Separation correction four-equation time scale turbulence model method for frozen wing streaming

Abstract

The invention relates to a method for separating and correcting a four-equation time scale turbulence model for frozen wing streaming, which comprises the following steps: constructing a four-equation turbulence model introducing a time scale, the four-equation turbulence model being formed based on three Reynolds normal stress transport equations and a turbulence time scale equation; reynolds shear stress is constructed through an algebraic relation, and a general form is obtained; introducing a separation correction function into the four-equation turbulence model to obtain a separation correction four-equation time scale turbulence model; and constructing flow field grid data of the to-be-simulated icing wing streaming, setting a flow field boundary condition and a flow field initial condition of the to-be-simulated icing wing streaming, and performing numerical solution on the separation correction four-equation time scale turbulence model based on the flow field grid data to obtain a numerical simulation result of the icing wing streaming. The method has the advantages that the number of equations is small, the calculation efficiency is high, and non-physical backflow does not occur to reattachment points.

Description

Technical Field

[0001] The present invention relates to the field of computational fluid dynamics, and particularly to a method for a separated modified four-equation time-scale turbulence model for the flow around an ice-covered wing. Background Art

[0002] Ice on the lift area of an aircraft will destroy its original streamlined shape, seriously affecting the operation of the aircraft, such as causing a decrease in lift, an increase in drag, and a non-linear change in pitching moment. The shapes of ice accretion on the wing are generally divided into rough ice, streamwise ice, horn ice, and spanwise ridge ice. Except for rough ice, the other three mainly feature two-dimensional flow structures. Taking the flow around a horn ice airfoil as an example, in the recirculation region, due to the influence of the adverse pressure gradient, the non-equilibrium characteristics of turbulence are very prominent, which poses a challenge to computational fluid dynamics (CFD) simulations.

[0003] In principle, scale-resolving methods such as large-eddy simulation (LES) and hybrid RANS / LES should be able to produce accurate results. In recent years, researchers have done a lot of work in this field. They applied the dynamic hybrid RANS / LES method to the simulation of the GLC305 horn ice airfoil, analyzed the performance of two length scales ( and ) in IDDES prediction and the flow around airfoils with horn ice or ridge ice accumulation, and simulated the flow of 5 NACA23012 ice-covered airfoils using the wall-adapting LES method. However, the above work all requires time-accurate three-dimensional (3-D) calculations, which are relatively costly. To achieve a balance between accuracy and computational cost, there is still a need to improve the RANS method, especially when it comes to streamwise ice, horn ice, or spanwise ridge ice.

[0004] Reynolds stress models (RSMs) are considered the most advanced models among RANS turbulence models. They directly solve the Reynolds stress, thus eliminating the weaknesses of eddy viscosity models (EVMs) such as the Spalart-Allmaras (SA) model and the shear stress transport (SST) model. For example, in tip vortex flow, wing-body junction flow, and square duct corner flow, the RSM can exhibit more potential performance. However, in separated flows caused by adverse pressure gradients, some unsatisfactory characteristics are still observed. Therefore, there is an urgent need for a new Reynolds stress model for the numerical calculation of the flow around ice-covered wings. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for a separated modified four-equation time-scale turbulence model for the flow around an ice-covered wing.

[0006] To achieve the above invention object, the present invention provides a method for a separated modified four-equation time-scale turbulence model for the flow around an ice-covered wing, including the following steps: S1. Construct a four - equation turbulence model incorporating a time scale, where the four - equation turbulence model is composed of three Reynolds normal stress transport equations and one turbulence time - scale equation, and is expressed as:

[0007]

[0008]

[0009]

[0010] Wherein, is the time - averaged density, is the time, , , are the three - direction Reynolds normal stresses, , are the three - direction velocity components respectively, , are the three - direction coordinate components respectively, with subscripts , , is the turbulence time scale, obtained from the turbulence time - scale equation and can be expressed as , is Menter's specific dissipation rate scale equation, , , are the generation terms of the three - direction Reynolds normal stress transport equations respectively, and , , are the generations of the three - direction Reynolds normal stresses respectively, , , are the pressure - strain correlation terms of the three - direction Reynolds normal stress transport equations respectively, and , , are the density - free pressure - strain correlation terms respectively, is the turbulent kinetic energy dissipation rate and is expressed as , is the turbulence empirical coefficient, is the dynamic viscosity coefficient, is the cross - diffusion term coefficient in the Reynolds normal stress equation, is the turbulent kinetic energy and is expressed as , is the equation diffusion term coefficient of the specific dissipation rate scale, is the turbulent kinetic energy generation term and is expressed as , is the dissipation term coefficient of the equation for the specific dissipation rate scale, is the diffusion term coefficient of the scale equation, is the equivalent eddy viscosity coefficient, and , is the cross-derivative term coefficient of the equation for the specific dissipation rate scale; S2. Construct the Reynolds shear stress from the algebraic relationship to obtain its general form; S3. Introduce the separation correction function in the four-equation turbulence model to obtain the separated corrected four-equation time-scale turbulence model; S4. Construct the flow field grid data for simulating the flow around the icing wing, set the flow field boundary conditions and the flow field initial conditions for simulating the flow around the icing wing, and numerically solve the separated corrected four-equation time-scale turbulence model based on the flow field grid data to obtain the numerical simulation results of the flow around the icing wing.

[0011] According to one aspect of the present invention, in step S1, in the step of constructing the four-equation turbulence model introducing the time scale, the three-direction Reynolds normal stresses , , are respectively obtained based on the Reynolds normal stress expression, where the Reynolds normal stress expression is expressed as:

[0012] where, , is used to respectively refer to the Reynolds normal stresses , , , represents the density, represents the first-order derivative of the velocity, and the subscript , ; The generation terms , , of the three-direction Reynolds normal stress transport equations are respectively expressed as:

[0013] where, is used to respectively refer to the generation terms , , of the Reynolds normal stress transport equations, is used to respectively refer to the Reynolds stresses, is used to respectively refer to the three-direction velocity components, , and the subscript is used to indicate not summing over the subscript summation, subscript For ; The pressure-strain correlation terms of the Reynolds normal stress transport equations in three directions , , are respectively obtained based on the expressions of the pressure-strain correlation terms of the Reynolds normal stress transport equations, where the expression of the pressure-strain correlation term is expressed as:

[0014] Wherein, is used to respectively refer to the pressure-strain correlation terms of the Reynolds normal stress transport equations , , ; , , is used to refer to the anisotropy tensor in the Reynolds normal stress equation of this model, and its general expression is ; is used to refer to the strain rate tensor in the Reynolds normal stress equation of this model, and its general expression is ; is used to refer to the traceless strain rate tensor in the Reynolds normal stress equation of this model, and its general expression is: , and are the strain rate tensors, is the Kronecker operator; is used to refer to the rotation tensor in the Reynolds normal stress equation of this model, and its general expression is: , , are the velocity components, , are the coordinate components; ; , , , , , , are respectively the pressure-strain correlation term coefficients; the subscripts , , , , the subscript means not summing over the subscript .

[0015] According to one aspect of the present invention, the pressure-strain correlation term coefficients , , , , , , are obtained respectively based on a first blending function expression, where the first blending function expression is expressed as:

[0016] where are used to respectively refer to the coefficients of the pressure-strain correlation terms , , , , , , , is the blending function in the Menter-SST eddy viscosity model, is related to the mode in the SSG / LRR model, is related to the mode.

[0017] According to one aspect of the present invention, in the turbulent time scale equation, the coefficient of the equation diffusion term of the specific dissipation rate scale , the coefficient of the equation dissipation term of the specific dissipation rate scale , the coefficient of the scale equation diffusion term , and the coefficient of the equation cross derivative term of the specific dissipation rate scale are obtained respectively based on a second blending function expression, where the second blending function expression is expressed as:

[0018]

[0019] where respectively refer to the coefficients , , , , is a transition function, is related to the mode near the wall in the SSG / LRR model, is related to the mode outside the boundary layer, is a transition function judgment function, is the distance from the wall of the ice-covered airfoil to the nearest numerical grid point in the flow field, is the viscosity coefficient.

[0020] According to one aspect of the present invention, in step S2, in the step of constructing the Reynolds shear stress from algebraic relations, it includes: Adopting the anisotropic eddy viscosity hypothesis for the Reynolds shear stress And Carrying out modeling, and expressing it as:

[0021] Wherein, Is the anisotropic eddy viscosity coefficient, Is the new specific dissipation rate in the anisotropic eddy viscosity coefficient, Is the coefficient related to the Part in the pressure-strain correlation term coefficient , Characterizes the turbulence equilibrium, that is, the ratio of the turbulent kinetic energy generation dissipation rate, Is a constant coefficient and is set to 0.63, Is the turbulence empirical coefficient and is set to 0.09; Only considering the pressure-strain relationship on the two-dimensional plane, then obtaining the Reynolds shear stress And In general form, and expressing it as:

[0022]

[0023]

[0024] Wherein, , , Respectively represent the three-direction anisotropic eddy viscosity coefficients.

[0025] According to one aspect of the present invention, in step S3, in the step of introducing the separation correction function Into the four-equation turbulence model, the separation correction function Is expressed as:

[0026] Wherein, Is the ratio of the turbulent kinetic energy generation dissipation rate, Is the invariant of the Reynolds stress anisotropy tensor.

[0027] According to one aspect of the present invention, in step S3, in the step of introducing the separation correction function Into the four-equation turbulence model, the separation correction function Acts on the coefficient , and obtains the corrected coefficient , to generate the separated modified four - equation time - scale turbulence model.

[0028] 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 for the flow around the icing wing to be simulated, the flow field involved is a two - dimensional icing airfoil flow field or a three - dimensional icing wing flow field.

[0029] 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 for the flow around the icing wing to be simulated, the boundary conditions on the solid wall surface and in the far - field of the icing wing to be simulated are set and expressed as:

[0030] where, is the scale at the wall surface, is the scale in the far - field, is the anisotropic eddy viscosity coefficient in the far - field, is the time - averaged density, is the turbulent kinetic energy, and the subscripts and represent the wall surface and the far - field respectively; The flow field initial conditions include: free - stream Mach number, Reynolds number.

[0031] According to one aspect of the present invention, in step S4, in the step of numerically solving the separated modified four - equation time - scale turbulence model based on the flow field grid data, 12 independent variables included in the separated modified four - equation time - scale turbulence model are solved: , , , , , , , , and The results of, and then the numerical solutions of other variables are derived through relational expressions.

[0032] According to one solution of the present invention, the present invention uses three Reynolds normal stress transport equations and one scale equation to form a four - equation model, represents the Reynolds shear stress using algebraic relations, and introduces separation modification, thus obtaining the method of the separated modified four - equation time - scale turbulence model.

[0033] 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, higher computational efficiency, etc.; at the same time, it effectively eliminates the inherent defects of the traditional model and provides an excellent modification scheme for the traditional model. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a step block diagram of a method for a separated modified four - equation time - scale turbulence model for the flow around an ice - covered wing according to an embodiment of the present invention; Figure 2 It is a schematic diagram of predicting the separated flow of an ice - covered airfoil by a method for a separated modified four - equation time - scale turbulence model for the flow around an ice - covered wing according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0035] The present invention will be described in detail below in conjunction with the drawings and specific embodiments. The embodiments cannot be enumerated one by one here, but the embodiments of the present invention are not limited to the following embodiments.

[0036] As Figure 1 shown, according to an embodiment of the present invention, a method for a separated modified four - equation time - scale turbulence model for the flow around an ice - covered wing of the present invention includes the following steps: S1. Construct a four - equation turbulence model introducing a time scale, where the four - equation turbulence model is composed of three normal stress equations and a turbulence time - scale equation, and is expressed as:

[0037]

[0038]

[0039]

[0040] Wherein, is the time - averaged density, is the time, , , are the three - direction Reynolds normal stresses, , are the velocity components in the three directions respectively, , are the coordinate components in the three directions respectively, and the subscripts , , is the turbulence time scale, obtained from the turbulence time - scale equation, and can be expressed as , is Menter's specific dissipation rate scale equation, , , are the generation terms of the three - direction Reynolds normal stress transport equations respectively, and , , For the generation of Reynolds normal stresses in three directions respectively, , , are the pressure-strain correlation terms in the transport equations of Reynolds normal stresses in three directions respectively, and , , are the pressure-strain correlation terms without density respectively, is the turbulent kinetic energy dissipation rate and is expressed as , is the turbulent empirical coefficient, is the dynamic viscosity coefficient, is the coefficient of the cross-diffusion term in the Reynolds normal stress equation, is the turbulent kinetic energy and is expressed as , is the coefficient of the diffusion term in the equation of the specific dissipation rate scale, is the generation term of the turbulent kinetic energy and is expressed as , is the coefficient of the dissipation term in the equation of the specific dissipation rate scale, is the coefficient of the diffusion term in the scale equation, is the equivalent eddy viscosity coefficient (the subscript t is time), and , is the coefficient of the cross-derivative term in the equation of the specific dissipation rate scale; S2. Construct the Reynolds shear stress from the algebraic relationship to obtain its general form; S3. Introduce the separation correction function in the four-equation turbulence model to obtain the separated corrected four-equation time-scale turbulence model: S4. Construct the flow field grid data of the flow around the icing wing to be simulated, set the flow field boundary conditions and the flow field initial conditions of the flow around the icing 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 the numerical simulation results of the flow around the icing wing.

[0041] As Figure 1 shown, according to an embodiment of the present invention, in step S1, in the step of constructing the four-equation turbulence model introducing the time scale, the Reynolds normal stresses , , are respectively obtained based on the Reynolds normal stress expressions. Among them, for the four-equation turbulence model, a general Reynolds normal stress expression is constructed, and it is expressed as:

[0042] wherein, represents the Reynolds normal stress in the general Reynolds normal stress expression, represents density, represents the first derivative of velocity, with subscript , ; Based on the general Reynolds normal stress expression, it is deformed to obtain the Reynolds normal stress expression of the Reynolds normal stress in the constructed four-equation turbulence model, and it is expressed as:

[0043] Furthermore, the production terms of the Reynolds normal stress transport equations in three directions , , are respectively expressed as: , wherein, is used to respectively refer to the production terms of the Reynolds normal stress transport equations , , , is used to respectively refer to the Reynolds stress, is used to respectively refer to the velocity components in three directions, , with subscript used to indicate not summing over the subscript , with subscript indicating ; Furthermore, the pressure-strain correlation terms of the Reynolds normal stress transport equations in three directions , , are respectively obtained based on the pressure-strain correlation term expressions of the Reynolds normal stress transport equations, wherein the pressure-strain correlation term expression is expressed as:

[0044] wherein, is used to respectively refer to the pressure-strain correlation terms of the Reynolds normal stress transport equations , , ; , , are used to refer to the anisotropy tensor in the Reynolds normal stress equation of this model, and its general expression is , , , is the subscript in three directions, indicating not summing over the subscript ; is used to refer to the strain rate tensor in the Reynolds normal stress equation of this model, and its general expression is , , is a three - direction subscript, indicating no summation over the subscript ; is used to refer 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, is the Kronecker operator; is used to refer to the rotation tensor in the Reynolds normal - stress equation of this model, and its general expression is: , , are velocity components, , are coordinate components; ; , , , , , , are the coefficients of the pressure - strain correlation term respectively. The subscript , , , .

[0045] It should be noted that the subscript is mainly to highlight that its values can be 11, 22, and 33, used to represent the terms of normal stress. The subscript is mainly to highlight that its values can be in the general case, belonging to the general form, used to indicate that the solution of the tensor is realized based on the general case. The subscript is for the distinction between different tensors. Using different subscripts is for taking different terms according to the calculation requirements.

[0046] As Figure 1 shown, according to an embodiment of the present invention, the coefficients of the pressure - strain correlation term , , , , , , are respectively obtained based on the first mixing - function expression. Among them, the first mixing - function expression is expressed as:

[0047] Among them, respectively refer to the coefficients of the pressure - strain correlation term , , , , , , , is the blending function in the Menter SST eddy viscosity model, is related to the mode in the SSG / LRR model, is related to the mode; among them, the SSG / LRR model can be referred to the turbulence model resource website, https: / / turbmodels.larc.nasa.gov .

[0048] In this embodiment, the values of the pressure-strain correlation term coefficients , , , , , , are shown in Table 1 below.

[0049] Table 1

[0050] Among them, .

[0051] In this embodiment, the modeling of the diffusion term and the dissipation term is consistent with the equation modeling in the SST model. The correlation coefficients of the diffusion term are and .

[0052] As Figure 1 shown, according to an embodiment of the present invention, in the turbulence time scale equation, the diffusion term coefficient of the specific dissipation rate scale equation, the dissipation term coefficient of the specific dissipation rate scale equation, the diffusion term coefficient of the scale equation, and the cross-derivative term coefficient of the specific dissipation rate scale equation are respectively obtained based on the second blending function expression, among which, the above-mentioned correlation coefficients ( , , , ) are composed of the part near the wall and the part outside the boundary layer (the SSG / LRR Reynolds stress model consists of the SSG model based on and the It consists of the LRR model. Among them, the LRR model mainly operates near the wall surface, and the SSG model acts in the outer boundary layer and free shear flow); thus, the expression of the second mixing function is:

[0053]

[0054] Wherein, respectively refer to the coefficients , , , , is the transition function, is related to the part of the mode near the wall surface in the SSG / LRR model (the same as above), is related to the part of the mode outside the boundary layer, is the transition function judgment function, is the distance from the wall surface of the ice-airfoil to the nearest numerical grid point in the flow field, is the kinematic viscosity coefficient.

[0055] In this embodiment, the aforementioned correlation coefficients ( , , , ) take the values as shown in Table 2 below.

[0056] Table 2

[0057] As Figure 1 shown, according to an embodiment of the present invention, in step S2, in the step of constructing the Reynolds shear stress by algebraic relations, it includes: Adopting the anisotropic eddy viscosity hypothesis to model the Reynolds shear stress and and expressing it as:

[0058] Wherein, is the anisotropic eddy viscosity coefficient, is the new specific dissipation rate in the anisotropic eddy viscosity coefficient, is the coefficient related to the part in the pressure-strain correlation term coefficient , characterizes the turbulence equilibrium (the ratio of turbulent kinetic energy generation to dissipation rate), is a constant coefficient and is set to 0.63, is the turbulent empirical coefficient and is set to 0.09; Only considering the pressure-strain relationship in a two-dimensional plane, the Reynolds shear stress constructed by an algebraic relationship is obtained and in general form, and is expressed as:

[0059]

[0060]

[0061] where , , respectively represent the three-direction anisotropic eddy viscosity coefficients.

[0062] As Figure 1 shown, according to an embodiment of the present invention, in step S3, in the four-equation turbulence model, when introducing the separation correction function , the separation correction function is expressed as:

[0063] where is the ratio of the generation and dissipation rate of turbulent kinetic energy, is the invariant of the Reynolds stress anisotropic tensor.

[0064] As Figure 1 shown, according to an embodiment of the present invention, in step S3, in the four-equation turbulence model, when introducing the separation correction function , the separation correction function acts on the coefficient , to obtain the corrected coefficient , so as to generate a separated corrected four-equation time-scale turbulence model.

[0065] As Figure 1 shown, according to an embodiment of the present invention, in step S4, when setting the flow field boundary conditions and flow field initial conditions for the flow around the icing wing to be simulated, the flow field involved is a two-dimensional icing airfoil flow field or a three-dimensional icing wing flow field.

[0066] As Figure 1 shown, according to an embodiment of the present invention, in step S4, when setting the flow field boundary conditions and flow field initial conditions for the flow around the icing wing to be simulated, the boundary conditions on the solid wall surface and the far field of the icing wing to be simulated are set, and are expressed as:

[0067] where is the scale at the wall scale is the scale in the far field scale is the anisotropic eddy viscosity coefficient in the far field is the time-averaged density is the turbulent kinetic energy, with subscripts and represent the wall and the far field respectively Furthermore, the initial conditions of the flow field include: free-stream Mach number and Reynolds number

[0068] As Figure 1 shown, according to an embodiment of the present invention, in step S4, in the step of numerically solving the separated modified four-equation time-scale turbulence model based on the flow field grid data, 12 independent variables included in the separated modified four-equation time-scale turbulence model are solved: , , , , , , , , and The results of are used to derive the numerical solutions of other variables through relational expressions

[0069] According to an embodiment of the present invention, an apparatus for implementing the method of the separated modified four-equation time-scale turbulence model for the flow around an ice-covered wing of the present invention includes: A model construction module for constructing a four-equation turbulence model introducing time scale, where the four-equation turbulence model is composed of three Reynolds normal stress transport equations and one turbulence time scale equation, and is expressed as:

[0070]

[0071]

[0072]

[0073] Wherein, is the time-averaged density is the time , , are the three-direction Reynolds normal stresses , are the three-direction velocity components respectively , are the three - direction coordinate components, with subscripts , , is the turbulent time scale, obtained from the turbulent time - scale equation and can be expressed as , is Menter's specific dissipation rate scale equation, , , are the generation terms of the Reynolds normal stress transport equations 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 equations in three directions, and , , are the pressure - strain correlation terms without density, is the turbulent kinetic energy dissipation rate and is expressed as , is the turbulent empirical coefficient, is the dynamic viscosity coefficient, is the cross - diffusion term coefficient in the Reynolds normal stress equation, is the turbulent kinetic energy and is expressed as , is the equation diffusion term coefficient of the specific dissipation rate scale, is the turbulent kinetic energy generation term and is expressed as , is the equation dissipation term coefficient of the specific dissipation rate scale, is the scale equation diffusion term coefficient, is the equivalent eddy viscosity coefficient, and , is the equation cross - derivative term coefficient of the specific dissipation rate scale; Construct the Reynolds shear stress from algebraic relations to obtain its general form; Introduce the separation correction function in the four - equation turbulence model to obtain the separated - corrected four - equation time - scale turbulence model: Input module, construct the flow - field grid data of the flow around the icing wing to be simulated, and set the flow - field boundary conditions and flow - field initial conditions of the flow around the icing wing to be simulated; Numerical simulation module, numerically solve the separated - corrected four - equation time - scale turbulence model based on the flow - field grid data to obtain the numerical simulation results of the flow around the icing wing.

[0074] To further elaborate on this solution, an example is given for it.

[0075] The numerical simulation results of the two-dimensional GLC305-944 ice airfoil (6-degree angle of attack) using the method of the separated modified four-equation time-scale turbulence model for the flow around an ice-covered wing of the present invention are shown in Figure 2 . The background is colored by the dimensionless eddy viscosity coefficient . This model method gives the predicted value of the reattachment point position , and avoids the irregular streamline (the non-physical backward bending of the streamline that is difficult to solve by the original Reynolds stress model) near the reattachment. The maximum height of the separation bubble is also more reasonable.

[0076] The above content is only an example of the specific solution of the present invention. For the equipment and structures not described in detail therein, it should be understood that the existing general equipment and general methods in the art are adopted for implementation.

[0077] The above is only one solution of the present invention and is not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A separated modified four-equation time-scale turbulence model method for the flow around an iced wing, characterized in that: The following steps are involved: S1. Construct a four-equation turbulence model introducing 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, , , is the Reynolds normal stress in three directions, , are the velocity components in three directions, , They are the coordinate components in three directions, and the subscripts , , 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 generated 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 without 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; 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 corrected 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.

2. The separation-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 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 the Reynolds stress, Used to refer to the velocity components in three directions 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 is used to refer 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 Croneco 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 , , , , subscript Indicates incorrect subscript Sum.

3. The separation-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 , , , , , , , 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 separation-corrected four-equation time-scale turbulence model method according to claim 3, characterized in that: In the turbulence time scale equation, the diffusion term coefficient of the equation for the specific dissipation rate scale is , the coefficient of the dissipation term of the equation for the specific dissipation rate scale , diffusion coefficient of the scaling equation , the coefficient of the cross derivative term 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 coefficient , , , , is the transition function, for Compared with the near-wall surface in the SSG / LRR model The mode-related part, for Outside the boundary layer The mode-related part, is the transition function judgment function, is the distance from the ice airfoil wall to the nearest numerical grid point in the flow field, is the viscosity coefficient.

5. The separation-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 by using the anisotropic eddy viscosity assumption. and Modeling is performed 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 The coefficient of partial correlation , 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 separation-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, the separation correction function It is expressed as: in, is the turbulent kinetic energy generation and dissipation rate ratio, is the Reynolds stress anisotropy tensor invariant.

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

8. The separation-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 flow field involved is a two-dimensional flow field around the iced airfoil or a three-dimensional flow field around the iced wing.

9. The separation-corrected four-equation time-scale turbulence model method according to claim 8, 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 ice wing to be simulated, the boundary conditions on the actual wall surface and the far field of the ice 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.

10. The separation-corrected four-equation time-scale turbulence model method according to claim 9, characterized in that: 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, 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.

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