A grid-adaptive turbulence simulation method based on turbulence energy spectrum coupled v2-f series models

Abstract

The present invention discloses a grid-adaptive turbulence simulation method based on turbulence energy spectrum coupling v2-f series models, and the main process of its implementation includes: step one, judging whether to apply a shielding function; step two, identifying the local grid scale; step three, constructing a scale-related adjustment function based on the turbulence energy spectrum integral coupling v2-f series model; step four, using the adjustment function to reconstruct the turbulent viscosity of the v2-f series model; step five, based on the v2-f series model, using the reconstructed turbulent viscosity to perform turbulence simulation. The present invention determines 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, which effectively overcomes the problem of high empirical dependence of existing RANS / LES hybrid models on grids, greatly reduces computational costs, and significantly accelerates the turbulence simulation process, providing an efficient numerical simulation method for solving fast and high-precision simulation of complex engineering flow problems.

Description

Technical Field

[0001] The invention relates to the field of engineering fluid mechanics calculation, and in particular to a grid adaptive turbulence simulation method based on turbulence energy spectrum coupled V2-F 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. Taking the internal flow of fluid machinery as an example, its flow structure is very complex, and there are widespread complex turbulent flow phenomena such as multi-scale, nonlinear, and unsteady. These complex turbulences have a great impact on the performance of fluid machinery. 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 fluid machinery.

[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 refined study of the complex flow mechanism in engineering problems such as the internal flow of fluid machinery, which seriously restricts the improvement of the design level in the field of fluid machinery. As a high-precision numerical simulation method, the large eddy simulation (LES) method has high requirements on 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 fluid machinery, the Reynolds number is often high. Under the existing computing power, the LES method is still difficult to apply to 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 relatively rich experience in high-precision numerical simulation, and therefore has limited predictive ability for complex engineering flows such as internal flow in fluid machinery. Therefore, reducing the RANS-LES hybrid model's empirical dependence on the grid is of great significance to better achieve accurate, efficient and high-precision simulation of multi-scale, nonlinear, unsteady and other turbulent flow phenomena in complex engineering flow problems. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] The purpose of the present invention is to propose a grid-adaptive turbulence simulation method based on the turbulence energy spectrum coupled v2-f series model, which effectively overcomes 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, and significantly accelerating the turbulence simulation process, 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.

[0007] (II) Technical solution

[0008] In order to solve the above technical problems, the present invention provides a grid adaptive turbulence simulation method based on turbulence energy spectrum coupled V2-F series model, comprising the following steps:

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

[0010] Step 2: Identify the local grid scale;

[0011] Step 3: construct a scale-dependent adjustment function based on the turbulence energy spectrum integral coupling v2-f series model;

[0012] Step 4, reconstruct the turbulent viscosity of the v2-f series model using the adjustment function;

[0013] Step 5: Based on the v2-f series model, turbulence simulation is performed using the reconstructed turbulent viscosity;

[0014] ① The determination of whether to apply the shielding function includes:

[0015] 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, the shielding function is used;

[0016] ② The identification of the local grid scale includes:

[0017] Combined with the shielding function F in step 1 GAS , determine the local grid length scale Δ * ;

[0018] The local grid length scale Δ * Given by:

[0019] Δ * =C GAS [(1-F GAS )Δ vol +F GAS Δ max ]

[0020] Δ max =max(Δ x ,Δ y ,Δ z )

[0021]

[0022] Among them, Δ max is the local maximum grid size, Δ vol is the local grid volume length scale, 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 taken as 0.6;

[0023] ③ The scale-related adjustment functions constructed based on the turbulence energy spectrum integral coupling v2-f series model include:

[0024] According to the modeling method of turbulent kinetic energy in the v2-f series model, the original modeled turbulent kinetic energy k is obtained. m , 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 ;

[0025] The actual simulated turbulent kinetic energy k u It is obtained from the following formula:

[0026]

[0027] 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:

[0028]

[0029] 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:

[0030]

[0031] l GAS =(1-F GAS ) u +F GAS l m

[0032]

[0033] Among them, l u is the grid-related scale, l m is the turbulence length scale given for the v2-f series of models;

[0034] ④ The turbulent viscosity of the v2-f series model reconstructed using the adjustment function includes:

[0035] Adopt the dynamic scale-related adjustment function D described in step 3 f Turbulent viscosity ν for the v2-f series model t By adjusting the turbulent viscosity ν, we can obtain the reconstructed turbulent viscosity ν. sfs , obtained from the following formula:

[0036] ν sfs =D f ·ν t

[0037] ⑤ The turbulence simulation based on the v2-f series model using the reconstructed turbulent viscosity includes:

[0038] Using the reconstructed turbulent viscosity ν described in step 4 sfs Calculate the Reynolds stress and update the transport equation of the v2-f series model, replacing the turbulent viscosity ν in the original transport equation of the v2-f series model t , combined with the v2-f series models, the grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled v2-f series models is obtained.

[0039] (III) Beneficial effects

[0040] The present invention provides a grid-adaptive turbulence simulation method based on turbulence energy spectrum coupling V2-F series models, which has the following beneficial effects: by identifying the local grid size, determining the 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, which effectively overcomes the problem of high empirical dependence of the existing RANS-LES hybrid model on the grid. While improving the calculation accuracy, it greatly reduces the calculation cost and significantly accelerates the turbulence simulation process, 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. The method of the present invention is concise in form and highly portable. It can be well combined with the v2-f series models, and is easy to be implanted into existing CFD codes for application and expansion, and has broad academic and engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of the grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled v2-f series model of the present invention;

[0042] Figure 2 The present invention constructs a dynamic scale-related adjustment function D based on the turbulence energy spectrum. f Schematic diagram of .

[0043] Figure 3 This is a diagram of the turbulent vortex structure of a periodic mountain flow example calculated using the v2-f turbulence model;

[0044] Figure 4 This is a diagram of the turbulent vortex structure of a periodic mountain flow example calculated by the grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled V2-F series model of the present invention. DETAILED DESCRIPTION

[0045] The following is a further detailed description of the specific implementation of the present invention by taking the v2-f turbulence model as an example in conjunction with the accompanying drawings. The following embodiments are only used to illustrate the present invention but are not used to limit the scope of the present invention.

[0046] The periodic mountain flow example is selected as the calculation example, and the high-quality hexahedral grid is used to spatially discretize the calculation domain. The total number of grids is about 220,000.

[0047] The present invention provides a grid adaptive turbulence simulation method based on turbulence energy spectrum coupling V2-F series model, comprising the following steps:

[0048] Step 1, determine whether to apply the shielding function;

[0049] In this step, the type of flow state being simulated is considered to determine whether to use the screening 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.

[0050] In this embodiment, the F in the DDES-SA model is used. d The shielding function is:

[0051] F GAS =F d

[0052]

[0053]

[0054] Among them, U i,j is the velocity gradient tensor; ν t is the turbulent viscosity given by the v2-f 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;

[0055] Step 2: Identify the local grid scale;

[0056] In this step, combined with the shielding function F in step 1 GAS , determine the local grid length scale Δ * ;

[0057] Local grid length scale Δ * Given by:

[0058] Δ * =C GAS [(1-F GAS )Δ vol +F GAS Δ max ]

[0059] Δ max =max(Δ x ,Δ y ,Δ z )

[0060]

[0061] Among them, Δ max is the local maximum grid size, Δ vol is the local grid volume length scale, 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 is the empirical coefficient, which is taken as 0.6;

[0062] Step 3: Construct a scale-dependent adjustment function based on the turbulence energy spectrum integral coupling v2-f series model:

[0063] In this step, according to the modeling method of turbulent kinetic energy in the v2-f turbulence model, the original modeled turbulent kinetic energy k is obtained. m ;

[0064] According to the local grid length scale Δ in step 2 * Based on the turbulence energy spectrum, the actual simulated turbulent kinetic energy k is obtained by integration u , is given by:

[0065]

[0066] 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:

[0067]

[0068] 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 2 As 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 ratio of the dynamic scale-related adjustment function D f is a function related to the scale ratio, which is obtained by the following formula:

[0069]

[0070] l GAS =(1-F GAS ) u +F GAS l m

[0071]

[0072] Among them, l u is the grid-related scale, l m is the turbulence length scale given by the v2-f turbulence model and is given by:

[0073]

[0074] Among them, km is the original modeled turbulent kinetic energy given by the v2-f model, ε m is the dissipation rate of the original model given by the v2-f model, ν is the viscosity coefficient of the fluid, C L and C η is a constant coefficient in the v2-f turbulence model, where C L Take 0.25, C η Take 85;

[0075] Step 4: Use the adjustment function to reconstruct the turbulent viscosity of the v2-f turbulence model:

[0076] In this step, the dynamic scale-related adjustment function D in step 3 is used f The turbulent viscosity ν obtained from the v2-f turbulence model t By adjusting the turbulent viscosity ν, we can obtain the reconstructed turbulent viscosity ν. sfs , as shown below:

[0077]

[0078] Where T is the turbulence time scale in the v2-f turbulence model, and its expression is:

[0079]

[0080] In particular, C μ and C T is a constant coefficient in the v2-f turbulence model, C μ Take 0.22, C T Take 6;

[0081] Step 5: Perform turbulence simulation based on the v2-f turbulence model using the reconstructed turbulent viscosity:

[0082] In this step, the turbulent viscosity ν reconstructed in step 4 is used sfs Calculate the Reynolds stress and update the transport equation of the v2-f turbulence model, replacing the turbulent viscosity ν in the original transport equation of the v2-f turbulence model t , the new transport equation is shown as follows:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] In particular, the constant coefficient C1 is 1.4, the constant coefficient C2 is 0.45, and the constant coefficient σ v2 Take 1;

[0090] The new transport equation obtained is combined with the v2-f turbulence model to obtain a grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled v2-f series model, and is used for the numerical simulation of periodic mountain flow examples.

[0091] 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 v2-f turbulence model is selected to perform numerical simulation on the periodic mountain flow example, and the numerical simulation results are compared with those of the grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled v2-f series model.

[0092] Figure 3 This is a diagram of the turbulent vortex structure of a periodic mountain flow example calculated using the v2-f turbulence model, colored using the dimensionless streamwise velocity.

[0093] Figure 4 This is a turbulent vortex structure diagram of a periodic mountain flow example calculated by the grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled V2-F series model of the present invention, and is colored using the dimensionless streamwise velocity.

[0094] Figure 3 , Figure 4 Comparative analysis shows that the turbulent eddy structure analysis capability obtained by the grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled v2-f series models proposed in the present invention is stronger than the result obtained by the v2-f turbulence model calculation. It can capture richer turbulence structures with the same number of grids and provide more accurate flow field details.

[0095] 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.

[0096] In summary, the embodiment of the present invention determines 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, which effectively overcomes the problem of high empirical dependence of existing turbulent mixing models on grids. While improving calculation accuracy, it can greatly reduce calculation costs and significantly accelerate the turbulence simulation process, providing a new method for flow prediction in complex engineering fields.

Claims

1. A grid-adaptive turbulence simulation method based on the turbulence energy spectrum coupled v2-f series model, It is characterized in that The following steps are involved: 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 coupling v2-f series model; Step 4, reconstruct the turbulent viscosity of the v2-f series model using the adjustment function; Step 5: Based on the v2-f series model, turbulence simulation is performed using the reconstructed turbulent viscosity; 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 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, the shielding function is used; ② The identification of the local grid scale includes: Combined with the shielding function F 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 max is the local maximum grid size, Δ vol is the local grid volume length scale, 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 taken as 0.6; ③ The scale-related adjustment functions constructed based on the turbulence energy spectrum integral coupling v2-f series model include: According to the modeling method of turbulent kinetic energy in the v2-f series model, the original modeled turbulent kinetic energy k is obtained. m , 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 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 for the v2-f series of models; ④ The turbulent viscosity of the v2-f series model reconstructed using the adjustment function includes: Adopt the dynamic scale-related adjustment function D described in step 3 f Turbulent viscosity ν for the v2-f 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 ⑤ The turbulence simulation based on the v2-f series model using the reconstructed turbulent viscosity includes: Using the reconstructed turbulent viscosity ν described in step 4 sfs Calculate the Reynolds stress and update the transport equation of the v2-f series model, replacing the turbulent viscosity ν in the original transport equation of the v2-f series model t , combined with the v2-f series models, the grid adaptive turbulence simulation method based on the turbulence energy spectrum coupled v2-f series models is obtained.

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