Method and equipment for constructing non-reflecting boundary condition model for aviation aeroacoustics

Abstract

The present invention discloses a method and device for constructing a non-reflecting boundary condition model for aviation aeroacoustics, which belongs to the field of aviation aerodynamic test and is used to provide effective non-reflecting boundary conditions for the boundary of the calculation domain during aviation aeroacoustics calculation to reduce / avoid non-physical reflection of sound waves on the boundary. The method comprises the following steps: arranging the general control equation into a standard form; rearranging the standard form control equation in the x-axis direction to obtain the characteristic equation along the x-axis; performing characteristic decomposition on the matrix [A] to obtain the eigenvalue Λ and the left and right eigenvectors L and R of the matrix [A]; obtaining the characteristic wave equation and characteristic variables in the x-axis direction; determining the control equation at the boundary; considering the lateral characteristic terms perpendicular to the x-axis; considering the influence of the Mach number on the characteristic variables; and applying the characteristic non-reflecting boundary conditions in a given area. The present invention improves the stability and numerical accuracy of aeroacoustic calculations.

Description

Technical Field

[0001] The invention belongs to the field of aviation aerodynamic test, and in particular relates to a method and a device for constructing a non-reflecting boundary condition model for aviation aeroacoustics. Background Art

[0002] In aviation aeroacoustic simulation, there are a lot of problems that need to be solved for infinite or semi-infinite regions. However, due to the limitation of computing resources, the computational region cannot be infinite, and the computational domain needs to be truncated. The solution on the new bounded region should be an approximation of the solution on the original unbounded region. In order to ensure the stability of the calculation and the correctness of the calculation results, the outer boundary of the computational domain needs to adopt a non-reflecting boundary condition. The function of this boundary is to prevent various waves in the computational domain from reflecting when passing through the boundary, and to avoid introducing some non-physical disturbances into the computational domain.

[0003] In the process of simulating sound waves, the treatment of non-reflecting boundary conditions is a prominent problem. Since the energy of sound waves is much smaller than the energy of the surrounding flow field, and the wavelength scale of sound waves is larger than the scale of change of the surrounding flow field, this requires that the proposed boundary conditions can not only allow the small average flow to flow out smoothly, but also prevent the sound waves from producing non-physical reflections on the boundary. If the boundary conditions are not handled properly, the non-physical disturbance errors caused will return to the calculation domain, propagate and diffuse as the calculation proceeds, affecting the accuracy of the calculation results. Therefore, non-reflecting boundaries play an important role in the accurate numerical calculation of aviation aeroacoustics. Summary of the invention

[0004] Based on the above shortcomings, the present invention provides a method for constructing a reflection-free boundary condition model for aviation aeroacoustics to reduce / avoid non-physical reflections of sound waves on the boundaries and ensure the stability and numerical accuracy of aeroacoustic calculations.

[0005] To achieve the above-mentioned purpose of the invention, the present invention provides the following technical solution: a method for constructing a non-reflecting boundary condition model for aviation aeroacoustics, the steps of which are as follows:

[0006] Step 1: Arrange the linearized Euler equation, Euler equation or Navier-Stokes equation into the following standard form equation:

[0007]

[0008] Where t is time, x and y represent the directions of the two coordinate axes in the Cartesian coordinate system; [U] is the vector containing the original perturbation variable, [A] and [B] are the flux Jacobian matrices, T0 is the viscosity term, and S0 is the source term;

[0009] Step 2: Rearrange the standard form control equation in the x-axis direction to obtain the characteristic equation along the x-axis. Simply shift the terms of equation (16) according to the flux along the x-axis to obtain the following equation:

[0010]

[0011] Step 3: Perform eigendecomposition on the matrix [A] according to equation (17) to obtain the eigenvalue Λ and the left eigenvector L and right eigenvector R of the matrix [A]. The eigenvalue Λ is expressed in ascending order as:

[0012] Λ(diag)=(u0-1,u0,u0,u0+1) (3)

[0013] Where u0 is the initial velocity in the x direction. The relationship between Λ, [A], [L] and [R] satisfies [A] = [R][Λ][L]. Substituting it into equation (17) and multiplying both ends of the equation by the matrix [L] on the left, we get the following equation:

[0014]

[0015] Step 4: Obtain the characteristic wave equation and characteristic variables in the x-axis direction. Further organize equation (19) to obtain the characteristic equation as follows:

[0016]

[0017] Among them, the characteristic differential variable Defined as is the horizontal term, which contains the characteristic variables that intersect the x-axis. represents the source term, which contains all the right-hand side variables except the lateral term. By expanding the second term in equation (20), the four characteristic variables are expressed as:

[0018]

[0019]

[0020]

[0021]

[0022] in, For the upward sound wave, For the downward sound wave, is the entropy wave, is the vorticity wave, p is the pressure, u and v are the velocities in the x and y directions respectively, and ρ represents the density. In order to avoid the acoustic reflection at the boundary of the subsonic outflow domain, the upstream wave The amplitude of the wave needs to be set to zero. If the downstream boundary is supersonic, the related pulsation will not be returned to the computational domain, so no related processing is required.

[0023] Step 5: At the boundary, solve the control equation according to the characteristic quantity. The control equation is:

[0024]

[0025] where [d] is defined as

[0026]

[0027] Step 6: Consider the lateral characteristic term perpendicular to the x-axis. The lateral term in equation (20) is The specific expressions of the four eigenvectors are:

[0028]

[0029]

[0030]

[0031]

[0032] Where v0 is the initial velocity in the y direction;

[0033] Step 7: Consider the influence of Mach number on characteristic variables, and the expression used is:

[0034]

[0035] Where A = 0.29, B = 0.7, M is the Mach number;

[0036] Step 8: Apply the characteristic non-reflecting boundary condition in the given area:

[0037] Apply the current characteristic non-reflecting boundary to the strip region with a length of l near the boundary to form a strip lateral characteristic boundary condition. The incident characteristic wave is set to:

[0038]

[0039] in, and is the incident acoustic characteristic wave before and after non-reflecting boundary treatment, where σ is given by:

[0040]

[0041] Where β sets the shape of the zone damping curve, l is the length of the zone, and h is the distance to the inner boundary.

[0042] On the other hand, the object of the present invention is achieved through a computer device, which includes a processor and a computer-readable storage medium communicatively connected to the processor, wherein computer instructions are stored in the computer-readable storage medium, and when the computer instructions are executed by the processor, the steps of the construction method of the present invention as described above are implemented.

[0043] On the other hand, the object of the present invention is achieved through a computer-readable storage medium, on which computer instructions are stored. When the computer instructions are executed by a processor, the steps of the construction method of the present invention as described above are implemented.

[0044] Beneficial effects and advantages of the present invention: Compared with the prior art, the present invention takes into account the lateral characteristic term in the process of establishing the model to better eliminate the oblique wave, and introduces additional parameters for controlling the performance of the boundary conditions: the buffer length l and the buffer forcing parameters α and β. The present invention extends the existing non-reflecting boundary conditions to a wide range of angular frequencies, flow Mach numbers, and cut-in ratio changes, broadens the application scope of non-reflecting boundary conditions in aviation aeroacoustic calculations, improves the stability and numerical accuracy of aeroacoustic calculations, and thus improves the efficiency of aviation aeroacoustic simulation tests. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a flow chart of a general non-reflecting boundary condition algorithm based on an eigenvalue method of the present invention;

[0046] Figure 2 This is a schematic diagram of a non-reflective boundary test case;

[0047] Figure 3 The figure is a curve diagram of the change of the numerical reflection with the wave direction angle obtained by the model constructed based on the present invention under different incoming flow Mach numbers, wherein the figure marks are: 1, sound wave, 2, analysis point. DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0049] Example 1

[0050] like Figure 1 As shown in FIG. 1 , a method for constructing a non-reflecting boundary condition model for aviation aeroacoustics is shown in FIG. 1 . The steps are as follows:

[0051] Step 1: Arrange the linearized Euler equation, Euler equation or Navier-Stokes equation into the following standard form equation:

[0052]

[0053] Where t is time, x and y represent the directions of the two coordinate axes in the Cartesian coordinate system; [U] is the vector containing the original perturbation variable, [A] and [B] are the flux Jacobian matrices, T0 is the viscosity term, and S0 is the source term;

[0054] Step 2: Rearrange the standard form control equation in the x-axis direction to obtain the characteristic equation along the x-axis. Simply shift the terms of equation (16) according to the flux along the x-axis to obtain the following equation:

[0055]

[0056] Step 3: Perform eigendecomposition on the matrix [A] according to equation (17) to obtain the eigenvalue Λ and the left eigenvector L and right eigenvector R of the matrix [A]. The eigenvalue Λ is expressed in ascending order as:

[0057] Λ(diag)=(u0-1,u0,u0,u0+1) (18)

[0058] Where u0 is the initial velocity in the x direction. The relationship between Λ, [A], [L] and [R] satisfies [A] = [R][Λ][L]. Substituting it into equation (17) and multiplying both ends of the equation by the matrix [L] on the left, we get the following equation:

[0059]

[0060] Step 4: Obtain the characteristic wave equation and characteristic variables in the x-axis direction. Further organize equation (19) to obtain the characteristic equation as follows:

[0061]

[0062] Among them, the characteristic differential variable Defined as is the horizontal term, which contains the characteristic variables that intersect the x-axis. represents the source term, which contains all the right-hand side variables except the lateral term. By expanding the second term in equation (20), the four characteristic variables are expressed as:

[0063]

[0064]

[0065]

[0066]

[0067] in, For the upward sound wave, For the downward sound wave, is the entropy wave, is the vorticity wave, p is the pressure, u and v are the velocities in the x and y directions respectively, and ρ represents the density. In order to avoid the acoustic reflection at the boundary of the subsonic outflow domain, the upstream wave The amplitude of the wave needs to be set to zero. If the downstream boundary is supersonic, the related pulsation will not be returned to the computational domain, so no related processing is required.

[0068] Step 5: At the boundary, solve the control equation according to the characteristic quantity. The control equation is:

[0069]

[0070] where [d] is defined as

[0071]

[0072] Step 6: Consider the lateral characteristic term perpendicular to the x-axis. The lateral term in equation (20) is The specific expressions of the four eigenvectors are:

[0073]

[0074]

[0075]

[0076]

[0077] Where v0 is the initial velocity in the y direction;

[0078] Step 7: Consider the influence of Mach number on characteristic variables, and the expression used is:

[0079]

[0080] Where A = 0.29, B = 0.7, M is the Mach number;

[0081] Step 8: Apply the characteristic non-reflecting boundary condition in the given area:

[0082] Apply the current characteristic non-reflecting boundary to the strip region with a length of l near the boundary to form a strip lateral characteristic boundary condition. The incident characteristic wave is set to:

[0083]

[0084] in, and is the incident acoustic characteristic wave before and after non-reflecting boundary treatment, where σ is given by:

[0085]

[0086] Where β sets the shape of the region damping curve, l is the length of the region, and h is the distance to the inner boundary, such as Figure 2 shown.

[0087] like Figure 3 As shown, it is shown that for a wide range of Mach numbers and wave angles, the numerical reflection obtained based on the current model is still less than 5%, verifying the good non-reflection performance of the current model.

Claims

1. A method for constructing a non-reflecting boundary condition model for aviation aeroacoustics, characterized in that: Here are the steps: Step 1: Arrange the linearized Euler equation, Euler equation or Navier-Stokes equation into the following standard form equation: Where t is time, x and y represent the directions of the two coordinate axes in the Cartesian coordinate system; [U] is the vector containing the original perturbation variable, [A] and [B] are the flux Jacobian matrices, T0 is the viscosity term, and S0 is the source term; Step 2: Rearrange the standard form control equation in the x-axis direction to obtain the characteristic equation along the x-axis. Simply shift the terms of equation (1) according to the flux along the x-axis to obtain the following equation: Step 3: Perform eigendecomposition on the matrix [A] according to equation (2) to obtain the eigenvalue Λ and the left eigenvector L and right eigenvector R of the matrix [A]. The eigenvalue Λ is expressed in ascending order as: Λ(diag)=(u0-1,u0,u0,u0+1) (3) Where u0 is the initial velocity in the x direction. The relationship between Λ, [A], [L] and [R] satisfies [A] = [R][Λ][L]. Substituting it into equation (2) and multiplying both ends of the equation by the matrix [L] on the left, we get the following equation: Step 4: Get the characteristic wave equation and characteristic variables in the x-axis direction. Further sort out equation (4) to get the characteristic equation as follows: Among them, the characteristic differential variable Defined as is the horizontal term, which contains the characteristic variables that intersect the x-axis. represents the source term, including all right-hand side variables except the lateral term. By expanding the second term in equation (5), the four characteristic variables are expressed as: in, For the upward sound wave, For the downward sound wave, is the entropy wave, is the vorticity wave, p is the pressure, u and v are the velocities in the x and y directions respectively, and ρ represents the density. In order to avoid the acoustic reflection at the boundary of the subsonic outflow domain, the upstream wave The amplitude of the wave needs to be set to zero. If the downstream boundary is supersonic, the related pulsation will not be returned to the computational domain, so no related processing is required. Step 5: At the boundary, solve the control equation according to the characteristic quantity. The control equation is: where [d] is defined as Step 6: Consider the lateral characteristic term perpendicular to the x-axis. The lateral term in equation (5) is The specific expressions of the four eigenvectors are: Where v0 is the initial velocity in the y direction; Step 7: Consider the influence of Mach number on characteristic variables, and the expression used is: Where A = 0.29, B = 0.7, M is the Mach number; Step 8: Apply the characteristic non-reflecting boundary condition in the given area: Apply the current characteristic non-reflecting boundary to the strip region with a length of l near the boundary to form a strip lateral characteristic boundary condition. The incident characteristic wave is set to: in, and is the incident acoustic characteristic wave before and after non-reflecting boundary treatment, where σ is given by: Where β sets the shape of the zone damping curve, l is the length of the zone, and h is the distance to the inner boundary.

2. A computer device comprising a processor and a computer-readable storage medium communicatively connected to the processor, wherein the computer-readable storage medium stores computer instructions, characterized in that: When the computer instructions are executed by the processor, the steps of the construction method described in claim 1 are implemented.

3. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed by a processor, the steps of the construction method described in claim 1 are implemented.

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