Strong shear turbulence grid adaptive simulation method coupled with v2-f series model

Abstract

The invention discloses a strong shear turbulence grid adaptive simulation method coupled with a v2-f series model. The method mainly comprises the following steps of: 1, judging whether a shielding function is applied or not; step 2, identifying a self-adaptive length scale of a shear layer; 3, constructing a scale-related adjustment function based on the turbulence energy spectrum integral; 4, using an adjustment function to reconstruct the turbulence viscosity of the v2-f series model; and 5, performing turbulence simulation by using the reconstructed turbulence viscosity. According to the method, the self-adaptive sub-grid length scale of the shear layer is constructed and introduced into the initial region of the quasi-two-dimensional free shear layer, so that the sub-grid length scale of the initial region of the free shear layer is effectively reduced, and the problem that an existing RANS-LES hybrid model is highly dependent on grids is solved. The calculation accuracy is improved, meanwhile, the calculation consumption is greatly reduced, the turbulence simulation process is remarkably accelerated, and an effective numerical simulation method is provided for solving low-consumption and high-precision simulation of strong shear flow in the complex engineering flow problem.

Description

Technical Field

[0001] The present invention relates to the field of complex fluid mechanics calculations for aeroengines and gas turbines, and particularly to a strongly sheared turbulent grid adaptive simulation method that couples v2-f series models. Background Art

[0002] Turbulence phenomena widely exist in nature and engineering fields. Among them, strongly sheared flows are complex turbulent types that cannot be ignored in many engineering applications. Strongly sheared flows are usually accompanied by extremely large velocity gradients and the interaction between large-scale and small-scale turbulences, with flow characteristics such as non-equilibrium transport and anisotropy. Achieving accurate prediction of strongly sheared turbulence is a major challenge in current turbulence research. To improve the accuracy and reliability of engineering designs, there is an urgent need to develop a turbulence simulation method that can accurately capture the characteristics of strongly sheared flows, is efficient, and scalable.

[0003] The commonly used turbulence simulation methods in existing engineering mainly solve the Reynolds-averaged N-S (RANS) equations. Although the computational cost is relatively small, the prediction accuracy for multi-scale, unsteady flows and complex flows with non-equilibrium transport and anisotropic turbulence is not good, making it difficult to achieve refined research on complex flow mechanisms, and severely restricting the improvement of the design level in fields such as fluid machinery. As a high-precision numerical simulation method, the large eddy simulation (LES) method has high accuracy, but its computational cost is much higher than what can be tolerated in engineering applications. With the existing computing power, it is difficult for the LES method to be applied 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 has balanced computational accuracy and computational efficiency by using the RANS method in the near-wall region and the LES method in the mainstream region, providing a good solution to the problem of high computational cost for high-precision simulation of complex flows. However, the classical RANS-LES hybrid model has relatively strict requirements for grids and requires users to have rich experience in high-precision numerical simulations, so its prediction ability for complex engineering flows is limited. Currently, various new types of grid adaptive turbulence simulations have been proposed, which can effectively improve the prediction ability for complex flows, but the definition of their grid scales cannot adapt to complex geometric grids, and a more suitable grid length scale needs to be combined for strongly sheared layers.

[0005] In order to improve the accuracy of the RANS-LES hybrid simulation of strong shear turbulence, the present invention proposes a shear layer adaptive subgrid length scale. By introducing this scale in the initial region of the quasi-two-dimensional free shear layer, the subgrid length scale in the initial region of the free shear layer is effectively reduced. Without significantly increasing the computational cost, the accuracy and efficiency of the turbulence simulation in the shear layer are improved, thus providing a new approach to solve complex turbulent flow problems. Compared with the publicly disclosed invention patents CN114970403 A and CN 117787130 A, the influence of strongly anisotropic grids on the development of the shear layer can be significantly reduced, the prediction accuracy of the grid adaptive turbulence simulation method can be further improved, and the computational cost can be effectively reduced. Summary of the Invention

[0006] (I) Technical Problems to be Solved

[0007] The purpose of the present invention is to propose a grid adaptive simulation method for strong shear turbulence coupled with the v2-f series model. By constructing a shear layer adaptive subgrid length scale and introducing it into the initial region of the quasi-two-dimensional free shear layer, the subgrid length scale in the initial region of the free shear layer is effectively reduced, and the problem of high grid dependence of the existing RANS-LES hybrid model is overcome. While improving the computational accuracy, the computational cost is significantly reduced, the turbulence simulation process is significantly accelerated, and an effective numerical simulation method is provided for the low-cost and high-precision simulation of strong shear flows in complex engineering flow problems.

[0008] (II) Technical Solutions

[0009] To solve the above technical problems, the present invention provides a grid adaptive simulation method for strong shear turbulence coupled with the v2-f series model, including the following steps:

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

[0011] Step 2, identify the shear layer adaptive length scale;

[0012] Step 3, construct a scale-related adjustment function based on the turbulent energy spectrum integral;

[0013] Step 4, reconstruct the turbulent viscosity of the v2-f series model using the adjustment function;

[0014] Step 5, perform turbulence simulation using the reconstructed turbulent viscosity;

[0015] ① The determination of whether to apply a shielding function in Step 1 includes:

[0016] Combined with the type of flow state being simulated, determine whether to adopt the shielding function F GAS , specifically, when the type of flow state is free shear flow, the shielding function is not adopted, and at this time the shielding function FGAS = 0; When the flow state type is near-wall flow, a shielding function is adopted, and the shielding function F GAS Selectively use the F1 shielding function, the F2 shielding function from the DDES-SST model and the F from the DDES-SA model d Shielding function;

[0017] ② The identification of the shear layer adaptive length scale in Step 2 includes:

[0018] Adopt the shielding function F described in Step 1 GAS , to determine the local grid length scale Δ * ; The local grid length scale Δ * Is given by the following formula:

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

[0020]

[0021] Δ max = max(Δ x , Δ y , Δ z )

[0022]

[0023]

[0024] Among them, C GAS Is an empirical coefficient, taking 0.6; 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 position vector of the cell vertex, Is the position vector of the cell center;

[0025] Take values according to the following formula:

[0026]

[0027] Among them, Is the strain rate tensor, Is the vorticity vector, ω 2 ​is the square of the vorticity vector; θ takes 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 v2 - f series model, v t∞ is the far - field turbulent viscosity given by the v2 - f series model;

[0028] <vtm>is the average value of the local VTM function value and the VTM function values of adjacent grids, F KH is based on the said <vtm>Two-segment linear function of values;

[0029] ③ The scale-dependent adjustment function constructed based on the integral of the turbulent energy spectrum described in Step 3 includes:

[0030] According to the way of modeling the turbulent kinetic energy in the v2-f series model, the originally modeled turbulent kinetic energy k is obtained m , based on the local grid length scale Δ described in Step 2 * , the actually modeled turbulent kinetic energy k is obtained by integrating based on the turbulent energy spectrum u ; the actually modeled turbulent kinetic energy k u is obtained by the following formula:

[0031]

[0032] where E(κ) is the Kolmogorov turbulent energy spectrum, κ is the turbulent wave number, C k is the Kolmogorov constant coefficient, taking 1.5, ε is the actual turbulent dissipation rate, κ c is the resolvable turbulent truncation wave number, which is determined by the local grid length scale Δ described in Step 2 * :

[0033]

[0034] where π is the pi, taking 3.14;

[0035] According to the actually modeled turbulent kinetic energy k u , the originally modeled turbulent kinetic energy k m and the shielding function F described in Step 1 GAS , a dynamic scale-dependent adjustment function D is constructed f ; define the scale ratio as the ratio of the actually modeled turbulent kinetic energy k u and the originally modeled turbulent kinetic energy k m , and the dynamic scale-dependent adjustment function D f is a function related to the scale ratio, and is obtained by the following formula:

[0036]

[0037] l GAS =(1 - F GAS )l u + F GAS l m

[0038]

[0039] where l u is the grid-related scale, l m Turbulent length scale given for the v2-f series model;

[0040] ④ The reconstruction of the turbulent viscosity of the v2-f series model using the adjustment function described in step four includes:

[0041] Adopt the dynamically scale-dependent adjustment function D described in step three f For the turbulent viscosity ν in the v2-f series model t Perform regulation to obtain the reconstructed turbulent viscosity ν sfs which is obtained from the following formula:

[0042] ν sfs = D f ·ν t

[0043] ⑤ The turbulent simulation using the reconstructed turbulent viscosity described in step five includes:

[0044] Adopt the reconstructed turbulent viscosity ν described in step four sfs Calculate the Reynolds stress and update the transport equation of the v2-f series model; adopt the reconstructed turbulent viscosity ν described in step four sfs Replace the turbulent viscosity ν in the v2-f series model t to obtain the strongly sheared turbulent grid adaptive simulation method of the coupled v2-f series model in combination with the v2-f series model.

[0045] (III) Beneficial effects

[0046] A strongly sheared turbulent grid adaptive simulation method of a coupled v2-f series model provided by the present invention has the following beneficial effects: by identifying the local grid size, combining the shear layer adaptive sub-grid length scale to determine the local grid length scale, and then reconstructing the turbulent viscosity through the turbulent energy spectrum integral to construct a scale-dependent function, grid adaptive simulation is realized, effectively improving the problems of large computational cost and poor accuracy in the simulation of the shear layer by the RANS-LES hybrid simulation method, and significantly accelerating the turbulent simulation process.

[0047] Compared with the prior arts CN 114970403 A and CN 117787130 A, the method of the present invention can significantly reduce the influence of the grid on the development of the shear layer by introducing the SLA length scale, further improve the prediction accuracy of the grid adaptive turbulent simulation method, effectively reduce the computational cost, and provide an important means for solving the problem of strong sheared multi-scale complex flow in aeroengines.

[0048] The present invention has the characteristics of simplicity and strong portability. It can be well combined with various grid-adaptive turbulence simulations and is easy to be implanted into existing CFD codes for application and expansion. It has broad academic and engineering application prospects and provides an effective, low-cost, and high-precision numerical simulation method for solving the strong shear flow prediction in complex engineering flow problems such as internal flow in aircraft engines. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of a grid adaptive simulation method for strong shear turbulence coupled with a V2-F series model of the present invention;

[0050] Figure 2 The invention is a method for the adaptive simulation of strong shear turbulence grids coupled with the v2-f series model. The method is applied to a specific embodiment of a circular pipe jet flow based on the shear layer adaptive sub-grid length scale D. f Distribution cloud map;

[0051] Figure 3 The turbulent vortex structure diagram of the circular pipe jet example calculated using the original standard v2-f model;

[0052] Figure 4 The figure shows the turbulent vortex structure of a circular pipe jet example calculated using a strong shear turbulence grid adaptive simulation method coupled with a V2-F series model of the present invention. DETAILED DESCRIPTION

[0053] The following, in conjunction with the accompanying drawings and examples, uses the standard V2-F model from the V2-F series as an example, and uses a circular pipe jet flow as a calculation example to further explain the specific embodiments of the present invention. The following examples are intended to illustrate the present invention only and are not intended to limit the scope of the present invention.

[0054] The present invention provides a grid adaptive simulation method for strong shear turbulence coupled with a V2-F 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 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.

[0057] In the circular pipe jet example of the embodiment of the present invention, a high-quality hexahedral mesh is used to spatially discretize the computational domain, and the total number of meshes is approximately 6.05 million.

[0058] Using the F in the DDES-SA model d function, then there is:

[0059] F GAS = F d

[0060]

[0061]

[0062] where U ij is the velocity gradient tensor, ν t is the turbulent viscosity given by the v2-f series model, and in this embodiment, it is the turbulent viscosity given by the standard v2-f model; ν is the viscosity coefficient of the fluid, d is the distance from the local mesh to the wall, κ is the von Kármán constant, and its value is 0.41; C d1 , C d2 are empirical coefficients, taking 20 and 3 respectively.

[0063] Step 2: Identify the shear layer adaptive length scale;

[0064] In this step, the shielding function F in Step 1 is used GAS to determine the local mesh length scale Δ * ; the local mesh length scale Δ * is given by the following formula:

[0065] Δ * = C GAS [(1 - F GAS )Δ SLA + F GAS Δ max

[0066]

[0067] Δ max = max(Δ x , Δ y , Δ z )

[0068]

[0069] where C GAS is an empirical coefficient, taking 0.6; Δ x is the length of the local hexahedral mesh, Δ y is the width of the local hexahedral mesh, Δ z ​is the height of the local hexahedral mesh; is the distance from the cell center to the i-th vertex, is the unit normal vector of the vorticity vector, is the position vector of the cell vertex, is the position vector of the cell center;

[0070] takes values according to the following formula:

[0071]

[0072] where, is the strain rate tensor, is the vorticity vector, ω 2 is the square of the vorticity vector; θ takes 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 v2-f series model, which is the turbulent viscosity given by the standard v2-f model in this embodiment; v t∞ is the far-field turbulent viscosity given by the v2-f series model, which is the far-field turbulent viscosity given by the standard v2-f model in this embodiment;

[0073] The value range of the above VTM function is between 0 and 1. In the quasi-two-dimensional region at the initial stage of separation, the vorticity vector is also the eigenvector of the strain rate tensor At this time, the value of the VTM function tends to 0; in fully developed three-dimensional turbulence, the direction of the vorticity vector and the eigenvector of the strain rate tensor have a weak correlation. At this time, the value of the VTM function tends to 1.

[0074] <vtm>is the average value of the local VTM function value and the VTM function values of adjacent grids, F KH is based on <vtm>Two-segment linear function of the value. When <vtm>When it is less than a certain threshold, the VTM function value is small. When <vtm>As the value of the VTM function increases gradually, it rapidly increases to 1, thereby reducing the mesh size in the early stages of separation. Using the subgrid stress model, it can be seen that when the value of the VTM function increases to 1, the turbulent viscosity coefficient also decreases as expected.

[0075] Step 3: construct a scale-dependent adjustment function based on the turbulence energy spectrum integral;

[0076] In this step, 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 In this embodiment, according to the modeling method of turbulent kinetic energy in the standard v2-f model, the original modeled turbulent kinetic energy k is obtained. m .

[0077] 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 The actual modeled turbulent kinetic energy k u It is obtained from the following formula:

[0078]

[0079] 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 To solve the turbulent cutoff wave number, the local grid length scale Δ * Decide:

[0080]

[0081] Where π is the ratio of circumference to circle, which is 3.14;

[0082] According to the actual 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-related adjustment function D f ,like Figure 2 shown.

[0083] The scale ratio is defined 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 scale ratio, which is obtained from the following formula:

[0084]

[0085] l GAS =(1 - F GAS )l u +F GAS l m

[0086]

[0087] wherein, l u is the grid-related scale, l m is the turbulence length scale given by the v2-f series model. In this embodiment, l m is the turbulence length scale given by the standard v2-f model and is obtained from the following formula:

[0088]

[0089] wherein, ε m is the original modeled dissipation rate given by the standard v2-f model, ν is the viscosity coefficient of the fluid, C L and C η are constant coefficients in the standard v2-f model. C L takes 0.25, and C η takes 85.

[0090] Step Four, use the adjustment function to reconstruct the turbulence viscosity of the v2-f series model;

[0091] In this step, the dynamic scale-related adjustment function D<s f is adopted to regulate the turbulence viscosity ν t in the v2-f series model to obtain the reconstructed turbulence viscosity ν sfs , which is obtained from the following formula:

[0092] ν sfs = D f ·ν t

[0093] In this embodiment, taking the standard v2-f model as an example, the turbulence viscosity ν t in the standard v2-f model is regulated to obtain the reconstructed turbulence viscosity ν sfs as follows:

[0094]

[0095] wherein, T is the turbulence time scale in the standard v2-f model, and its expression is;

[0096]

[0097] C μ and C T are constant coefficients in the standard v2-f model, C μ Take 0.22, C T Take 6.

[0098] Step 5, perform turbulence simulation using the reconstructed turbulent viscosity;

[0099] In this step, adopt the turbulent viscosity ν reconstructed in Step 4 sfs to calculate the Reynolds stress and update the transport equation of the v2-f series model. In this embodiment, taking the standard v2-f model in the v2-f series model as an example, adopt the turbulent viscosity ν reconstructed in Step 4 sfs to replace the turbulent viscosity ν in the standard v2-f model t , and the new obtained transport equation is shown as follows:

[0100]

[0101] Combine the obtained new transport equation with the standard v2-f model to obtain a strong shear turbulence grid adaptive simulation method for the coupled v2-f series model, and use it for the numerical simulation of the round pipe jet example.

[0102] Adopt the fully implicit coupled solution technique for transient calculation, and the time step satisfies the CFL condition in engineering computational fluid dynamics. At the same time, select the standard v2-f model in the v2-f series model to perform numerical simulation on the round pipe jet example of the embodiment of the present invention, and compare it with the numerical simulation results of a strong shear turbulence grid adaptive simulation method for the coupled v2-f series model of the present invention.

[0103] Figure 3 Figure is the turbulent vortex structure diagram of the round pipe jet example calculated by using the standard v2-f model in the v2-f series model, and is colored by the turbulent viscosity ratio.

[0104] Figure 4 Figure is the turbulent vortex structure diagram of the round pipe jet example calculated by using a strong shear turbulence grid adaptive simulation method for the coupled v2-f series model of the present invention, and is colored by the turbulent viscosity ratio.

[0105] Figure 3 , Figure 4 The comparative analysis shows that the analytical ability of the turbulent vortex structure obtained by calculating with a strong shear turbulence grid adaptive simulation method for the coupled v2-f series model proposed by the present invention is stronger than that of the vortex structure calculated by the standard v2-f model, and can capture more abundant turbulent structures under the same number of grids, and can provide more accurate flow field details.

[0106] The above are only the preferred embodiments of the present invention patent and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

[0107] In summary, a strong shear turbulence grid adaptive simulation method coupling the v2-f series model proposed by the present invention identifies the local shear layer to adaptively sub-grid length scale, improves the identification of the local grid length scale Δ * , and further reconstructs the turbulent viscosity by constructing a scale-related function through the integral of the turbulent energy spectrum to achieve a more efficient grid adaptive simulation. It not only significantly reduces the computational cost and significantly speeds up the turbulent simulation process, but also constructs a grid length scale more suitable for strong shear layers, providing an efficient and low-cost numerical simulation method for high-precision simulation of strong shear flows in complex engineering flow problems.< / vtm> < / vtm> < / vtm> < / vtm> < / vtm> < / vtm>

Claims

1. A grid adaptive simulation method for strongly sheared turbulence coupling the v2-f series models, characterized in that, It includes the following steps: Step 1: Determine whether to apply a shielding function; Step 2: Identify the adaptive length scale of the shear layer; Step 3: Construct a scale-dependent adjustment function based on the integral of the turbulent energy spectrum; Step 4: Use the adjustment function to reconstruct the turbulent viscosity of the v2-f series model; Step 5: Perform turbulent simulation using the reconstructed turbulent viscosity; ① The determination of whether to apply a shielding function in Step 1 includes: Determine whether to use the shielding function F in combination with the type of simulated flow state GAS , specifically, when the type of flow state is free shear flow, the shielding function is not used, and at this time the shielding function F GAS = 0; when the type of flow state is near-wall flow, the shielding function is used, and the shielding function F GAS Optionally use the F1 shielding function, F2 shielding function from the DDES-SST model and the F d shielding function from the DDES-SA model; ② The identification of the adaptive length scale of the shear layer in Step 2 includes: Adopt the shielding function F described in step one GAS , and determine the local grid length scale Δ * ; the local grid length scale Δ * is given by the following formula: Δ * = C GAS [(1 - F GAS )Δ SLA + F GAS Δ max ​ Δ max = max(Δ x , Δ y , Δ z ) Among them, C GAS is the empirical coefficient, taking 0.6; Δ x is the length of the local hexahedral mesh, Δ y is the width of the local hexahedral mesh, Δ z is the height of the local hexahedral mesh; is the distance from the cell center to the i-th vertex, is the unit normal vector of the vorticity vector, is the position vector of the cell vertex, is the position vector of the cell center; Take values according to the following formula: wherein, is the strain rate tensor, is the vorticity vector, ω 2 is the square of the vorticity vector; θ takes 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 v2-f series model, v t∞ is the far-field turbulent viscosity given by the v2-f series model; <vtm>is the average value of the local VTM function value and the VTM function values of adjacent grids, F KH is based on the said <vtm>A two-segment linear function of the value;< / vtm> < / vtm> ③ The construction of a scale-dependent adjustment function based on the integral of the turbulent energy spectrum in Step 3 includes: According to the modeling method of turbulent kinetic energy in the v2-f series model, the originally modeled turbulent kinetic energy k is obtained m , according to the local grid length scale Δ described in step 2 * , the actually modeled turbulent kinetic energy k is obtained by integration based on the turbulent energy spectrum u ; the actually modeled turbulent kinetic energy k u is obtained by the following formula: Among them, E(κ) is the Kolmogorov turbulence energy spectrum, κ is the turbulence wave number, and C k is the Kolmogorov constant coefficient, taking 1.5, ε is the actual turbulence dissipation rate, and κ c is the resolvable turbulence cutoff wave number, which is determined by the local grid length scale Δ * described in Step 2: where π is the ratio of a circle's circumference to its diameter, taking 3.14; According to the actual turbulent kinetic energy k to be modeled u , the original modeled turbulent kinetic energy k m and the shielding function F described in step one GAS , construct a dynamic scale-dependent adjustment function D f ; define the scale ratio as the ratio of the actual turbulent kinetic energy k to be modeled u and the original modeled turbulent kinetic energy k m , and the dynamic scale-dependent adjustment function D f is a function related to the scale ratio and is obtained by the following formula: l GAS = (1 - F GAS )l u + F GAS l m where, l u is the grid-related scale, and l m is the turbulent length scale given by the v2-f series model; ④ The reconstruction of the turbulent viscosity of the v2-f series model using the adjustment function in Step 4 includes: Adopt the dynamic scale-related adjustment function D described in Step 3 f for the turbulent viscosity ν in the v2-f series model t to perform regulation and obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula: ν sfs = D f · ν t ⑤ The performance of turbulent simulation using the reconstructed turbulent viscosity in Step 5 includes: Adopt 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; adopt the reconstructed turbulent viscosity ν described in Step 4 sfs Replace the turbulent viscosity ν in the v2-f series model t , and combine it with the v2-f series model to obtain the strong shear turbulent grid adaptive simulation method of the coupled v2-f series model

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