane vortex wave propagating in the x positive direction from infinity is as follows: ； Among them, are respectively the density of the vortex wave perturbation, x the direction velocity, y the direction velocity and the pressure; ε is the vortex wave intensity, c ∞ is the sound speed at infinity, f 0 is the vortex wave frequency, u ∞ is the vortex wave propagation velocity, and the vortex wave wavelength λ = u ∞ / f 0, t is the time; The background flow expression in Step 4.4 is: ； Among them, ρ 0, u 0, v 0 and p 0 are respectively the density, x directional velocity, y directional velocity and pressure of the background flow, u ∞ is the vortex wave propagation velocity, U v is the maximum tangential velocity, x is the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction, R is the vortex core radius, M v is the vortex intensity, γ represents the adiabatic index, ρ ∞ and c ∞ are respectively the density and the speed of sound at infinity, , U c is the vortex convection velocity, t is the time, r represents the distance from the spatial coordinate ( x , y ) to the vortex center; The calculation method of subtracting the perturbation amount corresponding to the vortex wave at the current moment from the calculation result to obtain the prediction result of the background noise of the low-speed open wind tunnel is: ； Among them, is the density of the acoustic wave perturbation, x the direction velocity, y the direction velocity, and the pressure; ρ ′, u ′, v ′, and p ′ are respectively the density of the perturbation in the flow, x the direction velocity, y the direction velocity, and the pressure; is the density of the vortex wave perturbation, x the direction velocity, y the direction velocity, and the pressure, x is the spatial coordinate in the mainstream direction, y is the transverse spatial coordinate perpendicular to the mainstream direction.

2. The background noise prediction method for a low-speed open wind tunnel according to claim 1, characterized in that, The calculated physical domain is X 1 ≤ x ≤ X 2, Y 1 ≤ y ≤ Y 2, and a sponge layer with a thickness of 2.5 is set around the physical domain λ . λ is the wavelength of the vortex wave, X1 and X2 respectively represent the left and right boundaries of the calculation domain, and Y1 and Y2 respectively represent the lower and upper boundaries of the calculation domain.

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