Numerical simulation method of two-equation eddy viscosity turbulence model based on general time root square scale

Abstract

The present application relates to a numerical simulation method, apparatus, computer equipment, and storage medium for a two-equation eddy viscosity turbulence model based on a general time root square scale. The method comprises: based on the ω-scale equation of an existing SST model, obtaining the #imgabs2# scale equation of turbulence with respect to the #imgabs1# scale according to the relationship between the #imgabs0# general time root square scale and the ω-scale; coupling the #imgabs3# scale equation with the predicted turbulence-based k-equation of the SST model to obtain the #imgabs4# model; and then coupling the #imgabs5# model with the predicted RANS equations to obtain a coupled equation set. When performing numerical simulation of an aircraft turbulent flow field, grid data of the aircraft flow field to be simulated is constructed, and the coupled equation set is numerically solved based on the grid data to obtain numerical simulation results of the aircraft turbulent flow field. The present invention strictly ensures that the wall boundary condition is zero when n is a positive integer, and can achieve numerical stability when using high-precision discrete or complex structured / unstructured grids.

Description

Technical Field

[0001] The present application relates to the field of computational fluid dynamics, and in particular to a numerical method, apparatus, computer equipment and storage medium for a two-equation eddy viscosity turbulence model based on a general time root square scale. Background Art

[0002] With the advancement of computing technology, computational fluid dynamics (CFD) has become one of the three major approaches (theoretical, experimental, and computational) for studying the generation and evolution of turbulent structures and solving practical engineering turbulence problems. The rapid development of CFD software, in particular, has brought significant benefits to designers and researchers. Traditionally, numerical simulation methods for turbulence fall into three categories: Reynolds-averaged simulation (RANS), large eddy simulation (LES), and direct numerical simulation (DNS). Due to limitations in computer hardware, RANS remains the primary approach for solving engineering problems.

[0003] The eddy viscosity turbulence model is the most important type of turbulence model in the RANS method, based on the Boussinesq hypothesis:

[0004]

[0005] Eddy viscosity coefficient μ t =ρν t is the scaling factor of the Boussinesq approximation. Two-equation turbulence models have been the foundation of theoretical research on turbulence patterns for the past fifty years. These models typically solve for equivalent values ​​of the turbulent kinetic energy, k, and the turbulent length scale, l.

[0006] Turbulence scales primarily provide variables for the kinetic energy dissipation rate, energetic length scales, and energetic time scales. The first type is commonly used in current commercial CFD software. The isotropic dissipation rate ε equation, derived from a direct closure of the dissipation term in the Reynolds stress equation or the turbulent kinetic energy equation, was first derived by Professor Zhou Peiyuan.

[0007] After decades of development, the ε model has evolved into many versions and is widely used.

[0008]

[0009] However, there are two problems with ε as a characteristic scale: first, the dissipation rate lacks natural boundary conditions; second, high-order correlations need to be processed near the wall. These two problems have an adverse impact on the stability of the model and the simulation accuracy near the wall. To address these two problems, researchers have adopted different improvements, such as the specific dissipation rate ω:

[0010]

[0011] The concept of specific dissipation rate was first proposed by Kolmogorov in 1942, but its real success came through the work of Wilcox, Menter, and others. While the ω-scaling equation improves the numerical rigidity issues caused by the ε-equation in handling high-order correlations, it still lacks natural boundary conditions. This leads to numerical instabilities when using high-precision discretization or complex structured or unstructured meshes in engineering applications such as numerical simulation of turbulent flow fields for aircraft and other aerodynamic problems. Consequently, existing technologies suffer from poor adaptability. Summary of the Invention

[0012] Based on this, it is necessary to provide a numerical method, device, computer equipment and storage medium based on a two-equation eddy viscosity turbulence model on a general time root square scale that can solve the numerical instability problem when high-precision discrete or complex structured / unstructured grids are used in aircraft flow field simulation to address the above technical problems.

[0013] A numerical method for a two-equation eddy viscosity turbulence model based on a general time root square scale, the method comprising:

[0014] Obtain the ω-scaling equations for the turbulent SST-based model; ω represents the specific dissipation rate scale;

[0015] Get pre-derived The relationship between the general time root square scale and the ω scale is obtained based on the relationship and the ω scale equation. The equation of the scale; where τ represents the energetic time scale, and n represents the nth root, which is a positive integer;

[0016] Get the k equation of the turbulent SST model; k represents the turbulent kinetic energy;

[0017] Modify the relevant terms of the K equation to the The two-equation eddy viscosity turbulence model based on the general time root square scale is obtained by coupling the scale equations. Model;

[0018] The known Reynolds-averaged Navier-Stokes (RANS) equations are coupled with a two-equation eddy-viscosity turbulence model based on general time root square scaling to obtain a coupled equation system.

[0019] Grid data of the aircraft flow field to be simulated is constructed, and the coupled equations are numerically solved according to the grid data to obtain numerical simulation results of the aircraft turbulent flow field.

[0020] In one embodiment, the method further includes: obtaining the ω-scale equation of the turbulence based on the SST model as follows:

[0021]

[0022] in, is the time-averaged density, ω is the specific dissipation rate scale, t is time, and j is the subscript for the coordinate index. is the three components of Favre average velocity, x j (j=1,2,3) are the three-directional coordinate components, γ is the coefficient of the specific dissipation rate scaling equation, ν t is the kinetic eddy viscosity coefficient, P is the turbulence generation, β is the dissipation term coefficient of the specific dissipation rate scaling equation, μ is the dynamic viscosity coefficient, σ ω is the diffusion coefficient, μ t is the eddy viscosity coefficient, F1 is the first transition function, σ ω2 is the coefficient of the cross-derivative term of the specific dissipation rate scaling equation, and k is the turbulent kinetic energy.

[0023] In one embodiment, the method further includes: The general relationship between the time root square scale and the ω scale is:

[0024]

[0025] Where n is Adjustment coefficients for general time root square and ω scales.

[0026] In one embodiment, the method further includes: obtaining a pre-derived The relationship between the general time root square scale and the ω scale is obtained based on the relationship and the ω scale equation. The scaling equation is:

[0027]

[0028] in, express The general time root square scale, α ω is the coefficient of the dissipation term of the general time root square scaling equation, β ω Generates the term coefficients for the general time root square scaling equation, σ d is the coefficient of the cross derivative term of the general time root square scaling equation.

[0029] In one embodiment, the method further includes: obtaining a k-equation of a turbulent flow based on an SST model, including:

[0030] The k equation for the turbulence-based SST model is:

[0031]

[0032] Among them, σ k is the coefficient of the dissipation term in the k equation.

[0033] In one embodiment, the turbulent kinetic energy generation term is further comprised of:

[0034]

[0035] Where S is the dependent variable, δ ij is the Kronecker operator.

[0036] In one embodiment, the eddy viscosity coefficient is μ t :

[0037]

[0038] Among them, a1 is the correction coefficient of the eddy viscosity coefficient formula, Ω is the vorticity, F2 is the second transition function.

[0039] In one embodiment, the method further includes: modifying the relevant terms of the k equation to be the same as the The two-equation eddy viscosity turbulence model based on the general time root square scale is coupled with the scaling equations:

[0040]

[0041] In one embodiment, the predicted Reynolds-averaged Navier-Stokes (RANS) equations are:

[0042]

[0043] in is the time-averaged pressure, is the average temperature in Favre, is Favre's average total energy, c p is the constant pressure specific heat ratio, Pr is the laminar Prandtl constant, Pr t is the turbulent Prandtl constant;

[0044] in is the viscous stress tensor:

[0045]

[0046] τ ij is the Reynolds stress tensor, which is obtained through the Boussinesq relationship:

[0047]

[0048] That is, the coupling of the RANS equations and the two-equation eddy viscosity turbulence model based on the general time root square scale is completed.

[0049] In one embodiment, the method further includes: using a numerical method for partial differential equations to solve the seven independent variables included in the coupled equations according to the grid data. k and λ are numerically solved;

[0050] Then, the numerical solutions of other variables are obtained by deducing the relationship.

[0051] A numerical device for a two-equation eddy viscosity turbulence model based on a general time root square scale, the device comprising:

[0052] The ω scale equation acquisition module is used to obtain the ω scale equation of the turbulence based on the SST model; ω represents the specific dissipation rate scale;

[0053] The time root square equation determination module is used to obtain the pre-derived The relationship between the general time root square scale and the ω scale is obtained based on the relationship and the ω scale equation. The equation of the scale; where τ represents the energetic time scale, and n represents the nth root, which is a positive integer;

[0054] The two-equation eddy viscosity turbulence model determination module based on the general time root square scale is used to obtain the k equation of turbulence based on the SST model; k represents the turbulent kinetic energy; the relevant terms of the k equation are modified to match the The two-equation eddy viscosity turbulence model based on the general time root square scale is obtained by coupling the scale equations. Model; The known Reynolds-averaged Navier-Stokes (RANS) equations are coupled with a two-equation eddy-viscosity turbulence model based on general time root square scaling to obtain a coupled equation system;

[0055] The numerical simulation module is used to construct grid data of the aircraft flow field to be simulated, and numerically solve the coupled equations according to the grid data to obtain the numerical simulation results of the aircraft turbulent flow field.

[0056] A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0057] Obtain the ω-scaling equations for the turbulent SST-based model; ω represents the specific dissipation rate scale;

[0058] Get pre-derived The relationship between the general time root square scale and the ω scale is obtained based on the relationship and the ω scale equation. The equation of the scale; where τ represents the energetic time scale, and n represents the nth root, which is a positive integer;

[0059] Get the k equation of the turbulence based on the SST model; k represents the turbulent kinetic energy;

[0060] Modify the relevant terms of the K equation to the The two-equation eddy viscosity turbulence model based on the general time root square scale is obtained by coupling the scale equations. Model;

[0061] The known Reynolds-averaged Navier-Stokes (RANS) equations are coupled with a two-equation eddy-viscosity turbulence model based on general time root square scaling to obtain a coupled equation system.

[0062] Grid data of the aircraft flow field to be simulated is constructed, and the coupled equations are numerically solved according to the grid data to obtain numerical simulation results of the aircraft turbulent flow field.

[0063] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the following steps:

[0064] Obtain the ω-scaling equations for the turbulent SST-based model; ω represents the specific dissipation rate scale;

[0065] Get pre-derived The relationship between the general time root square scale and the ω scale is obtained based on the relationship and the ω scale equation. The equation of the scale; where τ represents the energetic time scale, and n represents the nth root, which is a positive integer;

[0066] Get the k equation of the turbulence based on the SST model; k represents the turbulent kinetic energy;

[0067] Modify the relevant terms of the K equation to the The two-equation eddy viscosity turbulence model based on the general time root square scale is obtained by coupling the scale equations. Model;

[0068] The known Reynolds-averaged Navier-Stokes (RANS) equations are coupled with a two-equation eddy-viscosity turbulence model based on general time root square scaling to obtain a coupled equation system.

[0069] Grid data of the aircraft flow field to be simulated is constructed, and the coupled equations are numerically solved according to the grid data to obtain numerical simulation results of the aircraft turbulent flow field.

[0070] The numerical method, apparatus, computer equipment and storage medium of the two-equation eddy viscosity turbulence model based on the general time root square scale are based on the ω scale equation of the existing SST model and are derived according to the The general relationship between the time root square scale and the ω scale is obtained by combining the two to obtain the relationship between the turbulence and the ω scale. Scale Scaling equation; The scaling equation and the predicted turbulence are coupled based on the k-equation of the SST model to obtain a two-equation eddy viscosity turbulence model based on the general time root square scale, namely: Model, then The model is coupled with the known Reynolds-averaged Navier-Stokes (RANS) equations to obtain a coupled equation group. When performing numerical simulation of the aircraft turbulent flow field, the grid data of the aircraft flow field to be simulated is constructed, and the coupled equation group is numerically solved based on the grid data to obtain the numerical simulation results of the aircraft turbulent flow field. In the model, when n is a positive integer, the wall boundary condition is strictly 0, which helps to reduce the dependence of the equation on wall information; further, when n is a positive even number greater than 2, the calculated value of λ will not affect the dissipation term in the k equation. This is very beneficial for maintaining the positive turbulent kinetic energy and can achieve numerical stability when using high-precision discretization or complex structured / unstructured grids. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 1 is a flow chart of a numerical method for a two-equation eddy viscosity turbulence model based on a general time root square scale in one embodiment;

[0072] Figure 2 Schematic diagram of the flow around a pointed leading edge delta wing in one embodiment: surface grid and station division, where (a) is a schematic diagram of the surface grid and (b) is a schematic diagram of the station division;

[0073] Figure 3 The SST in the flow around the sharp leading edge delta wing in one embodiment Schematic diagram of convergence results for different values ​​of model parameter n;

[0074] Figure 4 The SST in the flow around the sharp leading edge delta wing in one embodiment Schematic diagram of the pressure distribution obtained by the model at different stations, where (a) is x / c r = 0.40, (b) is the pressure distribution diagram obtained by x / c r = 0.60, (c) is x / c r = 0.80, (d) is the pressure distribution diagram obtained by x / c r = 0.95 obtained by the pressure distribution diagram;

[0075] Figure 51 is a block diagram of a numerical device for a two-equation eddy viscosity turbulence model based on a general time root square scale in one embodiment;

[0076] Figure 6 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0078] In one embodiment, Figure 1 As shown in FIG, a numerical method based on a two-equation eddy viscosity turbulence model with a general time root square scale is provided, which includes the following steps:

[0079] Step 102: Obtain the ω-scale equation of the turbulence based on the SST model.

[0080] ω represents the specific dissipation rate scale.

[0081] The numerical simulation of aircraft turbulent flow field is based on the proposed physical model. The existing eddy viscosity turbulence models are mostly based on the ε scale or ω scale, which do not have natural boundary conditions at the viscous wall. This will lead to numerical instability when using high-precision discrete or complex structured / unstructured grids, which will have an adverse effect on the numerical simulation of aircraft flow field. The present invention proposes a scaling equation with natural boundaries at the viscous wall, based on the general time root square scale. And coupled with the turbulent kinetic energy K equation, a two-equation eddy viscosity model is formed, namely Model.

[0082] Specifically, the ω-scale equation in the SST model proposed by Menter is:

[0083]

[0084] in, is the time-averaged density, ω is the specific dissipation rate scale, t is time, and j is the subscript for the coordinate index. is the three components of Favre average velocity, x j (j=1,2,3) are the three-directional coordinate components, γ is the coefficient of the specific dissipation rate scaling equation, ν t is the kinetic eddy viscosity coefficient, P is the turbulence generation, β is the dissipation term coefficient of the specific dissipation rate scaling equation, μ is the dynamic viscosity coefficient, σ ω is the diffusion coefficient, μ t is the eddy viscosity coefficient, F1 is the first transition function, σ ω2is the coefficient of the cross-derivative term of the specific dissipation rate scaling equation, and k is the turbulent kinetic energy.

[0085] Step 104, obtain the pre-derived The general relationship between the time root square scale and the ω scale is obtained based on the relationship and the ω scale equation. Scale Scale equation.

[0086] Where τ represents the energetic time scale, and n represents the nth root, which is a positive integer.

[0087] The present invention derives from the The relationship between the time root square scale and the ω scale is:

[0088]

[0089] Where n is Adjustment coefficients for general time root square and ω scales.

[0090] Combined with the ω-scaling equation, we can get Scaling equation:

[0091]

[0092] Where n is a positive integer that regulates the numerical properties of the scaling equation. A special case, n = 1, restores the time scaling equation proposed by Spezia1e in 1992. The second term on the right-hand side of this equation is a constant, meaning there are no generated terms, which can lead to serious numerical rigidity issues.

[0093] in, express Generally, the time root square scale, α ω is the coefficient of the dissipation term of the general time root square scaling equation, β ω Generates the term coefficients for the general time root square scaling equation, σ d is the coefficient of the cross derivative term of the general time root square scaling equation.

[0094] Step 106: Obtain the k-equation of the turbulence based on the SST model.

[0095] k represents the turbulent kinetic energy.

[0096] The k equation based on the SST model is:

[0097]

[0098] Among them, σ k is the coefficient of the dissipation term in the k equation.

[0099] The generated items are:

[0100]

[0101] The dissipative term is:

[0102]

[0103] The eddy viscosity coefficient is obtained by the following formula:

[0104]

[0105] The vorticity and strain are:

[0106]

[0107]

[0108] The coefficients in the scaling equation are weighted by the transition function F1:

[0109] φ=F1φ (ω) +(1-F1)φ (ε)

[0110] Specific values ​​are shown in Table 1.

[0111] Table 1 Coefficients in general time root square scaling equations

[0112]

[0113] The coefficients in the turbulent kinetic energy equation are also obtained through the transition function:

[0114] c k =F1c k (ω) +(1-F1)c k (ε)

[0115] in:

[0116] c k (ω) =1.0,c k (ε) =0.85

[0117] The remaining coefficients are:

[0118] C μ =0.09

[0119] The transition function F1 is:

[0120]

[0121] in:

[0122] arg1=min[max(Term1,Term2),Term3]

[0123]

[0124]

[0125] The transition function F2 is:

[0126] arg2=max(2Term1,Term2)

[0127] Finally, it is important to emphasize that the turbulent kinetic energy and scale variables are both taken to be zero at the viscous wall.

[0128] Step 108, modify the relevant terms of the k equation to The two-equation eddy viscosity turbulence model based on the general time root square scale is obtained by coupling the scaling equations.

[0129] The two-equation eddy viscosity turbulence model based on the general time root square scale is Model.

[0130] The two-equation eddy viscosity turbulence model based on the general time root square scale is:

[0131]

[0132] Among them, C μ is the dissipation coefficient.

[0133] In step 110 , the predicted Reynolds-averaged Navier-Stokes (RANS) equations are coupled with a two-equation eddy-viscosity turbulence model based on a general time root square scale to obtain a coupled equation set.

[0134] Specifically, the predicted Reynolds-averaged Navier-Stokes (RANS) equations are:

[0135]

[0136] in is the time-averaged pressure, is the average temperature in Favre, is Favre's average total energy, c p is the ratio of specific heats at constant pressure, Pr is the laminar Prandtl constant, and Pr is the turbulent Prandtl constant;

[0137] in is the viscous stress tensor:

[0138]

[0139] τij is the Reynolds stress tensor, which is obtained through the Boussinesq relationship:

[0140]

[0141] That is, the coupling of the RANS equations and the two-equation eddy viscosity turbulence model based on the general time root square scale is completed.

[0142] Step 112 : constructing grid data of the aircraft flow field to be simulated, numerically solving the coupled equations according to the grid data, and obtaining numerical simulation results of the aircraft turbulent flow field.

[0143] After constructing the two-equation eddy viscosity turbulence model based on the general time root square scale, the corresponding grid data is established according to the aircraft flow field to be simulated. The grid data includes the shape of the grid and the position of the grid nodes. Based on the grid data, the numerical method for the partial differential equations is used to solve the 7 independent variables contained in the coupled equations. k and λ are numerically solved; then the numerical solutions of other variables are derived through relationship equations.

[0144] In the numerical method of the two-equation eddy viscosity turbulence model based on the general time root square scale, based on the ω-scale equation of the existing SST model, the derived The general relationship between the time root square scale and the ω scale is obtained by combining the two to obtain the relationship between the turbulence and the ω scale. scale Scaling equation; The scaling equation and the predicted turbulence are coupled based on the k-equation of the SST model to obtain a two-equation eddy viscosity turbulence model based on the general time root square scale, namely: Model, then The model is coupled with the known Reynolds-averaged Navier-Stokes (RANS) equations to obtain a coupled equation group. When performing numerical simulation of the aircraft turbulent flow field, the grid data of the aircraft flow field to be simulated is constructed, and the coupled equation group is numerically solved based on the grid data to obtain the numerical simulation results of the aircraft turbulent flow field. In the model, when n is a positive integer, the wall boundary condition is strictly 0, which is conducive to reducing the dependence of the equation on wall information; further, when n is a positive even number greater than 2, the calculated value of λ will not affect the dissipation term -C in the k equation μ ρk / λ n This is very beneficial for maintaining the positive turbulent kinetic energy and can achieve numerical stability when using high-precision discretization or complex structured / unstructured grids.

[0145] It should be understood that although Figure 1The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0146] In a specific embodiment, NASA Langley Center used the National Transonic Facility (NTF) to conduct a multi-factor wind tunnel experimental study on a 65° swept delta wing, specifically examining the effects of Mach number, Reynolds number, angle of attack, and leading edge bluntness on the flow. As the free stream Mach number reaches transonic speed, the morphology of the separation vortex at the leading edge of the delta wing gradually changes. In particular, the shock wave makes the flow field extremely complex, and many phenomena different from the subsonic flow field appear. Therefore, the second international vortex flowexperiment (VFE) conducted a series of studies specifically on the shock wave / vortex interference and vortex breakup phenomena that appear on the upper surface of the delta wing under transonic conditions. Here, the shape of the pointed leading edge delta wing at the Reynolds number Re c =6×10 6 , Mach number Ma ref Numerical simulations were carried out under the conditions of ΔH = 0.85 and angle of attack α = 22.6°. Figure 2 A schematic diagram of the multi-block structured grid used is given, with a grid size of approximately 2.35 million.

[0147] Figure 3 The convergence results of the calculation of the flow around the sharp leading edge delta wing with different values ​​of parameter n are given. For the model, only when n=2 will the high-order calculation diverge. However, using the other three values ​​can achieve calculation convergence for the second-order MUSCL format, the fifth-order WCNS-E5 format, the seventh-order WNCS-E7 format, and the ninth-order WCNS-E9 format.

[0148] Because the calculated angle of attack in this example is less than the critical angle for vortex breakdown, the flow can still be considered steady with a complex vortex structure. Specifically, as the flow passes the leading edge, a primary detached vortex and a secondary detached vortex form on the leeward side of the delta wing. These two detached vortices can be distinguished by the suction peak in the wall pressure distribution. Figure 4 SST The wall pressure distribution calculated by the model, where n = 8. Comparison with experimental values ​​shows that the second-order MUSCL scheme on this grid cannot clearly resolve the structure of the secondary vortex. In contrast, the results of the higher-order WCNS scheme agree well with the experimental data.

[0149] In one embodiment, Figure 5 As shown, a numerical device for a two-equation eddy viscosity turbulence model based on a general time root square scale is provided, comprising: an ω scale equation acquisition module 502, a general time root square scale equation determination module 504, a two-equation eddy viscosity turbulence model determination module 506 based on a general time root square scale, and a numerical simulation module 508, wherein:

[0150] The ω scale equation acquisition module 502 is used to obtain the ω scale equation of the turbulence based on the SST model; ω represents the specific dissipation rate scale;

[0151] The general time root square equation determination module 504 is used to obtain the pre-derived The general relationship between the time root square scale and the ω scale is obtained based on the relationship and the ω scale equation. The equation of the scale; where τ represents the energetic time scale, and n represents the nth root, which is a positive integer;

[0152] The two-equation eddy viscosity turbulence model determination module 506 based on the general time root square scale is used to obtain the k equation of turbulence based on the SST model; k represents turbulent kinetic energy; the relevant terms of the k equation are modified and The two-equation eddy viscosity turbulence model based on the general time root square scale is obtained by coupling the scale equations. Model; The known Reynolds-averaged Navier-Stokes (RANS) equations are coupled with a two-equation eddy-viscosity turbulence model based on general time root square scaling to obtain a coupled equation system;

[0153] The numerical simulation module 508 is used to construct grid data of the aircraft flow field to be simulated, and numerically solve the coupled equations according to the grid data to obtain the numerical simulation results of the aircraft turbulent flow field.

[0154] The ω scale equation acquisition module 502 is further used to obtain the ω scale equation of the turbulence based on the SST model:

[0155]

[0156] in, is the time-averaged density, ω is the specific dissipation rate scale, t is time, and j is the subscript for the coordinate index. is the three components of Favre average velocity, x j(j=1,2,3) are the three-directional coordinate components, γ is the coefficient of the specific dissipation rate scaling equation, ν t is the kinetic eddy viscosity coefficient, P is the turbulence generation, β is the dissipation term coefficient of the specific dissipation rate scaling equation, μ is the dynamic viscosity coefficient, σ ω is the diffusion coefficient, μ t is the eddy viscosity coefficient, F1 is the first transition function, σ ω2 is the coefficient of the cross-derivative term of the specific dissipation rate scaling equation, and k is the turbulent kinetic energy.

[0157] The general time root square equation determination module 504 is also used to obtain the pre-derived The general relationship between the time root square scale and the ω scale is obtained based on the relationship and the ω scale equation. Scale The scaling equation is:

[0158]

[0159] in, express Generally, the time root square scale, α ω is the coefficient of the dissipation term of the general time root square scaling equation, β ω Generates the term coefficients for the general time root square scaling equation, σ d is the coefficient of the cross derivative term of the general time root square scaling equation.

[0160] The two-equation eddy viscosity turbulence model determination module 506 based on the general time root square scale is also used to obtain the turbulence

[0161] The k equation of the flow based on the SST model is:

[0162]

[0163] Among them, σ k is the coefficient of the dissipation term in the k equation.

[0164] The two-equation eddy viscosity turbulence model determination module 506 based on the general time root square scale is also used to modify the relevant terms of the K equation and The two-equation eddy viscosity turbulence model based on the general time root square scale is coupled with the scaling equations:

[0165]

[0166] Among them, C μ is the dissipation coefficient.

[0167] The numerical simulation module 508 is also used to use the numerical method for the partial differential equations to simulate the 7 independent variables included in the coupled equations according to the grid data. k and λ are numerically solved; then the numerical solutions of other variables are derived through relationship equations.

[0168] Regarding the specific limitations of the numerical device of the two-equation eddy viscosity turbulence model based on the general time root square scale, please refer to the limitations of the numerical method of the two-equation eddy viscosity turbulence model based on the general time root square scale above, which will not be repeated here. Each module in the above-mentioned numerical device of the two-equation eddy viscosity turbulence model based on the general time root square scale can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

[0169] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 6 As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a numerical method of a two-equation eddy viscosity turbulence model based on a general time root square scale is implemented. The display screen of the computer device can be a liquid crystal display or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a button, trackball or touchpad provided on the computer device housing, or an external keyboard, touchpad or mouse.

[0170] Those skilled in the art will understand that Figure 6 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0171] In one embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiment when executing the computer program.

[0172] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above method embodiment are implemented.

[0173] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0174] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0175] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

Claims

1. A numerical simulation method based on a two-equation eddy viscosity turbulence model with general time root square scaling, characterized in that: The method comprises: Get turbulence based on SST model ω Scaling equations; ω represents the specific dissipation rate scale; Get pre-derived General time root square scale and ω The relationship between the scale, according to the relationship and the ω The scaling equations give the turbulence about The equation of scale; where represents the energetic time scale, express The second root is a positive integer; Get turbulence based on SST model k equation; k represents turbulent kinetic energy; Will k The equation is the same as The two-equation eddy viscosity turbulence model based on the general time root square scale is obtained by coupling the scale equations. k - Model; The predicted Reynolds-averaged Navier-Stokes equations are coupled with a two-equation eddy-viscosity turbulence model based on general time root square scaling to obtain a coupled equation system. Constructing grid data of the aircraft flow field to be simulated, numerically solving the coupled equations according to the grid data, and obtaining numerical simulation results of the aircraft turbulent flow field; The pre-derived General time root square scale and ω The scale relationship is: in, n for General time root square scale and ω The adjustment coefficient of the scale; Get pre-derived General time root square scale and ω The relationship between the scale, according to the relationship and the ω The scaling equations give the turbulence about The scaling equation is: in, ,express Generally, the time root square scale is is the coefficient of the dissipation term of the general time root square scaling equation, Generate term coefficients for the general time root square scaling equation, is the cross-derivative coefficient of the general time root square equation, is the time-averaged density, is the specific dissipation rate scale, For time, Make the subscript the coordinate index, is the three components of Favre average velocity, are the three-direction coordinate components, For turbulence generation, is the dynamic viscosity coefficient, is the diffusion coefficient, is the eddy viscosity coefficient.

2. The method according to claim 1, characterized in that Get turbulence based on SST model ω Scaling equations, including: Get turbulence based on SST model ω The scaling equation is: in, Generate term coefficients for the specific dissipation rate scaling equation, is the kinematic eddy viscosity coefficient, is the coefficient of the dissipation term in the specific dissipation rate scaling equation, is the first transition function, is the coefficient of the cross-derivative term of the specific dissipation rate scaling equation, is turbulent kinetic energy.

3. The method according to claim 1, characterized in that Get turbulence based on SST model k Equations, including: Get turbulence based on SST model k The equation is: in, for k The coefficient of the dissipation term in the equation, To generate items, is the dissipation coefficient.

4. The method according to claim 3, characterized in that The generated items are: in, is the dependent variable, , , is the Kronecker operator.

5. The method according to claim 1, wherein The eddy viscosity coefficient is : in, is the correction coefficient of the eddy viscosity coefficient formula, is the vorticity, , , is the second transition function.

6. The method according to claim 5, characterized in that Will k The equation is the same as The two-equation eddy viscosity turbulence model based on the general time root square scale is coupled with the scaling equations, which includes: Will k The relevant terms of the equation are modified as described The two-equation eddy viscosity turbulence model based on the general time root square scale is coupled with the scaling equations: 。 7. The method according to claim 6, characterized in that The predicted Reynolds-averaged Navier-Stokes equations are: in, is the time-averaged pressure, is the average temperature in Favre, For Favre's average total energy, is the specific heat ratio at constant pressure, Pr is the laminar Prandtl constant, Pr t is the turbulent Prandtl constant; in is the viscous stress tensor: is the Reynolds stress tensor, which is obtained through the Boussinesq relationship: That is, the coupling of the Reynolds-averaged Navier-Stokes equations and the two-equation eddy-viscosity turbulence model based on the general time root square scale is completed.

8. The method according to claim 7, characterized in that Numerically solving the coupled equations according to the grid data includes: According to the grid data, the 7 independent variables included in the coupled equations are solved using the numerical method for the partial differential equations. 、 、 、 k and λ Perform numerical solutions; Then, the numerical solutions of other variables are obtained by deducing the relationship.

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