Numerical prediction method, device and equipment based on nine-equation transition model

Abstract

The present invention relates to a numerical prediction method, device and equipment based on a nine-equation transition model. The method comprises: based on the specific dissipation rate scale equation of the existing nine-equation transition model, according to the derived relationship between the time root square scale and the specific dissipation rate scale, a turbulence time scale equation is obtained; the time scale equation is coupled with the predicted SSG / LRR equation of Reynolds stress, the improved intermittency factor equation and the critical transition Reynolds number equation to obtain an improved nine-equation transition model; the predicted Reynolds-averaged Navier-Stokes equation is coupled with the improved nine-equation transition model to obtain a coupled equation group. When performing a numerical simulation of an aircraft flow field, the coupled equation group is numerically solved according to the grid data of the aircraft flow field to be simulated to obtain a numerical prediction result of the aircraft transition flow field. The present method can improve the prediction accuracy of low-speed flat plates (zero pressure gradient and pressure gradient) and transonic airfoils.

Description

Technical Field

[0001] The present invention relates to the technical field of computational fluid dynamics, and in particular to a numerical prediction method, apparatus and device based on a nine-equation transition model. Background Art

[0002] Flow in nature can be categorized into two regimes: laminar and turbulent. The transition between these two regimes is called transition. The study of transition dates back over a century, coinciding with the emergence of turbulence. Initially, scientists approached transition as a flow stability problem. However, the development of computer technology and the urgent need for transition prediction in engineering in the 1970s led to the rapid development of model theories based on empirical relationships. Consequently, transition model theories are divided into two main categories: those based on stability theory and those not.

[0003] Among the methods not based on stability theory, the intermittent factor model is currently the most popular. In 1958, Dhawan and Narasimha, based on Emmons' "turbulent patch" theory, proposed using intermittent factors to quantitatively describe the turbulence generation process. In 1975, Libby used intermittent factors to dynamically control the state of the turbulent quantity transport equation based on the intermittent characteristics of the turbulent field boundary, laying the framework for the intermittent factor model. In the 1990s, Cho and Chung constructed the intermittent factor transport equation based on the k-ε model, forming the k-ε-γ three-equation turbulence model that can predict transition. Subsequently, Suzen et al. added the intermittent factor transport equation to the SST model and were able to accurately calculate the transition position and transition interval length under a range of conditions, such as the T3 series flat plate boundary layer. However, transition models of this period required the use of global parameters to some extent, which limited their application in parallel computing and unstructured grids.

[0004] In this century, Menter and Langtry proposed the γ-Re theory based on local correlation. θt The model has become a milestone engineering transition model. This model organically combines the empirical correlation function and the intermittent factor method, controls the generation of the intermittent factor in the boundary layer through the empirical correlation function, and then controls the generation of turbulence in the turbulence model through the intermittent factor. θt The "localized" parameters used in the model framework are beneficial to unstructured grids, parallel computing, and complex shape calculations. On the other hand, they also facilitate the writing of CFD codes. Therefore, this idea was quickly recognized by the industry and received positive responses from scholars. θt The model needs to be coupled with the SST k-ω model proposed by it to solve, which belongs to the four-equation turbulence model, namely k-ω-γ-Re θtModel.

[0005] However, the four-equation transition model based on the isotropy hypothesis cannot handle the more complex flow separation transition problem. Therefore, Nie et al. tried to use the γ-Re θt By combining this model with the Reynolds stress model, Wang et al. introduced the general time root square scale and achieved high-precision solutions for the SSG-LRR Reynolds stress transition model for the first time. However, the original model still fails to provide accurate predictions for some cases involving pressure gradient transitions and transonic transitions. Therefore, the existing technology suffers from poor adaptability. Summary of the Invention

[0006] Based on this, it is necessary to provide a numerical prediction method, device and equipment based on the nine-equation transition model that can improve the accuracy of predicted pressure gradient and transonic transition to address the above technical problems.

[0007] A numerical prediction method based on a nine-equation transition model, the method comprising:

[0008] Construct a nine-turn equation transition model on a general time root square scale.

[0009] According to the intermittent factor γ equation and critical transition Reynolds number in the transition model of the nine-transformation equation γ-Re of the equation θt The empirical correlation function is combined with the experimental value to make corrections, and the correction factor is added to compress the transition model of the nine-turn equation to obtain the corrected intermittent factor γ equation and the corrected critical transition Reynolds number. equation.

[0010] According to the modified intermittent factor γ equation and the modified critical transition Reynolds number Equation coupling The scaling equation and the predicted SSG / LRR equation of Reynolds stress are used to obtain the modified nine-turn transition model.

[0011] The predicted Reynolds-averaged Navier-Stokes equations are coupled with the modified nine-turn transition model to obtain a coupled equation system.

[0012] The grid data of the simulated aircraft flow field is constructed, and the coupled equations are numerically solved based on the grid data to obtain the numerical prediction results of the aircraft transition flow field.

[0013] A numerical prediction device based on a nine-equation transition model, comprising:

[0014] The Nine-turn Equation Transition Model Construction Module is used to construct the Nine-turn Equation Transition Model on a general time root square scale;

[0015] Parameter optimization module, used to optimize the intermittent factor γ equation and critical transition Reynolds number in the transition model of the nine-transition equation γ-Re of the equation θt The empirical correlation function is corrected in combination with the experimental value, and the correction factor is added to compress and correct the transition model of the nine-turn equation to obtain the corrected intermittent factor γ equation and the corrected critical transition Reynolds number. equation.

[0016] Model optimization module, used to calculate the critical transition Reynolds number based on the modified intermittent factor γ equation and the modified critical transition Reynolds number Equation coupling The scaling equation and the predicted SSG / LRR equation of Reynolds stress are used to obtain the modified nine-turn transition model.

[0017] The coupling module is used to couple the predicted Reynolds-averaged Navier-Stokes equations with the modified nine-turn transition model to obtain a coupled equation system.

[0018] The prediction module is used to construct grid data of the simulated aircraft flow field, numerically solve the coupled equations according to the grid data, and obtain the numerical prediction results of the aircraft transition flow field.

[0019] 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:

[0020] Construct a nine-turn equation transition model on a general time root square scale.

[0021] According to the intermittent factor γ equation and critical transition Reynolds number in the transition model of the nine-transformation equation γ-Re of the equation θt The empirical correlation function is combined with the experimental value to make corrections, and the correction factor is added to compress the transition model of the nine-turn equation to obtain the corrected intermittent factor γ equation and the corrected critical transition Reynolds number. equation.

[0022] According to the modified intermittent factor γ equation and the modified critical transition Reynolds number Equation coupling The scaling equation and the predicted SSG / LRR equation of Reynolds stress are used to obtain the modified nine-turn transition model.

[0023] The predicted Reynolds-averaged Navier-Stokes equations are coupled with the modified nine-turn transition model to obtain a coupled equation system.

[0024] The grid data of the simulated aircraft flow field is constructed, and the coupled equations are numerically solved based on the grid data to obtain the numerical prediction results of the aircraft transition flow field.

[0025] The numerical prediction method, apparatus, and device based on the nine-equation transition model first adjust the empirical correlation functions of the intermittency factor γ equation and the critical transition Reynolds number equation. By adding correction factors, the transition model of the nine-equation transition model is compressed. The improved intermittency factor correction yields the intermittency factor γ equation and the critical transition Reynolds number equation. These corrections improve the model's accuracy in complex flow environments, particularly for transition predictions under high-pressure gradients and transonic conditions. The corrected intermittency factor γ equation and critical Reynolds number equation are combined with the SSG / LRR Reynolds error equation, making the model more accurate for pressure gradient variations and transonic transitions, overcoming the shortcomings of traditional transition models in these areas. The model further couples the dynamic connection between the Reynolds coefficient distribution in the flow and complex turbulent structures, resulting in the improved nine-equation transition model. This model, coupled with the Reynolds-averaged Navier-Stokes equations, forms a coupled system of equations capable of describing complex flow phenomena. When flows with significant pressure gradients or transonic surface transitions occur, the modified model can better capture changes in the flow field and accurately predict the transition location and flow characteristics. The modified model also achieved significant improvements in predicting flows over low-speed flat plates (both with and without pressure gradients), enhancing the model's perception of different flow conditions. Next, using the mesh data of the aircraft flow field, the coupled equations were simulated through numerical simulation to predict the transition flow field under different coupled flow conditions. By combining the simulation of the aircraft flow field with numerical simulation, the improved nine-transition equation model achieved inertial predictions for complex flow fields. This not only improved the prediction accuracy for low-speed flat plates and transonic airfoil flows, but also further expanded its scope of use in practical engineering applications, achieving particularly remarkable results in the refinement of transition phenomenon predictions. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 1 is a flow chart of a numerical method for an improved nine-equation transition model based on a general time root square scale in one embodiment;

[0027] Figure 2 Schematic diagram of the computational grid for low-speed zero-pressure gradient and pressure-gradient transition flat plate flows in one embodiment. Figure 2 (a) is the zero pressure gradient flat grid (T3B), Figure 2 (b) is a flat grid with pressure gradient (T3C2, T3C5);

[0028] Figure 3In one embodiment, the low-speed transition flat plate flow Schematic diagram comparing the model calculation results with the experimental values, where: Figure 3 (a) is the calculated result of T3B flat plate transition experiment (Re θt Schematic diagram of comparison between the experimental value before and after correction (modified represents the corrected value). Figure 3 (b) is the calculated result of T3C2 flat plate transition experiment (Re θt Schematic diagram comparing the experimental values ​​(before and after correction), Figure 3 (c) is the calculated result of T3C5 flat plate transition experiment (Re θt Schematic diagram of comparison between (before and after correction) and experimental values;

[0029] Figure 4 A schematic diagram of a computational grid for a transonic VA-2 airfoil in one embodiment;

[0030] Figure 5 Calculate the transition position (original Comparison of the transition position between the model and the modified model) and the experimental transition position, where modified represents Re θt Correction, c(original) represents the original compressible correction, c(modified) is the modified compressible correction adopted in this paper;

[0031] Figure 6 Calculate the wall friction coefficient distribution for a transonic VA-2 airfoil in one embodiment (raw Comparison of the transition position between the model and the modified model) and the experimental transition position, where modified represents Re θt Correction, c(original) represents the original compressible correction, c(modified) is the modified compressible correction adopted in this paper;

[0032] Figure 7 is a structural block diagram of a numerical prediction device based on a nine-equation transition model in one embodiment;

[0033] Figure 8 FIG. 1 is a diagram showing the internal structure of a computer device in one embodiment. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0035] In one embodiment, Figure 1As shown, a numerical prediction method based on a nine-equation transition model is provided, comprising the following steps:

[0036] Step 102: construct a nine-transition equation transition model of general time root square scale.

[0037] Specifically, the ω-scale equation of turbulence based on the SSG / LRR-ω model is obtained, where ω represents the specific dissipation rate scale. The numerical simulation of the aircraft flow field is based on the proposed physical model. In the engineering application of the numerical simulation of the aircraft flow field, the γ-Re commonly used in current CFD commercial software is used. θt The model needs to be coupled with the proposed SST k-ω model to solve it. The ω-scale equation does not have natural boundary conditions at the viscous wall, which will lead to some numerical instabilities when using high-precision discretization or complex structured / unstructured grids, and have an adverse effect on the numerical simulation of the aircraft flow field.

[0038] Furthermore, the ω-scale equation of turbulence based on the SSG / LRR-ω model is:

[0039]

[0040] Among them, among them, is the time-averaged density, ω is the specific dissipation rate scale, t is time, j is the subscript for the coordinate index, j = 1, 2, 3…n, n is the total number of j, is the three components of Favre average velocity, x j are the three-direction coordinate components, α ω is the coefficient of the specific dissipation rate scaling equation, P is the turbulence generation, β ω is the coefficient of the dissipation term in the specific dissipation rate scaling equation, σ ω is the diffusion coefficient, and k is the turbulent kinetic energy.

[0041] Furthermore, take 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. Scaling equation. Where τ represents the energetic time scale, and n represents the nth root, which is a positive integer.

[0042] By deduction, we can get The relationship between the time root square scale and the ω scale is:

[0043]

[0044] Where n is Adjustment coefficients for the time root square and ω scales.

[0045] Combined with the ω-scaling equation, we can get Scaling equation:

[0046]

[0047] in, express The general time root square scale, σ d is the coefficient of the cross derivative term of the general time root square scaling equation.

[0048] Here, 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.

[0049] Step 104: According to the intermittent factor γ equation and the critical transition Reynolds number in the nine-transition equation transition model γ-Re of the equation θt The empirical correlation function is combined with the experimental value to make corrections, and the correction factor is added to compress the transition model of the nine-turn equation to obtain the corrected intermittent factor γ equation and the corrected critical transition Reynolds number. equation.

[0050] Specifically, Scaling equation and predicted SSG / LRR equation, improved intermittency factor γ equation and critical transition Reynolds number The improved nine-equation transition model based on the general time root square scale is obtained by coupling the equations. The predicted Reynolds stress equation is:

[0051]

[0052] Among them, the right side of the equation is the generation term, pressure-strain correlation term, dissipation term, diffusion term and mass flux term.

[0053] Generated items do not need to be modeled and can be written as:

[0054]

[0055] The form after modeling the dissipation term is:

[0056]

[0057] The pressure-strain correlation is modeled as follows:

[0058]

[0059] The diffusion term uses a simplified diffusion model instead of the generalized gradient diffusion model in the original version. The specific form is:

[0060]

[0061] The correlation coefficient between the pressure-strain correlation term and the diffusion term in the Reynolds stress transport equation needs to be calculated using the F1 mixing function, namely:

[0062] φ=F1φ (LRR) +(1-F1)φ (SSG)

[0063] The improved intermittent factor γ equation is:

[0064]

[0065] Among them, γ is the intermittent factor, P γ is the generated term in the intermittent factor γ equation, E γ is the dissipative term in the intermittent factor γ equation, is the diffusion term in the intermittent factor γ equation, σ f is the diffusion term coefficient of the intermittent factor γ equation.

[0066] Improved critical transition Reynolds number The equation is:

[0067]

[0068] Among them, P θt is the critical transition Reynolds number Equation generator, is the critical transition Reynolds number, is the critical transition Reynolds number The diffusion term in the equation, σ θt is the diffusion term coefficient of the intermittent factor γ equation.

[0069] Step 106: According to the modified intermittent factor γ equation and the modified critical transition Reynolds number Equation coupling The scaling equation and the predicted SSG / LRR equation of Reynolds stress are used to obtain the modified nine-turn transition model.

[0070] Specifically, the SSG / LRR equation, Scaling equation, improved intermittency factor γ equation and critical transition Reynolds number The improved nine-equation transition model based on the general time root square scale is obtained by coupling the equations:

[0071]

[0072] The variables and functions involved in the source term of the γ transport equation are as follows:

[0073]

[0074] F turb =exp[-(R T / 4) 4 ]

[0075] F onset =max(0,F onset2 -F onset3 )

[0076] F onset1 =Re V / 2.193Re θc,comp

[0077]

[0078] F onset3 =max[0,1-(R T / 3) 3 ]

[0079] F length =F length,1 (1-F sublayer )+40F sublayer

[0080]

[0081] F sublayer =exp[-(Re ω / 200) 2 ]

[0082] Re θc,comp =ψRe θc

[0083]

[0084] a1=0.44, a2=-0.31, a3=1.00, b1=2.40, c1=0.38, c2=-0.27

[0085] Among them, F onset is a dimensionless function that controls the starting position of the transition; Re θc,comp is the critical momentum thickness Reynolds number at which the intermittency factor in the new compressible-corrected boundary layer begins to increase, which is located at the transition momentum thickness Reynolds number Upstream position of F length is the empirical correlation function that controls the length of the transition region.

[0086] The coefficients in the γ transport equation are as follows:

[0087] c a1 =2.0c a2 =0.06ce1 =1.0c e2 =50.0σ f =1.0

[0088] In the Cartesian coordinate system, The transport equation is as follows:

[0089]

[0090] Among them, the source term P θt Outside the boundary layer Equal to Re θt , which is specifically defined as:

[0091]

[0092] Source term P θt The variables and functions in are as follows:

[0093]

[0094] F wake =exp[-(Re ω / 10 5 ) 2 ]

[0095]

[0096] Re θt =f(Tu,λ θ )

[0097] Where T is the time scale, which is obtained from dimensional analysis. θt is a mixing function that closes P in the boundary layer θt , thus allowing Diffusion from the free stream into the boundary layer, that is, in the free stream F θt =0 and in the boundary layer F θt =1;F wake is used to ensure that the mixing function F θt Not activated in the wake area; Re θt is the local turbulence Tu and the local pressure gradient parameter λ θ The empirical correlation function of .

[0098] New Re θt The empirical expression of can be written as:

[0099]

[0100] in,

[0101]

[0102] Local turbulence Tu and local pressure gradient parameter λ θ is defined as:

[0103]

[0104] Note that due to Re θt The expression of θ is also t Therefore, it is common to iterate θ t The value of Re θt .also, is the acceleration along the flow direction, and its specific solution is:

[0105]

[0106] Due to Re θt The local turbulence Tu and the local pressure gradient parameter λ θ Calculation shows that it is not practical to use it directly in the boundary layer. The transport equations, which make the By Re θt The empirical correlation function of the boundary layer is obtained. is obtained by free flow diffusion. In addition, the following restrictions are imposed on some variables to achieve numerical robustness:

[0107] -0.1≤λ θ ≤0.1Tu≥0.027Re θt ≥20

[0108] In order to improve the simulation effect of separation transition, the intermittent factor needs to be corrected as follows:

[0109] γ eff =max(γ,γ sep )

[0110] in,

[0111] γ sep =min{2max[0,Re V / (3.235Re θc )-1]F reattach ,2}F θt

[0112] F reattach =exp[-(R T / 20) 4 ]

[0113] γ-Re θ The far-field boundary conditions of the transition model are:

[0114] γ ∞ =1

[0115]

[0116] At the wall, γ and Re should be guaranteed θ The normal flux is 0, that is:

[0117]

[0118] Furthermore, for the convection term, let γ out =γ in and Even if the convection flux is zero at the wall, for the viscous term, let γ = 1 / c at the wall (1 / 2 point) e2 , so that the destruction terms of the γ equation and The generated term of the equation is 0 at the wall, and The viscous flux is set to 0 to ensure that it is obtained only by diffusion outside the boundary layer through the transport equation.

[0119] Step 108 : Couple the predicted Reynolds-averaged Navier-Stokes equations with the modified nine-turn transition model to obtain a coupled equation system.

[0120] The predicted Reynolds-averaged Navier-Stokes equations are:

[0121]

[0122] 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;

[0123] in is the viscous stress tensor:

[0124]

[0125] τ ij is the Reynolds stress tensor, which is obtained through the Boussinesq relationship:

[0126]

[0127] Complete the coupling of the Reynolds-averaged Navier-Stokes equations and the improved nine-equation transition model based on the general time root square scale.

[0128] Step 110 : constructing grid data of the simulated aircraft flow field, numerically solving the coupled equations based on the grid data, and obtaining numerical prediction results of the aircraft transition flow field.

[0129] Specifically, according to the grid data of the aircraft flow field to be simulated, the numerical method for the partial differential equations is used to solve the 14 independent variables contained in the coupled equations: λ, γ, etc. to obtain numerical solutions; and then derive numerical solutions for other variables through relational expressions.

[0130] exist 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 will not affect the SSG / LRR 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.

[0131] In the numerical prediction method based on the nine-equation transition model, empirical correlation functions are first adjusted for the intermittency factor γ equation and the critical transition Reynolds number equation. By adding correction factors, the transition model of the nine-equation transition model is compressed. The improved intermittency factor correction yields the intermittency factor γ equation and the critical transition Reynolds number equation. These corrections improve the model's accuracy in complex flow environments, particularly for transition predictions under high-pressure gradients and transonic conditions. The modified intermittency factor γ equation and the critical Reynolds number equation are combined with the SSG / LRR Reynolds error equation, making the model more accurate for pressure gradient variations and transonic transitions. This overcomes the shortcomings of traditional transition models in these areas and further couples the dynamic connection between the Reynolds coefficient distribution in the flow and complex turbulent structures, resulting in the improved nine-equation transition model. This model, coupled with the Reynolds-averaged Navier-Stokes equations, forms a coupled system of equations capable of describing complex flow phenomena. When flows with significant pressure gradients or transonic surface transitions occur, the modified model can better capture changes in the flow field and accurately predict the transition location and flow characteristics. The modified model also achieved significant improvements in predicting flows over low-speed flat plates (both with and without pressure gradients), enhancing the model's perception of different flow conditions. Next, using the mesh data of the aircraft flow field, the coupled equations were simulated through numerical simulation to predict the transition flow field under different coupled flow conditions. By combining the simulation of the aircraft flow field with numerical simulation, the improved nine-transition equation model achieved inertial predictions for complex flow fields. This not only improved the prediction accuracy for low-speed flat plates and transonic airfoil flows, but also further expanded its scope of use in practical engineering applications, achieving particularly remarkable results in the refinement of transition phenomenon predictions.

[0132] In one embodiment, the turbulence is obtained based on the ω-scale equation of the SSG / LRR-ω model:

[0133]

[0134] in, is the time-averaged density, ω is the specific dissipation rate scale, t is time, j is the subscript for the coordinate index, j = 1, 2, 3…n, n is the total number of j, is the three components of Favre average velocity, x j are the three-direction coordinate components, α ω is the coefficient of the specific dissipation rate scaling equation, P is the turbulence generation, β ω is the coefficient of the dissipation term in the specific dissipation rate scaling equation, σ ω is the diffusion coefficient, k is the turbulent kinetic energy;

[0135] Get 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. Scaling equation:

[0136]

[0137] in, for The general time root square scale, σ d is the cross derivative coefficient of the general time root square equation, n is Adjustment coefficients for the time root square scale and the specific dissipation rate scale ω.

[0138] In one embodiment, according to the intermittent factor γ equation and the critical transition Reynolds number in the nine-transition equation transition model, γ-Re of the equation θt The empirical correlation function is modified based on historical values:

[0139]

[0140] F turb =exp[-(R T / 4) 4 ]

[0141] F onset =max(0,F onset2 -F onset3 )

[0142] F onset1 =Re V / 2.193Re θc

[0143]

[0144] F onset3 =*max[0,1-(R T / 2.5) 3 ]

[0145] F length =F length,1 (1-F sublayer )+40F sublayer

[0146]

[0147] F sublayer =exp[-(Re ω / 200) 2 ]

[0148]

[0149] Among them, P γ is the generated term in the intermittent factor γ equation, c a1 、c a2 are constants of 2.0 and 0.06 respectively, γ is the intermittent factor, F onset 、F onset2 、F onset3 are the dimensionless functions that control the starting position of the transition, F length is the empirical correlation function that controls the length of the transition region, is the time-averaged density, is the strain rate modulus, c e1 、c e2 are constants of 1.0 and 50.0 respectively, E γ is the dissipative term in the intermittent factor γ equation, is the vorticity modulus, R T is the turbulent Reynolds number, Re V is the vorticity Reynolds number, Re θc is the critical momentum thickness Reynolds number, is the critical transition Reynolds number, Re ω is the dissipation rate Reynolds number;

[0150] And add F onset2 The correction factor performs compression correction on the transition model of the nine-turn equation:

[0151]

[0152] Among them, f bp is the mixing function, F onsetn is the dimensionless function that controls the transition starting position, is the dimensionless function of the original control transition starting position, is the critical transition Reynolds number;

[0153] The critical momentum thickness Reynolds number Re when the intermittent factor in the boundary layer begins to increase in the modified nine-turn equation transition model is θc Use Re θc,comp replace:

[0154] Re θc,comp =ψRe θc

[0155]

[0156] a1=0.44, a2=-0.31, a3=1.00, b1=2.40, c1=0.38, c2=-0.27

[0157] Where ψ is the correction coefficient, a1, a2, b1, c1, c2 are all constants, M e is the boundary layer Mach number, λ θ,e is the local pressure gradient parameter, Tu ∞ is the turbulence;

[0158] The corrected intermittent factor γ equation is obtained:

[0159]

[0160] in, is the time-averaged density, is the three components of Favre average velocity, x j are the three-direction coordinate components, μ is the molecular viscosity coefficient, μ t is the turbulent viscosity coefficient, σ f is the diffusion coefficient of the intermittent factor γ equation, is the diffusion term in the intermittent factor γ equation;

[0161] and the corrected critical transition Reynolds number equation:

[0162]

[0163] Among them, P θt is the critical transition Reynolds number Equation generator, where is the critical transition Reynolds number, and the generated term expression is:

[0164]

[0165] Among them, Re θt is the empirical correlation function. In the modified nine-transition equation transition model, the empirical correlation function is expressed as:

[0166]

[0167] in, is the critical transition Reynolds number The diffusion term in the equation, σ θt is the diffusion coefficient of the intermittent factor γ equation, F(λ θ ) is λ θ function of , Tu is the local turbulence.

[0168] In one embodiment, the pre-derived The general relationship between the time root square scale and the ω scale is:

[0169]

[0170] Where n is Adjustment coefficients for the time root square scale and the specific dissipation rate scale ω;

[0171] The predicted Reynolds stress SSG / LRR equation is:

[0172]

[0173] Among them, the right side of the equation is the generation term, pressure-strain correlation term, dissipation term, diffusion term and mass flux term in order;

[0174] The generated items are:

[0175]

[0176] in, is the time-averaged density, P ij is the turbulence generation term, is the Reynolds stress component, is the three components of Favre average velocity, x k is the coordinate component, k is the turbulent kinetic energy, is the velocity component.

[0177] The dissipation term is modeled as follows:

[0178]

[0179] Among them, ε ij is the dissipation term, ε is the isotropic dissipation term, δ ij is the Kronecker operator, is the time-averaged density;

[0180] The pressure-strain correlation is modeled as follows:

[0181]

[0182] Among them, Π ij is the pressure-strain correlation term, C1, C2, C3, C4, C5, is a constant, is the time-averaged density, P kk To generate items, is the anisotropic operator, is the turbulent kinetic energy, is the traceless anisotropy tensor, is the strain rate tensor, is the rotation tensor;

[0183] The diffusion term is modeled using a simplified diffusion model as follows:

[0184]

[0185] Among them, D ij is the diffusion term, is the time-averaged density, D is the isotropic diffusion term, C μ is a constant, x k are coordinate components, is the Reynolds stress component;

[0186] The correlation coefficient between the pressure-strain correlation term and the diffusion term in the Reynolds stress transport equation is calculated using the F1 mixing function:

[0187] φ=F1φ (LRR) +(1-F1)φ (SSG)

[0188] Among them, F1 is the mixing function, φ is the mixed coefficient, φ (LRR) is the LRR coefficient, φ (SSG) is the SSG coefficient.

[0189] In one embodiment, according to the modified intermittent factor γ equation and the modified critical transition Reynolds number Equation coupling The scale equation and the predicted SSG / LRR equation of Reynolds stress give the modified nine-turn transition model:

[0190]

[0191] in, is the time-averaged density, is the velocity component, is the Reynolds stress separation, λ is the scale variable, is the three components of Favre average velocity, α ω Generates the coefficient for the specific dissipation rate scaling equation, β ω is the coefficient of the dissipation term in the specific dissipation rate scaling equation, σ ω is the diffusion coefficient, P θt is the source term, σ θt is the diffusion coefficient of the intermittent factor γ equation, σ f is a constant of 1.0, x i is the coordinate component, M ij is the additional gradient term, σ d is the coefficient of the cross derivative term of the general time root square scaling equation.

[0192] It is worth noting that the second-order MUSCL format and the fifth-order WCNS-E5 format are used to analyze the SSG / LRR- The model was evaluated using the T3 series low-speed flat plate flow. Specifically, three flat plate transition experiments were conducted: T3B, T3C2, and T3C5. T3B was a high-turbulence bypass transition, while T3C2 and T3C5 were flat plates with pressure gradients. The grid used in the calculations is shown in [1]. Figure 2 As shown, pre-treatment technology is used to adapt to low-speed flow. Figure 2 (a) is the zero pressure gradient flat grid (T3B), Figure 2 (b) is a flat grid with pressure gradient (T3C2, T3C5). Figure 3 The results show that the improved Model (simplified in the figure as modifiedγ-Re θt RSM) has a better prediction effect on low-speed flat plate flow than the original version, where modified represents Re θt Empirical correlation formula after correction; Exp. represents the experimental value.

[0193] In one embodiment, based on the grid data, a numerical method for partial differential equations is used to solve the independent variables included in the coupled equations: λ, γ, After numerical solution, the numerical solutions of the remaining variables are obtained by deducing the relational expressions.

[0194] In one embodiment, the predicted Reynolds-averaged Navier-Stokes equations are:

[0195]

[0196] in, is the time-averaged pressure, is the time-averaged density, 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;

[0197] is the viscous stress tensor:

[0198]

[0199] S ij is the strain rate tensor, μ is the viscosity coefficient, x k are coordinate components, is the velocity component, δ ij is the Kronecker operator;

[0200] τ ij is the Reynolds stress tensor:

[0201]

[0202] S ij For x k are coordinate components, is the velocity component, μ t is the turbulent viscosity coefficient, is the time-averaged density, and k is the turbulent kinetic energy.

[0203] In one embodiment, the example used is the transonic flow of VA-2 airfoil, and the grid is as follows: Figure 4 As shown, the calculation results are as follows Figure 5 (Transition position calculation) and Figure 6 (Distribution of wall friction coefficient) is shown, where modified represents Re θt Correction, c(original) represents the original compressibility correction, c(modified) is the modified compressibility correction used in this paper, Exp. represents the experimental value, and you can see the final modified (The simplified expression in the figure is modifiedγ-Re θt RSM-c(modified)) achieved better prediction results.

[0204] It should be understood that although Figure 1 The 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.

[0205] In one embodiment, Figure 7 As shown, a numerical prediction device based on the nine-equation transition model is provided, comprising: a nine-equation transition model construction module 702, a parameter optimization module 704, a model optimization module 706, a coupling module 708 and a prediction module 710, wherein:

[0206] A nine-turn equation transition model construction module 702 is used to construct a nine-turn equation transition model of a general time root square scale;

[0207] Parameter optimization module 704 is used to optimize the intermittent factor γ equation and the critical transition Reynolds number in the nine-transition equation transition model. γ-Re of the equation θt The empirical correlation function is corrected in combination with the experimental value, and the correction factor is added to compress and correct the transition model of the nine-turn equation to obtain the corrected intermittent factor γ equation and the corrected critical transition Reynolds number. equation.

[0208] Model optimization module 706 is used to optimize the model according to the modified intermittent factor γ equation and the modified critical transition Reynolds number. Equation coupling The scaling equation and the predicted SSG / LRR equation of Reynolds stress are used to obtain the modified nine-turn transition model.

[0209] The coupling module 708 is used to couple the predicted Reynolds-averaged Navier-Stokes equations with the modified nine-turn transition model to obtain a coupled equation set.

[0210] The prediction module 710 is used to construct grid data of the simulated aircraft flow field, numerically solve the coupled equations according to the grid data, and obtain the numerical prediction results of the aircraft transition flow field.

[0211] Regarding the specific limitations of the numerical prediction device based on the nine-equation transition model, please refer to the limitations of the numerical prediction method based on the nine-equation transition model above, which will not be repeated here. The various modules in the above-mentioned numerical prediction device based on the nine-equation transition model 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 modules.

[0212] 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 8As 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 prediction method based on a nine-equation transition model is implemented. The display screen of the computer device can be a liquid crystal display screen 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 key, trackball or touchpad provided on the computer device housing, or an external keyboard, touchpad or mouse.

[0213] Those skilled in the art will understand that Figure 7-8 The structure shown in the figure is merely a block diagram of a portion of the structure related to the solution of the present invention and does not constitute a limitation on the computer device to which the solution of the present invention 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.

[0214] In one embodiment, a computer device is provided, including 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:

[0215] Construct a nine-turn equation transition model on a general time root square scale.

[0216] According to the intermittent factor γ equation and critical transition Reynolds number in the transition model of the nine-transformation equation γ-Re of the equation θt The empirical correlation function is combined with the experimental value to make corrections, and the correction factor is added to compress the transition model of the nine-turn equation to obtain the corrected intermittent factor γ equation and the corrected critical transition Reynolds number. equation.

[0217] According to the modified intermittent factor γ equation and the modified critical transition Reynolds number Equation coupling The scaling equation and the predicted SSG / LRR equation of Reynolds stress are used to obtain the modified nine-turn transition model.

[0218] The predicted Reynolds-averaged Navier-Stokes equations are coupled with the modified nine-turn transition model to obtain a coupled equation system.

[0219] The grid data of the simulated aircraft flow field is constructed, and the coupled equations are numerically solved based on the grid data to obtain the numerical prediction results of the aircraft transition flow field.

[0220] Those skilled in the art will appreciate that all or part of the processes in the above-described 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 above-described embodiments. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention 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 DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct RAM bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM).

[0221] 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.

[0222] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A numerical prediction method based on a nine-equation transition model, characterized in that: The method comprises: Construct a nine-turn equation transition model for general time root square scale; According to the intermittent factor in the transition model of the nine-transition equation γ Equation and critical transition Reynolds number Equation The empirical correlation function is corrected in combination with the experimental value, and the correction factor is added to compress and correct the transition model of the nine-turn equation to obtain the corrected intermittent factor γ Equation and modified critical transition Reynolds number equation; According to the modified intermittent factor γ Equation and the modified critical transition Reynolds number Equation coupling Scaling equation and preset Reynolds stress SSG / LRR Equation, the modified nine-turn equation transition model is obtained as in, is the time-averaged density, is the velocity component, is the Reynolds stress separation, is a scale variable, 、 are the three components of Favre mean velocity, Generates term coefficients for the specific dissipation rate scaling equation, is the coefficient of the dissipation term in the specific dissipation rate scaling equation, is the diffusion coefficient, is the source term, Intermittent factor γ The diffusion coefficient of the equation, is a constant of 1.0, For time, 、 、 are the coordinate components, is the additional gradient term, is the cross-derivative coefficient of the general time root square equation, is the Reynolds stress generating term, is the pressure-strain correlation term, is the Reynolds stress dissipation term, is the Reynolds stress diffusion term, Generate terms for the scaling equation, n for Time root square scale and specific dissipation rate scale ω The adjustment coefficient, is the turbulent kinetic energy, is the viscosity coefficient, is the turbulent viscosity coefficient, Intermittent factor γ The generated term in the equation, Intermittent factor γ The dissipative term in Eq. The preset Reynolds-averaged Navier-Stokes equations are: in, is the time-averaged pressure, is the time-averaged density, 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; is the viscous stress tensor: is the strain rate tensor, is the viscosity coefficient, are coordinate components, is the velocity component, is the Kronecker operator; is the Reynolds stress tensor: for, is the turbulent viscosity coefficient, is the time-averaged density, is the turbulent kinetic energy; Coupling the preset Reynolds-averaged Navier-Stokes equations with the modified nine-turn transition model to obtain a coupled equation system; Grid data of the simulated aircraft flow field is constructed, and the coupled equations are numerically solved according to the grid data to obtain numerical prediction results of the aircraft transition flow field.

2. The method according to claim 1, characterized in that Construct a nine-turn equation transition model on a general time root square scale, including: Get turbulence based on SSG / LRR - ω Model ω Scaling equation: in, is the time-averaged density, is the specific dissipation rate scale, For time, Make the subscript the coordinate index, , for The total number of 、 are the three components of Favre mean velocity, are the three-direction coordinate components, Generates term coefficients for the specific dissipation rate scaling equation, For turbulence generation, is the coefficient of the dissipation term in the specific dissipation rate scaling equation, is the diffusion coefficient, is the turbulent kinetic energy, To generate items; 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 turbulent Scaling equation: in, for Generally, the time root square scale is is the cross-derivative coefficient of the general time root square equation, n for Time root square scale and specific dissipation rate scale ω The adjustment coefficient.

3. The method according to claim 2, characterized in that According to the intermittent factor in the transition model of the nine-transition equation γ Equation and critical transition Reynolds number Equation The empirical correlation function is corrected in combination with the experimental value, and the correction factor is added to compress and correct the transition model of the nine-turn equation to obtain the corrected intermittent factor γ Equation and modified critical transition Reynolds number Equations, including: According to the intermittent factor in the transition model of the nine-transition equation γ Equation and critical transition Reynolds number Equation The empirical correlation function is modified based on historical values: in, Intermittent factor γ The generated term in the equation, 、 are constants of 2.0 and 0.06 respectively, is the intermittent factor, 、 、 are the dimensionless functions that control the starting position of the transition, is the empirical correlation function that controls the length of the transition region, is the time-averaged density, is the strain rate norm, 、 are constants of 1.0 and 50.0 respectively, Intermittent factor γ The dissipation term in the equation, is the vorticity modulus, is the turbulent Reynolds number, is the vorticity Reynolds number, is the critical momentum thickness Reynolds number, is the critical transition Reynolds number, is the dissipation rate Reynolds number, Represents Related empirical functions; and add The correction factor performs compression correction on the nine-transition equation transition model: in, is a mixing function, is the dimensionless function that controls the transition starting position, is the dimensionless function of the original control transition starting position, is the critical transition Reynolds number; The critical momentum thickness Reynolds number at which the intermittent factor in the boundary layer begins to increase in the modified nine-turn equation transition model is use replace: in, is the correction factor, 、 、 、 、 、 are all constants, is the boundary layer Mach number, is the local pressure gradient parameter, is the turbulence; Get the corrected intermittent factor γ equation: in, is the time-averaged density, is the three components of Favre average velocity, are the three-direction coordinate components, is the molecular viscosity coefficient, is the turbulent viscosity coefficient, Intermittent factor γ The diffusion coefficient of the equation, Intermittent factor γ The diffusion term in the equation; and the corrected critical transition Reynolds number equation: in, is the critical transition Reynolds number Equation generator, where is the critical transition Reynolds number, and the generated term expression is: in, is the empirical correlation function. In the modified nine-transition equation transition model, the empirical correlation function is expressed as: in, is the critical transition Reynolds number The diffusion term in the equation, Intermittent factor γ The diffusion coefficient of the equation, For Related functions, is the local turbulence.

4. The method according to any one of claims 1 to 3, characterized in that Pre-derived General time root square scale and ω The scale relationship is: in, n for Time root square scale and specific dissipation rate scale ω The adjustment coefficient of The predicted Reynolds stress SSG / LRR The equation is: Among them, the right side of the equation is the generation term, pressure-strain correlation term, dissipation term, diffusion term and mass flux term in order; The generated items are: in, is the time-averaged density, is the turbulence generation term, is the Reynolds stress component, is the three components of Favre average velocity, are coordinate components, is the velocity component; The form after modeling the dissipation term is: in, is the dissipation term, is the isotropic dissipation term, is the Kronecker operator, is the time-averaged density; The pressure-strain correlation term is modeled as follows: in, is the pressure-strain correlation term, 、 、 、 、 、 、 is a constant, is the time-averaged density, To generate items, 、 、 、 are the anisotropic operators, is the turbulent kinetic energy, is the traceless anisotropy tensor, 、 、 are the strain rate tensor, is the rotation tensor; The diffusion term is modeled using a simplified diffusion model as follows: in, is the diffusion term, is the time-averaged density, is the isotropic diffusion term, is the viscosity coefficient, is a constant; The correlation coefficient between the pressure-strain correlation term and the diffusion term in the Reynolds stress transport equation is calculated using the F1 mixing function: in, is a mixing function, is the mixing coefficient, is the LRR coefficient, is the SSG coefficient.

5. The method according to claim 4, characterized in that Numerically solving the coupled equations according to the grid data includes: According to the grid data, the independent variables included in the coupled equations are solved using a numerical method for the partial differential equations: 、 、 、 、 λ、 、 After numerical solution, the numerical solutions of the remaining variables are obtained by deducing the relational expressions.

6. A numerical prediction device based on a nine-equation transition model, characterized in that: To implement the method according to any one of claims 1 to 5, the device comprises: The Nine-turn Equation Transition Model Construction Module is used to construct the Nine-turn Equation Transition Model on a general time root square scale; Parameter optimization module, used to optimize the intermittent factor in the transition model according to the nine-transition equation γ Equation and critical transition Reynolds number Equation The empirical correlation function is corrected in combination with the experimental value, and the correction factor is added to compress and correct the transition model of the nine-turn equation to obtain the corrected intermittent factor γ Equation and modified critical transition Reynolds number equation; A model optimization module is used to optimize the intermittent factor according to the modified intermittent factor. γ Equation and the modified critical transition Reynolds number Equation coupling Scaling equation and predicted Reynolds stress SSG / LRR Equation, and the modified nine-turn equation transition model is obtained; A coupling module is used to couple the predicted Reynolds-averaged Navier-Stokes equations with the modified nine-turn transition model to obtain a coupled equation system; The prediction module is used to construct grid data of the simulated aircraft flow field, numerically solve the coupled equations according to the grid data, and obtain the numerical prediction results of the aircraft transition flow field.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

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