A method for turbulent numerical simulation of incompressible separated flows

Abstract

The application relates to the technical field of computational fluid dynamics, and discloses a turbulent flow numerical simulation method for incompressible separated flow, which comprises the following steps: initializing flow physical quantities and turbulent characteristic quantities for the separated flow to be simulated; obtaining corrected Reynolds stress according to the flow physical quantities and the turbulent characteristic quantities; solving a corrected incompressible flow Reynolds average equation based on the corrected Reynolds stress to obtain average velocity and average pressure of each iteration step; obtaining turbulent kinetic energy, specific dissipation rate and turbulent vortex viscosity coefficient of each iteration step according to the flow physical quantities and a discretized turbulent flow model transport equation; and outputting final flow physical quantities and turbulent characteristic quantities and ending the numerical simulation until the residual error is less than a preset value or the maximum iteration step is reached. The application improves the prediction accuracy of the separated zone in the incompressible separated flow, and the size of the separated zone and the Reynolds stress distribution are closer to the direct numerical simulation result.

Description

Technical Field

[0001] This application relates to the field of computational fluid dynamics, and in particular to a numerical simulation method for incompressible separated flows. Background Technology

[0002] Incompressible separation flows are a type of flow with wide engineering applications in fluid mechanics. They exist under conditions such as surface constraints, channel expansion or contraction, vehicle outflow, and building wind engineering. A significant recirculation zone forms within the boundary layer, accompanied by complex vortex structure evolution and energy loss. Therefore, accurately predicting the flow field characteristics, separation point, and reattachment location of incompressible separation flows is of great importance.

[0003] The Reynolds-Average Navier-Stokes (RANS) method is the most commonly used numerical evaluation method in industry. Compared with methods such as Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES), it has advantages such as requiring fewer computational grids and higher computational efficiency. One of the key techniques of the RANS method is the turbulence model, such as... The model is one of the most widely used models in engineering. It performs well and is applied in typical flows such as those with attached boundary layers and shear layers, but it cannot yet predict incompressible separation flows very well.

[0004] Numerical simulation methods for incompressible separated flows include RANS methods, LES methods, RANS-LES hybrid methods, and direct numerical simulations. Due to its advantages such as smaller computational grid and higher computational efficiency, RANS remains the most commonly used numerical evaluation method in industry. It mainly includes the eddy viscosity model (EVM) based on the eddy viscosity assumption and the Reynolds stress model (RSM) based on the Reynolds stress transport equation framework. The former has higher efficiency and computational stability and is the most widely used in industrial software, with shear stress transport (SST) being the most typical example. A two-equation model. However, the SST model presents challenges when dealing with clearly separated turbulent flows. Related improvements include revising the coefficients in the turbulence model and refining existing terms in the turbulence model equations.

[0005] The original SST model overestimates the recirculation region of incompressible separated flows and its ability to simulate Reynolds stress distribution needs improvement. Summary of the Invention

[0006] In view of this, this application provides a turbulent numerical simulation method for incompressible separated flows. By adding two nonlinear components to the Reynolds stress constitutive relation, the prediction accuracy of the original SST model is improved without significantly increasing computational costs.

[0007] This application discloses a turbulent numerical simulation method for incompressible separated flows, which includes: Step 1: For the separated flow to be simulated, initialize the flow physical quantities and turbulence characteristic quantities; the flow physical quantities include the average velocity. and pressure Turbulent characteristic quantities include turbulent kinetic energy. Specific dissipation rate and turbulent eddy viscosity coefficient ; Step 2: Construct and calculate the flow field characteristic quantities based on the flow physical quantities and turbulence characteristic quantities. ~ The flow physical quantity includes average velocity. Mean pressure The turbulent characteristic quantities include turbulent kinetic energy. Specific dissipation rate Turbulent eddy viscosity coefficient ; Step 3: Based on the flow physical quantities, turbulence characteristic quantities, and flow field characteristic quantities ~ The correction term for Reynolds stress is obtained. ; Step 4: According to the The original Reynolds stress of the iteration step and the correction term for Reynolds stress Calculation yields the first Reynolds stress after iterative step correction The corrected Reynolds stress The expression replaces the original Reynolds-averaged equation for incompressible flow. The modified Reynolds-averaged equations for incompressible flow are obtained. By solving the modified Reynolds-averaged equations for incompressible flow, the first... Average speed of iteration steps and average pressure ; Step 5: Solve The transport equations of the turbulent model are used to calculate the first... Turbulent characteristics of the iteration step, including turbulent characteristics. , Based on the turbulence characteristic quantities, the first... Turbulent eddy viscosity coefficient of the iterative step ;in, For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps For the first Turbulent eddy viscosity coefficient of the iteration step; Step 6: Repeat steps 4 and 5 iteratively until the residual is found. Less than the preset value or iterative steps Equal to the maximum number of iterations When the time is right, stop the calculation; among them, For the first Incompressible flow under iterative steps: Reynolds-averaged Navier-Stokes equations and The residuals of the turbulence model equations; Step 7: Output the final flow physical quantities and turbulence characteristic quantities to end the numerical simulation; the final flow physical quantities include , The final turbulence characteristic quantities include , , , For the first The average speed of the iteration step For the first Average pressure of iteration steps For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps For the first Turbulent eddy viscosity coefficient of the iteration step.

[0008] Further, step 2 includes: For the flow field to be simulated, which includes the separation region, flow physical quantities and turbulence characteristic quantities are extracted, and the following feature set is constructed. ~ :

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] in, The trace is the combination of the dimensionless strain rate and rotation rate tensors. The trace is the combination of the turbulent kinetic energy gradient correlation tensor and the strain rate tensor. The ratio of generating terms to dissipating terms. The turbulent Reynolds number is based on the wall distance. This represents the ratio of the turbulent timescale to the mean flow timescale. It is the ratio of turbulent viscosity to molecular viscosity. The operators for calculating the trace of a matrix. The dimensionless rotation rate tensor. The dimensionless strain rate tensor For the first The first indicator and the first The components of the dimensionless twitch rate tensor of each index For the first The first indicator and the first The components of the dimensionless twitch rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index The result is obtained by cross product of the negative diagonal matrix and the turbulent kinetic energy gradient vector, followed by dimensionless transformation. and All The amount, For the turbulent kinetic energy generation term, for The velocity component in the direction of the index, for The coordinate components of the indicator direction, These are the components of the Reynolds stress tensor. It is a constant. For turbulent kinetic energy, For specific dissipation rate, for The velocity component in the direction of the index, for The coordinate components of the indicator direction, The function for calculating the minimum value, The distance between the walls. The coefficient of kinematic viscosity, These are the strain rate tensor components. The turbulent eddy viscosity coefficient, velocity gradient , velocity gradient , for The velocity component in the direction of the index, for The coordinate components of the indicator direction, For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The rotation rate tensor components of each index For the first The first indicator and the first The components of the cross product tensor of the turbulent kinetic energy gradient of each index. and Levi-Civita notation (permutation notation) is used for indices in a three-dimensional Cartesian coordinate system. Its definition and The specific content and arrangement are related: If If any two of them are equal, then ;like yes If the even permutations are..., then ;like yes If the odd permutation is..., then Even permutations are those with an even number of inversions, and odd permutations are those with an odd number of inversions; the number of inversions is the total number of inversion pairs; and the definition of an inversion pair is as follows: Assume there is a permutation... (i.e., an ordered sequence in which no elements are repeated), if the index is correct satisfy and This is called an ordered pair. It is an inversion pair; in the formula In the middle, repeated subscripts Indicates to l Summing 1, 2, and 3, this expression defines an antisymmetric tensor. In the The first indicator and the first The components under each indicator for The coordinate components of the indicator direction, for p The coordinate components of the indicator direction, To find the sign of the partial derivative, and All are positive integers; denoted as the Frobenius norm of the turbulent kinetic energy gradient tensor before normalization.

[0019] Further, step 3 includes: Correction terms for calculating Reynolds stress :

[0020] in, For coefficient functions, For the first Tensor base for each index.

[0021] Furthermore, tensor bases exist The expressions for the values ​​equal to 1, 2, and 3 are:

[0022] in, For Kronecker notation, For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The rotation rate tensor components of each index For the first The first indicator and the first The rotation rate tensor components of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For Kronecker notation, For the first The first indicator and the first Components of the dimensionless strain rate tensor of each index; Based on data obtained through DNS methods, and obtained by employing deep symbolic regression. , , Corresponding coefficient function The expressions are as follows:

[0023]

[0024] .

[0025] Furthermore, the first is calculated using the following formula. Reynolds stress after iterative step correction :

[0026]

[0027] in, For the first The iteration step is based on the linear eddy viscosity proposed by the Boussinesq assumption. For the first Turbulent kinetic energy of the iteration step For the first Turbulent eddy viscosity coefficient of the iteration step For the first The average speed of the iteration step; The modified Reynolds-averaged equation for incompressible flow is expressed as follows:

[0028]

[0029] in, For average pressure, For the first The coordinate position of a tensor index. For the first The coordinate position of a tensor index. For average density, The coefficient of kinematic viscosity, For the corrected Reynolds stress, For time, For the first The velocity field of each index For the first The velocity field of each index; The SIMPLEC algorithm is used to handle pressure-velocity coupling, and a multigrid solver is employed to accelerate the solution of the modified Reynolds-averaged equations for incompressible flow, where inviscid flux... Upwind configuration is adopted to ensure transport characteristics and viscous flux. The discretization is performed using a second-order Gaussian linear correction scheme, and the gradient calculation is performed using Gaussian linear interpolation. That is, the gradient is calculated by interpolating from the unit volume center value to the surface center value, and then the gradient is obtained. The flow field variables of the iteration step, the first step The flow field variables of the iteration step include , .

[0030] Further, step 5 includes: Solving iteratively using the stable biconjugate gradient method The transport equations of the turbulent model are derived, and corresponding relaxation factors are used to ensure numerical stability; the first... Turbulent characteristic quantities of the iteration step, including , According to the first Magnitude of strain rate tensor of iteration step and the Mixed function of iteration steps Calculate the first Turbulent eddy viscosity coefficient of the iterative step .

[0031] Furthermore, the first is calculated using the following formula. Turbulent eddy viscosity coefficient of the iterative step :

[0032] in, For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps For the first The magnitude of the strain rate tensor of the iteration step , It is a positive number.

[0033] Furthermore, the first is calculated using the following formula. Mixed function of iteration steps :

[0034] in, For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps It is a positive number. The distance to the nearest wall. It is the molecular kinematic viscosity coefficient. It is a function for maximizing the value.

[0035] Further, step 6 includes: Repeat steps 4 and 5 to continuously iterate and solve the problem. N The iterations continue until the preset convergence condition is met, or the maximum set number of computation iterations is reached. until.

[0036] Furthermore, prior to step 1, the procedure also includes: The average velocity in the Reynolds-averaged Navier-Stokes equations for initializing incompressible flow Mean pressure ,as well as Turbulent kinetic energy in turbulence models Specific dissipation rate and turbulent eddy viscosity coefficient ; , , , , These are the average velocity, average pressure, turbulent kinetic energy, specific dissipation rate, and turbulent eddy viscosity coefficient at the 0th iteration step.

[0037] Due to the adoption of the above technical solution, this application has the following advantages: the improved SST-SR turbulence model proposed in this application can obtain better calculation results. Specifically, its advantages over the original SST-OR model are: the simulation of the separation zone is more accurate, and the distribution of Reynolds stress is better matched. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings.

[0039] Figure 1 This is a flowchart illustrating a turbulence numerical simulation method for incompressible separated flow according to an embodiment of this application. Figure 2(a) is a schematic diagram of Reynolds stress distribution in a periodic simulation example under different numerical simulation methods according to the embodiments of this application; Figure 2(b) is a schematic diagram of Reynolds stress distribution in a periodic mountain simulation example under different numerical simulation methods according to the embodiments of this application. Detailed Implementation

[0040] The present application will be further described iteratively with reference to the accompanying drawings and embodiments. The described embodiments are only some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art should fall within the protection scope of the present application.

[0041] For incompressible separated flows, classic numerical simulation methods in engineering (such as those using Sparlart) Significant differences remain between RANS simulations of the Allmaras turbulence model and the SST turbulence model. Specifically, the numerical predictions of the separation zone, surface pressure, and frictional drag are inaccurate, and the anisotropic Reynolds stress components in the turbulence cannot be obtained. By comparing periodic turbulent flows, it is found that the classical models commonly used in industry... The separation region predicted by the turbulence model is significantly larger than that obtained by direct numerical simulation (DNS).

[0042] Based on this, see Figure 1 This application provides an embodiment of a turbulent numerical simulation method for incompressible separated flows, comprising: Step 1: For the separated flow to be simulated, initialize the flow physical quantities and turbulence characteristic quantities; the flow physical quantities include the average velocity. and pressure Turbulent characteristic quantities include turbulent kinetic energy. Specific dissipation rate and turbulent eddy viscosity coefficient ; Step 2: Construct and calculate the flow field characteristic quantities based on the flow physical quantities and turbulence characteristic quantities. ~ The flow physical quantity includes average velocity. Mean pressure The turbulent characteristic quantities include turbulent kinetic energy. Specific dissipation rate Turbulent eddy viscosity coefficient ; Step 3: Based on the flow physical quantities, turbulence characteristic quantities, and flow field characteristic quantities ~ The correction term for Reynolds stress is obtained. ; Step 4: According to the The original Reynolds stress of the iteration step and the correction term for Reynolds stress Calculation yields the first Reynolds stress after iterative step correction The corrected Reynolds stress The expression replaces the original Reynolds-averaged equation for incompressible flow. The modified Reynolds-averaged equations for incompressible flow are obtained. By solving the modified Reynolds-averaged equations for incompressible flow, the first... Average speed of iteration steps and average pressure ; Step 5: Solve The transport equations of the turbulent model are used to calculate the first... Turbulent characteristics of the iteration step, including turbulent characteristics. , Based on the turbulence characteristic quantities, the first... Turbulent eddy viscosity coefficient of the iterative step ;in, For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps For the first Turbulent eddy viscosity coefficient of the iteration step; Step 6: Repeat steps 4 and 5 iteratively until the residual is found. Less than the preset value or iterative steps Equal to the maximum number of iterations When the time is right, stop the calculation; among them, For the first Incompressible flow under iterative steps: Reynolds-averaged Navier-Stokes equations and The residuals of the turbulence model equations; Step 7: Output the final flow physical quantities and turbulence characteristic quantities to end the numerical simulation; the final flow physical quantities include , The final turbulence characteristic quantities include , , , For the first The average speed of the iteration step For the first Average pressure of iteration steps For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps For the first Turbulent eddy viscosity coefficient of the iteration step.

[0043] This application improves the prediction accuracy of the separation zone in incompressible separation flows, and the size of the separation zone and the Reynolds stress distribution are closer to the actual numerical simulation results.

[0044] Optionally, step 2 includes: For the flow field to be simulated, which includes the separation region, flow physical quantities and turbulence characteristic quantities are extracted, and the following feature set is constructed. ~ :

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] in, The trace is the combination of the dimensionless strain rate and rotation rate tensors. The trace is the combination of the turbulent kinetic energy gradient correlation tensor and the strain rate tensor. The ratio of generating terms to dissipating terms. The turbulent Reynolds number is based on the wall distance. This represents the ratio of the turbulent timescale to the mean flow timescale. It is the ratio of turbulent viscosity to molecular viscosity. The operators for calculating the trace of a matrix. The dimensionless rotation rate tensor. The dimensionless strain rate tensor For the first The first indicator and the first The components of the dimensionless twitch rate tensor of each index For the first The first indicator and the first The components of the dimensionless twitch rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index The result is obtained by cross product of the negative diagonal matrix and the turbulent kinetic energy gradient vector, followed by dimensionless transformation. and All The amount, For the turbulent kinetic energy generation term, for The velocity component in the direction of the index, for The coordinate components of the indicator direction, These are the components of the Reynolds stress tensor. It is a constant (an empirical constant that can take the value 0.09). For turbulent kinetic energy, For specific dissipation rate, for The velocity component in the direction of the index, for The coordinate components of the indicator direction, The function for calculating the minimum value, The distance between the walls. The coefficient of kinematic viscosity, These are the strain rate tensor components. The turbulent eddy viscosity coefficient, velocity gradient , velocity gradient , for The velocity component in the direction of the index, for The coordinate components of the indicator direction, For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The rotation rate tensor components of each index For the first The first indicator and the first The components of the cross product tensor of the turbulent kinetic energy gradient of each index. and Levi-Civita notation (permutation notation) is used for indices in a three-dimensional Cartesian coordinate system. Its definition and The specific content and arrangement are related: If If any two of them are equal, then ;like yes If the even permutations are..., then ;like yes If the odd permutation is..., then Even permutations are those with an even number of inversions, and odd permutations are those with an odd number of inversions; the number of inversions is the total number of inversion pairs; and the definition of an inversion pair is as follows: Assume there is a permutation... (i.e., an ordered sequence in which no elements are repeated), if the index is correct satisfy and This is called an ordered pair. It is an inversion pair; in the formula In the middle, repeated subscripts Indicates to l Summing 1, 2, and 3, this expression defines an antisymmetric tensor. In the The first indicator and the first The components under each indicator for The coordinate components of the indicator direction, for p The coordinate components of the indicator direction, To find the sign of the partial derivative, and All are positive integers; denoted as the Frobenius norm of the turbulent kinetic energy gradient tensor before normalization.

[0055] Optionally, step 3 includes: Correction terms for calculating Reynolds stress :

[0056] in, For coefficient functions, For the first Tensor base for each index.

[0057] Optionally, tensor base exist The expressions for the values ​​equal to 1, 2, and 3 are:

[0058] in, For Kronecker notation, For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The rotation rate tensor components of each index For the first The first indicator and the first The rotation rate tensor components of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For Kronecker notation, For the first The first indicator and the first Components of the dimensionless strain rate tensor of each index; Based on data obtained through DNS methods, and obtained by employing deep symbolic regression. , , Corresponding coefficient function ) The expressions are as follows:

[0059]

[0060] .

[0061] Optionally, the first step is calculated using the following formula. Reynolds stress after iterative step correction :

[0062]

[0063] in, For the first The iteration step is based on the linear eddy viscosity proposed by the Boussinesq assumption. For the first Turbulent kinetic energy of the iteration step For the first Turbulent eddy viscosity coefficient of the iteration step For the first The average speed of the iteration step; The modified Reynolds-averaged equation for incompressible flow is expressed as follows:

[0064]

[0065] in, For average pressure, For the first The coordinate position of a tensor index. For the first The coordinate position of a tensor index. For average density, The coefficient of kinematic viscosity, For the corrected Reynolds stress, For time, For the first The velocity field of each index For the first The velocity field of each index; The SIMPLEC algorithm is used to handle pressure-velocity coupling, and a multigrid solver is employed to accelerate the solution of the modified Reynolds-averaged equations for incompressible flow, where inviscid flux... Upwind configuration is adopted to ensure transport characteristics and viscous flux. The discretization is performed using a second-order Gaussian linear correction scheme, and the gradient calculation is performed using Gaussian linear interpolation. That is, the gradient is calculated by interpolating from the unit volume center value to the surface center value, and then the gradient is obtained. The flow field variables of the iteration step, the first step The flow field variables of the iteration step include , .

[0066] Optionally, step 5 includes: Solving iteratively using the stable biconjugate gradient method The transport equations of the turbulent model are derived, and corresponding relaxation factors are used to ensure numerical stability; the first... Turbulent characteristic quantities of the iteration step, including , According to the first Magnitude of strain rate tensor of iteration step and the Mixed function of iteration steps Calculate the first Turbulent eddy viscosity coefficient of the iterative step .

[0067] Optionally, the first step is calculated using the following formula. Turbulent eddy viscosity coefficient of the iterative step :

[0068] in, For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps For the first The magnitude of the strain rate tensor of the iteration step , For example, positive numbers a The limit of 1=0.31 ensures that the eddy viscosity coefficient is not too large in the separated flow, thereby improving the prediction accuracy.

[0069] Optionally, the first step is calculated using the following formula. Mixed function of iteration steps :

[0070] in, For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps It is a positive number. The distance to the nearest wall. It is the molecular kinematic viscosity coefficient. It is a function for maximizing the value.

[0071] Optionally, step 6 includes: Repeat steps 4 and 5 to continuously iterate and solve the problem. Iterate step by step until the preset convergence condition (such as residual) is met. Less than (or reaching the maximum set number of computation iterations), until.

[0072] Optionally, before step 1, the method further includes: The average velocity in the Reynolds-averaged Navier-Stokes equations for initializing incompressible flow Mean pressure ,as well as Turbulent kinetic energy in turbulence models Specific dissipation rate and turbulent eddy viscosity coefficient ; , , , , These are the average velocity, average pressure, turbulent kinetic energy, specific dissipation rate, and turbulent eddy viscosity coefficient at the 0th iteration step.

[0073] The following examples are used to evaluate the effectiveness of the modified SST turbulence model on periodic hill examples.

[0074] The example flow velocity was 0.028 m / s, the Reynolds number was 5600, the slope factor α = 0.8, and the iteration was 20000. The DNS results were used as the standard results, and a comparative study was carried out by using the standard SST-OR turbulence model and the modified SST-SR turbulence model.

[0075] Figures 2(a) and 2(b) show a comparison of the Reynolds stress component contour maps under different numerical simulation methods. It can be seen that the SST-SR turbulence numerical simulation method significantly improves the prediction results compared to the SST-OR turbulence numerical simulation method. The incoming flow velocity is 0.028 m / s. Dimensionless Direction coordinates Dimensionless Direction coordinates As a feature scale, These represent the three diagonal components of the anisotropic Reynolds stress tensor, reflecting the relative strengths of the turbulent kinetic energy in the flow direction, normal direction, and spanwise direction. It is an off-diagonal component of the anisotropic Reynolds stress tensor, reflecting the degree of anisotropy in the correlation between flow-direction and normal-direction turbulent fluctuations.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.

Claims

1. A numerical simulation method for turbulent flows incompressible separation, characterized in that, include: Step 1: For the separated flow to be simulated, initialize the flow physical quantities and turbulence characteristic quantities; the flow physical quantities include the average velocity. and pressure Turbulent characteristic quantities include turbulent kinetic energy. Specific dissipation rate and turbulent eddy viscosity coefficient ; Step 2: Construct and calculate the flow field characteristic quantities based on the flow physical quantities and turbulence characteristic quantities. ~ The flow physical quantity includes average velocity. Mean pressure The turbulent characteristic quantities include turbulent kinetic energy. Specific dissipation rate Turbulent eddy viscosity coefficient ; Step 3: Based on the flow physical quantities, turbulence characteristic quantities, and flow field characteristic quantities ~ The correction term for Reynolds stress is obtained. ; Step 4: According to the The original Reynolds stress of the iteration step and the correction term for Reynolds stress Calculation yields the first Reynolds stress after iterative step correction The corrected Reynolds stress The expression replaces the original Reynolds-averaged equation for incompressible flow. The modified Reynolds-averaged equations for incompressible flow are obtained. By solving the modified Reynolds-averaged equations for incompressible flow, the first... Average speed of iteration steps and average pressure ; Step 5: Solve The transport equations of the turbulent model are used to calculate the first... Turbulent characteristics of the iteration step, including turbulent characteristics. , ; Based on the turbulence characteristic quantities, the first... Turbulent eddy viscosity coefficient of the iterative step ;in, For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps For the first Turbulent eddy viscosity coefficient of the iteration step; Step 6: Repeat steps 4 and 5 iteratively until the residual is found. Less than the preset value or iterative steps Equal to the maximum number of iterations When the time is right, stop the calculation; among them, For the first Incompressible flow under iterative steps: Reynolds-averaged Navier-Stokes equations and The residuals of the turbulence model equations; Step 7: Output the final flow physical quantities and turbulence characteristic quantities to end the numerical simulation; the final flow physical quantities include , The final turbulence characteristic quantities include , , , For the first The average speed of the iteration step For the first Average pressure of iteration steps For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps For the first Turbulent eddy viscosity coefficient of the iteration step.

2. The method according to claim 1, characterized in that, Step 2 includes: For the flow field to be simulated, which includes the separation region, flow physical quantities and turbulence characteristic quantities are extracted, and the following feature set is constructed. ~ : in, The trace is the combination of the dimensionless strain rate and rotation rate tensors. The trace is the combination of the turbulent kinetic energy gradient correlation tensor and the strain rate tensor. The ratio of generating terms to dissipating terms. The turbulent Reynolds number is based on the wall distance. This represents the ratio of the turbulent timescale to the mean flow timescale. It is the ratio of turbulent viscosity to molecular viscosity. The operators for calculating the trace of a matrix. The dimensionless rotation rate tensor. The dimensionless strain rate tensor For the first The first indicator and the first The components of the dimensionless twitch rate tensor of each index For the first The first indicator and the first The components of the dimensionless twitch rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index The result is obtained by cross product of the negative diagonal matrix and the turbulent kinetic energy gradient vector, followed by dimensionless transformation. and All The amount, For the turbulent kinetic energy generation term, for The velocity component in the direction of the index, for The coordinate components of the indicator direction, These are the components of the Reynolds stress tensor. It is a constant. For turbulent kinetic energy, For specific dissipation rate, for The velocity component in the direction of the index, for The coordinate components of the indicator direction, The function for calculating the minimum value, The distance between the walls. The coefficient of kinematic viscosity, These are the strain rate tensor components. The turbulent eddy viscosity coefficient, velocity gradient , velocity gradient , for The velocity component in the direction of the index, for The coordinate components of the indicator direction, For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The rotation rate tensor components of each index For the first The first indicator and the first The components of the cross product tensor of the turbulent kinetic energy gradient of each index. and The symbol for Levi-Civita. Define antisymmetric tensors In the The first indicator and the first The components under each indicator for The coordinate components of the indicator direction, with repeated subscripts. Indicates to Summation, for p The coordinate components of the indicator direction, To find the sign of the partial derivative, and All are positive integers; denoted as the Frobenius norm of the turbulent kinetic energy gradient tensor before normalization.

3. The method according to claim 1, characterized in that, Step 3 includes: Correction terms for calculating Reynolds stress : in, For coefficient functions, For the first Tensor base for each index.

4. The method according to claim 3, characterized in that, tensor bases exist The expressions for the values ​​equal to 1, 2, and 3 are: in, For Kronecker notation, For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The rotation rate tensor components of each index For the first The first indicator and the first The rotation rate tensor components of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For the first The first indicator and the first The components of the dimensionless strain rate tensor of each index For Kronecker notation, For the first The first indicator and the first Components of the dimensionless strain rate tensor of each index; Based on data obtained through DNS methods, and obtained by employing deep symbolic regression. , , Corresponding coefficient function ) The expressions are as follows: 。 5. The method according to claim 4, characterized in that, The number is calculated using the following formula. Reynolds stress after iterative step correction : in, For the first The iteration step is based on the linear eddy viscosity proposed by the Boussinesq assumption. For the first Turbulent kinetic energy of the iteration step For the first Turbulent eddy viscosity coefficient of the iteration step For the first The average speed of the iteration step; The modified Reynolds-averaged equation for incompressible flow is expressed as follows: in, For average pressure, For the first The coordinate position of a tensor index. For the first The coordinate position of a tensor index. For average density, The coefficient of kinematic viscosity, For the corrected Reynolds stress, For time, For the first The velocity field of each index For the first The velocity field of each index; The SIMPLEC algorithm is used to handle pressure-velocity coupling, and a multigrid solver is employed to accelerate the solution of the modified Reynolds-averaged equations for incompressible flow, where inviscid flux... Upwind configuration is adopted to ensure transport characteristics and viscous flux. The discretization is performed using a second-order Gaussian linear correction scheme, and the gradient calculation is performed using Gaussian linear interpolation. That is, the gradient is calculated by interpolating from the unit volume center value to the surface center value, and then the gradient is obtained. The flow field variables of the iteration step, the first step The flow field variables of the iteration step include , .

6. The method according to claim 1, characterized in that, Step 5 includes: Solving iteratively using the stable biconjugate gradient method The transport equations of the turbulent model are derived, and corresponding relaxation factors are used to ensure numerical stability; the first... Turbulent characteristic quantities of the iteration step, including , According to the first Magnitude of strain rate tensor of iteration step and the Mixed function of iteration steps Calculate the first Turbulent eddy viscosity coefficient of the iterative step .

7. The method according to claim 6, characterized in that, The number is calculated using the following formula. Turbulent eddy viscosity coefficient of the iterative step : in, For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps For the first The magnitude of the strain rate tensor of the iteration step , It is a positive number.

8. The method according to claim 6 or 7, characterized in that, The number is calculated using the following formula. Mixed function of iteration steps : in, For the first Turbulent kinetic energy of the iteration step For the first Specific dissipation rate of iteration steps It is a positive number. The distance to the nearest wall. It is the molecular kinematic viscosity coefficient. It is a function for maximizing the value.

9. The method according to claim 1, characterized in that, Step 6 includes: Repeat steps 4 and 5 to continuously iterate and solve the problem. N The iterations continue until the preset convergence condition is met, or the maximum set number of computation iterations is reached. until.

10. The method according to claim 1, characterized in that, Before step 1, the following are also included: The average velocity in the Reynolds-averaged Navier-Stokes equations for initializing incompressible flow Mean pressure ,as well as Turbulent kinetic energy in turbulence models Specific dissipation rate and turbulent eddy viscosity coefficient ; , , , , These are the average velocity, average pressure, turbulent kinetic energy, specific dissipation rate, and turbulent eddy viscosity coefficient at the 0th iteration step.

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