A grid-adaptive turbulence simulation method based on SA series models coupled with turbulence energy spectrum

Abstract

The present invention discloses a grid adaptive turbulence simulation method based on the coupling of the turbulence energy spectrum and the SA series models. The main implementation process includes: Step 1, determining whether to apply a shielding function; Step 2, identifying the local grid scale; Step 3, constructing a scale-dependent adjustment function based on the integral of the turbulence energy spectrum and coupling with the SA series models; Step 4, using the adjustment function to reconstruct the turbulent viscosity of the SA series models; Step 5, based on the SA series models, performing turbulence simulation using the reconstructed turbulent viscosity. The present invention realizes grid adaptive simulation by identifying the local grid size, determining the local grid length scale Δ<supgt;*< / supgt;, and then reconstructing the turbulent viscosity through constructing a scale-dependent function by integrating the turbulence energy spectrum; constructs a new algebraic empirical formula to characterize the turbulent kinetic energy and the corresponding turbulent length scale, overcomes the problem of high empirical dependence of the existing turbulence mixing models on the grid, effectively improves the calculation accuracy, greatly reduces the calculation cost, and significantly speeds up the turbulence simulation process.

Description

Technical Field

[0001] The present 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 turbulence energy spectrum coupled SA series model. Background Art

[0002] Aircraft engines and gas turbines are a major national need 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 significant impact on the performance of aircraft engines and gas turbines. Therefore, in engineering design, there is an urgent need 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 current engineering projects is primarily based on solving the Reynolds-averaged NS equations (RANS) method. Although computationally intensive, it is based on simple basic flows and lacks accuracy in predicting complex turbulent flows such as those found in engineering problems, such as multi-scale, unsteady, and highly separated turbulent flows. This makes it difficult to conduct detailed studies of complex flow mechanisms in engineering problems, such as the internal flow of aircraft engines and gas turbines, and severely restricts the advancement of design capabilities in these fields. Large eddy simulation (LES), a high-precision numerical simulation method, places high demands on the number of grids, making its computational cost exponentially higher than that of RANS methods, far exceeding the computational cost acceptable for engineering applications. For engineering flow problems such as the internal flow of aircraft engines and gas turbines, the Reynolds number is often high. With current computing power, the LES method is still difficult to apply to flow prediction in complex engineering fields at the engineering design level.

[0004] The RANS-LES hybrid simulation method has emerged in the past two decades. By using the RANS method in the near-wall region and the LES method in the mainstream region, it balances computational accuracy and efficiency, providing a good solution to the problem of high computational costs in high-precision simulation of complex flows. However, the current classic RANS-LES hybrid model has relatively strict requirements on the mesh, requiring the user to have extensive experience in high-precision numerical simulation. Therefore, its predictive ability for complex engineering flows, such as the internal flow of aircraft engines and gas turbines, is limited. Therefore, reducing the RANS-LES hybrid model's reliance on empirical meshing is of great significance for achieving accurate, efficient, and high-precision simulation of multi-scale, nonlinear, and unsteady turbulent flow phenomena in complex engineering flow problems.

[0005] The previously published invention patents (CN 115034162 A, CN 115186607 A, CN 115186608 A, CN114970403 A) all use multi-equation turbulence models as the basis, which are more computationally expensive than the single-equation SA series turbulence models. In addition, the basis models in the previously published invention patents (CN 115034162 A, CN 115186607 A, CN 115186608 A, CN114970403 A) all solve the transport equations related to turbulent kinetic energy, thereby directly obtaining the turbulent length scale; however, the SA series model in the present invention does not contain turbulent kinetic energy, so the corresponding turbulent length scale cannot be obtained. 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, and then proposes a grid-adaptive turbulence simulation method based on the turbulent energy spectrum coupled to the SA series model. Summary of the Invention

[0006] (1) Technical issues to be solved

[0007] The purpose of the present invention is to propose a grid-adaptive turbulence simulation method based on the SA series of models coupled with the turbulence energy spectrum. This method effectively overcomes the high empirical dependence of existing RANS-LES hybrid models on the grid, significantly reduces computational cost while improving computational accuracy, and significantly accelerates the turbulence simulation process. This method provides an efficient numerical simulation method for fast, high-precision simulation of multi-scale, nonlinear, and unsteady turbulent flows in complex engineering flow problems. Furthermore, compared with existing technologies, since the SA series of models do not contain a 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, thereby proposing a grid-adaptive turbulence simulation method based on the SA series of models coupled with the turbulence energy spectrum.

[0008] (2) Technical solution

[0009] In order to solve the above technical problems, the present invention provides a grid-adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model, comprising the following steps:

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

[0011] Step 2: Identify the local grid scale;

[0012] Step 3: Construct a scale-dependent adjustment function based on the turbulence energy spectrum integral coupled SA series model;

[0013] Step 4: Use the adjustment function to reconstruct the turbulent viscosity of the SA series model;

[0014] Step 5: Based on the SA series model, turbulence simulation is performed using the reconstructed turbulent viscosity;

[0015] 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 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 For example, the F from the DDES-SA model can be used. d The shielding function and F from the IDDES-SA model B Shield function;

[0017] Step 2 of identifying the local grid scale includes:

[0018] Combined with the shielding function F described in step 1 GAS , determine the local grid length scale Δ * ;

[0019] The local grid length scale Δ * It is given by:

[0020] Δ * =C GAS [(1-F GAS )Δ vol +F GAS Δ max ]

[0021] Δ max =max(Δ x ,Δ y ,Δ z )

[0022]

[0023] Among them, Δ x is the length of the local hexahedral grid, Δ y is the width of the local hexahedral grid, Δ z The height of the local hexahedral grid, C GAS The empirical coefficient is 0.016;

[0024] The scale-dependent adjustment function constructed based on the turbulence energy spectrum integral coupled SA series model in step 3 includes:

[0025] 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:

[0026]

[0027] According to the local grid length scale Δ * Based on the turbulence energy spectrum, the actual modeled turbulent kinetic energy k is obtained by integration. u ;

[0028] The actual simulated turbulent kinetic energy k u It is obtained from the following formula:

[0029]

[0030] Among them, C k is the Kolmogorov constant coefficient, which is 1.5, ε is the actual turbulence dissipation rate; κ c To solve the turbulent cutoff wave number, the local grid length scale Δ * Decide:

[0031]

[0032] According to the actual modeled 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-related adjustment function D f ; Define the scale ratio as the actual modeled turbulent kinetic energy k u and the 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:

[0033]

[0034] l GAS =(1-F GAS )l u +F GAS l m

[0035]

[0036] Among them, l u is the grid-related scale, l m is the turbulence length scale;

[0037] The turbulence length scale l m The expression is as follows:

[0038]

[0039] Among them, ν t is the original turbulent viscosity of the SA series model, U i,j is the velocity gradient tensor obtained from the SA series model; a0 is the empirical coefficient, which is 5.794;

[0040] The turbulent viscosity of the SA series model is reconstructed using the adjustment function described in step 4, including:

[0041] Adopt the dynamic scale-related adjustment function D described in step 3 f For the turbulent viscosity ν in the SA series model t By regulating, we can obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula:

[0042] ν sfs =D f ν t

[0043] Step 5 describes the turbulence simulation based on the SA series model using the reconstructed turbulent viscosity, including:

[0044] Use the turbulent viscosity ν reconstructed in step 4 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 grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model.

[0045] (3) Beneficial effects

[0046] The present invention provides a grid-adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model, which has the following beneficial effects:

[0047] By identifying the local grid size, determine the local grid length scale Δ *, and then reconstruct the turbulent viscosity by constructing a scale-related function through the turbulent energy spectrum integral to realize grid adaptive simulation, effectively overcome the problem of high empirical dependence of the existing RANS-LES hybrid model on the grid, while improving the calculation accuracy, greatly reducing the calculation cost, significantly accelerating the turbulence simulation process, and providing 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 view of the fact that the SA series model does 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 has the characteristics of simple form and strong portability, can be well combined with the SA series model, and is convenient for implanting into existing CFD codes for application and expansion, and has broad academic and engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flow chart of a grid-adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model of the present invention;

[0049] Figure 2 The present invention is a grid adaptive turbulence simulation method based on turbulence energy spectrum coupling SA series model. Based on the turbulence energy spectrum, a dynamic scale-related adjustment function D is constructed. f Schematic diagram of;

[0050] Figure 3 Schematic diagram of the turbulent vortex structure of the flow around a cylinder calculated using the SA-noft2 turbulence model in the SA series of models;

[0051] Figure 4 The figure is a schematic diagram of the turbulent vortex structure of a flow example around a cylinder calculated by using a grid adaptive turbulence simulation method based on the turbulence energy spectrum coupling SA series model of the present invention. DETAILED DESCRIPTION

[0052] 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 embodiments of the present invention. The following examples are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0053] The flow around a cylinder is selected as a calculation example, and high-quality hexahedral meshes are used to spatially discretize the computational domain. The total number of meshes is about 280,000.

[0054] The present invention provides a grid-adaptive turbulence simulation method based on a turbulence energy spectrum coupled SA series model, comprising the following steps:

[0055] Step 1: determine whether to apply the shielding function;

[0056] In this step, the type of flow state being simulated is used to determine whether to use the shielding function F GAS 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, the shielding function is used. The shielding function F GAS For example, the F from the DDES-SA model can be used. d The shielding function and F from the IDDES-SA model B Masking function.

[0057] In this embodiment, the F B Examples of functions include:

[0058] F GAS =F B

[0059] F B =min[2exp(-9α 2 ),1.0]

[0060] α=0.25-d w / Δ max

[0061] Δ max =max(Δ x ,Δ y ,Δ z )

[0062] 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.

[0063] Step 2: Identify the local grid scale;

[0064] In this step, combined with the shielding function F in step 1 GAS , determine the local grid length scale Δ * ;

[0065] Local grid length scale Δ * It is given by:

[0066] Δ * =C GAS [(1-F GAS )Δ vol +F GAS Δ max ]

[0067] Δ max =max(Δ x ,Δ y ,Δ z )

[0068]

[0069] 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, C GAS The empirical coefficient is 0.016;

[0070] Step 3: Construct a scale-dependent adjustment function based on the turbulence energy spectrum integral coupled SA series model:

[0071] In this step, the local modeled turbulent viscosity ν is obtained according to the SA series model. t and the velocity gradient tensor U i,j , 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 To characterize.

[0072] Taking the SA-noft2 turbulence model in the SA series 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 , 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 Characterization:

[0073]

[0074] According to the local grid length scale Δ in step 2 * Based on the turbulence energy spectrum, the actual modeled turbulent kinetic energy k is obtained by integration. u , obtained from the following formula:

[0075]

[0076] 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 grid length scale Δ in step 2 is * Decide:

[0077]

[0078] According to the actual turbulent kinetic energy k u , modeled turbulent kinetic energy k m and the shielding function F in step 1 GAS , construct the dynamic scale-related adjustment 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 ratio of the dynamic scale-related adjustment function D f is a function related to the scale ratio, which is obtained from the following formula:

[0079]

[0080] l GAS =(1-F GAS )l u +F GAS l m

[0081]

[0082] Among them, l u is the grid-related scale, l m is the turbulence length scale; since there is no turbulence kinetic energy related quantity in the SA-noft2 turbulence model, the corresponding turbulence length scale cannot be obtained. Therefore, the present invention constructs a new algebraic empirical formula to express the turbulence kinetic energy and the corresponding turbulence length scale; the constructed turbulence length scale l m The expression is as follows:

[0083]

[0084] Among them, ν t is the original turbulent viscosity of the SA-noft2 turbulence model, U i,j is the velocity gradient tensor obtained by the SA-noft2 turbulence model; a0 is the empirical coefficient, which is 5.794.

[0085] Step 4: Use the adjustment function to reconstruct the turbulent viscosity of the SA series model;

[0086] In this step, the dynamic scale-related adjustment function D described in step 3 is used. f For the turbulent viscosity ν in the SA series model t By regulating, we can obtain the reconstructed turbulent viscosity ν sfs .

[0087] Taking the SA-noft2 turbulence model in the SA series as an example, the dynamic scale-dependent adjustment function D in step 3 is used.f The turbulent viscosity ν in the SA-noft2 turbulence model t By regulating, we can obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula:

[0088]

[0089] 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 the constant coefficient in the SA-noft2 turbulence model, which is taken as 7.1;

[0090] Step 5: Based on the SA series model, use the reconstructed turbulent viscosity to perform turbulence simulation:

[0091] In this step, the turbulent viscosity ν reconstructed in step 4 is used 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 grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model.

[0092] Taking the SA-noft2 turbulence model in the SA series as an example, the turbulent viscosity ν reconstructed in step 4 is used. sfs , calculate the Reynolds stress, and update the mass, momentum, and energy transport equations. Combined with the SA-noft2 turbulence model, the grid-adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model is obtained, and used for the numerical simulation of the flow around a cylinder.

[0093] 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. Furthermore, to better demonstrate the advantages of the embodiments of the present invention, a numerical simulation of the flow around a cylinder using the SA-noft2 turbulence model from the SA series of models was performed. The simulation results were compared with those of the present invention's grid-adaptive turbulence simulation method based on the turbulence energy spectrum coupled to the SA series of models.

[0094] Figure 3 Schematic diagram of the turbulent vortex structure of the flow around a cylinder calculated using the SA-noft2 turbulence model in the SA series of models, colored by the turbulent viscosity ratio.

[0095] Figure 4 This is a schematic diagram of the turbulent vortex structure of a flow example around a cylinder calculated by a grid-adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model of the present invention, and is colored using the turbulent viscosity ratio.

[0096] Figure 3 、 Figure 4Comparative analysis shows that the turbulent eddy structure analysis capability obtained by the grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model proposed in the present invention is stronger than the results obtained by the SA-noft2 turbulence model. With the same number of grids, it can capture richer turbulent structures and provide more accurate flow field details.

[0097] 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.

[0098] In summary, the present invention provides a grid-adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model, which determines the local grid length scale Δ by identifying the local grid size. * , and then reconstruct the turbulent viscosity by constructing a scale-dependent function through the turbulent energy spectrum integral, realizing grid-adaptive simulation. Given that the SA series models do not contain turbulent kinetic energy and cannot directly obtain the corresponding turbulent length scale, this paper constructs a new algebraic empirical formula to characterize the turbulent kinetic energy and the corresponding turbulent length scale. This effectively overcomes the problem of existing turbulent mixing models' high empirical dependence on the grid. While improving calculation accuracy, it can significantly reduce computational costs, significantly accelerate 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 turbulence energy spectrum coupled SA series model, characterized in that: The steps include: Step 1, determine whether to apply the shielding function; Step 2: Identify the local grid scale; Step 3: Construct a scale-dependent adjustment function based on the turbulence energy spectrum integral coupled SA series model; Step 4, reconstruct the turbulent viscosity of the SA series model using the adjustment function; Step 5: Based on the SA series model, turbulence simulation is performed using the reconstructed turbulent viscosity; 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 , when the flow state type is free shear flow, the shielding function is not used. At this time, 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 For example, the F from the DDES-SA model can be used. d The screening function and F from the IDDES-SA model B Masking function; Step 2 of identifying the local grid scale includes: Combined with the shielding function F described in step 1 GAS , determine the local grid length scale Δ * ; The local grid length scale Δ * Given by: D * =C GAS [(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 The height of the local hexahedral grid, C GAS The empirical coefficient is taken as 0.016; The scale-dependent adjustment function constructed based on the turbulence energy spectrum integral coupling SA series model in step 3 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 in the following formula: According to the local 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 grid length scale Δ * Decide: 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 original turbulent viscosity of the SA series model, U i,j is the velocity gradient tensor obtained by the SA series model; a0 is the empirical coefficient, which is 5.794; Step 4 describes the use of adjustment functions to reconstruct the turbulent viscosity of the SA series model, including: Adopt the dynamic scale-related adjustment function D described in step 3 f For the 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 Step 5 describes the turbulence simulation based on the SA series model using the reconstructed turbulent viscosity, including: Using the reconstructed turbulent viscosity ν described in step 4 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 grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled SA series model.

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