CN114722734B - Acoustic velocity time domain extrapolation method based on permeable surface - Google Patents
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Abstract
The invention discloses an acoustic velocity time domain extrapolation method based on a permeable surface, which utilizes uniform average flow density, pressure and velocity, sound velocity and flow characteristic size to dimensionless time, space and flow parameters; according to the high-precision numerical simulation result of computational fluid dynamics, a static permeable surface is selected, so that the phenomena of sound wave generation, reflection, refraction and the like are enclosed in the permeable surface; determining and outputting dimensionless disturbance density, disturbance pressure and disturbance speed on a permeable surface, and gradient of the disturbance pressure and gradient and divergence of the disturbance speed; determining key parameters of the sound source on the permeable surface; substituting the dimensionless sound source information on the permeable surface into an acoustic velocity time domain integral formula, extrapolating the dimensionless acoustic velocity of the far-field observation point, and converting the dimensionless acoustic velocity into a dimensionality value. Under the condition that the geometric parameters and the flow parameters of the permeable surface are the same, the calculation accuracy of the method is greatly improved compared with the existing method.
Description
Technical Field
The invention belongs to the technical field of aeroacoustics, and particularly relates to an acoustic velocity time domain extrapolation method.
Background
In the acoustic field, the selection of sound absorption and insulation control schemes, and the identification and positioning of pneumatic sound sources all require the analysis of sound propagation paths by using sound intensities, which are sound pressuresAnd acoustic speed->Is a function of (2). In addition, non-tight boundaries on aerodynamic noise propagation paths induce acoustic scattering, the analysis of which requires prediction of scattering edgesAcoustic speed at the boundary>As boundary conditions.
Consider aerodynamic noise propagating in a uniform average flow. Uniform average flow density, pressure and velocity ofAnd->Sound velocity of +.>Acoustic Density->Sound pressure->And acoustic speed->Defined as->Andwherein->And->Respectively instantaneous density, pressure and velocity. The existing acoustic velocity calculation method is to +.>As acoustic variables, the following non-homogeneous convective wave equation was established
Wherein, above the symbol or parameter, -represents a dimensional value, f=0 represents a permeable surface, f>0 and f<0 is the permeable surface outer and inner region, respectively;time of presentation->For the initial time +.>Is an integral variable; substance derivative-> Delta (f) is a Dirac function and H (f) is a Heaviside function; />And->Representing a quadrupole source, a load source and a thickness source, respectively, which are negligible when the phenomena of sound generation, reflection and refraction are surrounded by permeable surfaces>Is a contribution of (a).
For a surface that is permeable to static electricity,and->Defined as-> And->Wherein->Representing the fluid viscosity stress tensor. The above-described convective wave equation has three drawbacks: firstly, mathematical expression is very complex, which is unfavorable for integral solution of an equation; secondly, in the process of establishing the equation, the load source is incorrectly processed, and partial sound sources are ignored, so that the integral solution of the equation is difficult to obtain a correct prediction result; thirdly, the source item depends on the initial conditions, +.>Is +.>And in the application is taken as +.>Errors in the initial conditions can also cause unnecessary numerical errors.
In summary, in the prior art, there is a problem that the accuracy of acoustic velocity field prediction is low due to the inherent defect of the acoustic control equation.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an acoustic velocity time domain extrapolation method based on a permeable surface, which utilizes uniform average flow density, pressure and velocity, sound velocity and flow characteristic size to dimensionless time, space and flow parameters; according to the high-precision numerical simulation result of computational fluid dynamics, a static permeable surface is selected, so that the phenomena of sound wave generation, reflection, refraction and the like are enclosed in the permeable surface; determining and outputting dimensionless disturbance density, disturbance pressure and disturbance speed on a permeable surface, and gradient of the disturbance pressure and gradient and divergence of the disturbance speed; determining key parameters of the sound source on the permeable surface; substituting the dimensionless sound source information on the permeable surface into an acoustic velocity time domain integral formula, extrapolating the dimensionless acoustic velocity of the far-field observation point, and converting the dimensionless acoustic velocity into a dimensionality value. Under the condition that the geometric parameters and the flow parameters of the permeable surface are the same, the calculation accuracy of the method is greatly improved compared with the existing method.
The technical scheme adopted by the invention for solving the technical problems comprises the following steps:
step 1: according to known uniform average flow densitySound velocity->And flow characteristic dimension->By-> And->Space with dimension ∈>Time->Density ofPressure->And speed->Dimensionless;
step 2: according to known uniform average flow pressureAnd speed->By->And determining disturbance pressure p' =p-p ∞ And disturbance speed u' =u-u ∞ Simultaneously determining the disturbance density ρ' =ρ -1;
step 3: according to the high-precision simulation result of computational fluid dynamics, selecting a static permeable surface f=0, so that the generation, reflection and refraction phenomena of sound waves are enclosed in the permeable surface;
step 4: according to the high-precision simulation result of computational fluid dynamics, determining parameters of a sound source on a permeable surface through a dimensionless non-homogeneous convection wave equation which is shown in a formula (1) and takes a disturbance speed u' as a variable;
wherein f=0 represents a permeable surface, f>0 and f<0 is the permeable surface outer and inner region, respectively; h (f) is the Heaviside function, delta (f) is the Dirac function,is the unit external normal vector of the permeable surface, the objectMass derivativeThe term containing H (f) at the right end of the equation is a volume source and is ignored because of small contribution to the sound field; the term containing δ (f) is a non-point source, which is decisive for the sound field, where the parameters W, F, L, P and Q are defined as:
wherein γ=1.4 is an air specific heat ratio;
step 5: determining dimensionless acoustic velocity u' (x, t) from the sound source parameters on the permeable surface by equation (3) for an observation point x outside the permeable surface;
wherein x and y represent the positions of the observation point and the sound source, respectively, t and τ represent the time of the observation point and the sound source, respectively, and the variables areAnd R is defined as:
wherein:
[…] ret indicating the delay time tau ret The value of =t-R, the remaining variables are defined as follows:
tensors of eachThe subscripts i, j, k=1, 2,3 denote x in the cartesian coordinate system 1 ,x 2 ,x 3 Components in three directions;
step 6: multiplying dimensionless acoustic velocity u' (x, t) by sound velocityObtaining the dimensional acoustic velocity +.>
Further, the process of determining the sound source parameters on the permeable surface according to the formula (1) includes:
step 4-1: selecting a static permeable surface f=0 according to a computational fluid dynamics high-precision simulation result, and outputting geometric parameters of all grid cells of the permeable surface, wherein the geometric parameters comprise a grid cell unit external normal vector n, a dimensionless central point position y and an area s;
step 4-2: calculating time steps for each unsteady flow, outputting unsteady flow parameters of the permeable surface including time τ, density ρ and disturbance density ρ ', disturbance pressure p ' and disturbance velocity u ', and disturbance pressure gradientAnd disturbance speed gradient->And (3) degree of divergence->
Step 4-3: for each grid cell for each unsteady time step, W, F, L, P and Q are calculated separately using equation (2) to determine the sound source parameters on the permeable surface.
Further, the solving process of the formula (3) includes:
step 5-1: determining a far field stationary acoustic viewpoint x and discretizing equation (3) into the following form
Where D is the number of permeable surface mesh cells, d=1, 2,3, …, D is the number of mesh cells, s d Is the grid cell area numbered d;
step 5-2: for each grid cell of each unsteady time step, A is calculated using equation (6) i 、B i And E is ij The method comprises the steps of carrying out a first treatment on the surface of the Calculating the parameter L using finite difference algorithm i 、E ij And Q is the value of the derivative of the dimensionless time tau;
step 5-3: for each grid cell, parameters are calculated using equations (4) and (5)And R, and determining the maximum value R of R max And a minimum value R min Simultaneously calculate the parameters +.>And->
Step 5-4: determining a dimensionless start time t of a received sound wave at a viewpoint x s ＝τ s +R max And expiration time t e ＝τ e +R min Wherein τ s And τ e Dimensionless start time and end time for the sound source; the observation point time t is discretized according to the fixed step length delta tau of the sound source time tau, and the m-th time step discretization time is t m MΔτ, where m is in the range of [ int (t s /Δτ)+1,int(t c /Δτ)]；
Step 5-5: for the first time step of the d-th grid unit, calculating the time when the radiated sound wave reaches the observation point xWherein R is d R is the value between the d-th grid unit and the observation point x; determine->Corresponding time stepsAnd its dimensionless deviation->
Step 5-6: if it isOr->The d-th grid-cell sound source of the first time step contributes 0 to the sound field; otherwise, determining the contribution ++of the grid cell using equation (7)>
Step 5-7: determining a d-th grid-cell sound source pair for a first time stepTime-step sound field contributionThe mesh unit sound source pair +.>Time-step sound field contribution
Step 5-8: and summing the contributions of all the grid cell sound sources to each observation point time step to obtain dimensionless acoustic velocity u' (x, t).
The beneficial effects of the invention are as follows:
the acoustic velocity convection wave equation and the time domain analysis integral formula thereof in the prior art depend on unknown initial conditions, and the acoustic velocity convection wave equation and the time domain analysis integral formula thereof in the invention are irrelevant to the initial conditions; the acoustic velocity convection wave equation in the prior art ignores part of sound sources on the permeable surface, and the acoustic velocity convection wave equation does not lose sound source information on the permeable surface; under the condition that the geometric parameters of the permeable surface and the flow parameters are the same, the calculation accuracy of the acoustic velocity time domain extrapolation method is greatly improved compared with the existing method.
Drawings
Fig. 1 is a schematic view of the observation point and observation angle according to an embodiment of the present invention.
Fig. 2 is a schematic representation of a discrete permeable surface according to an embodiment of the present invention.
Fig. 3 shows an example of the present invention at an observation angle θ=120° x 2 The invention relates to a method numerical solution of directional acoustic velocity time history, and a comparison diagram of the existing method numerical solution and a theoretical analysis solution;
FIG. 4 shows the embodiment of the present invention at x 1 Directional acoustic velocity effective value directivity distribution the method of the invention is a comparison graph of the existing method numerical solution and the theoretical analysis solution.
Reference numerals illustrate:
1. even average flow; 2. a stationary dipole point source; 3. an observation point x; 4. an observation angle θ; 5. a permeable surface; 6. a permeable surface mesh cell center point y; 7. the permeable surface grid unit external normal vector n; 8. an acoustic velocity time history theoretical analytical solution; 9. the acoustic velocity time history has a method numerical solution; 10. acoustic velocity time history the method of the invention solves the numerical value; 11. the effective value directivity distribution theory of the acoustic velocity is analyzed and solved; 12. the directivity distribution of the effective value of the acoustic velocity is solved by the existing method; 13. the effective value directivity distribution of the acoustic velocity is calculated by the method.
Detailed Description
The invention will be further described with reference to the drawings and examples.
The invention provides an acoustic velocity time domain extrapolation method based on a permeable surface, which is used for solving the problem that the acoustic velocity calculation accuracy is low when the uniform average flow convection effect is considered in the existing acoustic velocity prediction method.
An acoustic velocity time domain extrapolation method based on a permeable surface, comprising the steps of:
step 1: according to known uniform average flow densitySound velocity->And flow characteristic dimension->By-> And->Space with dimension ∈>Time->Density ofPressure->And speed->Dimensionless;
step 2: according to known uniform average flow pressureAnd speed->By->And determining disturbance pressure p' =p-p ∞ And disturbance speed u' =u-u ∞ Simultaneously determining the disturbance density ρ' =ρ -1;
step 3: according to the high-precision simulation result of computational fluid dynamics, selecting a static permeable surface f=0, so that the generation, reflection and refraction phenomena of sound waves are enclosed in the permeable surface;
step 4: according to the high-precision simulation result of computational fluid dynamics, determining parameters of a sound source on a permeable surface through a dimensionless non-homogeneous convection wave equation which is shown in a formula (1) and takes a disturbance speed u' as a variable;
wherein f=0 represents a permeable surface, f>0 and f<0 is the permeable surface outer and inner region, respectively; h (f) is the Heaviside function, delta (f) is the Dirac function,as the unit external normal vector of the permeable surface, the derivative of the substanceThe term containing H (f) at the right end of the equation is a volume source and is ignored because of small contribution to the sound field; the term containing delta (f) is a non-point source and plays a decisive role in the sound field, wherein the parameters W, F, L, P and Q are defined as
Wherein γ=1.4 is an air specific heat ratio;
step 5: determining dimensionless acoustic velocity u' (x, t) from the sound source parameters on the permeable surface by equation (3) for an observation point x outside the permeable surface;
wherein x and y represent the positions of the observation point and the sound source, respectively, t and τ represent the time of the observation point and the sound source, respectively, and the variables areAnd R is defined as:
wherein:
[…] ret indicating the delay time tau ret The value of =t-R, the remaining variables are defined as follows:
the subscripts i, j, k=1, 2,3 of each tensor in the formula denote x in the Cartesian coordinate system 1 ,x 2 ,x 3 Components in three directions;
step 6: multiplying dimensionless acoustic velocity u' (x, t) by sound velocityObtaining the dimensional acoustic velocity +.>
Further, the process of determining the sound source parameters on the permeable surface according to the formula (1) includes:
step 4-1: selecting a static permeable surface f=0 according to a computational fluid dynamics high-precision simulation result, and outputting geometric parameters of all grid cells of the permeable surface, wherein the geometric parameters comprise a grid cell unit external normal vector n, a dimensionless central point position y and an area s;
step 4-2: calculating time steps for each unsteady flow, outputting unsteady flow parameters of the permeable surface including time τ, density ρ and disturbance density ρ ', disturbance pressure p ' and disturbance velocity u ', and disturbance pressure gradientAnd disturbance speed gradient->And (3) degree of divergence->
Step 4-3: for each grid cell for each unsteady time step, W, F, L, P and Q are calculated separately using equation (2) to determine the sound source parameters on the permeable surface.
Further, the solving process of the formula (3) includes:
step 5-1: determining a far field stationary acoustic viewpoint x and discretizing equation (3) into the following form
Where D is the number of permeable surface mesh cells, d=1, 2,3, …, D is the number of mesh cells, s d Is the grid cell area numbered d;
step 5-2: for each grid cell of each unsteady time step, A is calculated using equation (6) i 、B i And E is ij The method comprises the steps of carrying out a first treatment on the surface of the Calculating the parameter L using finite difference algorithm i 、E ij And Q is the value of the derivative of the dimensionless time tau;
step 5-3: for each grid cell, parameters are calculated using equations (4) and (5)And R, and determining the maximum value R of R max And a minimum value R min Simultaneously calculate the parameters +.>And->
Step 5-4: determining a dimensionless start time t of a received sound wave at a viewpoint x s ＝τ s +R max And expiration time t e ＝τ e +R min Wherein τ s And τ e Dimensionless start time and end time for the sound source; the observation point time t is discretized according to the fixed step length delta tau of the sound source time tau, and the m-th time step discretization time is t m MΔτ, where m is in the range of [ int (t s /Δτ)+1,int(t c /Δτ)]；
Step 5-5: for the first time step of the d-th grid unit, calculating the time when the radiated sound wave reaches the observation point xWherein R is d For the d-th grid cell andr values between observation points x; determine->Corresponding time stepsAnd its dimensionless deviation->
Step 5-6: if it isOr->The d-th grid-cell sound source of the first time step contributes 0 to the sound field; otherwise, determining the contribution ++of the grid cell using equation (7)>
Step 5-7: determining a d-th grid-cell sound source pair for a first time stepTime-step sound field contributionThe mesh unit sound source pair +.>Time-step sound field contribution
Step 5-8: and summing the contributions of all the grid cell sound sources to each observation point time step to obtain dimensionless acoustic velocity u' (x, t).
Specific examples:
the embodiment of the invention provides an acoustic velocity time domain extrapolation method based on a permeable surface by taking a stationary dipole point source in uniform average flow as an example.
As shown in FIG. 1, at Mach number M ∞ = (0.3,0,0), densityAnd pressure->Has a stationary dipole point source at the origin of coordinates, and the wave number k=2, period of the radiated sound waveTake the sound velocity +.>Average flow speed->Assuming that the dipole axis is along x 2 The direction, the dimensional transient parameter of the flow may be determined by a velocity potential function:
wherein i is an imaginary unit
Has a dimensional velocity of
Has a dimensional pressure of
Has a dimensional density of
Based on the uniform rectangular coordinate grid, selecting the dimensional time step asSelf-programming is used to calculate the dimensional transient density, pressure and velocity of the dipole flow.
The specific process of the embodiment comprises the following steps:
1. selecting a flow characteristic length asAccording to the known uniform mean flow density +.>Sound velocity->And flow characteristic dimension->By->And->Space with dimension ∈>Time->Density->Pressure->And speed->Dimensionless;
2. step 2: according to known uniform average flow pressureAnd speed->By->Anddetermining disturbance pressure p' =p-p ∞ And disturbance speed u' =u-u ∞ Simultaneously determining the disturbance density ρ' =ρ -1;
3. selecting the point source as the center and the side lengthIs a permeable integration surface surrounding the dipole point source. For each surface of the cube, it was discretized into 60×60=3600 uniformly sized structured grid cells, with a total of 21600 grid cells for the permeable face, as shown in fig. 2.
4. By using the flow high-precision calculation result, the key parameters of the sound source on the permeable surface are determined through the following dimensionless non-homogeneous convection wave equation taking the acoustic velocity u' as a variable:
wherein f=0 represents a permeable surface, f>0 and f<0 is respectivelyA permeable surface outer and inner region; h (f) is the Heaviside function, delta (f) is the Dirac function,as the unit external normal vector of the permeable surface, the derivative of the substanceThe term containing H (f) at the right end of the equation is a volume source and is ignored because of small contribution to the sound field; the term containing delta (f) is a non-point source and plays a decisive role in the sound field, wherein the parameters W, F, L, P and Q are defined as
Wherein γ=1.4 is an air specific heat ratio;
the specific process of sound source parameter determination is as follows:
a. and selecting a proper static permeable surface f=0 according to a computational fluid dynamics high-precision simulation result, and outputting geometric parameters of all grid cells of the permeable surface, wherein the geometric parameters comprise a normal vector n outside the grid cells and a dimensionless central point position y and an area s.
b. Calculating time steps for each unsteady flow, outputting unsteady flow parameters of the permeable surface including time τ, density ρ and disturbance density ρ ', disturbance pressure p ' and disturbance velocity u ', and disturbance pressure gradientAnd a disturbance velocity gradientAnd (3) degree of divergence->
c. For each grid cell for each unsteady time step, W, F, L, P and Q are calculated separately using equation (2) to determine the sound source parameters on the permeable surface.
Step 5, placing the observation pointIn the plane, 36 observation points are uniformly arranged at the radius of +.>And to determine the dimensionless coordinates of the observation point x. Determining dimensionless acoustic velocity u' (x, t) from an unsteady sound source parameter on the permeable surface by the following equation (3);
wherein x and y represent the positions of the observation point and the sound source, respectively, t and τ represent the time of the observation point and the sound source, respectively, and the variables areAnd R is defined as:
wherein:
[…] ret indicating the delay time tau ret The value of =t-R, the remaining variables are defined as follows:
the subscripts i, j, k=1, 2,3 of each tensor in the formula denote x in the Cartesian coordinate system 1 ,x 2 ,x 3 Components in three directions;
the specific calculation process is as follows:
a. step 5-1, wherein n=21600 is the number of permeable face mesh cells;
b. step 5-2: for each grid cell of each unsteady time step, A is calculated using equation (6) i 、B i And E is ij The method comprises the steps of carrying out a first treatment on the surface of the Calculating the parameter L by using five-point fourth-order precision finite difference algorithm i 、E ij And Q is the value of the derivative of the dimensionless time tau;
c. for each grid cell, parameters are calculated using equations (4) and (5)And R, and determining the maximum value R of R max And a minimum value R min Simultaneously calculate the parameters +.>And->
d. Determining a dimensionless start time t of a received sound wave at a viewpoint x s ＝τ s +R max And expiration time t e ＝τ e +R min Wherein τ s And τ e Dimensionless start time and end time for the sound source; the observation point time t is discretized according to the fixed step length delta tau of the sound source time tau, and the m-th time step discretization time is t m MΔτ, where m is in the range of [ int (t s /Δτ)+1,int(t c /Δτ)]；
e. For the first time step of the d-th grid unit, calculating the time when the radiated sound wave reaches the observation point x Wherein R is d R is the value between the d-th grid unit and the observation point x; determine->Corresponding time step-> And its dimensionless deviation->
f. If it isOr->The d-th grid-cell sound source of the first time step contributes 0 to the sound field; otherwise, determining the contribution ++of the grid cell using equation (7)>
g. Determining a d-th grid-cell sound source pair for a first time stepTime-step sound field contribution-> The mesh unit sound source pair +.>Time-step sound field contribution->
h. And summing the contributions of all the grid cell sound sources to each observation point time step to obtain dimensionless acoustic velocity u' (x, t).
6. Multiplying dimensionless acoustic velocity u' (x, t) by sound velocityObtaining the dimensional acoustic velocity +.>Selecting data in a period, and drawing a change history curve chart of the acoustic speed of the observation point along with time; meanwhile, the root mean square value of data in one period is calculated, and a directivity distribution diagram of an effective value of the acoustic velocity is drawn.
Observation point x at observation angle θ=120° under the same conditions of permeable surface geometry and flow parameters 2 Directional acoustic velocity time history a pair of the present method value solution, the existing method value solution, and the theoretical analytical solution is shown in fig. 3, where curve 8 is the theoretical analytical solution, curve 9 is the existing method value solution, and curve 10 is the present method value solution. X is x 1 Directional Acoustic velocity effective value directivity distribution the present method value solution, the existing method value solution, and the theoretical analytical solution pair are shown in FIG. 4, wherein curve 11 is the theoretical analytical solution, curve 12 is the existing method value solution, and curve 13 is the present method value solution. The numerical solution of the existing method is identical to the theoretical solution, so that the correctness of the method is proved, and the superiority of the method is demonstrated.
Claims (3)
1. A method for time-domain extrapolation of acoustic velocity based on a permeable surface, comprising the steps of:
step 1: according to known uniformity levelsDensity of uniform flowSound velocity->And flow characteristic dimension->By-> And->Space with dimension ∈>Time->Density ofPressure->And speed->Dimensionless;
step 2: according to known uniform average flow pressureAnd speed->By->And-> Determining disturbance pressure p' =p-p ∞ And disturbance speed u' =u-u ∞ Simultaneously determining the disturbance density ρ' =ρ -1;
step 3: according to the high-precision simulation result of computational fluid dynamics, selecting a static permeable surface f=0, so that the generation, reflection and refraction phenomena of sound waves are enclosed in the permeable surface;
step 4: according to the high-precision simulation result of computational fluid dynamics, determining parameters of a sound source on a permeable surface through a dimensionless non-homogeneous convection wave equation which is shown in a formula (1) and takes a disturbance speed u' as a variable;
wherein f=0 represents the permeable surface, f > 0 and f < 0 being the outer and inner regions of the permeable surface, respectively; h (f) is the Heaviside function, delta (f) is the Dirac function,as the unit external normal vector of the permeable surface, the derivative of the substanceThe term containing H (f) at the right end of the equation is a volume source and is ignored because of small contribution to the sound field; the term containing δ (f) is a non-point source, which is decisive for the sound field, where the parameters W, F, L, P and Q are defined as:
wherein γ=1.4 is an air specific heat ratio;
step 5: determining dimensionless acoustic velocity u' (x, t) from the sound source parameters on the permeable surface by equation (3) for an observation point x outside the permeable surface;
wherein x and y represent the positions of the observation point and the sound source, respectively, t and τ represent the time of the observation point and the sound source, respectively, and the variables areAnd R is defined as:
wherein:
[…] ret indicating the delay time tau ret The value of =t-R, the remaining variables are defined as follows:
the subscripts i, j, k=1, 2,3 of each tensor in the formula denote x in the Cartesian coordinate system 1 ，x 2 ，x 3 Components in three directions;
step 6: multiplying dimensionless acoustic velocity u' (x, t) by sound velocityObtaining the dimensional acoustic velocity +.>
2. The permeable-surface-based acoustic velocity time-domain extrapolation method according to claim 1, wherein the determining of the sound source parameters of the permeable surface according to formula (1) comprises:
step 4-1: selecting a static permeable surface f=0 according to a computational fluid dynamics high-precision simulation result, and outputting geometric parameters of all grid cells of the permeable surface, wherein the geometric parameters comprise a grid cell unit external normal vector n, a dimensionless central point position y and an area s;
step 4-2: calculating time steps for each unsteady flow, outputting unsteady flow parameters of the permeable surface including time τ, density ρ and disturbance density ρ ', disturbance pressure p ' and disturbance velocity u ', and disturbance pressure gradientAnd disturbance speed gradient->And (3) degree of divergence->
Step 4-3: for each grid cell for each unsteady time step, W, F, L, P and Q are calculated separately using equation (2) to determine the sound source parameters on the permeable surface.
3. A method of time-domain extrapolation of acoustic velocity based on a permeable surface according to claim 2 wherein the solving of equation (3) comprises:
step 5-1: determining a far field stationary acoustic viewpoint x and discretizing equation (3) into the following form
Where D is the number of permeable face mesh cells, d=1, 2,3,..d is the number of mesh cells, s d Is the grid cell area numbered d;
step 5-2: for each grid cell of each unsteady time step, A is calculated using equation (6) i 、B i And E is ij The method comprises the steps of carrying out a first treatment on the surface of the Calculating the parameter L using finite difference algorithm i 、E ij And Q is the value of the derivative of the dimensionless time tau;
step 5-3: for each grid cell, parameters are calculated using equations (4) and (5)And R, and determining the maximum value R of R max And a minimum value R min Simultaneously calculate the parameters +.>And->
Step 5-4: determining a dimensionless start time t of a received sound wave at a viewpoint x s ＝τ s +R max And expiration time t e ＝τ e +R min Wherein τ s And τ e Dimensionless start time and end time for the sound source; the observation point time t is discretized according to the fixed step length delta tau of the sound source time tau, and the m-th time step discretization time is t m MΔτ, where m is in the range of [ int (t s /Δτ)+1，int(t c /Δτ)]；
Step 5-5: for the first time step of the d-th grid unit, calculating the time when the radiated sound wave reaches the observation point xWherein R is d R is the value between the d-th grid unit and the observation point x; determine->Corresponding time stepsAnd its dimensionless deviation->
Step 5-6: if it isOr->The d-th grid-cell sound source of the first time step contributes 0 to the sound field; otherwise, determining the contribution ++of the grid cell using equation (7)>
Step 5-7: determining a d-th grid-cell sound source pair for a first time stepTime-step sound field contributionThe mesh unit sound source pair +.>Time stepIs of sound field contribution of (a)
Step 5-8: and summing the contributions of all the grid cell sound sources to each observation point time step to obtain dimensionless acoustic velocity u' (x, t).
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