A grid-adaptive turbulence simulation method based on Vreman dynamic coefficient coupled SA series model

Abstract

The present invention discloses a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled SA series model, and the main process of its implementation includes: step 1, judging whether to apply shielding function; step 2, calculating Vreman dynamic coefficient; step 3, determining local dynamic grid length scale; step 4, constructing scale-related adjustment function; step 5, reconstructing turbulent viscosity of SA series model; step 6, using reconstructed turbulent viscosity to perform turbulence simulation. The present invention constructs Vreman dynamic coefficient based on local velocity gradient tensor, identifies local grid size, and determines local grid length scale Δ * , the turbulent viscosity is reconstructed by constructing scale-related functions through turbulent energy spectrum integration, and a new algebraic empirical formula is constructed to characterize the turbulent kinetic energy and turbulent length scale. This overcomes the problem of high dependence of existing turbulent mixing models on grid experience, broadens grid adaptability, improves calculation accuracy, reduces calculation cost, and significantly accelerates the turbulence simulation process.

Description

Technical Field

[0001] The invention relates to the field of complex flow calculation of aircraft engines and gas turbines, and in particular to a grid adaptive turbulence simulation method based on a Vreman dynamic coefficient coupled SA series model. Background Art

[0002] Aircraft engines and gas turbines are a major national demand and a key development area for my country's high-end equipment manufacturing. Turbulence is ubiquitous in nature and engineering, and accurate prediction of turbulence is a major challenge in studying complex flow problems. Turbulent flows in aircraft engines and gas turbines are extremely complex, with multi-scale, nonlinear, and unsteady characteristics. These complex turbulences have a great impact on the performance of aircraft engines and gas turbines. Therefore, in engineering design, it is urgent to develop turbulence simulation methods with high prediction accuracy and high computational efficiency, so that they can accurately simulate turbulent flows in complex engineering problems such as the internal flow of aircraft engines and gas turbines.

[0003] The turbulence simulation method commonly used in existing engineering projects is mainly based on solving the Reynolds-averaged NS equations (RANS) method. Although the amount of calculation is small, it is based on simple basic flows and has poor prediction accuracy for complex turbulent flows such as multi-scale, unsteady, and large separation in engineering problems. Therefore, it is difficult to achieve a detailed study of the complex flow mechanism in engineering problems such as the internal flow of aircraft engines and gas turbines, which seriously restricts the improvement of the design level in the fields of aircraft engines and gas turbines. As a high-precision numerical simulation method, the large eddy simulation (LES) method has a high requirement for the number of grids, which makes its computational cost increase exponentially compared to the RANS method, which is much higher than the computational cost that can be tolerated in engineering applications. For engineering flow problems such as the internal flow of aircraft engines and gas turbines, the Reynolds number is often high. Under the existing computing power, the LES method is still difficult to apply to the flow prediction in complex engineering fields at the engineering design level.

[0004] In the past two decades, the RANS-LES hybrid simulation method was born. By using the RANS method in the near-wall area and the LES method in the mainstream area, the calculation accuracy and efficiency are balanced, which provides a good solution to the problem of high-precision simulation and high computational cost of complex flows. However, the current classic RANS-LES hybrid model has relatively strict requirements on the grid, requiring users to have rich experience in high-precision numerical simulation. The existing RANS-LES hybrid simulation method is highly dependent on the experience-based grid distribution arrangement for the prediction accuracy of complex engineering flows such as the internal flow of aircraft engines and gas turbines, and the grid demand is large, making it difficult to apply to daily engineering design. Therefore, reducing the empirical dependence of the RANS-LES hybrid model on the grid is of great significance to better realize the accurate, efficient and high-precision simulation of multi-scale, nonlinear, unsteady and other turbulent flow phenomena in complex engineering flow problems.

[0005] The multi-equation turbulence model used in the disclosed invention patents (CN 115034162 A, CN 115186607 A, CN 115186608 A, CN114970403 A) is used as the basis, which is more computationally expensive than the single-equation SA series turbulence model. In addition, the basis models in the disclosed invention patents (CN 115034162A, CN 115186607 A, CN 115186608 A, CN114970403 A) all solve the transport equation related to turbulent kinetic energy, so that the turbulent length scale can be directly obtained; while the SA series model in the present invention does not contain turbulent kinetic energy, so the corresponding turbulent length scale cannot be obtained. In order to solve the above problems, the present invention constructs a new algebraic empirical formula to characterize the turbulent kinetic energy and the corresponding turbulent length scale.

[0006] In addition, the present invention further improves the prediction accuracy and grid adaptability of the grid adaptive turbulence simulation method by introducing the Vreman dynamic coefficient. Compared with the disclosed invention patents (CN 115034162 A, CN 115186607 A, CN 115186608 A, CN 114970403 A), the prediction accuracy of the grid adaptive turbulence simulation method can be further improved, and the calculation cost can be greatly reduced. Summary of the invention

[0007] 1. Technical issues to be resolved

[0008] The purpose of the present invention is to propose a grid-adaptive turbulence simulation method based on the SA series model coupled with the Vreman dynamic coefficient, aiming to improve the adaptive ability of turbulence simulation to the grid, effectively overcome the problem of the high empirical dependence of the existing RANS-LES hybrid model on the grid, and greatly reduce the computational cost while improving the calculation accuracy, significantly speed up the turbulence simulation process, and provide an efficient numerical simulation method for solving the fast and high-precision simulation of multi-scale, nonlinear, unsteady turbulent flows in complex engineering flow problems. In addition, compared with the prior art, since the SA series model does not contain the turbulent kinetic energy term, the corresponding turbulent length scale cannot be obtained. The present invention aims to construct a new algebraic empirical formula to characterize the turbulent kinetic energy and the corresponding turbulent length scale, and further improve the prediction accuracy of the grid-adaptive turbulence simulation method by introducing the Vreman dynamic coefficient, and then propose a grid-adaptive turbulence simulation method based on the SA series model coupled with the Vreman dynamic coefficient.

[0009] (II) Technical solution

[0010] In order to solve the above technical problems, the present invention provides a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled SA series model, comprising the following steps:

[0011] Step 1, determine whether to apply the shielding function;

[0012] Step 2, calculate the Vreman dynamic coefficient;

[0013] Step 3, determine the local dynamic grid length scale;

[0014] Step 4: construct a scale-dependent adjustment function;

[0015] Step 5, reconstruct the turbulent viscosity of the SA series model;

[0016] Step 6, use the reconstructed turbulent viscosity to perform turbulence simulation;

[0017] The step 1 of determining whether to apply the shielding function includes:

[0018] Combined with the type of flow state being simulated, determine whether to use the shielding function F GAS Specifically, when the flow state type is free shear flow, the shielding function is not used. In this case, the shielding function F GAS = 0; when the flow state type is near-wall flow, a shielding function is used, and the shielding function F GAS Choose one from the F in the DDES-SA model d The screening function and F from the IDDES-SA model B Masking function;

[0019] The calculation of the Vreman dynamic coefficient in step 2 includes:

[0020] Based on the local velocity gradient tensor α ij , construct the Vreman dynamic coefficient C DGAS ;

[0021] The Vreman dynamic coefficient C DGAS It is obtained by the following formula:

[0022]

[0023] β ij =α mi α mj

[0024]

[0025] Where S is the strain rate, C GAS The empirical coefficient is taken as 0.016;

[0026] Determining the local dynamic grid length scale in step 3 includes:

[0027] Combined with the shielding function F described in step 1 GAS , and the Vreman dynamic coefficient C described in step 2 DGAS , determine the local dynamic grid length scale Δ * ;

[0028] The local dynamic grid length scale Δ * Given by:

[0029] Δ * =C DGAS [(1-F GAS )Δ vol +F GAS Δ max ]

[0030] Δ max =max(Δ x ,Δ y ,Δ z )

[0031]

[0032] Among them, Δ x is the length of the local hexahedral grid, Δ y is the width of the local hexahedral grid, Δ z is the height of the local hexahedral grid;

[0033] The construction scale-related adjustment function described in step 4 includes:

[0034] According to the SA series model, the local modeled turbulent viscosity ν is obtained t and the velocity gradient tensor U i,j , given by the locally modeled turbulent viscosity ν t and the velocity gradient tensor U i,j Construct a new algebraic empirical formula for the modeled turbulent kinetic energy k m It is characterized as shown below:

[0035]

[0036] According to the local dynamic grid length scale Δ * Based on the turbulence energy spectrum, the actual simulated turbulent kinetic energy k is obtained by integration u ;

[0037] The actual simulated turbulent kinetic energy k u It is obtained by the following formula:

[0038]

[0039] Among them, C k is the Kolmogorov constant coefficient, which is taken as 1.5; ε is the actual turbulence dissipation rate; κ c To solve the turbulent cutoff wave number, the local dynamic grid length scale Δ * Determine as follows:

[0040]

[0041] Among them, π is the ratio of pi, which is 3.14;

[0042] According to the actual simulated turbulent kinetic energy k u , the modeled turbulent kinetic energy k m and the shielding function F described in step 1 GAS , construct the dynamic scale-dependent regulation function D f ; Define the scale ratio as the actual simulated turbulent kinetic energy k u and the modeled turbulent kinetic energy k m The dynamic scale-dependent regulation function D f is a function related to the ratio of the scales, which is obtained by the following formula:

[0043]

[0044] l GAS =(1-F GAS ) u +F GAS l m

[0045]

[0046] Among them, l u is the grid-related scale, l m is the turbulence length scale;

[0047] The turbulence length scale l m The expression is as follows:

[0048]

[0049] Among them, ν t is the local modeled turbulent viscosity, U i,j is the velocity gradient tensor obtained by the SA series model; a0 is the empirical coefficient, which is taken as 6.0;

[0050] Step 5 describes the reconstruction of the turbulent viscosity of the SA series model, including:

[0051] Adopt the dynamic scale-dependent adjustment function D described in step 4 f The local modeled turbulent viscosity ν in the SA series model t By adjusting the turbulent viscosity ν, we can obtain the reconstructed turbulent viscosity ν. sfs , obtained from the following formula:

[0052] ν sfs =D f ·ν t

[0053] The turbulence simulation using the reconstructed turbulent viscosity described in step 6 includes:

[0054] Using the reconstructed turbulent viscosity ν described in step 5 sfs , calculate the Reynolds stress, and update the mass, momentum, and energy transport equations, and combine them with the SA series model to obtain the Vreman dynamic grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model.

[0055] (III) Beneficial effects

[0056] The grid adaptive turbulence simulation method based on the Vreman dynamic coefficient coupled SA series model provided by the present invention has the following beneficial effects: constructing the Vreman dynamic coefficient based on the local velocity gradient tensor, and then determining the local grid length scale Δ by identifying the local grid size. *, and then reconstruct the turbulent viscosity by constructing scale-related functions through turbulent energy spectrum integration to achieve grid adaptive simulation, effectively overcome the problem of high empirical dependence of the existing RANS-LES hybrid model on the grid, further broaden its grid adaptability, while improving the calculation accuracy, greatly reducing the calculation cost, significantly accelerating the turbulence simulation process, and providing an efficient numerical simulation method for fast and high-precision simulation of multi-scale, nonlinear, unsteady and other turbulent flows in complex engineering flow problems.

[0057] In view of the fact that the SA series models do not contain turbulent kinetic energy and the corresponding turbulent length scale cannot be directly obtained, the present invention constructs a new algebraic empirical formula to characterize the turbulent kinetic energy and the corresponding turbulent length scale, and further improves the prediction accuracy of the grid adaptive turbulence simulation method by introducing the Vreman dynamic coefficient. It can stimulate the unsteady characteristics of the flow more quickly, has the characteristics of concise form and strong portability, can be well combined with the SA series models, and is easy to implant into existing CFD codes for application and expansion, and has broad academic and engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled SA series model of the present invention;

[0059] Figure 2 The dynamic scale-dependent adjustment function D is constructed for the grid adaptive turbulence simulation method based on the Vreman dynamic coefficient coupled SA series model of the present invention. f Schematic diagram of

[0060] Figure 3 The schematic diagram of the turbulent vortex structure of the back step example calculated using the SA-noft2 turbulence model in the SA series model;

[0061] Figure 4 The figure is a schematic diagram of the turbulent vortex structure of a back-step example calculated by a grid adaptive turbulence simulation method based on the Vreman dynamic coefficient coupled SA series model of the present invention. DETAILED DESCRIPTION

[0062] The following, in conjunction with the accompanying drawings, takes the SA-noft2 turbulence model in the SA series model as an example to further describe the specific implementation of the present invention in detail. The following examples are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0063] The back step example is selected as the calculation example, and the high-quality hexahedral mesh is used to spatially discretize the calculation domain. The total number of meshes is about 280,000.

[0064] The present invention provides a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled SA series model, comprising the following steps:

[0065] Step 1, determine whether to apply the shielding function;

[0066] In this step, the type of flow state being simulated is considered to determine whether to use the screening function F GAS Specifically, when the flow state type is free shear flow, the shielding function is not used. In this case, the shielding function F GAS = 0; when the flow state type is near-wall flow, a shielding function is used, and the shielding function F GAS Choose one from the F in the DDES-SA model d The screening function and F from the IDDES-SA model B Masking function.

[0067] In this embodiment, the F from the IDDES-SA model is used. B Examples of functions include:

[0068] F GAS =F B

[0069] F B =min[2exp(-9α 2 ),1.0]

[0070] α=0.25-d w / Δ max

[0071] Δ max =max(Δ x ,Δ y ,Δ z )

[0072] Among them, d w is the distance from the local grid to the wall, Δ x is the length of the local hexahedral grid, Δ y is the width of the local hexahedral grid, Δ z is the height of the local hexahedral grid.

[0073] Step 2, calculate the Vreman dynamic coefficient;

[0074] In this step, based on the local velocity gradient tensor α ij , construct the Vreman dynamic coefficient C DGAS ;

[0075] The Vreman dynamic coefficient C DGAS It is obtained by the following formula:

[0076]

[0077] β ij =α mi α mj

[0078]

[0079] Where S is the strain rate, C GAS The empirical coefficient is taken as 0.016.

[0080] Step 3, determine the local dynamic grid length scale;

[0081] In this step, combined with the shielding function F in step 1 GAS , and the Vreman dynamic coefficient C in step 2 DGAS , determine the local dynamic grid length scale Δ * ;

[0082] Local dynamic grid length scale Δ * Given by:

[0083] Δ * =C DGAS [(1-F GAS )Δ vol +F GAS Δ max ]

[0084] Δ max =max(Δ x ,Δ y ,Δ z )

[0085]

[0086] where Δ x is the length of the local hexahedral grid, Δ y is the width of the local hexahedral grid, Δ z is the height of the local hexahedral grid;

[0087] Step 4: Construct a scale-dependent adjustment function:

[0088] In this step, the local modeled turbulent viscosity ν is obtained according to the SA series turbulence model. t and the velocity gradient tensor U i,j , given by the locally modeled turbulent viscosity ν t and the velocity gradient tensor U i,j Construct a new algebraic empirical formula for the modeled turbulent kinetic energy k mIn this embodiment, taking the SA-noft2 turbulence model in the SA series model as an example, the local modeled turbulent viscosity ν is obtained according to the SA-noft2 turbulence model. t and the velocity gradient tensor U i,j , the local modeled turbulent viscosity ν obtained according to the SA-noft2 turbulence model t and the velocity gradient tensor U i,j Construct a new algebraic empirical formula for the modeled turbulent kinetic energy k m It is characterized as shown below:

[0089]

[0090] According to the local dynamic grid length scale Δ in step 3 * Based on the turbulence energy spectrum, the actual simulated turbulent kinetic energy k is obtained by integration u ;

[0091] The actual simulated turbulent kinetic energy k u It is obtained by the following formula:

[0092]

[0093] Among them, C k is the Kolmogorov constant coefficient, which is taken as 1.5; ε is the actual turbulence dissipation rate; κ c To solve the turbulent cutoff wave number, the local dynamic grid length scale Δ in step 3 is * Determine as follows:

[0094]

[0095] Among them, π is the ratio of pi, which is 3.14;

[0096] According to the actual simulated turbulent kinetic energy k u , modeled turbulent kinetic energy k m and the shielding function F in step 1 GAS , construct the dynamic scale-dependent regulation function D f ,like Figure 2 As shown; the scale ratio is defined as the actual simulated turbulent kinetic energy k u and the modeled turbulent kinetic energy k m The dynamic scale-dependent regulation function D f is a function related to the scale ratio, which is obtained by the following formula:

[0097]

[0098] l GAS =(1-F GAS ) u +FGAS l m

[0099]

[0100] Among them, l u is the grid-related scale, l m is the turbulence length scale;

[0101] The turbulence length scale l m The expression is as follows:

[0102]

[0103] Among them, ν t is the local modeled turbulent viscosity, U i,j is the velocity gradient tensor obtained by the SA-noft2 turbulence model; a0 is the empirical coefficient, which is taken as 6.0.

[0104] Step 5, reconstruct the turbulent viscosity of the SA series model;

[0105] In this step, the dynamic scale-dependent adjustment function D in step 4 is used f For the turbulent viscosity ν in the SA series turbulence models t By adjusting the turbulent viscosity ν, we can obtain the reconstructed turbulent viscosity ν. sfs In this embodiment, the SA-noft2 turbulence model in the SA series model is taken as an example, and the turbulent viscosity ν in the SA-noft2 turbulence model is t By adjusting the turbulent viscosity ν, we can obtain the reconstructed turbulent viscosity ν. sfs , obtained from the following formula:

[0106]

[0107] Where ν is the viscosity coefficient of the fluid, is the turbulent viscosity directly obtained from the transport equation of the SA-noft2 turbulence model, C v1 is a constant coefficient in the SA-noft2 turbulence model and is taken as 7.1.

[0108] Step 6, use the reconstructed turbulent viscosity to perform turbulence simulation;

[0109] In this step, the turbulent viscosity ν reconstructed in step 5 is used sfs , calculate the Reynolds stress, and update the mass, momentum, and energy transport equations, and combine with the SA series model to obtain the Vreman dynamic grid adaptive turbulence simulation method based on the turbulence energy spectrum coupling SA series model. In this embodiment, taking the SA-noft2 turbulence model in the SA series model as an example, the turbulent viscosity ν reconstructed in step 5 is used. sfs, calculate the Reynolds stress, and update the mass, momentum, and energy transport equations, and combine them with the SA-noft2 turbulence model to obtain the Vreman dynamic grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model, and use it for the numerical simulation of the back-step example.

[0110] The fully implicit coupling solution technology is used for transient calculations, and the time steps all meet the CFL conditions in engineering computational fluid dynamics. In addition, in order to better demonstrate the advantages of the embodiments of the present invention, the SA-noft2 turbulence model in the SA series model is selected to perform numerical simulations on the back step example, and the numerical simulation results are compared with those of the grid adaptive turbulence simulation method based on the Vreman dynamic coefficient coupled SA series model of the present invention.

[0111] Figure 3 This is a schematic diagram of the turbulent eddy structure of the back-step example calculated using the SA-noft2 turbulence model in the SA series of models, colored using the turbulent viscosity ratio.

[0112] Figure 4 It is a schematic diagram of the turbulent eddy structure of a back-step example calculated by a grid adaptive turbulence simulation method based on the Vreman dynamic coefficient coupled SA series model of the present invention, and is colored by the turbulent viscosity ratio.

[0113] Figure 3 , Figure 4 Comparative analysis shows that the turbulent eddy structure analysis capability obtained by calculating the grid adaptive turbulence simulation method based on the Vreman dynamic coefficient coupled SA series model proposed in the present invention is stronger than the result calculated by the SA-noft2 turbulence model. It can capture richer turbulent structures with the same number of grids and provide more accurate flow field details.

[0114] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

[0115] In summary, the grid adaptive turbulence simulation method based on the Vreman dynamic coefficient coupled SA series model proposed in the present invention constructs the Vreman dynamic coefficient based on the local velocity gradient tensor, and then determines the local grid length scale Δ by identifying the local grid size. *, and then the scale-related function is constructed by integrating the turbulent energy spectrum to reconstruct the turbulent viscosity and realize grid adaptive simulation. In view of the fact that the SA series models do not contain turbulent kinetic energy and the corresponding turbulent length scale cannot be directly obtained, the present invention constructs a new algebraic empirical formula to characterize the turbulent kinetic energy and the corresponding turbulent length scale, which effectively overcomes the problem of high empirical dependence of the existing turbulent mixing model on the grid. By introducing the Vreman dynamic coefficient, the grid adaptability of the grid adaptive turbulence simulation method is further broadened. While improving the calculation accuracy, it can greatly reduce the calculation cost, significantly speed up the turbulence simulation process, and provide a new method for flow prediction in complex engineering fields.

Claims

1. A grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled SA series model, characterized in that: The steps include: Step 1, determine whether to apply the shielding function; Step 2, calculate the Vreman dynamic coefficient; Step 3, determine the local dynamic grid length scale; Step 4: construct a scale-dependent adjustment function; Step 5, reconstruct the turbulent viscosity of the SA series model; Step 6, use the reconstructed turbulent viscosity to perform turbulence simulation; The step 1 of determining whether to apply the shielding function includes: Combined with the type of flow state being simulated, determine whether to use the shielding function F GAS Specifically, when the flow state type is free shear flow, the shielding function is not used. In this case, the shielding function F GAS = 0; when the flow state type is near-wall flow, a shielding function is used, and the shielding function F GAS Choose one from the F in the DDES-SA model d The screening function and F from the IDDES-SA model B Masking function; The calculation of the Vreman dynamic coefficient in step 2 includes: Based on the local velocity gradient tensor α ij , construct the Vreman dynamic coefficient C DGAS ; The Vreman dynamic coefficient C DGAS It is obtained by the following formula: β ij ＝α mi α mj Where S is the strain rate, C GAS The empirical coefficient is taken as 0.016; Determining the local dynamic grid length scale in step 3 includes: Combined with the shielding function F described in step 1 GAS , and the Vreman dynamic coefficient C described in step 2 DGAS , determine the local dynamic grid length scale Δ * ; The local dynamic grid length scale Δ * Given by: D * =C DGAS [(1-F GAS )D vol +F GAS D max ] D max =max(Δ x ,D y ,D z ) Among them, Δ x is the length of the local hexahedral grid, Δ y is the width of the local hexahedral grid, Δ z is the height of the local hexahedral grid; The construction scale-related adjustment function described in step 4 includes: According to the SA series model, the local modeled turbulent viscosity ν is obtained t and the velocity gradient tensor U i,j , given by the locally modeled turbulent viscosity ν t and the velocity gradient tensor U i,j Construct a new algebraic empirical formula for the modeled turbulent kinetic energy k m It is characterized as shown below: According to the local dynamic grid length scale Δ * Based on the turbulence energy spectrum, the actual simulated turbulent kinetic energy k is obtained by integration u ; The actual simulated turbulent kinetic energy k u It is obtained by the following formula: Among them, C k is the Kolmogorov constant coefficient, which is taken as 1.5; ε is the actual turbulence dissipation rate; κ c To solve the turbulent cutoff wave number, the local dynamic grid length scale Δ * Determine as follows: Among them, π is the ratio of pi, which is 3.14; According to the actual simulated turbulent kinetic energy k u , the modeled turbulent kinetic energy k m and the shielding function F described in step 1 GAS , construct the dynamic scale-dependent regulation function D f ; Define the scale ratio as the actual simulated turbulent kinetic energy k u and the modeled turbulent kinetic energy k m The dynamic scale-dependent regulation function D f is a function related to the ratio of the scales, which is obtained by the following formula: the GAS =(1-F GAS )l u +F GAS the m Among them, l u is the grid-related scale, l m is the turbulence length scale; The turbulence length scale l m The expression is as follows: Among them, ν t is the local modeled turbulent viscosity, U i,j is the velocity gradient tensor obtained by the SA series model; a0 is the empirical coefficient, which is taken as 6.0; Step 5 describes the reconstruction of the turbulent viscosity of the SA series model, including: Adopt the dynamic scale-dependent adjustment function D described in step 4 f The local modeled turbulent viscosity ν in the SA series model t By adjusting the turbulent viscosity ν, we can obtain the reconstructed turbulent viscosity ν. sfs , obtained from the following formula: n sfs =D f ·n t The turbulence simulation using the reconstructed turbulent viscosity described in step 6 includes: Using the reconstructed turbulent viscosity ν described in step 5 sfs , calculate the Reynolds stress, and update the mass, momentum, and energy transport equations, and combine them with the SA series model to obtain the Vreman dynamic grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model.

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