Separated Corrected Four-Equation Time-Scale Turbulence Model Method for Flow Around Iced Wing

Abstract

The present invention relates to a method for a separated and corrected four-equation time-scale turbulence model for flow around an iced wing. The method comprises: constructing a four-equation turbulence model with a time scale, wherein the four-equation turbulence model is based on three Reynolds normal stress transport equations and one turbulence time-scale equation; constructing Reynolds shear stress from an algebraic relationship to obtain its general form; introducing a separated correction function into the four-equation turbulence model to obtain a separated and corrected four-equation time-scale turbulence model; constructing flow field grid data for the flow around an iced wing to be simulated, setting flow field boundary conditions and flow field initial conditions for the flow around the iced wing to be simulated, and numerically solving the separated and corrected four-equation time-scale turbulence model based on the flow field grid data to obtain numerical simulation results of the flow around an iced wing. The method has the advantages of a small number of equations, high computational efficiency, and no non-physical backflow at re-addition points.

Description

Technical Field

[0001] The present invention relates to the field of computational fluid dynamics, and in particular to a method for separating and correcting a four-equation time-scale turbulence model for flow around an icing wing. Background Art

[0002] Ice on the lifting area of an aircraft will destroy its original streamlined shape and seriously affect the operation of the aircraft, such as reducing lift, increasing drag, and nonlinear changes in pitch moment. The shapes of ice accumulation on wings are generally divided into rough ice, stream ice, angular ice, and spanwise ridged ice. Except for rough ice, the other three types are mainly two-dimensional flow structures. Taking the flow around the angular ice airfoil as an example, in the recirculation area, due to the influence of the adverse pressure gradient, the non-equilibrium characteristics of turbulence are very prominent, which brings challenges to computational fluid dynamics (CFD) simulation.

[0003] In principle, scale-resolved methods like large eddy simulation (LES) and hybrid RANS / LES should produce accurate results. In recent years, researchers have done a lot of work in this area. They applied the dynamic hybrid RANS / LES method to the simulation of the GLC305 corner ice airfoil and analyzed the two length scales ( and ) In the context of IDDES predictions and the performance of flows around airfoils with angular or ridged ice accumulation, the wall-adapted LES method was used to simulate flows around five NACA 23012 iced airfoils. However, all of these works require time-accurate three-dimensional (3-D) computations, which are relatively expensive. To strike a balance between accuracy and computational cost, improvements to RANS methods are still needed, especially when dealing with streamwise ice, angular ice, or spanwise ridged ice.

[0004] Reynolds stress models (RSMs) are considered the most advanced RANS turbulence models. They directly solve for Reynolds stresses, thereby eliminating the weaknesses of eddy viscosity models (EVMs) such as the Spalart-Allmaras (SA) model and the shear stress transport (SST) model. For example, RSMs demonstrate promising performance in wingtip vortex flows, wing-body junction flows, and square duct corner flows. However, some undesirable characteristics are still observed in separated flows caused by adverse pressure gradients. Therefore, a new Reynolds stress model is urgently needed for the numerical calculation of flows around icing wings. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for separating and correcting a four-equation time-scale turbulence model for the flow around an iced wing.

[0006] To achieve the above-mentioned object, the present invention provides a method for separating and correcting a four-equation time-scale turbulence model for the flow around an iced wing, comprising the following steps:

[0007] S1. Construct a four-equation turbulence model that introduces a time scale, wherein the four-equation turbulence model is based on three Reynolds normal stress transport equations and one turbulence time scale equation, and is expressed as:

[0008]

[0009]

[0010]

[0011]

[0012] in, is the time-averaged density, For time, 、 、 are the Reynolds normal stresses in three directions, 、 are the three-directional velocity components, 、 They are the three-direction coordinate components, subscript 、 , is the turbulence time scale, obtained from the turbulence time scale equation, and can be expressed as , is Menter's specific dissipation rate scaling equation, 、 、 are the generating terms of the Reynolds normal stress transport equation in three directions, and 、 、 are the generation of Reynolds normal stress in three directions, 、 、 are the pressure-strain correlation terms of the Reynolds normal stress transport equation in three directions, and 、 、 are the pressure-strain correlation terms excluding density, is the turbulent kinetic energy dissipation rate and is expressed as , is the empirical coefficient of turbulence, is the dynamic viscosity coefficient, is the cross-diffusion coefficient in the Reynolds normal stress equation, is the turbulent kinetic energy and is expressed as , is the diffusion coefficient of the equation for the specific dissipation rate scale, is the turbulent kinetic energy generation term and is expressed as , is the coefficient of the dissipation term of the equation for the specific dissipation rate scale, is the diffusion coefficient of the scaling equation, is the equivalent eddy viscosity coefficient, and , is the coefficient of the cross-derivative term of the equation for the specific dissipation rate scale;

[0013] S2. Construct the Reynolds shear stress from algebraic relations and obtain its general form;

[0014] S3. Introducing a separation correction function into the four-equation turbulence model , to obtain the separated corrected four-equation time-scale turbulence model;

[0015] S4. Construct flow field grid data of the flow around the iced wing to be simulated, set the flow field boundary conditions and flow field initial conditions of the flow around the iced wing to be simulated, and numerically solve the separated corrected four-equation time-scale turbulence model based on the flow field grid data to obtain numerical simulation results of the flow around the iced wing.

[0016] According to one aspect of the present invention, in step S1, in the step of constructing a four-equation turbulence model introducing a time scale, the Reynolds normal stress in three directions is 、 、 are obtained based on the Reynolds normal stress expression, wherein the Reynolds normal stress expression is expressed as:

[0017]

[0018] in, , Reynolds normal stress 、 、 , represents density, represents the first-order derivative of velocity, subscript , ;

[0019] Generated terms of the Reynolds normal stress transport equation in three directions 、 、 Respectively expressed as:

[0020]

[0021] in, Used to refer to the generated terms of the Reynolds normal stress transport equation 、 、 , Used to refer to Reynolds stress, Used to refer to the three-directional velocity components respectively, , subscript Used to indicate incorrect subscript Sum, subscript for ;

[0022] Pressure-strain correlation terms of the Reynolds normal stress transport equation in three directions 、 、 are obtained based on the pressure-strain correlation expression of the Reynolds normal stress transport equation, wherein the pressure-strain correlation expression is expressed as:

[0023]

[0024] in, Used to refer to the pressure-strain correlation terms of the Reynolds normal stress transport equation 、 、 ; 、 、 It is used to refer to the anisotropy tensor in the Reynolds normal stress equation of this model, and its general expression is ; It is used to refer to the strain rate tensor in the Reynolds normal stress equation of this model, and its general expression is ; It refers to the traceless strain rate tensor in the Reynolds normal stress equation of this model, and its general expression is: , and is the strain rate tensor, for the Croneko operator; It is used to refer to the rotation tensor in the Reynolds normal stress equation of this model, and its general expression is: , 、 is the velocity component, 、 is the coordinate component; ; 、 、 、 、 、 、 are pressure-strain correlation coefficients; 、 、 、 , subscript Indicates incorrect subscript Summation.

[0025] According to one aspect of the present invention, the pressure-strain correlation coefficient 、 、 、 、 、 、 are respectively obtained based on a first mixed function expression, wherein the first mixed function expression is expressed as:

[0026]

[0027] in, Used to refer to the pressure-strain correlation coefficients respectively 、 、 、 、 、 、 , is the mixing function in the Menter-SST eddy viscosity model, for Compared with the SSG / LRR model The mode-related part, for and Mode-related parts.

[0028] According to one aspect of the present invention, in the turbulence time scale equation, the diffusion term coefficient of the equation of the specific dissipation rate scale is , the coefficient of the dissipation term of the equation of specific dissipation rate scale , diffusion coefficient of the scaling equation , the cross-derivative coefficient of the equation for the specific dissipation rate scale are respectively obtained based on a second mixed function expression, wherein the second mixed function expression is expressed as:

[0029]

[0030]

[0031] in, Respectively refer to the coefficients 、 、 、 , is the transition function, for Compared with the SSG / LRR model near the wall The mode-related part, for Outside the boundary layer The mode-related part, is the transition function judgment function, is the distance from the iced airfoil wall to the nearest numerical grid point in the flow field, is the viscosity coefficient.

[0032] According to one aspect of the present invention, in step S2, the step of constructing the Reynolds shear stress from an algebraic relationship includes:

[0033] The Reynolds shear stress is calculated using the anisotropic eddy viscosity assumption. and Modeled and expressed as:

[0034]

[0035] in, is the anisotropic eddy viscosity coefficient, is the new specific dissipation rate in the anisotropic eddy viscosity coefficient, is the pressure-strain correlation coefficient Partial correlation coefficient , Characterizes the turbulence balance, that is, the ratio of turbulent kinetic energy generation and dissipation rate, is a constant coefficient and is set to 0.63, is the empirical coefficient of turbulence and is set to 0.09;

[0036] Considering only the pressure-strain relationship on the two-dimensional plane, the Reynolds shear stress constructed by the algebraic relationship is obtained and The general form of is expressed as:

[0037]

[0038]

[0039]

[0040] in, 、 、 represent the anisotropic eddy viscosity coefficients in three directions respectively.

[0041] According to one aspect of the present invention, in step S3, a separation correction function is introduced into the four-equation turbulence model. In the step of Expressed as:

[0042]

[0043] in, is the turbulent kinetic energy generation and dissipation rate ratio, is the Reynolds stress anisotropy tensor invariant.

[0044] According to one aspect of the present invention, in step S3, a separation correction function is introduced into the four-equation turbulence model. In the step of Acting on the coefficient , and obtain the corrected coefficient , to generate the separated modified four-equation time-scale turbulence model.

[0045] According to one aspect of the present invention, in step S4, in the step of setting the flow field boundary conditions and the flow field initial conditions of the flow around the iced wing to be simulated, the flow field involved is a two-dimensional flow field around an iced airfoil or a three-dimensional flow field around an iced wing.

[0046] According to one aspect of the present invention, in step S4, in the step of setting the flow field boundary conditions and the flow field initial conditions of the flow around the iced wing to be simulated, the boundary conditions on the actual wall surface and the far field of the iced wing to be simulated are set and expressed as:

[0047]

[0048] in, For the wall scale, For the far field scale, is the anisotropic eddy viscosity coefficient in the far field, is the time-averaged density, is the turbulent kinetic energy, subscript and Represent the locations at the wall and the far field respectively;

[0049] The initial conditions of the flow field include: free flow Mach number and Reynolds number.

[0050] According to one aspect of the present invention, in step S4, in the step of numerically solving the separation-corrected four-equation time-scale turbulence model based on the flow field grid data, the 12 independent variables included in the separation-corrected four-equation time-scale turbulence model are solved: 、 、 、 、 、 、 、 、 and The numerical solutions of other variables are then derived through the relationship.

[0051] According to one solution of the present invention, the present invention adopts three Reynolds normal stress transport equations and one scaling equation to form a four-equation model, uses algebraic relations to represent the Reynolds shear stress, and introduces separation correction, thereby obtaining a separation-corrected four-equation time-scale turbulence model method.

[0052] According to one solution of the present invention, compared with the traditional seven-equation Reynolds stress model, the present invention has the advantages of fewer equations, lower computational cost, and higher computational efficiency; at the same time, it effectively eliminates the inherent defects of the traditional model and provides an excellent correction solution for the traditional model. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A flowchart of a method for separating and correcting a four-equation time-scale turbulence model for flow around an iced wing according to an embodiment of the present invention;

[0054] Figure 2 This is a schematic diagram of an embodiment of the present invention for predicting the separated flow of an iced airfoil using a modified four-equation time-scale turbulence model method for the flow around an iced airfoil. DETAILED DESCRIPTION

[0055] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described one by one here, but the embodiments of the present invention are not limited to the following embodiments.

[0056] like Figure 1 As shown, according to one embodiment of the present invention, a method for separating and correcting a four-equation time-scale turbulence model for flow around an iced wing of the present invention includes the following steps:

[0057] S1. Construct a four-equation turbulence model that introduces a time scale. The four-equation turbulence model is based on three normal stress equations and one turbulence time scale equation, and is expressed as:

[0058]

[0059]

[0060]

[0061]

[0062] in, is the time-averaged density, For time, 、 、 are the Reynolds normal stresses in three directions, 、 are the three-directional velocity components, 、 They are the three-direction coordinate components, subscript 、 , is the turbulence time scale, obtained from the turbulence time scale equation, and can be expressed as , is Menter's specific dissipation rate scaling equation, 、 、 are the generating terms of the Reynolds normal stress transport equation in three directions, and 、 、 are the generation of Reynolds normal stress in three directions, 、 、 are the pressure-strain correlation terms of the Reynolds normal stress transport equation in three directions, and 、 、 are the pressure-strain correlation terms excluding density, is the turbulent kinetic energy dissipation rate and is expressed as , is the empirical coefficient of turbulence, is the dynamic viscosity coefficient, is the cross-diffusion coefficient in the Reynolds normal stress equation, is the turbulent kinetic energy and is expressed as , is the diffusion coefficient of the equation for the specific dissipation rate scale, is the turbulent kinetic energy generation term and is expressed as , is the coefficient of the dissipation term of the equation for the specific dissipation rate scale, is the diffusion coefficient of the scaling equation, is the equivalent eddy viscosity coefficient (subscript t is time), and , is the coefficient of the cross-derivative term of the equation for the specific dissipation rate scale;

[0063] S2. Construct the Reynolds shear stress from algebraic relations and obtain its general form;

[0064] S3. Introducing a separation correction function into the four-equation turbulence model , to obtain the separated corrected four-equation time-scale turbulence model:

[0065] S4. Construct the flow field grid data of the flow around the iced wing to be simulated, set the flow field boundary conditions and flow field initial conditions of the flow around the iced wing to be simulated, and numerically solve the separated modified four-equation time-scale turbulence model based on the flow field grid data to obtain the numerical simulation results of the flow around the iced wing.

[0066] like Figure 1 As shown, according to one embodiment of the present invention, in step S1, in the step of constructing a four-equation turbulence model introducing a time scale, the Reynolds normal stress in three directions is 、 、 They are obtained based on the Reynolds normal stress expression. For the four-equation turbulence model, a universal Reynolds normal stress expression is constructed, which is expressed as:

[0067]

[0068] in, represents the Reynolds normal stress in the general Reynolds normal stress expression, represents density, represents the first-order derivative of velocity, subscript , ;

[0069] The Reynolds normal stress expression of the constructed four-equation turbulence model is obtained by deformation based on the general Reynolds normal stress expression, and it is expressed as:

[0070]

[0071] Furthermore, the generated terms of the Reynolds normal stress transport equation in three directions are 、 、 Respectively expressed as:

[0072] ,

[0073] in, Used to refer to the generated terms of the Reynolds normal stress transport equation 、 、 , Used to refer to Reynolds stress, Used to refer to the three-directional velocity components respectively, , subscript Used to indicate incorrect subscript Sum, subscript express ;

[0074] Furthermore, the pressure-strain correlation terms of the Reynolds normal stress transport equation in three directions are 、 、 They are obtained based on the pressure-strain correlation expression of the Reynolds normal stress transport equation, where the pressure-strain correlation expression is expressed as:

[0075]

[0076] in, Used to refer to the pressure-strain correlation terms of the Reynolds normal stress transport equation 、 、 ; 、 、 It is used to refer to the anisotropy tensor in the Reynolds normal stress equation of this model, and its general expression is , , , For three-way subscript, Indicates incorrect subscript sum; It is used to refer to the strain rate tensor in the Reynolds normal stress equation of this model, and its general expression is , , For three-way subscript, Indicates incorrect subscript sum; It refers to the traceless strain rate tensor in the Reynolds normal stress equation of this model, and its general expression is: , and is the strain rate tensor, for the Croneko operator; It is used to refer to the rotation tensor in the Reynolds normal stress equation of this model, and its general expression is: , 、 is the velocity component, 、 is the coordinate component; ; 、 、 、 、 、 、 are the pressure-strain correlation coefficients, 、 、 、 .

[0077] It should be noted that the subscript The main purpose is to highlight that its value can be 11, 22 and 33, which is used to indicate the normal stress term. The main purpose is to highlight that its value can be a general case, belonging to the general form, used to indicate that the solution of the tensor is based on the general case, the subscript It is to distinguish between different tensors, and different subscripts are used to calculate different items.

[0078] like Figure 1 As shown, according to one embodiment of the present invention, the pressure-strain correlation coefficient 、 、 、 、 、 、 are respectively obtained based on the first mixed function expression, wherein the first mixed function expression is expressed as:

[0079]

[0080] in, Respectively refer to the pressure-strain correlation coefficient 、 、 、 、 、 、 , is Menter's mixing function in the SST eddy viscosity model, for Compared with the SSG / LRR model The mode-related part, for and Model-related parts; among them, the SSG / LRR model can be found on the turbulence model resource website. https: / / turbmodels.larc.nasa.gov .

[0081] In this embodiment, the pressure-strain correlation coefficient 、 、 、 、 、 、 The values of are shown in Table 1 below.

[0082] Table 1

[0083]

[0084] in, .

[0085] In this embodiment, the diffusion and dissipation terms are modeled in the same way as in the SST model. The correlation coefficients of the diffusion terms are and .

[0086] like Figure 1 As shown, according to one embodiment of the present invention, in the turbulence time scale equation, the diffusion term coefficient of the equation of the specific dissipation rate scale is , the coefficient of the dissipation term of the equation of specific dissipation rate scale , diffusion coefficient of the scaling equation , the cross-derivative coefficient of the equation for the specific dissipation rate scale are obtained based on the second mixed function expression, wherein the above correlation coefficient ( 、 、 、 ) by the near wall Partial and outside the boundary layer Part (SSG / LRR Reynolds stress model is based on The SSG model and The LRR model is composed of the LRR model, in which the LRR model mainly works near the wall, and the SSG model works in the outer layer of the boundary layer and the free shear flow); thus, the second mixing function expression is expressed as:

[0087]

[0088]

[0089] in, Respectively refer to the coefficients 、 、 、 , is the transition function, for Compared with the SSG / LRR model (same as above), Mode-related parts, for Outside the boundary layer Mode-related parts, is the transition function judgment function, is the distance from the iced airfoil wall to the nearest numerical grid point in the flow field, is the kinematic viscosity coefficient.

[0090] In this embodiment, the aforementioned correlation coefficient ( 、 、 、 ) are shown in Table 2 below.

[0091] Table 2

[0092]

[0093] like Figure 1 As shown, according to one embodiment of the present invention, in step S2, the step of constructing the Reynolds shear stress from the algebraic relationship includes:

[0094] The Reynolds shear stress is calculated using the anisotropic eddy viscosity assumption. and Modeled and expressed as:

[0095]

[0096] in, is the anisotropic eddy viscosity coefficient, is the new specific dissipation rate in the anisotropic eddy viscosity coefficient, is the pressure-strain correlation coefficient Partial correlation coefficient , Characterize the turbulence balance (ratio of turbulent kinetic energy generation and dissipation rate), is a constant coefficient and is set to 0.63, is the empirical coefficient of turbulence and is set to 0.09;

[0097] Considering only the pressure-strain relationship on the two-dimensional plane, the Reynolds shear stress constructed by the algebraic relationship is obtained and The general form of is expressed as:

[0098]

[0099]

[0100]

[0101] in, 、 、 represent the anisotropic eddy viscosity coefficients in three directions respectively.

[0102] like Figure 1 As shown, according to one embodiment of the present invention, in step S3, a separation correction function is introduced into the four-equation turbulence model. In the steps of Expressed as:

[0103]

[0104] in, is the turbulent kinetic energy generation and dissipation rate ratio, is the Reynolds stress anisotropy tensor invariant.

[0105] like Figure 1 As shown, according to one embodiment of the present invention, in step S3, a separation correction function is introduced into the four-equation turbulence model. In the steps of Acting on the coefficient , and obtain the corrected coefficient , to generate a separated corrected four-equation time-scale turbulence model.

[0106] like Figure 1 As shown, according to one embodiment of the present invention, in step S4, in the step of setting the flow field boundary conditions and the flow field initial conditions of the flow around the iced wing to be simulated, the flow field involved is a two-dimensional iced airfoil flow field or a three-dimensional iced wing flow field.

[0107] like Figure 1 As shown, according to one embodiment of the present invention, in step S4, in the step of setting the flow field boundary conditions and the flow field initial conditions of the flow around the iced wing to be simulated, the boundary conditions on the actual wall surface and the far field of the iced wing to be simulated are set and expressed as:

[0108]

[0109] in, For the wall scale, For the far field scale, is the anisotropic eddy viscosity coefficient in the far field, is the time-averaged density, is the turbulent kinetic energy, subscript and Represent the locations at the wall and the far field respectively;

[0110] Furthermore, the initial conditions of the flow field include: free flow Mach number and Reynolds number.

[0111] like Figure 1 As shown, according to one embodiment of the present invention, in step S4, in the step of numerically solving the separation-corrected four-equation time-scale turbulence model based on the flow field grid data, the 12 independent variables included in the separation-corrected four-equation time-scale turbulence model are solved: 、 、 、 、 、 、 、 、 and The numerical solutions of other variables are then derived through the relationship.

[0112] According to one embodiment of the present invention, a device of the present invention using the aforementioned separated modified four-equation time-scale turbulence model method for flow around an iced wing comprises:

[0113] A model building module is used to construct a four-equation turbulence model that introduces a time scale, wherein the four-equation turbulence model is based on three Reynolds normal stress transport equations and one turbulence time scale equation, and is expressed as:

[0114]

[0115]

[0116]

[0117]

[0118] in, is the time-averaged density, For time, 、 、 are the Reynolds normal stresses in three directions, 、 are the three-directional velocity components, 、 They are the three-direction coordinate components, subscript 、 , is the turbulence time scale, obtained from the turbulence time scale equation, and can be expressed as , is Menter's specific dissipation rate scaling equation, 、 、 are the generating terms of the Reynolds normal stress transport equation in three directions, and 、 、 are the generation of Reynolds normal stress in three directions, 、 、 are the pressure-strain correlation terms of the Reynolds normal stress transport equation in three directions, and 、 、 are the pressure-strain correlation terms excluding density, is the turbulent kinetic energy dissipation rate and is expressed as , is the empirical coefficient of turbulence, is the dynamic viscosity coefficient, is the cross-diffusion coefficient in the Reynolds normal stress equation, is the turbulent kinetic energy and is expressed as , is the diffusion coefficient of the equation for the specific dissipation rate scale, is the turbulent kinetic energy generation term and is expressed as , is the coefficient of the dissipation term of the equation for the specific dissipation rate scale, is the diffusion coefficient of the scaling equation, is the equivalent eddy viscosity coefficient, and , is the coefficient of the cross-derivative term of the equation for the specific dissipation rate scale;

[0119] The Reynolds shear stress is constructed from algebraic relations and its general form is obtained;

[0120] Introducing a separation correction function into the four-equation turbulence model , to obtain the separated corrected four-equation time-scale turbulence model:

[0121] An input module constructs flow field grid data of the flow around the icing wing to be simulated, and sets the flow field boundary conditions and flow field initial conditions of the flow around the icing wing to be simulated;

[0122] The numerical simulation module numerically solves the separated modified four-equation time-scale turbulence model based on the flow field grid data to obtain the numerical simulation results of the flow around the iced wing.

[0123] To further illustrate this solution, an example is given.

[0124] The numerical simulation results of the two-dimensional GLC305-944 ice airfoil (6 degrees angle of attack) using the separated modified four-equation time-scale turbulence model method for the flow around the ice wing of the present invention are shown in Figure 2 The background is determined by the dimensionless eddy viscosity coefficient Coloring, the model method gives the reattachment point location The predicted value is better than that of the original Reynolds stress model, and the irregular streamline shape near the reattachment is avoided (the non-physical backbend of the streamline that is difficult to solve in the original Reynolds stress model), and the maximum height of the separation bubble is more reasonable.

[0125] The above contents are merely examples of specific solutions of the present invention. For devices and structures not described in detail, it should be understood that they can be implemented by adopting general devices and methods available in the art.

[0126] The above description is merely one embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A separated modified four-equation time-scale turbulence model method for the flow around an iced wing, characterized by: The following steps are involved: S1. Construct a four-equation turbulence model that introduces a time scale, wherein the four-equation turbulence model is based on three Reynolds normal stress transport equations and one turbulence time scale equation, and is expressed as: in, is the time-averaged density, For time, 、 、 are the Reynolds normal stresses in three directions, 、 are the three-directional velocity components, 、 They are the three-direction coordinate components, subscript 、 , is the turbulence time scale, obtained from the turbulence time scale equation, and can be expressed as , is Menter's specific dissipation rate scaling equation, 、 、 are the generating terms of the Reynolds normal stress transport equation in three directions, and 、 、 are the generation of Reynolds normal stress in three directions, 、 、 are the pressure-strain correlation terms of the Reynolds normal stress transport equation in three directions, and 、 、 are the pressure-strain correlation terms excluding density, is the turbulent kinetic energy dissipation rate and is expressed as , is the empirical coefficient of turbulence, is the dynamic viscosity coefficient, is the cross-diffusion coefficient in the Reynolds normal stress equation, is the turbulent kinetic energy and is expressed as , is the diffusion coefficient of the equation for the specific dissipation rate scale, is the turbulent kinetic energy generation term and is expressed as , is the coefficient of the dissipation term of the equation for the specific dissipation rate scale, is the diffusion coefficient of the scaling equation, is the equivalent eddy viscosity coefficient, and , is the coefficient of the cross-derivative term of the equation for the specific dissipation rate scale; S2. Construct the Reynolds shear stress from algebraic relations and obtain its general form; S3. Introducing a separation correction function into the four-equation turbulence model , to obtain the separation-corrected four-equation time-scale turbulence model; wherein the separation correction function Expressed as: in, is the turbulent kinetic energy generation and dissipation rate ratio, is the Reynolds stress anisotropy tensor invariant; S4. Construct flow field grid data of the flow around the iced wing to be simulated, set the flow field boundary conditions and flow field initial conditions of the flow around the iced wing to be simulated, and numerically solve the separated corrected four-equation time-scale turbulence model based on the flow field grid data to obtain numerical simulation results of the flow around the iced wing.

2. The separated and corrected four-equation time-scale turbulence model method according to claim 1, characterized in that: In step S1, in the step of constructing a four-equation turbulence model with the introduction of time scale, the Reynolds normal stress in three directions 、 、 are obtained based on the Reynolds normal stress expression, wherein the Reynolds normal stress expression is expressed as: in, , Reynolds normal stress 、 、 , represents density, represents the first-order derivative of velocity, subscript , ; Generated terms of the Reynolds normal stress transport equation in three directions 、 、 Respectively expressed as: in, Used to refer to the generated terms of the Reynolds normal stress transport equation 、 、 , Used to refer to Reynolds stress, Used to refer to the three-directional velocity components respectively, , subscript Used to indicate incorrect subscript Sum, subscript for ; Pressure-strain correlation terms of the Reynolds normal stress transport equation in three directions 、 、 are obtained based on the pressure-strain correlation expression of the Reynolds normal stress transport equation, wherein the pressure-strain correlation expression is expressed as: in, Used to refer to the pressure-strain correlation terms of the Reynolds normal stress transport equation 、 、 ; 、 、 It is used to refer to the anisotropy tensor in the Reynolds normal stress equation of this model, and its general expression is ; It is used to refer to the strain rate tensor in the Reynolds normal stress equation of this model, and its general expression is ; It refers to the traceless strain rate tensor in the Reynolds normal stress equation of this model, and its general expression is: , and is the strain rate tensor, for the Croneko operator; It is used to refer to the rotation tensor in the Reynolds normal stress equation of this model, and its general expression is: , 、 is the velocity component, 、 is the coordinate component; ; 、 、 、 、 、 、 are pressure-strain correlation coefficients; 、 、 、 , subscript Indicates incorrect subscript Summation.

3. The separated and corrected four-equation time-scale turbulence model method according to claim 2, characterized in that: The pressure-strain correlation coefficient 、 、 、 、 、 、 are respectively obtained based on a first mixed function expression, wherein the first mixed function expression is expressed as: in, Used to refer to the pressure-strain correlation coefficients respectively 、 、 、 、 、 、 , is the mixing function in the Menter-SST eddy viscosity model, for Compared with the SSG / LRR model The mode-related part, for and Mode-related parts.

4. The separated and corrected four-equation time-scale turbulence model method according to claim 3, characterized in that: In the turbulence time scale equation, the diffusion coefficient of the equation of specific dissipation rate scale is , the coefficient of the dissipation term of the equation of specific dissipation rate scale , diffusion coefficient of the scaling equation , the cross-derivative coefficient of the equation for the specific dissipation rate scale are respectively obtained based on a second mixed function expression, wherein the second mixed function expression is expressed as: in, Respectively refer to the coefficients 、 、 、 , is the transition function, for Compared with the SSG / LRR model near the wall Mode-related parts, for Outside the boundary layer Mode-related parts, is the transition function judgment function, is the distance from the iced airfoil wall to the nearest numerical grid point in the flow field, is the viscosity coefficient.

5. The separated and corrected four-equation time-scale turbulence model method according to claim 4, characterized in that: In step S2, the step of constructing the Reynolds shear stress from an algebraic relationship includes: The Reynolds shear stress is calculated using the anisotropic eddy viscosity assumption. and Modeled and expressed as: in, is the anisotropic eddy viscosity coefficient, is the new specific dissipation rate in the anisotropic eddy viscosity coefficient, is the pressure-strain correlation coefficient Partial correlation coefficient , Characterizes the turbulence balance, that is, the ratio of turbulent kinetic energy generation and dissipation rate, is a constant coefficient and is set to 0.63, is the empirical coefficient of turbulence and is set to 0.09; Considering only the pressure-strain relationship on the two-dimensional plane, the Reynolds shear stress constructed by the algebraic relationship is obtained and The general form of is expressed as: in, 、 、 represent the anisotropic eddy viscosity coefficients in three directions respectively.

6. The separated and corrected four-equation time-scale turbulence model method according to claim 5, characterized in that: In step S3, a separation correction function is introduced into the four-equation turbulence model. In the step of Acting on the coefficient , and obtain the corrected coefficient , to generate the separated modified four-equation time-scale turbulence model.

7. The separated and corrected four-equation time-scale turbulence model method according to claim 6, characterized in that: In step S4, in the step of setting the flow field boundary conditions and the flow field initial conditions of the flow around the iced wing to be simulated, the flow field involved is a two-dimensional flow field around the iced airfoil or a three-dimensional flow field around the iced wing.

8. The separated and corrected four-equation time-scale turbulence model method according to claim 7, characterized in that: In step S4, in the step of setting the flow field boundary conditions and the flow field initial conditions of the flow around the iced wing to be simulated, the boundary conditions on the actual wall surface and the far field of the iced wing to be simulated are set and expressed as: in, For the wall scale, For the far field scale, is the anisotropic eddy viscosity coefficient in the far field, is the time-averaged density, is the turbulent kinetic energy, subscript and Represent the locations at the wall and the far field respectively; The initial conditions of the flow field include: free flow Mach number and Reynolds number.

9. The separated and corrected four-equation time-scale turbulence model method according to claim 8, characterized in that: In step S4, in the step of numerically solving the separated and corrected four-equation time-scale turbulence model based on the flow field grid data, 12 independent variables included in the separated and corrected four-equation time-scale turbulence model are solved: 、 、 、 、 、 、 、 、 and The numerical solutions of other variables are then derived through the relationship.

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