Numerical method for reynolds stress turbulence model based on general time-dependent root scale

Abstract

The application relates to a numerical method, device, computer equipment and storage medium based on a general time root scale Reynolds stress turbulence model. The method comprises the following steps: obtaining a scale equation of turbulence with respect to a scale based on a relationship between a general time root scale and an omega scale according to an omega scale equation of an existing SSG / LRR-omega Reynolds stress model; coupling the scale equation and a known turbulence equation based on the SSG / LRR-omega model to obtain a model; obtaining a RANS equation set, coupling the model, obtaining a coupled equation set, constructing grid data of a turbulent flow field of an aircraft to be simulated when performing numerical simulation of the flow field of the aircraft, performing numerical solution on the coupled equation set according to the grid data, and obtaining a numerical simulation result of the turbulent flow field of the aircraft. When n is a positive integer, the wall boundary condition is strictly 0, and numerical stability can be realized when high-precision discretization or a complex structure / non-structure grid is adopted.

Description

Technical Field

[0001] This application relates to the field of computational fluid dynamics, and in particular to a numerical method, apparatus, computer device, and storage medium based on a Reynolds stress turbulence model with a general root-square time scale. Background Technology

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

[0003] The RANS method dates back over a century, with Boussinesq proposing the famous eddy viscosity assumption to simulate Reynolds stress. Subsequently, many pioneers in fluid mechanics developed a series of semi-empirical theories, but because they only considered first-order turbulence statistics, these turbulence models are also called first-order moment models. Physically more complete closed-loop modeling methods are usually called higher-order moment models, such as the Reynolds stress model (RSM). In 1940, Zhou Peiyuan, a renowned Chinese mechanics master, established the transport differential equations satisfied by Reynolds stress in general turbulence and proposed closure assumptions for new unknowns such as the three-dimensional velocity correlation. In 1951, Rotta further developed Zhou Peiyuan's work and proposed the complete RSM model. Later, Donaldson et al. proposed the concept of model invariance, and Lumley developed the closure approximation, but these were still in the early stages of research.

[0004] In the 1990s, the rapid development of computer technology and the shortcomings of first-order moment models led to a renewed focus on second-order moment models. Speziale argued that the Reynolds stress model (RSM) bridged the gap between the LES and RANS methods for calculating complex turbulent flows. He further discussed the feasibility of the Reynolds stress model and proposed simplified design criteria. Subsequently, many scholars developed various RSM models based on these criteria, such as the LRR-ε model, LRR-ω model, SSG-ε model, and SSG / LRR-ω model. These RSM models have been integrated into numerous commercial CFD software programs and have been widely applied.

[0005] In engineering applications of numerical simulation of turbulent flow fields in aircraft, the aforementioned RSM model is commonly used. However, these RSM models are mostly based on the ε-scale or ω-scale, and lack natural boundary conditions at viscous walls, which can lead to numerical instability when using high-precision discretization or complex structured / unstructured meshes. Therefore, existing techniques suffer from poor adaptability. Summary of the Invention

[0006] Therefore, it is necessary to provide a numerical method, apparatus, computer equipment, and storage medium based on a Reynolds stress turbulence model with a general root-square time scale to address the above-mentioned technical problems and solve the numerical instability problem when using high-precision discretization or complex structured / unstructured meshes in aircraft flow field simulation.

[0007] A numerical method based on a Reynolds stress turbulence model with a general root-square time scale, the method comprising:

[0008] The ω-scale equation for turbulence based on the SSG / LRR-ω Reynolds stress model is obtained; ω represents the specific dissipation rate scale.

[0009] Obtain the pre-derived The relationship between the general root-square time scale and the ω-scale is used to derive the turbulence equation regarding... Scale The scaling equation; where τ represents the energy-containing time scale, and n represents the nth root, which is a positive integer;

[0010] Turbulence is obtained based on the SSG / LRR-ω model. equation; Represents the components of the Reynolds stress equation;

[0011] The Modification of relevant terms in the equation and the above By coupling the scaling equations, a Reynolds stress turbulence model based on the general root-square time scale is obtained, namely SSG / LRR- Model;

[0012] The Reynolds-averaged Navier-Stokes (RANS) equations are obtained and coupled with the Reynolds stress turbulence model based on the general root-square time scale to obtain the coupled equations.

[0013] A grid of flow field data for the aircraft to be simulated is constructed, and the coupled equations are numerically solved based on the grid data to obtain the numerical simulation results of the turbulent flow field of the aircraft.

[0014] In one embodiment, the method further includes: obtaining the ω-scale equation of the turbulence based on the SSG / LRR-ω Reynolds stress model as follows:

[0015]

[0016] in, This represents the time-averaged density, where t is time, and i, j, k are coordinate indices when used as subscripts. Let x be the three components of the Favre average velocity. j (j=1,2,3) represents the three-directional coordinate components, α ω P is the coefficient of the generating term in the ratio dissipation rate scaling equation. kk / 2=(P 11 +P 22 +P 33 ) / 2 represents the generation of turbulent kinetic energy, where P 11 P 22 P 33 For the generation of Reynolds normal stress in three directions, β ω Here, μ is the coefficient of the dissipation term in the specific dissipation rate scaling equation, μ is the kinetic viscosity coefficient, and σ is the coefficient of dissipation. ω σ is the coefficient of the diffusion term in the specific dissipation rate scaling equation. d The coefficients of the cross-derivative term in the specific dissipation rate scaling equation are... For turbulent kinetic energy, The Reynolds normal stress is in three directions.

[0017] In one embodiment, it further includes: the pre-derived... The general relationship between the root square time scale and the ω-scale is:

[0018]

[0019] Where n is Adjustment coefficients for the root square time scale and the ω-scale.

[0020] In one embodiment, it further includes: obtaining a pre-derived... The relationship between the root square time scale and the ω-scale is used to obtain the turbulence equation regarding... Scale The scaling equation is:

[0021]

[0022] in, express Typical time root square scale.

[0023] In one embodiment, it further includes: obtaining the turbulent SSG / LRR-ω model. The equation is:

[0024]

[0025] in, For generated items, For redistribution items, For dissipation terms, This is a diffusion term.

[0026] In one embodiment, it further includes:

[0027] The generated item is:

[0028]

[0029] The redistribution item is:

[0030]

[0031] in, For anisotropic tensors, As the dependent variable, C1 is a special dependent variable. C2, C3 C4 and C5 are coefficients in the known SSG / LRR Reynolds stress equation. It is vorticity.

[0032] The dissipation term is:

[0033]

[0034] Among them, isotropic dissipation rate C μ is the dissipation coefficient.

[0035] The diffusion term is:

[0036]

[0037] in, is the eddy viscosity coefficient.

[0038] In one embodiment, it further includes: placing the Modification of relevant terms in the equation and the above The scaling equations are coupled, based on the Reynolds stress turbulence model with a general root-square time scale, namely SSG / LRR- The model is:

[0039]

[0040] In one embodiment, the method further includes: obtaining the Reynolds-averaged Navier-Stokes (RANS) equations as follows:

[0041]

[0042] in, For time-averaged pressure, The average temperature of Favre. For Favre's average total energy, c p The specific heat ratio is given by Pr, where Pr is the Prandtl constant for laminar flow. t It is the Prandtl constant for turbulence;

[0043] in For the viscous stress tensor:

[0044]

[0045] τ ij Let Reynolds stress tensor be the tensor, and... The relationship is:

[0046]

[0047] Thus, the RANS equations and SSG / LRR- are completed. Model coupling.

[0048] In one embodiment, the method further includes: based on the grid data, using a numerical method for partial differential equations to determine the 12 independent variables contained in the coupled equations: Numerical solutions are obtained for λ and λ; then, numerical solutions for other variables are derived through relational derivation.

[0049] A numerical apparatus based on a Reynolds stress turbulence model with a general root-square time scale, the apparatus comprising:

[0050] The ω-scale equation acquisition module is used to obtain the ω-scale equation for turbulence based on the SSG / LRR-ω Reynolds stress model; ω represents the specific dissipation rate scale.

[0051] The general root-square time scaling equation determination module is used to obtain the pre-derived equation. The relationship between the general root-square time scale and the ω-scale is used to derive the turbulence equation regarding... The scaling equation; where τ represents the energy-containing time scale, and n represents the nth root, which is a positive integer;

[0052] A Reynolds stress turbulence model determination module based on a general root-square time scale is used to obtain turbulence based on the SSG / LRR-ω model. equation; Representing the components of the Reynolds stress equation; [The following is a list of components and their meanings, which are not Modification of relevant terms in the equation and the above By coupling the scaling equations, a Reynolds stress turbulence model based on the general root-square time scale is obtained, namely SSG / LRR- Model; Obtain the Reynolds-averaged Navier-Stokes (RANS) equations and couple them with the Reynolds stress turbulence model based on the general root-square time scale to obtain the coupled equations;

[0053] The numerical simulation module is used to construct grid data of the flow field of the aircraft (or other aerodynamic problems) to be simulated, and to numerically solve the coupled equations based on the grid data to obtain the numerical simulation results of the turbulent flow field of the aircraft.

[0054] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:

[0055] The ω-scale equation for turbulence based on the SSG / LRR-ω Reynolds stress model is obtained; ω represents the specific dissipation rate scale.

[0056] Obtain the pre-derived The relationship between the root square time scale and the ω-scale is used to obtain the turbulence equation regarding... Scale The scaling equation; where τ represents the energy-containing time scale, and n represents the nth root, which is a positive integer;

[0057] Turbulence is obtained based on the SSG / LRR-ω model. equation; Represents the components of the Reynolds stress equation;

[0058] The Modification of relevant terms in the equation and the above By coupling the scaling equations, a Reynolds stress turbulence model based on the general root-square time scale is obtained, namely SSG / LRR- Model;

[0059] The Reynolds-averaged Navier-Stokes (RANS) equations are obtained and coupled with the Reynolds stress turbulence model based on the general root-square time scale to obtain the coupled equations.

[0060] A grid of flow field data for the aircraft (or other aerodynamic problem) to be simulated is constructed. The coupled equations are numerically solved based on the grid data to obtain the numerical simulation results of the turbulent flow field of the aircraft.

[0061] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0062] The ω-scale equation for turbulence based on the SSG / LRR-ω Reynolds stress model is obtained; ω represents the specific dissipation rate scale.

[0063] Obtain the pre-derived The relationship between the general root-square time scale and the ω-scale is used to derive the turbulence equation regarding... Scale The scaling equation; where τ represents the energy-containing time scale, and n represents the nth root, which is a positive integer;

[0064] Turbulence is obtained based on the SSG / LRR-ω model. equation; Represents the components of the Reynolds stress equation;

[0065] The Modification of relevant terms in the equation and the above By coupling the scaling equations, a Reynolds stress turbulence model based on the general root-square time scale is obtained, namely SSG / LRR- Model;

[0066] The Reynolds-averaged Navier-Stokes (RANS) equations are obtained and coupled with the Reynolds stress turbulence model based on the general root-square time scale to obtain the coupled equations.

[0067] A grid of flow field data for the aircraft to be simulated is constructed, and the coupled equations are numerically solved based on the grid data to obtain the numerical simulation results of the turbulent flow field of the aircraft.

[0068] The numerical method, apparatus, computer equipment, and storage medium described above, based on the Reynolds stress turbulence model using a general root-square time scale, are derived from the ω-scale equations of the existing SSG / LRR-ω Reynolds stress model. The relationship between the general root-square time scale and the ω-scale, combined with the two, yields the relationship between turbulence and... Scale Scaling equation; The scaling equations and predicted turbulence are based on the SSG / LRR-ω model. The equations are coupled to obtain a Reynolds stress turbulence model based on a general root-square time scale, namely SSG / LRR- The model obtains the Reynolds-averaged Navier-Stokes (RANS) equations and couples them with a Reynolds stress turbulence model based on a general root-square time scale to obtain a coupled equation set. When performing numerical simulations of the aircraft flow field, grid data of the turbulent flow field to be simulated is constructed, and the coupled equations are numerically solved based on the grid data to obtain the numerical simulation results of the aircraft turbulent flow field. The SSG / LRR- proposed in this invention... In the model, when n is a positive integer, the wall boundary conditions are strictly 0, which helps to reduce the dependence of the equation on wall information. Furthermore, when n is a positive even number greater than 2, the calculated value of λ will not affect the sign of the dissipation term in the Reynolds stress equation, which is very beneficial for obtaining a physically satisfying solution of the RSM and can achieve numerical stability when using high-precision discretization or complex structure / unstructured meshes. Attached Figure Description

[0069] Figure 1 This is a flowchart illustrating the numerical method based on a Reynolds stress turbulence model using a general root-square time scale in one embodiment.

[0070] Figure 2 The diagram shows the flow around a pointed leading-edge delta wing in a specific embodiment: surface mesh and station division, where (a) is a schematic diagram of the surface mesh and (b) is a schematic diagram of the station division;

[0071] Figure 3 In a specific embodiment, the SSG / LRR flow around a pointed leading-edge delta wing is described. A schematic diagram illustrating the convergence process for different values ​​of the model parameter n;

[0072] Figure 4 In a specific embodiment, the SSG / LRR flow around a pointed leading-edge delta wing is described. A schematic diagram of the pressure distribution obtained by the model at different stations, where (a) represents x / c. r =0.40, the pressure distribution diagram, (b) is x / c r =0.60, the pressure distribution diagram, (c) is x / c r =0.80, the pressure distribution diagram, (d) is x / c r A schematic diagram of the pressure distribution obtained with a value of 0.95;

[0073] Figure 5 This is a structural block diagram of a numerical apparatus based on a Reynolds stress turbulence model with a general root-square time scale in one embodiment.

[0074] Figure 6 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0075] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0076] In one embodiment, such as Figure 1As shown, a numerical method based on a Reynolds stress turbulence model with a general root-square time scale is provided, including the following steps:

[0077] Step 102: Obtain the ω-scale equation for turbulence based on the SSG / LRR-ω Reynolds stress model.

[0078] ω represents the specific dissipation rate scale.

[0079] Numerical simulations of turbulent flow fields in aircraft are based on the proposed physical model. Existing RSM models are mostly based on ε- or ω-scales, lacking natural boundary conditions at viscous walls. This leads to numerical instability when using high-precision discretization or complex structured / unstructured meshes, negatively impacting the numerical simulation of aircraft flow fields. This invention proposes a scale equation with natural boundaries at viscous walls, based on a general root-square time scale. And coupled with the Reynolds stress equation 6, forming SSG / LRR- Reynolds stress model.

[0080] Specifically, the ω-scale equation for turbulence based on the SSG / LRR-ω Reynolds stress model is obtained as follows:

[0081]

[0082] in, This represents the time-averaged density, where t is time, and i, j, k are coordinate indices when used as subscripts. Let x be the three components of the Favre average velocity. j (j=1,2,3) represents the three-directional coordinate components, α ω P is the coefficient of the generating term in the ratio dissipation rate scaling equation. kk / 2=(P 11 +P 22 +P 33 ) / 2 represents the generation of turbulent kinetic energy, where P 11 P 22 P 33 For the generation of Reynolds normal stress in three directions, β ω Here, μ is the coefficient of the dissipation term in the specific dissipation rate scaling equation, μ is the kinetic viscosity coefficient, and σ is the coefficient of dissipation. ω σ is the coefficient of the diffusion term in the specific dissipation rate scaling equation. d The coefficients of the cross-derivative term in the specific dissipation rate scaling equation are... For turbulent kinetic energy, The Reynolds normal stress is in three directions.

[0083] Step 104, obtain the pre-derived... The relationship between the general root-square time scale and the ω-scale is used to derive the equation for turbulence based on this relationship and the ω-scale equation. Scale Scaling equation.

[0084] Where τ represents the energy-containing time scale, and n represents the nth root, which is a positive integer.

[0085] This invention derives, through derivation, the following conclusions. The relationship between the root square time scale and the ω-scale is:

[0086]

[0087] Combining the ω-scale equation, we obtain information about Scaling equation:

[0088]

[0089] in, express Typical time root square scale.

[0090] Here, n is a positive integer used to adjust the numerical properties of the scaling equation. n=1 is a special case, which reverts to 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 generating terms, which can cause serious numerical rigidity problems.

[0091] Step 106, obtain the turbulence based on the SSG / LRR-ω model. equation.

[0092] This represents the components of the Reynolds stress equation.

[0093] Specifically, The equation is:

[0094]

[0095] in, For generated items, For redistribution items, For dissipation terms, This is a diffusion term.

[0096] The generated item is:

[0097]

[0098] The redistribution items are:

[0099]

[0100] in, For anisotropic tensors, As the dependent variable, C1 is a special dependent variable. C2, C3 C4 and C5 are coefficients in the known SSG / LRR Reynolds stress equation. It is vorticity.

[0101] The dissipation term is:

[0102]

[0103] in, C μ is the dissipation coefficient.

[0104] The diffusion term is:

[0105]

[0106] in, is the eddy viscosity coefficient.

[0107] The coefficients in the Reynolds stress equation above are obtained by weighting using the transition function F1:

[0108] φ=F1φ (LRR) +(1-F1)φ (SSG)

[0109] Similarly, the coefficients in the scaling equation are also obtained through weighted summation using the transition function F1:

[0110] φ=F1φ (ω) +(1-F1)φ (ε)

[0111] Where φ represents an arbitrary system, and the specific values ​​are shown in Table 1 and Table 2 respectively.

[0112] Table 1. Coefficients in the Reynolds stress equation

[0113]

[0114] Table 2. Coefficients in the general root square time scale equation

[0115]

[0116] Other coefficients include:

[0117]

[0118] C μ =0.09

[0119] The transition function F1 is:

[0120]

[0121] in:

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

[0123]

[0124]

[0125] Finally, it should be emphasized that the six components of Reynolds stress and the scale variable are all taken as 0 at the viscous wall.

[0126] Step 108, will Modification of related terms in the equation and By coupling the scaling equations, a Reynolds stress turbulence model based on a general root-square time scale is obtained.

[0127] The Reynolds stress turbulence model based on the general root-square time scale, namely SSG / LRR- The model. Specifically:

[0128]

[0129] Step 110: Obtain the Reynolds-averaged Navier-Stokes (RANS) equations and couple them with the Reynolds stress turbulence model based on the general root-square time scale to obtain the coupled equations.

[0130] Step 112: Construct grid data of the flow field of the aircraft to be simulated, and numerically solve the coupled equations based on the grid data to obtain the numerical simulation results of the turbulent flow field of the aircraft.

[0131] Based on grid data, numerical methods for partial differential equation systems were used to address the 12 independent variables contained in the coupled equation system: Numerical solutions are performed for λ;

[0132] Then, numerical solutions for other variables are derived through relational derivation.

[0133] After constructing the Reynolds stress turbulence model based on the general root-square time scale, corresponding mesh data is established according to the flow field of the aircraft to be simulated. The mesh data includes the shape of the mesh and the position of the mesh nodes. The Reynolds stress turbulence model based on the general root-square time scale is numerically solved based on the mesh data to obtain the analysis results of the turbulent flow field of the aircraft.

[0134] In the numerical method based on the general root-square time scale Reynolds stress turbulence model described above, the ω-scale equation of the existing SSG / LRR-ω Reynolds stress model is derived from... The relationship between the general root-square time scale and the ω-scale, combined with the two, yields the relationship between turbulence and... Scale Scaling equation; The scaling equations and predicted turbulence are based on the SSG / LRR-ω model. The equations are coupled to obtain a Reynolds stress turbulence model based on a general root-square time scale, namely SSG / LRR- The model obtains the Reynolds-averaged Navier-Stokes (RANS) equations and couples them with a Reynolds stress turbulence model based on a general root-square time scale to obtain a coupled equation set. When performing numerical simulations of the aircraft flow field, grid data of the turbulent flow field to be simulated is constructed, and the coupled equations are numerically solved based on the grid data to obtain the numerical simulation results of the aircraft turbulent flow field. The SSG / LRR- proposed in this invention... In the model, when n is a positive integer, the wall boundary conditions are strictly 0, which helps to reduce the dependence of the equation on wall information. Furthermore, when n is a positive even number greater than 2, the calculated value of λ will not affect the sign of the dissipation term in the Reynolds stress equation, which is very beneficial for obtaining a physically satisfying solution of the RSM and can achieve numerical stability when using high-precision discretization or complex structure / unstructured meshes.

[0135] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but may be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but may be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0136] In one specific embodiment, NASA's Langley Center conducted multi-factor wind tunnel experiments on a 65° swept delta wing using the National Transonic Facility (NTF), specifically examining the effects of Mach number, Reynolds number, angle of attack, and leading-edge bluntness on the flow. As the free-flow Mach number reaches transonic speeds, the morphology of the separated vortices at the leading edge of the delta wing gradually changes. In particular, the shock wave makes the flow field extremely complex, exhibiting many phenomena different from those in subsonic flow fields. Therefore, the Second International Vortex Flow Experiment (VFE) specifically conducted a series of studies on shock wave / vortex interference and vortex breaking phenomena appearing on the upper surface of the delta wing under transonic conditions.

[0137] This embodiment utilizes the method proposed in this invention to refine the shape of a sharp leading-edge delta wing at Reynolds number Re. c =6×10 6 Mach number Ma ref Numerical simulation studies were conducted under the conditions of α = 0.85 and angle of attack α = 22.6°. Figure 2 A schematic diagram of the multi-block structured mesh used is given, with a mesh size of approximately 2.35 million.

[0138] Figure 3 The calculated convergence results for different values ​​of parameter n in the flow around a sharp leading-edge delta wing are presented. For SSG / LRR- The model only diverges in higher-order calculations when n=2, while using the other three values ​​can achieve computational convergence for second-order MUSCL, fifth-order WCNS-E5, seventh-order WNCS-E7, and ninth-order WCNS-E9 formats.

[0139] Since the calculated angle of attack in this example is less than the critical angle of attack for vortex breakup, the flow can still be considered as a steady flow with a complex vortex system. Specifically, when the flow passes the leading edge, a main separation vortex and a secondary separation vortex will form on the leeward side of the delta wing. These two can be distinguished by the suction peak in the wall pressure distribution. Figure 4 SSG / LRR- was demonstrated The model calculates the wall pressure distribution, where n = 8. Comparison with experimental values ​​reveals that the second-order MUSCL scheme cannot clearly resolve the structure of the secondary vortex on this grid. Conversely, the results from the higher-order WCNS scheme agree well with the experimental data.

[0140] In one embodiment, such as Figure 5 As shown, a numerical apparatus for a Reynolds stress turbulence model based on a general root-square time scale is provided, comprising: an ω-scale equation acquisition module 502, a general root-square time scale equation determination module 504, a Reynolds stress turbulence model determination module based on a general root-square time scale 506, and a numerical simulation module 508, wherein:

[0141] The ω-scale equation acquisition module 502 is used to acquire the ω-scale equation for turbulence based on the SSG / LRR-ω Reynolds stress model; ω represents the specific dissipation rate scale.

[0142] The general root-square time scaling equation determination module 504 is used to obtain the pre-derived... The relationship between the general root-square time scale and the ω-scale is used to derive the equation for turbulence based on this relationship and the ω-scale equation. Scale The scaling equation; where τ represents the energy-containing time scale, and n represents the nth root, which is a positive integer;

[0143] The Reynolds stress turbulence model determination module 506, based on a general root-square time scale, is used to obtain the turbulence model based on the SSG / LRR-ω model. equation; Representing the components of the Reynolds stress equation; [The following is a list of components and their meanings, which are not Modification of relevant terms in the equation and the above By coupling the scaling equations, a Reynolds stress turbulence model based on the general root-square time scale is obtained, namely SSG / LRR- Model; Obtain the Reynolds-averaged Navier-Stokes (RANS) equations and couple them with the Reynolds stress turbulence model based on the general root-square time scale to obtain the coupled equations;

[0144] The numerical simulation module 508 is used to construct grid data of the flow field of the aircraft (or other aerodynamic problems) to be simulated, and to numerically solve the coupled equations based on the grid data to obtain the numerical simulation results of the turbulent flow field of the aircraft.

[0145] The ω-scale equation acquisition module 502 is also used to acquire the ω-scale equation for turbulence based on the SSG / LRR-ω Reynolds stress model, as follows:

[0146]

[0147] in, This represents the time-averaged density, where t is time, and i, j, k are coordinate indices when used as subscripts. Let x be the three components of the Favre average velocity. j (j=1,2,3) represents the three-directional coordinate components, α ω P is the coefficient of the generating term in the ratio dissipation rate scaling equation. kk / 2=(P 11 +P 22 +P 33 ) / 2 represents the generation of turbulent kinetic energy, where P 11 P 22 P 33 For the generation of Reynolds normal stress in three directions, β ω Here, μ is the coefficient of the dissipation term in the specific dissipation rate scaling equation, μ is the kinetic viscosity coefficient, and σ is the coefficient of dissipation. ω σ is the coefficient of the diffusion term in the specific dissipation rate scaling equation. d The coefficients of the cross-derivative term in the specific dissipation rate scaling equation are... For turbulent kinetic energy, The Reynolds normal stress is in three directions.

[0148] The general root-square time scaling equation determination module 504 is also used to obtain the pre-derived equation. The relationship between the general root-square time scale and the ω-scale is used to derive the equation for turbulence based on this relationship and the ω-scale equation. Scale The scaling equation is:

[0149]

[0150] in, express Typical time root square scale.

[0151] The Reynolds stress turbulence model determination module 506 based on the general root-square time scale is also used to obtain the turbulence SSG / LRR-ω model. The equation is:

[0152]

[0153] in, For generated items, For redistribution items, For dissipation terms, This is a diffusion term.

[0154] The Reynolds stress turbulence model determination module 506 based on the general root-square time scale is also used to determine the Reynolds stress turbulence model. Modification of related terms in the equation and The scaling equations are coupled, based on the Reynolds stress turbulence model with a general root-square time scale, namely SSG / LRR- The model is:

[0155]

[0156] The Reynolds stress turbulence model determination module 506 based on the general root-square time scale is also used to obtain the Reynolds-averaged Navier-Stokes (RANS) equations:

[0157]

[0158] in, For time-averaged pressure, The average temperature of Favre. For Favre's average total energy, c p The specific heat ratio is given by Pr, where Pr is the Prandtl constant for laminar flow. t It is the Prandtl constant for turbulence;

[0159] in For the viscous stress tensor:

[0160]

[0161] τ ij Let Reynolds stress tensor be the tensor, and... The relationship is:

[0162]

[0163] Thus, the RANS equations and SSG / LRR- are completed. Model coupling.

[0164] The numerical simulation module 508 is also used to perform numerical simulations on the 12 independent variables contained in the coupled equations based on the grid data, using numerical methods for partial differential equations: Numerical solutions are obtained for λ and λ; then, numerical solutions for other variables are derived through relational derivation.

[0165] Specific limitations on the numerical apparatus for the Reynolds stress turbulence model based on the general root-square time scale can be found in the limitations on the numerical methods for the Reynolds stress turbulence model based on the general root-square time scale mentioned above, and will not be repeated here. Each module in the numerical apparatus for the Reynolds stress turbulence model based on the general root-square time scale can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0166] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 6 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a numerical method based on a Reynolds stress turbulence model with a general root-square time scale. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0167] Those skilled in the art will understand that Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0168] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps in the above method embodiment.

[0169] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0170] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, 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), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0171] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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.

[0172] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A numerical method based on a Reynolds stress turbulence model with a general root-square time scale, characterized in that, The method includes: Turbulence acquisition based on SSG / LRR- ω Reynolds stress model ω Scaling equation; ω This represents a measure of specific dissipation rate; Obtain the pre-derived General time root square scale and ω The scale relationship, based on the relationship and the... ω The scaling equation yields turbulence with respect to Scaling equation; where, Indicates the energy timescale. express The second root is a positive integer; Turbulence acquisition based on SSG / LRR- ω Model equation; Represents the components of the Reynolds stress equation; The Equation and the above By coupling the scaling equations, a Reynolds stress turbulence model based on the general root-square time scale is obtained, namely SSG / LRR- Model; The Reynolds-averaged Navier-Stokes equations are obtained and coupled with the Reynolds stress turbulence model based on the general root-square time scale to obtain the coupled equations. A grid of flow field data for the aircraft to be simulated is constructed, and the coupled equations are numerically solved based on the grid data to obtain the numerical simulation results of the turbulent flow field of the aircraft. Turbulence acquisition based on SSG / LRR- ω Reynolds stress model ω Scaling equations, including: Turbulence acquisition based on SSG / LRR- ω Reynolds stress model ω The scaling equation is: in, For time-averaged density, For time, When creating subscripts, use coordinate indices. The three components of the Favre average velocity. These are the three-directional coordinate components. For the coefficients of the generating term in the specific dissipation rate scaling equation, It is generated by turbulent kinetic energy, where , , For the generation of Reynolds normal stress in three directions, The coefficients of the dissipation term in the dissipation rate scaling equation are given. The kinetic viscosity coefficient, The coefficients of the diffusion term in the specific dissipation rate scaling equation are... The coefficients of the cross-derivative term in the specific dissipation rate scaling equation are... For turbulent kinetic energy, , , Reynolds normal stress in three directions; The pre-derived General time root square scale and ω The relationship between scales is: in, n for root square scale of time ω The scaling factor; Obtain the pre-derived General time root square scale and ω The scale relationship, based on the relationship and the... ω The scaling equation yields turbulence with respect to Scaling equations, including: Obtain the pre-derived General time root square scale and ω The scale relationship, based on the relationship and the... ω The scaling equation yields turbulence with respect to Scale The scaling equation is: in, ,express General root-square time scale is the eddy viscosity coefficient.

2. The method according to claim 1, characterized in that, Obtaining turbulent SSG / LRR- ω Model Equations, including: Obtaining turbulent SSG / LRR- ω Model The equation is: in, For generated items, For redistribution items, For dissipation terms, This is a diffusion term.

3. The method according to claim 2, characterized in that, The generated item is: The redistribution item is: in, For isotropic dissipation rate, , , , , For anisotropic tensors, , , As the dependent variable, As a special dependent variable, , , , , , , The coefficients in the predicted SSG / LRR Reynolds stress equation, , It is vorticity; The dissipation term is: Among them, isotropic dissipation rate , The dissipation coefficient; The diffusion term is: in, is the eddy viscosity coefficient.

4. The method according to claim 3, characterized in that, The Equation and the above The scaling equations are coupled, based on the Reynolds stress turbulence model with a general root-square time scale, namely SSG / LRR- The model includes: The Modification of relevant terms in the equation and the above The scaling equations are coupled, based on the Reynolds stress turbulence model with a general root-square time scale, namely SSG / LRR- The model is: 。 5. The method according to claim 4, characterized in that, Obtain the Reynolds-averaged Navier-Stokes equations, including: The Reynolds-averaged Navier-Stokes equations are obtained as follows: in, For time-averaged pressure, The average temperature of Favre. For Favre's average total energy, For constant pressure specific heat ratio, Pr For laminar flow, Prandtl constant, Pr t It is the Prandtl constant for turbulence; in For the viscous stress tensor: Let Reynolds stress tensor be the constant, and... The relationship is: This completes the coupling between the Reynolds-averaged Navier-Stokes equations and the Reynolds stress turbulence model based on the general root-square time scale.

6. The method according to claim 5, characterized in that, Numerical solution of the coupled equations based on the grid data includes: Based on the grid data, the 12 independent variables contained in the coupled equation system are analyzed using numerical methods for partial differential equation systems: , , , , , , , , and λ Perform numerical solutions; Then, numerical solutions for other variables are derived through relational derivation.

7. A numerical apparatus for a Reynolds stress turbulence model based on a general root-square time scale, characterized in that, The device includes: ω The scaling equation acquisition module is used to acquire turbulence based on SSG / LRR- ω Reynolds stress model ω Scaling equations, including: Turbulence acquisition based on SSG / LRR- ω Reynolds stress model ω The scaling equation is: in, For time-averaged density, For time, When creating subscripts, use coordinate indices. The three components of the Favre average velocity. These are the three-directional coordinate components. For the coefficients of the generating term in the specific dissipation rate scaling equation, It is generated by turbulent kinetic energy, where , , For the generation of Reynolds normal stress in three directions, The coefficients of the dissipation term in the dissipation rate scaling equation are given. The kinetic viscosity coefficient, The coefficients of the diffusion term in the specific dissipation rate scaling equation are... The coefficients of the cross-derivative term in the specific dissipation rate scaling equation are... For turbulent kinetic energy, , , Reynolds normal stress in three directions; ω This represents a measure of specific dissipation rate; The general root-square time scaling equation determination module is used to obtain the pre-derived equation. General time root square scale and ω The scale relationship, based on the relationship and the... ω The scaling equation yields turbulence with respect to Scaling equations, including: Obtain the pre-derived General time root square scale and ω The scale relationship, based on the relationship and the... ω The scaling equation yields turbulence with respect to Scale The scaling equation is: in, ,express General root-square time scale Let be the eddy viscosity coefficient; where, Indicates the energy timescale. express The second root is a positive integer; the pre-derived... General time root square scale and ω The relationship between scales is: in, n for root square scale of time ω The scaling factor; The Reynolds stress turbulence model determination module based on the general root-square time scale is used to obtain turbulence based on SSG / LRR- ω Model equation; Representing the components of the Reynolds stress equation; [The following is a list of components and their meanings, which are not translated as they are not part of the main text] Equation and the above By coupling the scaling equations, a Reynolds stress turbulence model based on the general root-square time scale is obtained, namely SSG / LRR- Model; Obtain the Reynolds-averaged Navier-Stokes equations and couple them with the Reynolds stress turbulence model based on the general root-square time scale to obtain the coupled equations; The numerical simulation module is used to construct grid data of the flow field of the aircraft to be simulated, and to numerically solve the coupled equations based on the grid data to obtain the numerical simulation results of the turbulent flow field of the aircraft.

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