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

Abstract

The present invention discloses a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled k-ε 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 k-ε series model; step 6, using reconstructed turbulent viscosity to simulate turbulence. The present invention constructs Vreman dynamic coefficient based on local velocity gradient tensor, identifies local grid size, and determines local grid length scale Δ * , and then reconstruct the turbulent viscosity by constructing scale-related functions through turbulent energy spectrum integration to achieve grid adaptive simulation, effectively overcoming the problem of high empirical dependence of existing turbulent mixing models on grids, further broadening the grid adaptability, effectively improving the calculation accuracy, greatly reducing the calculation cost, and significantly accelerating 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 Vreman dynamic coefficient coupled k-ε series models. Background Art

[0002] Turbulence is ubiquitous in nature and engineering. 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 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 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 patent CN 115034162 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

[0006] 1. Technical issues to be resolved

[0007] The purpose of the present invention is to propose a grid-adaptive turbulence simulation method based on the Vreman dynamic coefficient coupled k-ε series model. The grid adaptability is further improved by introducing the Vreman dynamic coefficient, effectively overcoming the problem of the existing RANS-LES hybrid model's high empirical dependence on the grid. While improving the calculation accuracy, the calculation cost is greatly reduced, the turbulence simulation process is significantly accelerated, and the unsteady characteristics of the flow are stimulated more quickly, providing an efficient numerical simulation method for solving the fast and high-precision simulation of multi-scale, nonlinear, unsteady and other turbulent flows in complex engineering flow problems.

[0008] (II) Technical solution

[0009] In order to solve the above technical problems, the present invention provides a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled k-ε series model, comprising the following steps:

[0010] Step 1, determine whether to apply the shielding function;

[0011] Step 2, calculate the Vreman dynamic coefficient;

[0012] Step 3, determine the local dynamic grid length scale;

[0013] Step 4: construct a scale-dependent adjustment function;

[0014] Step 5, reconstruct the turbulent viscosity of the k-ε series model;

[0015] Step 6, use the reconstructed turbulent viscosity to perform turbulence simulation;

[0016] ① The determination of whether to apply the shielding function includes:

[0017] 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 GASThe following functions can be used: F1 shielding function, F2 shielding function from DDES-SST model and F from DDES-SA model d Masking function;

[0018] ② The calculation of the Vreman dynamic coefficient includes:

[0019] Based on the local velocity gradient tensor α ij , construct the Vreman dynamic coefficient C DGAS ;

[0020] The Vreman dynamic coefficient C DGAS It is obtained by the following formula:

[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 determination of the local dynamic grid length scale includes:

[0026] 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 * ;

[0027] The local dynamic grid length scale Δ * Given by:

[0028] Δ * =C DGAS [(1-F GAS )Δ vol +F GAS Δ max ]

[0029] Δ max =max(Δ x ,Δ y ,Δ z )

[0030]

[0031] Among them, Δ x is the length of the local hexahedral grid, Δ y is the width of the local hexahedral grid, Δz is the height of the local hexahedral grid;

[0032] ④ The structural scale-related adjustment functions include:

[0033] According to the modeling method of turbulent kinetic energy in the k-ε series model, the original modeled turbulent kinetic energy k is obtained. m , 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 ;

[0034] The actual simulated turbulent kinetic energy k u It is obtained by the following formula:

[0035]

[0036] 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:

[0037]

[0038] Among them, π is the ratio of pi, which is 3.14;

[0039] According to the actual simulated 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-dependent regulation function D f ; Define the scale ratio as the actual simulated turbulent kinetic energy k u and the original 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:

[0040]

[0041] l GAS =(1-F GAS ) u +F GAS l m

[0042]

[0043] Among them, l u is the grid-related scale, l mis the turbulence length scale given by the k-ε series model and is given by:

[0044]

[0045] Among them, ε m is the dissipation rate of the original model obtained according to the k-ε series model;

[0046] ⑤ The turbulent viscosity of the reconstructed k-ε series model includes:

[0047] Adopt the dynamic scale-dependent adjustment function D described in step 4 f The turbulent viscosity ν in the k-ε series model t By adjusting the turbulent viscosity ν, we can obtain the reconstructed turbulent viscosity ν. sfs , obtained from the following formula:

[0048] ν sfs =D f ·ν t

[0049] ⑥ The turbulence simulation using the reconstructed turbulent viscosity includes:

[0050] Using the reconstructed turbulent viscosity ν described in step 5 sfs , calculate the Reynolds stress, and update the transport equation of the k-ε series model, replacing the turbulent viscosity ν in the original transport equation of the k-ε series model t , combined with the k-ε series model, the grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupling k-ε series model is obtained.

[0051] (III) Beneficial effects

[0052] The present invention provides a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled k-ε series model, which has the following beneficial effects: constructing Vreman dynamic coefficient based on local velocity gradient tensor, determining local dynamic grid length scale Δ by identifying 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, which effectively overcomes the problem of high empirical dependence of the existing RANS-LES hybrid model on the grid.

[0053] Compared with the prior art CN 115034162 A, the grid adaptability of the grid adaptive turbulence simulation method is further broadened by introducing the Vreman dynamic coefficient. While improving the calculation accuracy, the calculation cost is greatly reduced, and the turbulence simulation process is significantly accelerated. This provides 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.

[0054] The method of the present invention is concise in form and highly portable, can be well combined with the k-ε series model, is easy to be implanted into the existing CFD code for application and expansion, and has broad academic and engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled k-ε series model of the present invention;

[0056] Figure 2 A dynamic scale-dependent adjustment function D is constructed for a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled k-ε series model of the present invention. f Schematic diagram of

[0057] Figure 3 The schematic diagram of the turbulent eddy structure of the back-step example calculated using the standard k-ε model in the k-ε series of models;

[0058] 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 k-ε series model of the present invention. DETAILED DESCRIPTION

[0059] The following is a further detailed description of the specific implementation of the present invention by taking the standard k-ε turbulence model in the k-ε series model as an example in conjunction with the accompanying drawings. The following examples are only used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0060] 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 410,000.

[0061] The present invention provides a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled k-ε series model, comprising the following steps:

[0062] Step 1, determine whether to apply the shielding function;

[0063] 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 The following functions can be used: F1 shielding function, F2 shielding function from DDES-SST model and F from DDES-SA model dMasking function.

[0064] In this embodiment, the F in the DDES-SA model is used. d The shielding function is:

[0065] F GAS =F d

[0066]

[0067] Among them, U i,j is the velocity gradient tensor; ν t is the turbulent viscosity given by the standard k-ε turbulence model, ν is the viscosity coefficient of the fluid, d is the distance from the local grid to the wall; κ is the Karman constant, which is 0.41; C d1 , C d2 are empirical coefficients, which are 20 and 3 respectively.

[0068] Step 2, calculate the Vreman dynamic coefficient;

[0069] In this step, based on the local velocity gradient tensor α ij , construct the Vreman dynamic coefficient C DGAS ;

[0070] The Vreman dynamic coefficient C DGAS It is obtained by the following formula:

[0071]

[0072] β ij =α mi α mj

[0073]

[0074] Where S is the strain rate, C GAS The empirical coefficient is taken as 0.6.

[0075] Step 3, determine the local dynamic grid length scale;

[0076] In this step, combined with the shielding function F in step 1 GAS , and the Vreman dynamic coefficient C in step 2 DGAS , the local dynamic grid length scale Δ * ;

[0077] Local dynamic grid length scale Δ * Given by:

[0078] Δ * =C DGAS [(1-FGAS )Δ vol +F GAS Δ max ]

[0079] Δ max =max(Δ x ,Δ y ,Δ z )

[0080]

[0081] 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.

[0082] Step 4: construct a scale-dependent adjustment function;

[0083] In this step, according to the modeling method of turbulent kinetic energy in the k-ε series model, the original modeled turbulent kinetic energy k is obtained. m ;

[0084] In this embodiment, the standard k-ε turbulence model in the k-ε series of models is taken as an example, and the original modeled turbulent kinetic energy k is obtained according to the modeling method of the turbulent kinetic energy in the standard k-ε turbulence model. m ;

[0085] 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 , is given by:

[0086]

[0087] 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:

[0088]

[0089] Among them, π is the ratio of pi, which is 3.14;

[0090] According to the actual simulated turbulent kinetic energy k u , the original 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 2As shown; the scale ratio is defined as the actual simulated turbulent kinetic energy k u and the original 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:

[0091]

[0092] Among them, l u is the grid-related scale, l m is the turbulence length scale given by the standard k-ε turbulence model, which is given by:

[0093]

[0094] Among them, ε m is the original modeled dissipation rate obtained according to the standard k-ε turbulence model.

[0095] Step 5, reconstruct the turbulent viscosity of the k-ε series model;

[0096] In this step, the dynamic scale-dependent adjustment function D in step 4 is used f The turbulent viscosity ν in the k-ε series model t By adjusting the turbulent viscosity ν, we can obtain the reconstructed turbulent viscosity ν. sfs In this embodiment, the standard k-ε turbulence model in the k-ε series of models is taken as an example, and the turbulent viscosity ν in the standard k-ε turbulence model is calculated. t By adjusting the turbulent viscosity ν, we can obtain the reconstructed turbulent viscosity ν. sfs , as shown below:

[0097]

[0098] Among them, C μ is a constant in the standard k-ε turbulence model and is taken as 0.09.

[0099] Step 6: Use the reconstructed turbulent viscosity to perform turbulence simulation:

[0100] In this step, the turbulent viscosity ν reconstructed in step 5 is used sfs , calculate the Reynolds stress, and update the transport equation of the k-ε series model, replacing the turbulent viscosity ν in the original transport equation of the k-ε series model t , combined with the k-ε series model, the grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupling k-ε series model is obtained. In this embodiment, the standard k-ε turbulence model in the k-ε series model is taken as an example, and the turbulent viscosity ν reconstructed in step 5 is used. sfs, calculate the Reynolds stress, and update the transport equation of the standard k-ε turbulence model, replacing the turbulent viscosity ν in the original transport equation of the standard k-ε turbulence model t , the new transport equation is shown as follows:

[0101]

[0102] The new transport equation obtained is combined with the standard k-ε turbulence model to obtain a grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled k-ε series models, which is used for the numerical simulation of the back-step example.

[0103] The fully implicit coupling solution technology is used for transient calculation, and the time step meets the CFL condition in engineering computational fluid dynamics. In addition, in order to better demonstrate the advantages of the embodiments of the present invention, the standard k-ε turbulence model in the k-ε series model is selected to perform numerical simulation 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 k-ε series model of the present invention.

[0104] Figure 3 This is a schematic diagram of the turbulent eddy structure of the back-step example calculated using the standard k-ε turbulence model in the k-ε series of models, colored using the turbulent viscosity ratio.

[0105] 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 k-ε series model of the present invention, and is colored by the turbulent viscosity ratio.

[0106] 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 k-ε series model proposed in the present invention is stronger than the result calculated by the standard k-ε model. It can capture richer turbulent structures with the same number of grids and provide more accurate flow field details.

[0107] 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.

[0108] In summary, the grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupled k-ε series model proposed in the present invention constructs Vreman dynamic coefficient based on local velocity gradient tensor, identifies local grid size, and determines local dynamic grid length scale Δ* , and then reconstruct the turbulent viscosity by constructing scale-related functions through turbulent energy spectrum integration to achieve grid adaptive simulation, effectively overcoming the problem of high empirical dependence of existing turbulent mixing models on grids. By introducing the Vreman dynamic coefficient, the grid adaptability of the grid adaptive turbulence simulation method is further broadened, which can greatly reduce the computational cost while improving the calculation accuracy, 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 k-ε 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 k-ε series model; Step 6, use the reconstructed turbulent viscosity to perform turbulence simulation; ① The determination of 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 Select one of the F1 shielding function and F2 shielding function from the DDES-SST model and the F from the DDES-SA model. d Masking function; ② The calculation of the Vreman dynamic coefficient 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 determination of the local dynamic grid length scale 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; ④ The structural scale-related adjustment functions include: According to the modeling method of turbulent kinetic energy in the k-ε series model, the original modeled turbulent kinetic energy k is obtained. m , 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 from 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 original 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 original 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 given by the k-ε series model and is given by: Among them, ε m is the dissipation rate of the original model obtained according to the k-ε series model; ⑤ The turbulent viscosity of the reconstructed k-ε series model includes: Adopt the dynamic scale-dependent adjustment function D described in step 4 f The turbulent viscosity ν in the k-ε 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 ⑥ The turbulence simulation using the reconstructed turbulent viscosity includes: Using the reconstructed turbulent viscosity ν described in step 5 sfs , calculate the Reynolds stress, and update the transport equation of the k-ε series model, replacing the turbulent viscosity ν in the original transport equation of the k-ε series model t , combined with the k-ε series model, the grid adaptive turbulence simulation method based on Vreman dynamic coefficient coupling k-ε series model is obtained.

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