Adaptive turbulence simulation method for high Reynolds number and highly separated turbulent flows

Abstract

The invention discloses an adaptive turbulence simulation method suitable for high Reynolds number large separation turbulent flow, and the steps are as follows: defining a resolution control function; calculating a filter scale coefficient in the resolution control function by applying a turbulence coherent structure parameter, thereby obtaining a filter scale, and further calculating the size of the resolution control function; as the computational grid scale changes, the resolution control function is adaptively adjusted to achieve an adaptive transition among an unsteady RANS mode, a LES mode and a DNS mode; based on the resolution control function, the turbulent viscosity coefficient in a turbulence model is modified to complete an adaptive turbulence simulation; the invention proposes to use a coherent structure function to calculate the filter scale coefficient in the resolution control function, which can more accurately reflect the characteristics of high Reynolds number large separation flow, and overcome the problem of limited accuracy of turbulence simulation when the filter scale coefficient is a constant in previous calculations.

Description

Technical Field

[0001] The invention belongs to the field of aerospace science and technology, and in particular relates to an adaptive turbulence simulation method suitable for high Reynolds number large separation turbulent flow. Background Art

[0002] In the field of aerospace, the Reynolds number of fluid flow is very high, and the flow presents a typical turbulent flow pattern. One of the important flow forms is the flow of fluid over solid obstacles, which is also the phenomenon of blunt body flow. Blunt body flow is widely present in the field of aerospace, such as aircraft engine combustion chambers, turbines, aircraft outflow, etc. A lot of research has been done on blunt body flow in some classic basic research, such as fluid flow over cylinders, square cylinders, spheres, etc. Blunt body flow at high Reynolds numbers will show typical Karman vortex street phenomenon and large flow separation, thus presenting complex unsteady turbulent pulsation. High-precision numerical prediction of large separation turbulence has always been a hot research issue and also a difficult point in research.

[0003] There are usually two types of flow separation around blunt bodies at high Reynolds numbers: the first is caused by a sudden change in the sharp geometric shape of the solid obstacle. In this case, the separation point of the fluid is fixed on the geometric shape of the solid; the second is that the geometric shape of the solid obstacle is smooth, and the separation point of the fluid keeps changing on the smooth solid surface during the flow, so there is no fixed fluid separation point. Flow around a cylinder is a typical example of the second type of flow separation. Since the separation point is not fixed, it is difficult to accurately predict it in numerical simulation, and it is a hot topic of research. Experimental studies on flow around a cylinder have found that the flow separation phenomena under different Reynolds numbers vary greatly, showing complex flow physics mechanisms. One of the complex phenomena is the "drag crisis" phenomenon, which is the phenomenon of flow around a cylinder at a Reynolds number of 10 5 When the Reynolds number increases to 10 6 When the drag coefficient drops sharply to about 0.2-0.4, the drag coefficient decreases sharply. Such a large change in the drag coefficient has a great impact on engineering applications. In order to accurately predict this phenomenon, high requirements are placed on the turbulence model in numerical simulation. Usually, some turbulence models can only accurately predict the Reynolds number of 10 5 The drag coefficient is 10 6 When the drag coefficient is one, it is impossible to simultaneously 5 and 10 6 The drag coefficient is accurately predicted for both cases simultaneously.

[0004] The numerical simulation methods of large separation turbulence represented by the flow around a cylinder mainly include three categories: direct numerical simulation method DNS, large eddy simulation method LES and Reynolds average method RANS. The direct numerical simulation method DNS cannot be used for simulation under high Reynolds number conditions due to its large amount of calculation; the Reynolds average method RANS averages the turbulent pulsations of all scales, with high calculation efficiency, but the calculation accuracy of the unsteady process caused by the separation flow is poor, and the deviation from the experimental results is large; the large eddy simulation method LES solves the large-scale turbulent structure and models the evolution of small-scale turbulence, with high calculation accuracy, but under high Reynolds number conditions, the calculation amount of LES is still very large. In order to accurately predict the "drag crisis" phenomenon of the flow around a cylinder, hundreds of millions of calculation grids are used in the literature published abroad. Therefore, it is difficult to meet the needs of engineering applications; based on this, under the current affordable computing resource supply, it is necessary to develop high-precision turbulence simulation methods, so as to accurately predict the high Reynolds number large separation turbulent flow represented by the flow around a cylinder, and provide calculation methods and design tools for a wide range of engineering application needs. Summary of the invention

[0005] In view of the above-mentioned deficiencies of the prior art, the object of the present invention is to provide an adaptive turbulence simulation method suitable for high Reynolds number large separation turbulent flow, so as to solve the problem of high computational cost required for accurate simulation in the existing turbulence simulation technology; the method of the present invention can simulate the flow around a high Reynolds number cylinder (Re=10 5 -10 6 ) Accurately simulate the resistance crisis phenomenon.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] The present invention provides an adaptive turbulence simulation method suitable for high Reynolds number large separation turbulent flow, the steps of which are as follows:

[0008] 1) Define the resolution control function;

[0009] 2) calculating the filter scale coefficient in the resolution control function in step 1) by using the turbulence coherent structure parameters, thereby obtaining the filter scale, and further calculating the size of the resolution control function;

[0010] 3) As the computational grid scale changes, the resolution control function in step 1) is adaptively adjusted to achieve adaptive transition among the unsteady RANS mode, the LES mode and the DNS mode;

[0011] 4) Based on the resolution control function, the turbulent viscosity coefficient μ in the Baseline k~ω turbulence model is t Modifications were made to complete adaptive turbulence simulation;

[0012] The filter scale coefficient C in step 2) x The expression is:

[0013] C x =max(C0(|F cs | 3 / 2 (1-F cs )) 1 / 2 ,C lim )

[0014] Among them, max(a,b) is the maximum value function; C0=2.0 and C lim =0.1, both are model constants; F cs is the coherent structure function,

[0015] Its expression is:

[0016]

[0017] Among them, u i ,u j They represent the velocity components in the x, y, and z directions respectively. i ,x j They represent the coordinates in the three directions of x, y, and z respectively, i, j = 1, 2, 3.

[0018] Furthermore, the step 1) resolution control function F r The expression is:

[0019]

[0020] in, is the minimum function, exp(d) = e d is a natural exponential function, n = 2 and β = 0.002 are model constants, L i , L c and L k are the integral length scale, the filtering scale and the Kolmogorov length scale, respectively, and their expressions are:

[0021] L c =C x (Δ x Δ y Δ z ) 1 / 3

[0022] L i =k 3 / 2 / (β * kω)

[0023] L k =v3 / 4 / (β * kω) 1 / 4

[0024] Among them, Δ x ,Δ y ,Δ z are the scales of the grid in the x, y, and z directions, k is the turbulent kinetic energy, ω is the turbulent specific dissipation rate, ν is the molecular motion viscosity coefficient, β * =0.09 is the model constant.

[0025] Furthermore, the adaptive transition of the solution mode in step 3) is specifically as follows: when the resolution control function F r When the size of approaches 1, the unsteady RANS mode dominates, and most of the turbulence is simulated by the Baseline k~ω turbulence model; when the resolution control function F r As the grid size decreases, the proportion of the unsteady RANS mode gradually decreases, and the proportion of the DNS mode gradually increases. At this time, it returns to the LES mode, the proportion of turbulence simulated by the Baseline k~ω turbulence model decreases, and the proportion of direct solution increases. When the resolution control function F r When it approaches 0, the DNS mode becomes dominant and all turbulence is directly solved.

[0026] Furthermore, the turbulent viscosity coefficient μ in the Baseline k~ω turbulence model in step 4) is t The expression is:

[0027] μ t =ρk / ω

[0028] Where ρ is the fluid density, k is the turbulent kinetic energy, and ω is the turbulent specific dissipation rate;

[0029] The turbulent viscosity coefficient μ in the Baseline k~ω turbulence model t After modification, the modified turbulent viscosity coefficient μ t * The expression is:

[0030] μ t * =F r ρk / ω

[0031] Among them, F r is the resolution control function, ρ is the fluid density, k is the turbulent kinetic energy, and ω is the turbulent specific dissipation rate;

[0032] Using the modified turbulent viscosity coefficient μ t * Numerical simulation of high Reynolds number and highly separated turbulent flows.

[0033] Beneficial effects of the present invention:

[0034] In the turbulence simulation method of the present invention, it is proposed to use the coherent structure function to calculate the filter scale coefficient in the resolution control function, which can more accurately reflect the characteristics of high Reynolds number large separation flow, overcome the problem of limited accuracy of turbulence simulation when the filter scale coefficient is a constant in previous calculations, and has more accurate characteristics in high Reynolds number large separation flow; at the same time, under the action of the resolution control function, the turbulence solution mode performs adaptive transition, which can ensure the calculation accuracy and effectively reduce the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The figure is a flow chart of the adaptive turbulence simulation method of the present invention.

[0036] Figure 2 This is a comparison chart of the calculated and experimental results of the drag coefficient and Reynolds number of the flow around a cylinder.

[0037] Figure 3 Reynolds number Re=10 predicted for adaptive turbulence simulation 5 Schematic diagram of the turbulent flow structure around a cylinder under working conditions.

[0038] Figure 4 Reynolds number Re=10 predicted for adaptive turbulence simulation 6 Schematic diagram of the turbulent flow structure around a cylinder under working conditions. DETAILED DESCRIPTION

[0039] In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

[0040] Reference Figure 1 As shown, an adaptive turbulence simulation method suitable for high Reynolds number and large separation turbulent flow of the present invention comprises the following steps:

[0041] 1) Define the resolution control function F r ;

[0042] Wherein, the step 1) resolution control function F r The expression is:

[0043]

[0044] in, is the minimum function, exp(d) = e d is a natural exponential function, n = 2 and β = 0.002 are model constants, L i , L c and Lk are the integral length scale, the filtering scale and the Kolmogorov length scale, respectively, and their expressions are:

[0045] L c =C x (Δ x Δ y Δ z ) 1 / 3

[0046] L i =k 3 / 2 / (β * kω)

[0047] L k =v 3 / 4 / (β * kω) 1 / 4

[0048] Among them, Δ x ,Δ y ,Δ z are the scales of the grid in the x, y, and z directions, k is the turbulent kinetic energy, ω is the turbulent specific dissipation rate, ν is the molecular motion viscosity coefficient, β * =0.09 is the model constant, C x is the filter scale coefficient.

[0049] 2) Calculating the filter scale coefficient C in the resolution control function in step 1) by using the turbulence coherent structure parameters x , thereby obtaining the filtering scale and further calculating the resolution control function size;

[0050] The filter scale coefficient C x The expression is:

[0051] C x =max(C0(|F cs | 3 / 2 (1-F cs )) 1 / 2 ,C lim )

[0052] Among them, max(a,b) is the maximum value function; C0=2.0 and C lim =0.1, both are model constants; F cs is the coherent structure function, and its expression is:

[0053]

[0054] Among them, u i ,u j They represent the velocity components in the x, y, and z directions respectively.i ,x j They represent the coordinates in the three directions of x, y, and z respectively, i, j = 1, 2, 3.

[0055] 3) As the computational grid scale changes, the resolution control function in step 1) is adaptively adjusted to achieve adaptive transition between the unsteady RANS mode, the LES mode, and the DNS mode (avoiding the delay caused by switching between different modes);

[0056] The adaptive transition of the solution mode is as follows: when the resolution control function F r When the size of approaches 1, the unsteady RANS mode dominates, and most of the turbulence is simulated by the Baseline k~ω turbulence model; when the resolution control function F r As the grid size decreases, the proportion of the unsteady RANS mode gradually decreases, and the proportion of the DNS mode gradually increases. At this time, it returns to the LES mode, the proportion of turbulence simulated by the Baseline k~ω turbulence model decreases, and the proportion of direct solution increases. When the resolution control function F r When it approaches 0, the DNS mode becomes dominant and all turbulence is solved directly. By adaptively adjusting the proportion between model simulation and direct solution through the grid scale, the separation process of the flow can be accurately simulated without increasing the amount of calculation.

[0057] 4) Based on the resolution control function F r , the turbulent viscosity coefficient μ in the Baseline (BSL) k~ω turbulence model t Modifications were made to complete adaptive turbulence simulation;

[0058] Turbulent viscosity coefficient μ in the baseline k~ω turbulence model t The expression is:

[0059] μ t =ρk / ω

[0060] Where ρ is the fluid density, k is the turbulent kinetic energy, and ω is the turbulent specific dissipation rate;

[0061] The turbulent viscosity coefficient μ in the Baseline k~ω turbulence model t After modification, the modified turbulent viscosity coefficient μ t * The expression is:

[0062] μ t * =F r ρk / ω

[0063] Among them, Fr is the resolution control function, ρ is the fluid density, k is the turbulent kinetic energy, and ω is the turbulent specific dissipation rate;

[0064] Using the modified turbulent viscosity coefficient μ t * Numerical simulation of high Reynolds number and highly separated turbulent flows.

[0065] Embodiment 1:

[0066] For the flow around the cylinder, a three-dimensional calculation area is set and a structured calculation grid is divided. The total number of grids is about 2.2 million. The calculation parameters are set, the incoming gas is air, and the Reynolds number is Re=10 5 and Re = 10 6 ; The inlet is a uniform flow, and the outlet is a pressure outlet; the cylindrical surface is set as a solid wall with no slip boundary conditions.

[0067] After the above steps 1) to 4), the turbulent viscosity coefficient μ modified by the resolution control function is obtained. t * , calculated in computational fluid dynamics software, and finally obtained the following results:

[0068] Figure 2 The horizontal axis is the incoming flow Reynolds number Re, and the vertical axis is the calculated cylinder flow resistance coefficient C D , when the Reynolds number increases from Re=10 5 Increase to Re = 10 5 When the load is high, the drag coefficient drops rapidly, which is called "drag crisis phenomenon". The results of the present invention can simulate this change well.

[0069] Figure 3 and Figure 4 The paper demonstrates the use of the above method to simulate the large separation flow field structure appearing at the tail of a cylinder.

[0070] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principle of the present invention. These improvements should also be regarded as the protection scope of the present invention.

Claims

1. An adaptive turbulence simulation method suitable for high Reynolds number and large separation turbulent flow, characterized in that: Here are the steps: 1) Define the resolution control function; 2) calculating the filter scale coefficient in the resolution control function in step 1) by using the turbulence coherent structure parameters, thereby obtaining the filter scale, and further calculating the size of the resolution control function; 3) As the computational grid scale changes, the resolution control function in step 1) is adaptively adjusted to achieve adaptive transition among the unsteady RANS mode, the LES mode and the DNS mode; 4) Based on the resolution control function, the turbulent viscosity coefficient μ in the Baseline k~ω turbulence model is t Modifications were made to complete adaptive turbulence simulation; The filter scale coefficient C in step 2) x The expression is: C x =max(C0(|F cs | 3 / 2 (1-F cs )) 1 / 2 ,C lim ) Among them, max(a,b) is the maximum value function; C0=2.0 and C lim =0.1, both are model constants; F cs is the coherent structure function, and its expression is: Among them, u i ,u j They represent the velocity components in the x, y, and z directions respectively. i ,x j Respectively represent the coordinates in the three directions of x, y, and z, i, j = 1, 2, 3; The step 1) resolution control function F r The expression is: in, is the minimum function, exp(d) = e d is a natural exponential function, n = 2 and β = 0.002 are model constants, L i , L c and L k are the integral length scale, the filtering scale and the Kolmogorov length scale, respectively, and their expressions are: L c =C x (D x D y D z ) 1 / 3 L i =k 3 / 2 / (b * (kω) L k =n 3 / 4 / (b * (kω) 1 / 4 Among them, Δ x ,Δ y ,Δ z are the scales of the grid in the x, y, and z directions, k is the turbulent kinetic energy, ω is the turbulent specific dissipation rate, ν is the molecular motion viscosity coefficient, β * =0.09 is the model constant.

2. The adaptive turbulence simulation method for high Reynolds number and large separation turbulent flow according to claim 1, characterized in that: The adaptive transition of the solution mode in step 3) is specifically: When the resolution control function F r When the size of approaches 1, the unsteady RANS mode dominates, and most of the turbulence is simulated by the Baseline k~ω turbulence model; when the resolution control function F r As the grid size decreases, the proportion of the unsteady RANS mode gradually decreases, and the proportion of the DNS mode gradually increases. At this time, it returns to the LES mode, the proportion of turbulence simulated by the Baseline k~ω turbulence model decreases, and the proportion of direct solution increases. When the resolution control function F r When it approaches 0, the DNS mode becomes dominant and all turbulence is directly solved.

3. The adaptive turbulence simulation method for high Reynolds number and large separation turbulent flow according to claim 1, characterized in that: The turbulent viscosity coefficient μ in the Baseline k~ω turbulence model in step 4) t The expression is: m t =ρk / ω Where ρ is the fluid density, k is the turbulent kinetic energy, and ω is the turbulent specific dissipation rate; The turbulent viscosity coefficient μ in the Baseline k~ω turbulence model t After modification, the modified turbulent viscosity coefficient μ t * The expression is: m t * =F r pk / w Among them, F r is the resolution control function, ρ is the fluid density, k is the turbulent kinetic energy, and ω is the turbulent specific dissipation rate; Using the modified turbulent viscosity coefficient μ t * Numerical simulation of high Reynolds number and highly separated turbulent flows.

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