A method for constructing a Cartesian grid wall model

Abstract

The invention discloses a method for constructing a Cartesian grid wall model, which relates to the field of computational fluid dynamics, including: constructing a flow field quantity calculation method for a wall modeling unit; correcting the turbulent viscosity coefficient of the wall modeling unit to obtain a correction result of the turbulent viscosity coefficient; calculating and obtaining a modeling height of a flat plate boundary layer to determine a wall modeling unit area; obtaining an outermost Cartesian grid spacing that meets a grid size requirement; calculating and obtaining the number of Cartesian grid wall modeling layers included in the wall modeling unit based on the spacing and the modeling height; constructing and obtaining a wall model based on the flow field quantity calculation method of the wall modeling unit, the correction result of the turbulent viscosity coefficient, the wall modeling unit area and the number of Cartesian grid wall modeling layers included in the wall modeling unit. The invention can solve the problem of applicability extension of the Cartesian grid coupled wall model under an immersed boundary and the problem of not being able to effectively meet the scale requirements of the Cartesian grid near the wall.

Description

Technical Field

[0001] The present invention relates to the field of computational fluid dynamics (CFD), and in particular to a method for constructing a Cartesian grid wall model. Background Art

[0002] As an orthogonal discrete grid, Cartesian grid has natural advantages in grid generation, which is different from body-fitted structured and unstructured grids. 1) The grid generation is fully automated, and high-quality orthogonal grids can be automatically and quickly generated for any complex shape; 2) It has strong adaptability and uses a fork tree data structure, which can easily adapt the grid according to needs. However, CFD simulations based on immersed Cartesian grids have difficulties in wall processing. For high Reynolds number flows, especially high Reynolds number wall turbulence problems, the strong anisotropy near the wall and the linear refinement of the Cartesian grid in all directions, the incoordination of the two makes it difficult to simulate wall-analytical turbulence with Cartesian grids. In order to obtain accurate wall flow information, the first layer of grid size often requires y + <1. At this time, the number of Cartesian grids in the boundary layer will increase exponentially with the Reynolds number, resulting in a large grid size. In traditional body-fitting structure / unstructured grids, wall models are usually used to relax the first layer grid size requirements to reduce the amount of calculation and accelerate convergence.

[0003] Among them, the wall model is a mathematical model used in CFD to simulate the behavior of fluid near the wall. It is based on the boundary layer theory and reduces the amount of calculation by simplifying the flow field near the wall into a quasi-steady area. The wall model covers not only wall functions, but also a series of physical modeling methods for dealing with flows near the wall. The wall function uses empirical formulas or semi-analytical formulas near the wall to describe the near-wall flow. Parameters such as wall distance, flow field velocity, and fluid properties are usually used to calculate the shear stress and friction coefficient at the wall, thereby affecting the velocity distribution of the flow and the development of the fluid boundary layer. By using the wall function in the wall model, the entire flow field can be accurately numerically simulated, while avoiding the computational difficulties and consumption of a large amount of computing resources of subdividing the entire flow field near the wall.

[0004] However, applying the wall model to the immersed Cartesian grid requires the applicability of the original body-fitting wall model method to be expanded accordingly. Specifically:

[0005] 1) If Figure 1 As shown, Figure 1This is a schematic diagram of the distribution of immersed adaptive Cartesian grids near the wall. Due to the non-body-fitting characteristics of the immersed Cartesian grid, the wall cannot be directly defined like a body-fitting grid, making it impossible to define the first layer of grid near the wall to implement the wall model, and it is impossible to effectively determine how many layers of grid are needed to implement the wall model.

[0006] 2) In the adaptive Cartesian grid of isotropic tree data (usually 4-tree in 2D and 8-tree in 3D), the grid transition will strictly follow the 1:2 growth ratio, and the growth ratio cannot be freely defined. The resulting problem is that the Cartesian grid scale near the wall modeling area cannot effectively meet the requirements of flow solution. Summary of the invention

[0007] The purpose of the present invention is to solve the problem of applicability extension of the Cartesian grid coupled wall model under immersed boundaries and the problem of not being able to effectively meet the scale requirements of the Cartesian grid near the wall.

[0008] To achieve the above-mentioned object of the invention, the present invention provides a method for constructing a Cartesian grid wall model, the method comprising:

[0009] Step 1: Construct a flow field calculation method for the wall modeling unit corresponding to the wall model;

[0010] Step 2: Correct the turbulent viscosity coefficient of the wall modeling unit corresponding to the wall model to obtain the corrected result of the turbulent viscosity coefficient;

[0011] Step 3: Calculate and obtain the modeling height of the flat plate boundary layer, and determine the wall modeling unit area based on the modeling height;

[0012] Step 4: Obtain the outermost Cartesian grid spacing that meets the grid size requirements;

[0013] Step 5: Based on the Cartesian grid spacing and the modeling height of the outermost layer, the number of Cartesian grid wall modeling layers included in the wall modeling unit corresponding to the wall model is calculated;

[0014] Step 6: Based on the flow field quantity calculation method of the wall modeling unit, the correction result of the turbulent viscosity coefficient, the wall modeling unit area and the number of Cartesian grid wall modeling layers included in the wall modeling unit, a wall model is constructed.

[0015] Among them, the principle of the present invention is: to construct a wall model based on Cartesian grids, aiming to solve several key problems in the background technology, especially the contradiction between the accuracy and computational efficiency of wall processing in traditional CFD simulation. By combining the flow field quantity calculation method, the correction of the turbulent viscosity coefficient, the regional division of the wall modeling unit and the number of grid layers, the present invention constructs a complete wall model. This method ensures that the accuracy of wall processing can be effectively improved in computational fluid dynamics simulation and reduces the computational cost by accurately controlling the flow characteristics near the wall and its grid division.

[0016] Wherein, the step 1 specifically includes:

[0017] The reference point information is obtained by interpolation, and the wall tangential and normal velocities at the reference point are calculated based on the reference point information and the outer normal of the wall;

[0018] Based on the reference point information and the wall tangential velocity at the reference point, the wall volume is obtained;

[0019] Based on the flow field quantity and wall quantity of the reference point, the flow field quantity calculation method of the wall modeling unit is reconstructed.

[0020] Among them, the wall tangential and wall normal velocities at the reference point are calculated as:

[0021] U n,r =(U r * n )* n ;

[0022] U t,r =U r -U n,r ;

[0023] Among them, U r is the velocity vector of the reference point, subscript r Indicates the reference point, n is the outer normal of the wall, subscript n represents the normal direction, t represents tangent direction, U n,r is the wall normal velocity at the reference point, U t,r is the wall tangential velocity at the reference point;

[0024] Among them, the flow field quantity of the wall modeling unit is calculated as follows:

[0025] ;

[0026] in, P f is the wall modeling unit pressure, T f is the wall modeling unit temperature, subscriptf represents the wall modeling unit, u t,f is the wall tangential velocity value of the wall modeling unit, u t,r is the wall tangential velocity at the reference point.

[0027] Among them, the calculation method of the wall normal velocity value and the wall tangential velocity value of the wall modeling unit is:

[0028] ;

[0029] in, y f is the distance from the wall modeling unit to the wall, y r is the distance from the reference point to the wall, u n,f is the wall normal velocity value of the wall modeling unit, u n,r is the wall normal velocity value of the reference point, y + is the dimensionless distance, u + is the dimensionless velocity, u τ is the wall friction velocity, is the dimensionless distance from the reference point, is the dimensionless distance of the wall modeling unit, For reference point u + about y + The derivative value of .

[0030] in, The calculation method is:

[0031] .

[0032] Among them, the correction method of the turbulent viscosity coefficient of the wall modeling unit corresponding to the wall model is:

[0033] ;

[0034] in, μ tur,f is the turbulent viscosity coefficient of the wall modeling unit, μ tur,r is the turbulent viscosity coefficient at the reference point, μ r is the molecular viscosity coefficient of the reference point, μ f is the molecular viscosity coefficient of the wall modeling unit.

[0035] The calculation method of the modeled height of the flat plate boundary layer is:

[0036] ;

[0037] in, H 模化 is the modeled height of the flat plate boundary layer, Re is the Reynolds number, L is the characteristic length, The expected wall model is valid according to the flat plate approximation formula y + value.

[0038] Among them, the calculation method of the outermost Cartesian grid spacing that meets the grid size requirements is:

[0039] ;

[0040] in, y + is the dimensionless distance, u + is the dimensionless velocity, with subscripts 1 and i Respectively represent the first or i The value at the layer.

[0041] The calculation method of the number of Cartesian grid wall modeling layers is:

[0042] ;

[0043] in, n 笛卡尔 is the number of Cartesian grid wall modeling layers, H 模化 is the modeled height of the flat plate boundary layer, The expected wall model is valid according to the flat plate approximation formula y + value.

[0044] The method further comprises: Step 7: performing turbulence numerical simulation calculation based on the wall model and the aircraft model. The high-precision wall model constructed by the method can accurately perform turbulence numerical simulation calculation on the aircraft model.

[0045] One or more technical solutions provided by the present invention have at least the following technical effects or advantages:

[0046] This method uses the construction idea based on the linearization of tangential velocity, the reference point flow field interpolation and the wall volume reconstruction method to achieve accurate modeling of the wall modeling unit flow field. This method can better fit the DNS data and y+ About 1~10 3 High-fidelity calibration is achieved within a wide range.

[0047] This method uses a prediction formula based on the thickness of the flat plate boundary layer: the prediction formula is used to estimate the thickness of the flat plate boundary layer, thereby determining the location of the wall modeling unit and the location of the reference point. This makes it easy to implement the wall model in an immersed Cartesian grid and ensure that the interpolation unit is surrounded by flow field units.

[0048] This method can make the Cartesian grid scale meet the requirements: according to the calibration du + / dy + = f ( y + ) formula can determine the outermost grid scale relationship between the wall modeling unit and the Cartesian grid, so as to achieve the matching of the calculation accuracy of the wall model and the grid scale near the wall. This can ensure that the modeling layers of the wall modeling unit meet the requirements of the velocity type grid distribution.

[0049] In summary, this method can improve the calculation accuracy of the wall model, conveniently implement the wall model, and ensure that the scale of the grid near the wall meets the requirements, which will have good application prospects and effects on complex fluid flow problems in numerical simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of the present invention, and do not constitute a limitation on the embodiments of the present invention;

[0051] Figure 1 Schematic diagram of the immersed adaptive Cartesian grid distribution near the wall;

[0052] Figure 2 A schematic diagram of a process for constructing a Cartesian grid wall model;

[0053] Figure 3 Schematic diagram of immersed Cartesian grid classification;

[0054] Figure 4 Schematic diagram of the comparison between the calibration formula proposed in this method and DNS and commonly used wall functions;

[0055] Figure 5 It is a schematic diagram of modeling height;

[0056] Figure 6 for Schematic diagram of the relationship between the number of modeling unit layers on the inner wall surface and the modeling height;

[0057] Figure 7for = Schematic diagram of friction distribution (logarithmic law area) under 90°;

[0058] Figure 8 for = Schematic diagram of friction distribution (logarithmic law area) under 60;

[0059] Fig. 9 for = 30 Schematic diagram of friction distribution (buffer zone);

[0060] Fig.10 for =20 Schematic diagram of friction distribution (buffer zone);

[0061] Fig.11 for = 10 Schematic diagram of friction distribution (viscous bottom layer);

[0062] Fig.12 for = 5 Schematic diagram of friction distribution (viscous bottom layer). DETAILED DESCRIPTION

[0063] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0064] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those within the scope of this description. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0065] Embodiment 1;

[0066] Please refer to Figure 2 , Figure 2 The present invention provides a method for constructing a Cartesian grid wall model, and the method comprises:

[0067] Step 1: Construct a flow field calculation method for the wall modeling unit corresponding to the wall model;

[0068] Step 2: Correct the turbulent viscosity coefficient of the wall modeling unit corresponding to the wall model to obtain the corrected result of the turbulent viscosity coefficient;

[0069] Step 3: Calculate and obtain the modeling height of the flat plate boundary layer, and determine the wall modeling unit area based on the modeling height;

[0070] Step 4: Obtain the outermost Cartesian grid spacing that meets the grid size requirements;

[0071] Step 5: Based on the Cartesian grid spacing and the modeling height of the outermost layer, the number of Cartesian grid wall modeling layers included in the wall modeling unit corresponding to the wall model is calculated;

[0072] Step 6: Based on the flow field quantity calculation method of the wall modeling unit, the correction result of the turbulent viscosity coefficient, the wall modeling unit area and the number of Cartesian grid wall modeling layers included in the wall modeling unit, a wall model is constructed.

[0073] Among them, in an embodiment of the present invention, the present invention relates to a wall model in CFD and a related grid generation method. The wall model is used to simulate the behavior of a fluid near a wall, such as wall shear stress and wall velocity. An immersed Cartesian grid solver is a method for numerically solving fluid mechanics equations, wherein Cartesian grid is a commonly used discretization grid method.

[0074] This method can be applied to practical engineering calculations to effectively guide the coupling calculations between the immersed Cartesian grid flow solver and the wall model, and improve the accuracy and reliability of computational fluid dynamics simulations. It is simple, robust and efficient, and can be used to conduct CFD wall function turbulence research.

[0075] Wherein, the method further includes: Step 7: performing turbulence numerical simulation calculation based on the wall model and the aircraft model.

[0076] Among them, the numerical simulation method of turbulence of the aircraft model is:

[0077] First, the wall model constructed by the method is implanted into the CFD simulation software, and then the corresponding aerodynamic parameters and aircraft model parameters are input, and then the aircraft model turbulence numerical simulation is started to obtain the simulation results. Since the wall model in the present invention has high precision, the accuracy of the aircraft model turbulence numerical simulation results finally obtained is also high. Among them, the aircraft model turbulence numerical simulation part can adopt the existing turbulence numerical simulation method, such as reference CN110489709A, CN116611368A, CN116776044A, CN118657090A, etc., and reference to high Reynolds number turbulence RANS numerical simulation based on embedded boundary method / wall model-"2016 Cross-Strait Fluid Mechanics Symposium Paper Abstracts"-Pu Tianmei, Zhou Chunhua, the present invention does not make corresponding repeated descriptions.

[0078] The adaptive Cartesian grid wall model construction method of the present invention belongs to a sharp immersion interface, so it is necessary to first classify the grids in the calculation domain. Figure 3 As shown, Figure 31-4 are fluid unit grids, r is the reference point, f is the wall modeling unit, n is the outer normal of the wall. According to the positional relationship between the grid center and the wall, it can be divided into fluid units (the grid center is located outside the wall), wall modeling units (usually 1~2 layers of grids near the wall, and this method can quantitatively derive the number of grid layers that meet the velocity type scale requirements), and internal units (the grid center is located inside the wall and does not participate in the calculation). Due to the non-body-fitting characteristics, each wall modeling unit needs to be pulled outward a certain distance according to the wall normal to find a reference point in the flow field, and the flow field needs to be interpolated. In order to ensure the interpolation accuracy, four surrounding fluid units are required to interpolate it in two dimensions.

[0079] The flow field construction of the wall modeling unit adopts the construction idea based on the linearization of tangential velocity. The specific steps are as follows:

[0080] a) Obtain reference point information (velocity, temperature, pressure, etc.) by interpolation and use the wall surface normal n Calculate the wall tangential and normal velocities at the reference point using the following formula:

[0081] U n,r =(U r * n )* n ;

[0082] U t,r =U r -U n,r ;

[0083] In the above formula, U is the velocity vector, and the subscript r Indicates reference point, subscript n represents the normal direction, t Indicates tangential direction.

[0084] b) Reconstruct the flow field value of the appropriate wall modeling unit through the flow field quantity at the reference point and the obtained wall quantity, where the pressure and temperature solutions are similar, namely:

[0085] ;

[0086] In the above formula P For pressure, T is the temperature, Pr is the Prandtl constant, c p is the specific heat capacity at constant pressure, f represents the wall modeling unit. The normal velocity and tangential velocity of the wall modeling unit are obtained by the following formula:

[0087] ;

[0088] In the above formulay is the distance to the wall, u is the speed magnitude, y + , u + and u τ are dimensionless distance, dimensionless velocity and wall friction velocity, respectively, which are obtained through specific wall function formulas. , given that the incompressible plate y + , u + With good similarity law, the present invention uses direct numerical simulation (DNS) of the flat plate Re θ =4060 cross section (based on momentum thickness θ A new scaling formula is proposed in the momentum thickness Reynolds number defined by the free flow, namely: du + / dy + = f ( y + ):

[0089] ;

[0090] Figure 4 DNS data and calibration formula are shown, as well as the Spalding formula y + right u + After the derivation, the comparison of the three is Figure 4 As can be seen, the classic Spalding formula can be well predicted du + / dy + Follow y + The new calibration formula in the present invention can fit the DNS data well, covering y + About 1~10 3 range, achieving high-fidelity calibration.

[0091] c) In order to ensure the shear stress balance of the boundary layer, it is also necessary to correct the turbulent viscosity coefficient of the wall modeling unit. The wall model assumes that the gradient of the tangential velocity below the reference point is constant, so the sum of the laminar and turbulent viscosity coefficients below the reference point must be equal, so:

[0092] ;

[0093] In order to better implement the wall model, the present invention adopts a prediction formula based on the thickness of the flat plate boundary layer to implement the scheme. Specifically, at a given Reynolds number Re , characteristic length L and The estimation formula for the flat plate boundary layer is:

[0094] ;

[0095] At this time, the schematic diagram of the wall model is as follows Figure 5 , that is, when the wall distance of the grid near the wall is less than H 模化 When , it is divided into wall modeling units. This makes it very convenient to implement the wall model in the immersed Cartesian grid; Figure 3 The position of the reference point can be determined, that is, the distance from the wall H 模化 + h The location ( h is the diagonal length of the wall modeling grid), so that the interpolation units around the reference point can be guaranteed to be flow field units.

[0096] In order to improve the calculation accuracy of the wall model and determine whether the scale of the grid near the wall meets the requirements, it is necessary to make Figure 5 The scale of the structured grid that directly solves the wall (without using the wall function) is equal to the scale of the outermost modeling unit of the wall model, that is, y i笛卡尔 = y i结构 The ideal grid distribution near the wall of the body-fitted structure grid is to generate the grid according to the wall velocity law. y 1 correspond y + When the velocity distribution is 1, the following relationship exists:

[0097] ;

[0098] exist Corresponding modeling height H 模化 In this case, the Cartesian grid is a uniform grid size. du + / dy + = f ( y +) formula can determine the Cartesian grid spacing of the outermost layer that meets the velocity type grid size requirements, thereby obtaining the number of Cartesian-wall function grid wall modeling layers that should be included in the modeling height n 笛卡尔 .

[0099] ;

[0100] The calibrated du + / dy + = f ( y + ) formula, we get n 笛卡尔 Follow The relationship curve of the change is as follows Figure 6 shown.

[0101] That is given The number of wall modeling unit layers contained in the modeling height is greater than Figure 6 When the value of the middle curve is , the outermost Cartesian grid can meet the grid distribution requirements of the velocity type. Figure 6 for Schematic diagram of the relationship between the number of modeling unit layers on the inner wall surface and the modeling height, from Figure 6 It can be seen from the figure that when the wall model of the present invention is used, if the wall model is effective in the logarithmic law region, it is only necessary to ensure that there are two layers of Cartesian grids within the modeling height to meet the scale requirement.

[0102] In order to facilitate the implementation of the immersed boundary-wall model, the present invention adopts a flat plate approximation formula to obtain a modeling height to quantitatively divide the wall modeling unit, and determines the pull-out distance of the reference point closest to the wall; further, a calibration formula is proposed du + / dy + = f ( y + ), through the calibrated new formula, the grid scale requirements that the wall modeling Cartesian grid unit needs to meet can be quantitatively derived (the number of Cartesian grid layers in the quantitative modeling unit).

[0103] To prove Figure 6 Consider the following example: for a flat plate, the incoming flow Mach number Ma=0.2, and the Reynolds number Re=1×10 based on a plate length of 1.6 m. 6 , design 6 different The specific grid settings of the 16 examples under the viscous bottom layer, buffer layer, and logarithmic law region are shown in Table 1. Table 1 is the grid setting table for the flat plate example, and the SST turbulence model is selected. Each time the maximum mesh refinement level is increased, the wall function mesh cells at the same modeling height will double.

[0104] Table 1

[0105]

[0106] Different in this case y + The results under the interval are shown in Figure 7-Figure 12 , first, when the modeling height range is set in the logarithmic law region, (i.e. for 90 and 60 cases), n 笛卡尔 The difference between 2 and 4 is very small, which is consistent with the experiment. When the effective interval of the wall function falls in the transition zone (i.e., 30 and 20), the prediction of friction resistance improves with the increase of the number of wall function layers. Finally, when the effective interval of the wall function is in the viscous bottom layer, the number of grid layers required within the modeling height is Figure 6 Prediction, will follow y + Increase and increase, and in y + The peak value is reached when it is 10. When is 10, the distribution of friction and velocity type is n 笛卡尔 When there are only 2 layers, the error will increase further until n 笛卡尔 The convergence is gradually achieved with 8 layers.

[0107] In summary, it is further verified Figure 6 The accuracy of the predicted grid scale requirements. Overall, it is recommended that the Cartesian grid immersed boundary-wall function falls within the logarithmic law interval. On the one hand, it can reduce the grid scale requirements and save program solution time; at the same time, only 2 to 4 layers of wall function units above the wall are needed to meet the grid scale requirements.

[0108] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0109] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for constructing a Cartesian grid wall model, characterized in that: The method comprises: Step 1: Construct a flow field calculation method for the wall modeling unit corresponding to the wall model; Step 2: Correct the turbulent viscosity coefficient of the wall modeling unit corresponding to the wall model to obtain the corrected result of the turbulent viscosity coefficient; Step 3: Calculate and obtain the modeling height of the flat plate boundary layer, and determine the wall modeling unit area based on the modeling height; Step 4: Obtain the outermost Cartesian grid spacing that meets the grid size requirements; Step 5: Based on the Cartesian grid spacing and the modeling height of the outermost layer, the number of Cartesian grid wall modeling layers included in the wall modeling unit corresponding to the wall model is calculated; Step 6: Based on the flow field quantity calculation method of the wall modeling unit, the correction result of the turbulent viscosity coefficient, the wall modeling unit area and the number of Cartesian grid wall modeling layers included in the wall modeling unit, a wall model is constructed; The step 1 specifically includes: The reference point information is obtained by interpolation, and the wall tangential and normal velocities at the reference point are calculated based on the reference point information and the outer normal of the wall; Based on the reference point information and the wall tangential velocity at the reference point, the wall volume is obtained; Based on the flow field quantity and wall quantity of the reference point, the calculation method of the flow field quantity of the wall modeling unit is reconstructed; The wall tangential and wall normal velocities at the reference point are calculated as: IN n,r =(U r * n )* n ; IN t,r =U r -IN n,r ; Among them, U r is the velocity vector of the reference point, subscript r Indicates the reference point, n is the outer normal of the wall, subscript n represents the normal direction, t represents tangent direction, U n,r is the wall normal velocity vector at the reference point, U t,r is the wall tangential velocity vector at the reference point; The flow field quantity of the wall modeling unit is calculated as follows: ； in, P f is the wall modeling unit pressure, T f is the wall modeling unit temperature, subscript f represents the wall modeling unit, u t,f is the wall tangential velocity value of the wall modeling unit, u t,r is the wall tangential velocity value at the reference point; The wall normal velocity and wall tangential velocity of the wall modeling unit are calculated as follows: ； in, y f is the distance from the wall modeling unit to the wall, y r is the distance from the reference point to the wall, u n,f is the wall normal velocity value of the wall modeling unit, u n,r is the wall normal velocity value of the reference point, y + is the dimensionless distance, u + is the dimensionless velocity, u τ is the wall friction velocity, is the dimensionless distance from the reference point, is the dimensionless distance of the wall modeling unit, For reference point u + about y + The derivative value of The calculation method is: ； The outermost Cartesian grid spacing that meets the grid size requirements is calculated as: ； in, y + is the dimensionless distance, u + is the dimensionless velocity, with subscripts 1 and i Respectively represent the first or i The value at the layer; The calculation method for the number of Cartesian grid wall modeling layers is: ； in, n 笛卡尔 is the number of Cartesian grid wall modeling layers, H 模化 is the modeled height of the flat plate boundary layer, The expected wall model is valid according to the flat plate approximation formula y + value.

2. A Cartesian grid wall model construction method according to claim 1, characterized in that: The correction method of the turbulent viscosity coefficient of the wall modeling unit corresponding to the wall model is: ； in, μ tur,f is the turbulent viscosity coefficient of the wall modeling unit, μ tur,r is the turbulent viscosity coefficient at the reference point, μ r is the molecular viscosity coefficient of the reference point, μ f is the molecular viscosity coefficient of the wall modeling unit.

3. A Cartesian grid wall model construction method according to claim 1, characterized in that: The modeled height of the flat plate boundary layer is calculated as: ； in, H 模化 is the modeled height of the flat plate boundary layer, Re is the Reynolds number, L is the characteristic length, The expected wall model is valid according to the flat plate approximation formula y + value.

4. A Cartesian grid wall model construction method according to claim 1, characterized in that: The method further comprises: Step 7: Perform turbulence numerical simulation based on the wall model and aircraft model.

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