Strong shear turbulence grid adaptive simulation method coupled with k-epsilon series model

Abstract

The invention discloses a strong shear turbulence grid adaptive simulation method coupled with a k-epsilon 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, reconstructing the turbulence viscosity of the k-epsilon series model by using an adjustment function; 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 coupled with the k-ε series model. Background Art

[0002] Turbulence phenomena widely exist in nature and engineering fields. Among them, strongly sheared flow is a complex type of turbulence that cannot be ignored in many engineering applications. Strongly sheared flow is usually accompanied by extremely large velocity gradients and the interaction between large-scale and small-scale turbulence, 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 design, there is an urgent need to develop a turbulence simulation method that can accurately capture the characteristics of strongly sheared flow, 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 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, which severely restricts 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. Under the existing computing power, the LES method is difficult 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 simulation, 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 published invention patents CN115034162 A and CN 118133701 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] (1) Technical problems to be solved

[0007] The object of the present invention is to propose a grid-adaptive simulation method for strong-shear turbulence coupled with the k-ε 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-accuracy simulation of strong-shear flows in complex engineering flow problems.

[0008] (2) 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 k-ε 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-dependent adjustment function based on the turbulent energy spectrum integral;

[0013] Step 4, reconstruct the turbulent viscosity of the k-ε 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 and 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 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] 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;

[0024] Take values according to the following formula:

[0025]

[0026] 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 k-ε series model, v t∞ is the far-field turbulent viscosity given by the k-ε series model;

[0027] <vtm>is the average of the local VTM function value and the VTM function values of adjacent grids, F KH is based on the aforesaid <vtm>Two-segment linear function of values;

[0028] ③ The scale-dependent adjustment function constructed based on the integral of the turbulent energy spectrum described in step three includes:

[0029] According to the modeling method of the turbulent kinetic energy in the k-ε series model, the originally modeled turbulent kinetic energy k is obtained m , based on the local grid length scale Δ described in step two * , 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:

[0030]

[0031] 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, determined by the local grid length scale Δ described in step two * :

[0032]

[0033] where π is the pi, taking 3.14;

[0034] 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 one 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 , the dynamic scale-dependent adjustment function D f is a function related to the scale ratio, obtained by the following formula:

[0035]

[0036] l GAS = (1 - F GAS )l u + F GAS l m

[0037]

[0038] where l u is the grid-related scale, l m The turbulent length scale given by the k-ε series model is obtained from the following formula:

[0039]

[0040] where ε m is the original modeled dissipation rate given by the k-ε series model;

[0041] ④ The reconstruction of the turbulent viscosity of the k-ε series model using the adjustment function described in Step 4 includes:

[0042] Adopt the dynamically scale-dependent adjustment function D described in Step 3 f to regulate the turbulent viscosity ν in the k-ε series model t to obtain the reconstructed turbulent viscosity ν sfs , which is obtained from the following formula:

[0043] ν sfs = D f ·ν t

[0044] ⑤ The turbulent simulation using the reconstructed turbulent viscosity described in Step 5 includes:

[0045] Adopt the reconstructed turbulent viscosity ν described in Step 4 sfs to calculate the Reynolds stress and update the transport equation of the k-ε series model; adopt the reconstructed turbulent viscosity ν described in Step 4 sfs to replace the turbulent viscosity ν in the k-ε series model t , and combine it with the k-ε series model to obtain the strong-shear turbulent grid adaptive simulation method of the coupled k-ε series model.

[0046] (III) Beneficial Effects

[0047] A strong-shear turbulent grid adaptive simulation method of a coupled k-ε 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, determining the local grid length scale, and then reconstructing the turbulent viscosity through the scale-dependent function constructed by the turbulent energy spectrum integration, grid adaptive simulation is realized, effectively improving the problems of large computational cost and poor accuracy in the shear layer simulation of the RANS-LES hybrid simulation method, and significantly accelerating the turbulent simulation process.

[0048] Compared with the prior arts CN 115034162 A and CN 118133701 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-shear multi-scale complex flow in aeroengines.

[0049] The present invention has the characteristics of simple form and strong portability, can be well combined with various grid-adaptive turbulence simulations, is convenient for implantation into existing CFD codes for application and expansion, has broad academic and engineering application prospects, and provides an effective numerical simulation method for solving the low-cost and high-precision simulation of strong shear flows in complex engineering flow problems. Brief Description of the Drawings

[0050] Figure 1 It is a flow chart of a strong shear turbulence grid-adaptive simulation method coupling the k-ε series model of the present invention;

[0051] Figure 2 It is the D f distribution cloud map based on the shear layer adaptive sub-grid length scale when a strong shear turbulence grid-adaptive simulation method coupling the k-ε series model of the present invention is applied to a specific example of a round pipe jet;

[0052] Figure 3 It is a turbulent vortex structure diagram of a round pipe jet example calculated by using the original standard k-ε model;

[0053] Figure 4 It is a turbulent vortex structure diagram of a round pipe jet example calculated by using a strong shear turbulence grid-adaptive simulation method coupling the k-ε series model of the present invention. Detailed Description of the Invention

[0054] The following combines the drawings and embodiments, taking the standard k-ε model in the k-ε series model as an example, and taking the round pipe jet flow as a calculation example, to further elaborate in detail on the specific implementation manner of the present invention. The following embodiments are only used to illustrate the present invention, but not to limit the scope of the present invention.

[0055] The present invention provides a strong shear turbulence grid-adaptive simulation method coupling the k-ε series model, including the following steps:

[0056] Step 1, determine whether to apply a shielding function;

[0057] In this step, in combination with the type of flow state to be 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 F GAS = 0; when the type of flow state is wall-adjacent flow, the shielding function is adopted, 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.

[0058] 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.

[0059] Using the F d function from the DDES-SA model, we have:

[0060] F GAS = F d

[0061]

[0062] where U ij is the velocity gradient tensor, ν t is the turbulent viscosity given by the standard k-ε 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 with a value of 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 masking function F GAS from Step 1 is used 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 unit vertex, is the position vector of the unit 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 said 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 k-ε series model, and in this embodiment, it is the turbulent viscosity given by the standard k-ε model; v t∞ is the far-field turbulent viscosity given by the k-ε series model, and in this embodiment, it is the far-field turbulent viscosity given by the standard k-ε model.

[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 , and at this time, the VTM function value tends to 0; in the fully developed three-dimensional turbulence, the direction of the vorticity vector has a weak correlation with the eigenvector of the strain rate tensor , and at this time, the VTM function value 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 the said <vtm>Two-segment linear function of the value. When <vtm>When the value is less than a certain threshold, the VTM function value is small. When <vtm>As the value gradually increases, the VTM function value rapidly increases to 1, thereby reducing the grid scale at the initial stage of separation. According to the sub-grid stress model, when the VTM function value increases to 1, the turbulent kinematic viscosity coefficient also decreases as expected.

[0075] Step 3: Construct a scale-dependent adjustment function based on the integral of the turbulent energy spectrum;

[0076] In this step, according to the way of modeling the turbulent kinetic energy in the k-ε series model, the originally modeled turbulent kinetic energy k m is obtained. In this embodiment, according to the way of modeling the turbulent kinetic energy in the standard k-ε model, the originally modeled turbulent kinetic energy k m is obtained.

[0077] According to the local grid length scale Δ * in Step 2, the actually modeled turbulent kinetic energy k u is obtained by integrating based on the turbulent energy spectrum; the actually modeled turbulent kinetic energy k u is obtained by the following formula:

[0078]

[0079] 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 * in Step 2:

[0080]

[0081] where π is the pi, taking 3.14;

[0082] According to the actually modeled turbulent kinetic energy k u , the originally modeled turbulent kinetic energy k m and the shielding function F GAS in Step 1, construct a dynamic scale-dependent adjustment function D f , as shown in Figure 2 .

[0083] Define the scale ratio as the ratio of the actually modeled turbulent kinetic energy k u to the originally modeled turbulent kinetic energy k m . The dynamic scale-dependent adjustment function D f is a function related to the scale ratio and is obtained by the following formula:

[0084]

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

[0086]

[0087] where l u is the grid-related scale, and l m is the turbulence length scale given by the k-ε series of models, which is obtained from the following formula:

[0088]

[0089] where ε m is the dissipation rate of the original modeling given by the k-ε series of models.

[0090] Step 4: Reconstruct the turbulent viscosity of the k-ε series of models using a tuning function;

[0091] In this step, the dynamic scale-related tuning function D f is adopted to regulate the turbulent viscosity ν t in the k-ε series of models, and the reconstructed turbulent viscosity ν sfs is obtained from the following formula:

[0092] ν sfs = D f ·ν t

[0093] In this embodiment, taking the standard k-ε turbulence model in the k-ε series of models as an example, the turbulent viscosity ν t in the standard k-ε turbulence model is regulated, and the reconstructed turbulent viscosity ν sfs is as follows:

[0094]

[0095] where C μ is a constant coefficient in the standard k-ε model, taking 0.09.

[0096] Step 5: Perform turbulent simulation using the reconstructed turbulent viscosity;

[0097] In this step, the reconstructed turbulent viscosity ν sfs in Step 4 is adopted to calculate the Reynolds stress and update the transport equation of the k-ε series of models. In this embodiment, taking the standard k-ε model in the k-ε series of models as an example, the reconstructed turbulent viscosity ν sfs in Step 4 is used to replace the turbulent viscosity ν t in the standard k-ε model, and the new transport equation obtained is as follows:

[0098]

[0099] Among them, the model coefficient C 1ε is 1.44, and C 2ε is 1.92.

[0100] The obtained new transport equation is combined with the standard k-ε model to obtain a strongly sheared turbulent grid adaptive simulation method for the coupled k-ε series model, and it is used for the numerical simulation of the circular pipe jet example.

[0101] The full implicit coupling solution technique is adopted for transient calculation, and the time step satisfies the CFL condition in engineering computational fluid dynamics. At the same time, the standard k-ε model in the k-ε series model is selected to conduct numerical simulation on the circular pipe jet example of the embodiment of the present invention, and the numerical simulation results are compared with those of the strongly sheared turbulent grid adaptive simulation method of the coupled k-ε series model of the present invention.

[0102] Figure 3 It is the turbulent vorticity structure diagram of the circular pipe jet example calculated by using the original standard k-ε model in the k-ε series model, and the turbulent viscosity ratio is used for coloring.

[0103] Figure 4 It is the turbulent vorticity structure diagram of the circular pipe jet example calculated by using a strongly sheared turbulent grid adaptive simulation method of a coupled k-ε series model of the present invention, and the turbulent viscosity ratio is used for coloring.

[0104] Figure 3 , Figure 4 The comparative analysis shows that the analytical ability of the turbulent vorticity structure obtained by using the strongly sheared turbulent grid adaptive simulation method of a coupled k-ε series model proposed by the present invention is stronger than that of the vorticity structure calculated by the standard k-ε model. It can capture richer turbulent structures under the same number of grids and can provide more accurate flow field details.

[0105] The above are only the preferred embodiments of the patent of the present invention, and they are not used to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0106] In summary, for the strongly sheared turbulent grid adaptive simulation method of a coupled k-ε series model proposed by the present invention, by identifying the local shear layer to adaptively sub-grid length scale, the local grid length scale Δ is improved * Recognition is further carried out by constructing a scale-dependent function through the integral of the turbulent energy spectrum to reconstruct the turbulent viscosity, realizing a more efficient grid adaptive simulation. This not only greatly 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 the 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 k-ε series model, 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 k-ε series model; Step 5: Perform turbulent simulation using the reconstructed turbulent viscosity; ① The determination of whether to apply a shielding function described 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 Selectively 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 described 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: 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 k-ε series model, v t∞ is the far-field turbulent viscosity given by the k-ε 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 described in Step 3 includes: According to the modeling method of the turbulent kinetic energy in the k-ε 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: where \(E(\kappa)\) is the Kolmogorov turbulence energy spectrum, \(\kappa\) is the turbulence wave number, \(C\) k is the Kolmogorov constant coefficient, taking 1.5, \(\varepsilon\) is the actual turbulence dissipation rate, \(\kappa\) c is the resolvable turbulence cut-off wave number, determined by the local grid length scale \(\Delta\) described in step two * as follows: where π is the pi, 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 turbulence length scale given by the k-ε series model, which is obtained from the following formula: where ε m is the original modeled dissipation rate given by the k-ε series of models; ④ The reconstruction of the turbulent viscosity of the k-ε series model using the adjustment function described in Step 4 includes: Adopt the dynamic scale-related adjustment function D described in Step 3 f For the turbulent viscosity ν in the k-ε series model t Perform regulation to 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 described in Step 5 includes: Adopt the reconstructed turbulent viscosity ν described in step four sfs Calculate the Reynolds stress and update the transport equation of the k-ε series model; adopt the reconstructed turbulent viscosity ν described in step four sfs Replace the turbulent viscosity ν in the k-ε series model t , and combine it with the k-ε series model to obtain the strong shear turbulent grid adaptive simulation method of the coupled k-ε series model

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