Strong shear turbulence dynamic grid adaptive simulation method coupled with RSM series model

Abstract

The invention discloses a strong shear turbulence dynamic grid adaptive simulation method coupled with an RSM series model. The method mainly comprises the following steps: step 1, judging whether a shielding function is applied or not; step 2, calculating a Vman dynamic coefficient; step 3, identifying the self-adaptive length scale of the shear layer; 4, constructing a scale-related adjustment function based on the turbulence energy spectrum integral coupling RSM series model; 5, reconstructing a Reynolds stress tensor and turbulence viscosity by using an adjustment function; and 6, performing turbulence simulation by using the reconstructed Reynolds stress tensor and turbulence viscosity. According to the method, the size of a local grid is identified by constructing a Vman dynamic coefficient, the length scale of the local grid is jointly determined in combination with the length scale of the shear layer adaptive sub-grid, and then the scale correlation function is constructed through the turbulence energy spectrum integral to reconstruct the turbulence viscosity, so that grid adaptive simulation is realized; an effective numerical simulation method is provided for solving low-consumption and high-precision simulation of strong shear turbulence in a complex engineering flow problem.

Description

Technical Field

[0001] The present invention relates to the field of complex fluid mechanics calculation of aircraft engines and gas turbines, and in particular to a dynamic grid adaptive simulation method for strong shear turbulence coupled with an RSM series model. Background Art

[0002] Strong shear flows in turbulent phenomena pose a challenge to engineering turbulence prediction due to their large velocity gradients, multi-scale turbulent interactions, and non-equilibrium transport. The current mainstream Reynolds-averaged NS (RANS) method, while computationally efficient, lacks sufficient accuracy for predicting multi-scale unsteady flows and anisotropic turbulence. Large eddy simulation (LES), while highly accurate, has an excessively high computational cost, far exceeding the requirements of engineering applications. Over the past two decades, the RANS-LES hybrid simulation method has found a balance between accuracy and computational efficiency by employing the RANS method in near-wall regions and the LES method in mainstream regions. This method resolves the contradiction between simulation accuracy and computational cost for complex flows and offers certain advantages. However, the traditional RANS-LES hybrid model places high demands on the mesh and requires the user to have extensive experience in high-precision numerical simulations, thus limiting its ability to predict complex engineering flows.

[0003] Although the emerging grid adaptive method has improved the ability to simulate complex flows, with the further increase in engineering demand for low-cost and high-precision flow prediction, typical flows such as jets and separation and reattachment have a large number of anisotropic grids under sparse grids, and the flow structure has multi-scale nonlinear characteristics during its development and evolution. Existing technologies require a large computational cost to analyze such complex flow scenarios coupled with strong shear flows, and still face challenges in predicting the strong velocity gradients and complex vortex structures within the sparse grids. It is urgent to develop more intelligent adaptive algorithms to improve the ability to simulate complex turbulence in lower-cost scenarios.

[0004] In order to improve the accuracy of RANS-LES hybrid simulation of strong shear turbulence, the present invention proposes an adaptive sub-grid length scale for the shear layer and simultaneously introduces an improved scheme for the Vreman dynamic coefficient. By introducing adaptive dynamic coefficients and improved grid scale definitions, the ability of sparse anisotropic grids to capture complex flows can be better improved. By coupling improvements to the grid scale and dynamic coefficients, the versatility of the grid adaptation method is further enhanced, and the cost of high-fidelity prediction of strong shear turbulence and complex multi-scale vortex structures is reduced. Compared with the disclosed invention patents CN 115186608 A and CN117763996 A, it can further optimize flow simulation without significantly increasing computational costs, providing higher prediction accuracy and better computational efficiency. Summary of the Invention

[0005] (1) Technical issues to be resolved

[0006] The purpose of this paper is to propose a dynamic mesh adaptive simulation method for strong shear turbulence coupled to the RSM series of models. By incorporating Vreman dynamic coefficients, the method dynamically adjusts the mesh size under strong shear flow and high Reynolds number conditions to optimize accuracy in strong shear regions, enhance adaptability to complex flow structures, balance high precision with high efficiency, significantly reduce computational overhead, and significantly accelerate turbulence simulation. This method aims to provide a low-cost, high-precision, and effective numerical simulation method for solving the complex strong shear flow problems encountered in engineering flows.

[0007] (2) Technical solution

[0008] In order to solve the above technical problems, the present invention provides a dynamic grid adaptive simulation method for strong shear turbulence coupled with an RSM series model, comprising the following steps:

[0009] Step 1: determine whether to apply the shielding function;

[0010] Step 2: Calculate the Vreman dynamic coefficient;

[0011] Step 3, identifying the shear layer adaptive length scale;

[0012] Step 4: Construct a scale-dependent adjustment function based on the turbulence energy spectrum integral coupled RSM series model;

[0013] Step 5: Reconstruct the Reynolds stress tensor and turbulent viscosity using the adjustment function;

[0014] Step 6: Use the reconstructed Reynolds stress tensor and turbulent viscosity to perform turbulence simulation;

[0015] ① The step 1 of determining whether to apply the shielding function includes:

[0016] 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 to use the F1 shielding function, F2 shielding function from the DDES-SST model and F from the DDES-SA model. d Shield function;

[0017] ② The calculation of the Vreman dynamic coefficient in step 2 includes:

[0018] Based on the local velocity gradient tensor α ij , construct the Vreman dynamic coefficient CDGAS ;

[0019] The Vreman dynamic coefficient C DGAS It is obtained from the following formula:

[0020]

[0021]

[0022] β ij =α mi α mj

[0023]

[0024] Where S is the strain rate, C GAS The empirical coefficient is taken as 0.6;

[0025] ③ The step 3 of identifying the shear layer adaptive length scale includes:

[0026] Use the shielding function F described in step 1 GAS And the Vreman dynamic coefficient C described in step 2 DGAS , determine the local grid length scale Δ*; the local grid length scale Δ* is given by the following formula:

[0027] Δ * =C GAS [(1-F GAS )Δ SLA +F GAS Δ max ]

[0028]

[0029] Δ max =max(Δ x ,Δ y ,Δ z )

[0030] Where m,n=1,2,...,8;

[0031] where i = 1, 2, ..., 8;

[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; is the distance from the cell center to the i-th vertex, is the unit normal vector of the vorticity vector, is the unit vertex position vector, is the unit center position vector;

[0033] According to the following formula:

[0034]

[0035] in, is the strain rate tensor, is the vorticity vector, ω 2 is the square of the vorticity vector; θ is taken as 0.99, a1=0.15,a2=0.3;ν is the viscosity coefficient of the fluid, v t is the turbulent viscosity given by the RSM series model, v t∞ The far-field turbulent viscosity given for the RSM series of models;

[0036] <vtm>is the average value of the local VTM function value and the VTM function value of the adjacent grid, F KH Based on the <vtm>A two-stage linear function of the value;

[0037] ④ The scale-related adjustment function constructed based on the turbulence energy spectrum integral coupled RSM series model in step 4 includes:

[0038] Isotropic velocity fluctuation u' solved according to the RSM series model m , the original modeled turbulent kinetic energy k m , as shown below:

[0039]

[0040] According to the local grid length scale Δ* described in step 3, the actual modeled turbulent kinetic energy k is obtained by integration based on the turbulent energy spectrum. u , the actual modeled turbulent kinetic energy k u It is obtained from the following formula:

[0041]

[0042] Where E(κ) is the Kolmogorov turbulence energy spectrum, κ is the turbulence wave number, C k is the Kolmogorov constant coefficient, which is 1.5, ε is the actual turbulence dissipation rate, κ c The cutoff wave number for resolvable turbulence is determined by the local grid length scale Δ* described in step 3:

[0043]

[0044] Where, π is the ratio of circumference to circle, which is 3.14;

[0045] According to the actual modeled turbulent kinetic energy k u , the original modeled turbulent kinetic energy k m and the shielding function F described in step 1 GAS , construct the dynamic scale-related adjustment function D f ; Define the scale ratio as the actual modeled turbulent kinetic energy k u and the original modeled turbulent kinetic energy k m The dynamic scale-related adjustment function D f is a function related to the ratio of the scales, which is obtained from the following formula:

[0046]

[0047] l GAS =(1-F GAS )l u +F GAS l m

[0048]

[0049] Among them, l u is the grid-related scale, l m is the turbulence length scale given by the RSM series model;

[0050] ⑤ The use of the adjustment function to reconstruct the Reynolds stress tensor and turbulent viscosity in step 5 includes:

[0051] Adopt the dynamic scale-related adjustment function D described in step 4 f The Reynolds stress tensor in the RSM model Control and obtain the reconstructed Reynolds stress tensor It is derived from the following formula:

[0052]

[0053] Adopt the dynamic scale-related adjustment function D described in step 4 f For the turbulent viscosity ν in the RSM model t By regulating, we can obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula:

[0054] ν sfs =D f ν t

[0055] ⑥ The turbulence simulation using the reconstructed Reynolds stress tensor and turbulent viscosity described in step 6 includes:

[0056] Use the reconstructed Reynolds stress tensor described in step 5 and the reconstructed turbulent viscosity ν sfs Update the transport equations of the RSM series model; use the reconstructed Reynolds stress tensor described in step 5 and the reconstructed turbulent viscosity ν sfs Reynolds stress tensor in the original transport equation of the RSM series model and turbulent viscosity ν t , combined with the RSM series model, the strong shear turbulence dynamic grid adaptive simulation method of the coupled RSM series model is obtained.

[0057] (3) Beneficial effects

[0058] The present invention provides a method for dynamic grid adaptive simulation of strong shear turbulence coupled with RSM series models, which has the following beneficial effects: constructing Vreman dynamic coefficients based on the local velocity gradient tensor, determining the local grid length scale by identifying the local grid size and combining it with the shear layer adaptive sub-grid length scale, and then reconstructing the turbulent viscosity by constructing a scale-related function through turbulent energy spectrum integration to achieve grid adaptive simulation, effectively improving the existing RANS-LES hybrid simulation method for the problems of high computational cost and poor accuracy in shear layer simulation, and significantly accelerating the turbulence simulation process.

[0059] Compared with the prior art CN 115186608 A and CN 117763996 A, the method of the present invention significantly reduces the influence of the grid on the development of the shear layer by introducing the SLA length scale and Vreman dynamic coefficient, and can dynamically adapt to strong shear turbulent flow, achieving more accurate simulation under high Reynolds number and strong shear flow conditions, further improving the prediction accuracy of the grid adaptive turbulence simulation method, and effectively reducing the computational cost, providing an important means for solving the strong shear multi-scale complex flow problem in aircraft engines.

[0060] This method boasts a concise form and strong portability. It integrates well with various grid-adaptive turbulence simulations and can be easily integrated into existing CFD codes for application and expansion. It has broad academic and engineering application prospects, providing an effective, low-cost, high-precision numerical simulation method for solving complex engineering flow problems involving strong shear. It holds significant application value in the prediction of complex flows involving strong shear, such as those in aircraft engines and gas turbines. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a flow chart of a dynamic grid adaptive simulation method for strong shear turbulence coupled with RSM series models of the present invention;

[0062] Figure 2 The invention is a method for dynamic grid adaptive simulation of strong shear turbulence coupled with RSM series models. The method is applied to a specific embodiment of circular pipe jet flow based on the shear layer adaptive sub-grid length scale D. f Distribution cloud map;

[0063] Figure 3 The turbulent vortex structure diagram of the circular pipe jet example calculated using the SSG-RSM model;

[0064] Figure 4 The figure shows the turbulent vortex structure of a circular pipe jet example calculated using a strong shear turbulence dynamic grid adaptive simulation method coupled with an RSM series model of the present invention. DETAILED DESCRIPTION

[0065] The following, in conjunction with the accompanying drawings and examples, takes the SSG-RSM model in the RSM series as an example and the circular pipe jet flow as a calculation example to further explain the specific embodiments of the present invention. The following examples are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0066] The present invention provides a dynamic grid adaptive simulation method for strong shear turbulence coupled with an RSM series model, comprising the following steps:

[0067] Step 1: determine whether to apply the shielding function;

[0068] In this step, the type of flow state being simulated is used to 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 to use the F1 shielding function, F2 shielding function from the DDES-SST model and F from the DDES-SA model. d Masking function.

[0069] In the circular pipe jet calculation example of the embodiment of the present invention, a high-quality hexahedral grid is used to spatially discretize the computational domain, and the total number of grids is approximately 6.05 million.

[0070] In this embodiment, the F d function, then:

[0071] F GAS =F d

[0072]

[0073] Among them, U ij is the velocity gradient tensor, ν t is the turbulent viscosity given by the SSG-RSM model, ν is the viscosity coefficient of the fluid, d is the distance from the local grid to the wall, and κ is the Karman constant, which is 0.41; C d1 、C d2 are empirical coefficients, which are 20 and 3 respectively.

[0074] Step 2: Calculate the Vreman dynamic coefficient

[0075] In this step, based on the local velocity gradient tensor α ij , construct the Vreman dynamic coefficient C DGAS ;

[0076] The Vreman dynamic coefficient C DGAS It is obtained from the following formula:

[0077]

[0078] β ij =α mi α mj

[0079]

[0080] Where S is the strain rate, C GAS The empirical coefficient is taken as 0.6;

[0081] Step 3, identifying the shear layer adaptive length scale;

[0082] In this step, the masking function F described in step 1 is used. GAS And the Vreman dynamic coefficient C described in step 2 DGAS , determine the local grid length scale Δ*; the local grid length scale Δ* is given by the following formula:

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

[0084]

[0085] Δ max =max(Δ x ,Δ y ,Δ z )

[0086] Where m,n=1,2,...,8;

[0087] where i = 1, 2, ..., 8;

[0088] 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; is the distance from the cell center to the i-th vertex, is the unit normal vector of the vorticity vector, is the unit vertex position vector, is the unit center position vector;

[0089] According to the following formula:

[0090]

[0091]

[0092] in, is the strain rate tensor, is the vorticity vector, ω 2 is the square of the vorticity vector; θ is taken as 0.99, a1=0.15,a2=0.3;ν is the viscosity coefficient of the fluid, v t is the turbulent viscosity given by the RSM series model, and in this embodiment is the turbulent viscosity given by the SSG-RSM model; v t∞ is the far-field turbulent viscosity given by the RSM series model, and in this embodiment is the far-field turbulent viscosity given by the SSG-RSM model.

[0093] The above VTM function ranges from 0 to 1. In the quasi-two-dimensional region at the initial stage of separation, the vorticity vector Also the strain rate tensor The characteristic vector of VTM function tends to 0. In fully developed three-dimensional turbulence, the vorticity vector Direction and strain rate tensors The eigenvector correlation is weak, and the VTM function value tends to 1.

[0094] <vtm>is the average value of the local VTM function value and the VTM function value of the adjacent grid, F KH Based on <vtm>A two-stage linear function of the value. <vtm>When it is less than a certain threshold, the VTM function value is small. <vtm>As the value of VTM increases gradually, it rapidly increases to 1, thus reducing the mesh size in the early stages of separation. Using the subgrid stress model, it can be seen that when the value of VTM increases to 1, the turbulent viscosity coefficient also decreases as expected.

[0095] Step 4: Construct a scale-dependent adjustment function based on the turbulence energy spectrum integral coupled RSM series model;

[0096] In this step, the isotropic velocity fluctuation u' is solved according to the RSM series model. m , the original modeled turbulent kinetic energy k m , as shown below:

[0097]

[0098] According to the local grid length scale Δ* in step 3, the actual modeled turbulent kinetic energy k is obtained by integration based on the turbulent energy spectrum. u , the actual modeled turbulent kinetic energy k u It is obtained from the following formula:

[0099]

[0100] Where E(κ) is the Kolmogorov turbulence energy spectrum, κ is the turbulence wave number, C k is the Kolmogorov constant coefficient, which is 1.5, ε is the actual turbulence dissipation rate, κ c The cutoff wave number for resolvable turbulence is determined by the local grid length scale Δ* in step 3:

[0101]

[0102] Where, π is the ratio of circumference to circle, which is 3.14;

[0103] According to the actual modeled turbulent kinetic energy k u , the original modeled turbulent kinetic energy k m and the shielding function F described in step 1 GAS , construct the dynamic scale-related adjustment function D f ; Define the scale ratio as the actual modeled turbulent kinetic energy k u and the original modeled turbulent kinetic energy k m The dynamic scale-related adjustment function D f is a function related to the ratio of the scales, which is obtained from the following formula:

[0104]

[0105] Among them, l u is the grid-related scale, l m is the turbulence length scale given by the RSM series model. In this embodiment, it is derived from the turbulence length scale of the SSG-RSM model, as shown in the following formula:

[0106]

[0107] Among them, ε m is the dissipation rate of the original model.

[0108] Step 5: Reconstruct the Reynolds stress tensor and turbulent viscosity using the adjustment function;

[0109] In this step, the dynamic scale-related adjustment function D described in step 4 is used. f The Reynolds stress tensor in the RSM model Control and obtain the reconstructed Reynolds stress tensor In this embodiment, the dynamic scale-related adjustment function D described in step 4 is used. f Reynolds stress tensor in SSG-RSM model Control and obtain the reconstructed Reynolds stress tensor It is derived from the following formula:

[0110]

[0111] Adopt the dynamic scale-related adjustment function D described in step 4 f For the turbulent viscosity ν in the RSM model t By regulating, we can obtain the reconstructed turbulent viscosity ν sfs In this embodiment, the dynamic scale-related adjustment function D described in step 4 is used. f The turbulent viscosity ν in the SSG-RSM model t By regulating, we can obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula:

[0112]

[0113] Among them, C μ is the constant coefficient in the SSG-RSM model and is set to 0.09.

[0114] Step 6: Use the reconstructed Reynolds stress tensor and turbulent viscosity to perform turbulence simulation;

[0115] In this step, the Reynolds stress tensor reconstructed in step 5 is used and the reconstructed turbulent viscosity ν sfs Update the transport equations of the RSM series model. Use the Reynolds stress tensor reconstructed in step 5 and the reconstructed turbulent viscosity ν sfs Reynolds stress tensor in the original transport equation of the RSM series model and turbulent viscosity ν t , combined with the RSM series model, the strong shear turbulence dynamic grid adaptive simulation method of the coupled RSM series model is obtained.

[0116] In this embodiment, the Reynolds stress tensor reconstructed in step 5 is used. and the reconstructed turbulent viscosity ν sfs Update the transport equation in the SSG-RSM model using the Reynolds stress tensor reconstructed in step 5 and the reconstructed turbulent viscosity ν sfs Replacing the Reynolds stress tensor in the original transport equation in the SSG-RSM model and turbulent viscosity ν t , the new transport equation is shown as follows:

[0117]

[0118] Among them, φ ij It is the pressure-strain related term of the SSG model, specifically:

[0119] φ ij =φ ij,1 +φ ij,2

[0120]

[0121] Among them, a ij is the anisotropy tensor, Ω ij is the curl tensor, is the generated term of the Reynolds stress transport equation, is the generated term of the dissipation rate transport equation and is calculated as follows:

[0122]

[0123] The model coefficients C involved s1 1.7, C s2 is -1.05, C r1 is 0.9, C r2 is 0.8, C r3 is 0.65, C r4 is 0.625, C r5 is 0.2, C ε1 is 1.45, C ε2 It is 1.83.

[0124] The new transport equation obtained is combined with the SSG-RSM model to obtain the strong shear turbulence dynamic grid adaptive simulation method of the coupled RSM series model, and is used for the numerical simulation of the circular pipe jet example.

[0125] Transient calculations were performed using a fully implicit coupled solution technique, with a time step that met the CFL condition in engineering computational fluid dynamics. The SSG-RSM model from the RSM series was also selected to perform numerical simulations of a circular pipe jet flow example from an embodiment of the present invention. The results were compared with the numerical simulation results of a dynamic mesh adaptive simulation method for strong shear turbulence coupled to the RSM series model.

[0126] Figure 3 This is a diagram of the turbulent vortex structure of a circular pipe jet flow example calculated using the SSG-RSM model in the RSM series of models, colored using the turbulent viscosity ratio.

[0127] Figure 4 This is a turbulent vortex structure diagram of a circular pipe jet example calculated using a strong shear turbulence dynamic grid adaptive simulation method coupled with an RSM series model of the present invention, and is colored using the turbulent viscosity ratio.

[0128] Figure 3 、 Figure 4 Comparative analysis shows that the turbulent vortex structure analysis capability calculated by the dynamic grid adaptive simulation method of strong shear turbulence coupled with the RSM series model proposed in the present invention is stronger than the vortex structure calculated by the SSG-RSM model. It can capture richer turbulent structures with the same number of grids and provide more accurate flow field details.

[0129] 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 scope of protection of the present invention.

[0130] In summary, the proposed method for dynamic grid-adaptive simulation of strong shear turbulence coupled to the RSM series of models introduces the Vreman dynamic coefficient to identify the local shear layer adaptive length scale, improving the identification of the local grid length scale Δ*. Furthermore, by integrating the turbulent energy spectrum to construct a scale-dependent function and reconstruct the turbulent viscosity, more efficient grid-adaptive simulation is achieved. This significantly reduces computational cost and significantly accelerates the turbulence simulation process. Furthermore, by dynamically adjusting the grid scale, it is more suitable for the numerical simulation of strong shear turbulence, providing a high-precision, low-cost numerical simulation method for solving high-precision simulations of strong shear turbulence in complex engineering flow problems.< / vtm> < / vtm> < / vtm> < / vtm> < / vtm> < / vtm>

Claims

1. A dynamic grid adaptive simulation method for strong shear turbulence coupled with RSM series models, characterized by: The steps include: Step 1: determine whether to apply the shielding function; Step 2: Calculate the Vreman dynamic coefficient; Step 3, identifying the shear layer adaptive length scale; Step 4: Construct a scale-dependent adjustment function based on the turbulence energy spectrum integral coupled RSM series model; Step 5: Reconstruct the Reynolds stress tensor and turbulent viscosity using the adjustment function; Step 6: Use the reconstructed Reynolds stress tensor and turbulent viscosity to perform turbulence simulation; ① 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 to use the F1 shielding function, F2 shielding function from the DDES-SST model and F from the DDES-SA model. d Shield function; ② 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 from the following formula: β ij ＝α mi α mj Where S is the strain rate, C GAS The empirical coefficient is taken as 0.6; ③ The step 3 of identifying the shear layer adaptive length scale includes: Use the shielding function F described in step 1 GAS And the Vreman dynamic coefficient C described in step 2 DGAS , determine the local grid length scale Δ*; the local grid length scale Δ* is given by the following formula: D * =C GAS [(1-F GAS )D SLA +F GAS D max ] D max =max(Δ x ,D y ,D z ) Where m,n=1,2,...,8; where i = 1, 2, ..., 8; 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; is the distance from the cell center to the i-th vertex, is the unit normal vector of the vorticity vector, is the unit vertex position vector, is the unit center position vector; According to the following formula: in, is the strain rate tensor, is the vorticity vector, ω 2 is the square of the vorticity vector; θ is taken as 0.99, a1=0.15,a2=0.3;ν is the viscosity coefficient of the fluid, v t is the turbulent viscosity given by the RSM series model, v t∞ The far-field turbulent viscosity given for the RSM series of models; <vtm>is the average value of the local VTM function value and the VTM function value of the adjacent grid, F KH Based on the <vtm> A two-stage linear function of the value;< / vtm> < / vtm> ④ The scale-related adjustment function constructed based on the turbulence energy spectrum integral coupled RSM series model in step 4 includes: Isotropic velocity fluctuation u' solved according to the RSM series model m , the original modeled turbulent kinetic energy k m , as shown below: According to the local grid length scale Δ* described in step 3, the actual modeled turbulent kinetic energy k is obtained by integration based on the turbulent energy spectrum. u , the actual modeled turbulent kinetic energy k u It is obtained from the following formula: Where E(κ) is the Kolmogorov turbulence energy spectrum, κ is the turbulence wave number, C k is the Kolmogorov constant coefficient, which is 1.5, ε is the actual turbulence dissipation rate, κ c The cutoff wave number for resolvable turbulence is determined by the local grid length scale Δ* described in step 3: Where, π is the ratio of circumference to circle, which is 3.14; According to the actual modeled turbulent kinetic energy k u , the original modeled turbulent kinetic energy k m and the shielding function F described in step 1 GAS , construct the dynamic scale-related adjustment function D f ; Define the scale ratio as the actual modeled turbulent kinetic energy k u and the original modeled turbulent kinetic energy k m The dynamic scale-related adjustment function D f is a function related to the ratio of the scales, which is obtained from 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 given by the RSM series model; ⑤ The use of the adjustment function to reconstruct the Reynolds stress tensor and turbulent viscosity in step 5 includes: Adopt the dynamic scale-related adjustment function D described in step 4 f The Reynolds stress tensor in the RSM model Control and obtain the reconstructed Reynolds stress tensor It is derived from the following formula: Adopt the dynamic scale-related adjustment function D described in step 4 f For the turbulent viscosity ν in the RSM model t By regulating, we can obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula: n sfs =D f ·n t ⑥ The turbulence simulation using the reconstructed Reynolds stress tensor and turbulent viscosity described in step 6 includes: Use the reconstructed Reynolds stress tensor described in step 5 and the reconstructed turbulent viscosity ν sfs Update the transport equations of the RSM series model; use the reconstructed Reynolds stress tensor described in step 5 and the reconstructed turbulent viscosity ν sfs Reynolds stress tensor in the original transport equation of the RSM series model and turbulent viscosity ν t , combined with the RSM series model, the strong shear turbulence dynamic grid adaptive simulation method of the coupled RSM series model is obtained.

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