Space complex curved surface turbulence boundary generation method

Abstract

The invention discloses a space complex curved surface turbulence boundary generation method, and relates to the technical field of turbulence boundary generation, the method comprises the following steps: obtaining a space curved surface grid of a free incoming flow boundary, and preprocessing the space curved surface grid to obtain data information of the space curved surface grid and data information of a cuboid space grid; calculating to obtain a theoretical pulsation speed based on a preset incoming flow turbulence degree and a free incoming flow speed; according to the data information of the cuboid space grid and the von K-alpha-rm-alpha-n-Pao turbulence energy spectrum model, calculating to obtain a space pulsation velocity vector field; the turbulence energy spectrum model comprises a theoretical pulsation speed; and based on the space pulsation velocity vector field, data interpolation is carried out on the surface center point of each surface grid block in the space curved surface grid by using a nearest space interpolation method, and a turbulence boundary which is suitable for a space complex curved surface and meets a real turbulence energy spectrum relationship is determined and obtained.

Description

Technical Field

[0001] The present application relates to the technical field of turbulent boundary generation, and in particular to a method for generating turbulent boundaries on complex spatial surfaces. Background Art

[0002] In the field of high-fidelity numerical simulation in computational fluid dynamics, the transition and turbulent boundary layers on the surface of objects are extremely sensitive to free-flow conditions. The proper and accurate setting of turbulent boundaries is directly related to the simulation accuracy of these two types of flow phenomena using high-fidelity numerical simulation methods such as Reynolds-Averaged Navier-Stokes (RANS) / Large Eddy Simulation (LES) hybrid simulations, LES, and direct numerical simulations. This is because the pulsating information at the turbulent inlet is unknown and highly stochastic. When performing high-fidelity numerical simulations, it is necessary to manually set turbulent boundaries that contain certain pulsating information. Whether this pulsating information accurately reflects the actual turbulence and whether it can reproduce the actual turbulent evolution process as it develops downstream is the key to achieving high-fidelity numerical simulations.

[0003] Currently, the methods for generating turbulence are mainly divided into two categories: pre-simulation method and artificial synthesis method. Among them, the pre-simulation method usually requires solving two computational domains. First, a stable flow field needs to be simulated in the auxiliary computational domain, and then the processed flow field information is transferred to the inlet boundary of the main computational domain. Although this method can provide relatively accurate turbulent boundary conditions, it is difficult to directly obtain a stable flow field with target turbulence characteristics. It requires multiple debugging and repeated calculations, which is inefficient and costly. The artificial synthesis method directly generates turbulent conditions by giving the corresponding turbulent pulsation information through random process simulation. Although this type of method is relatively simple, it has significant shortcomings. The artificial synthesis method based on white noise, Gaussian white noise, etc., because its noise component is incompatible with the NS (Navier-Stokes) equation, the turbulence obtained is quite different from the actual situation and decays rapidly, and cannot effectively restore the actual turbulence decay process.

[0004] At the same time, for complex shapes, especially those at hypersonic speeds, creating computational meshes suitable for high-fidelity numerical simulations requires both efficient mesh utilization and accurate capture of shock wave structures. Consequently, the generated computational meshes often feature complex three-dimensional curved incoming flow boundaries, making traditional two-dimensional planar turbulence generation methods difficult to apply to complex three-dimensional aircraft. Summary of the Invention

[0005] The purpose of this application is to provide a method for generating turbulent boundaries on complex spatial surfaces, which can simply and conveniently generate turbulent boundaries that are suitable for complex spatial surfaces and satisfy the real turbulent energy spectrum relationship, and provide certain technical support for high-fidelity numerical simulation research on complex three-dimensional aircraft in terms of boundary layer transition and turbulence development and evolution.

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] In a first aspect, the present application provides a method for generating turbulent boundaries on a spatially complex curved surface, comprising:

[0008] Acquire a spatial surface mesh of a free flow boundary, construct a spatial Cartesian coordinate system for the spatial surface mesh, and perform preprocessing operations on the spatial surface mesh to obtain data information of the spatial surface mesh and data information of a rectangular space mesh; the spatial surface mesh is composed of a plurality of surface mesh blocks; the data information of the spatial surface mesh includes the coordinates of the vertices of each surface mesh block and the coordinates of the center point of each surface mesh block; the rectangular space mesh is composed of a plurality of volume mesh blocks, and the rectangular space mesh can surround the spatial surface mesh; the volume mesh blocks are obtained based on mesh node division; the data information of the rectangular space mesh includes the scale information of the rectangular space mesh, the coordinates of the vertices of each volume mesh block, and the coordinates of the center point of each volume mesh block;

[0009] Based on the preset incoming flow turbulence and free incoming flow velocity, the theoretical pulsation velocity is calculated;

[0010] A spatial pulsating velocity vector field is calculated based on the data information of the rectangular space grid and the von Kármán-Pao turbulence energy spectrum model; the von Kármán-Pao turbulence energy spectrum model includes the theoretical pulsating velocity; the spatial pulsating velocity vector field includes the pulsating velocity of the body center point of each volume grid block;

[0011] Based on the spatial pulsating velocity vector field, a nearest neighbor spatial interpolation method is used to perform data interpolation on the surface center point of each surface grid block in the spatial curved surface grid to determine a turbulent boundary.

[0012] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0013] The present application provides a method for generating turbulent boundaries on complex spatial surfaces. First, by preprocessing the spatial surface mesh of the free flow boundary and converting it into a rectangular spatial mesh, a structured and regularized mesh data is provided for the calculation of the turbulent boundary, which effectively reduces the difficulty of complex surface meshes in numerical calculations and simplifies subsequent calculations without losing accuracy. Secondly, the von Kármán-Pao turbulence energy spectrum model is used for calculation, and combined with the theoretical pulsating velocity parameters, a spatial pulsating velocity vector field is obtained. The pulsating velocity field generated by this model can accurately describe the turbulent characteristics in the flow field, making the generation process of the turbulent boundary more consistent with actual fluid dynamics phenomena. After obtaining the spatial pulsating velocity vector field, the turbulent boundary suitable for complex spatial surfaces can be obtained by the nearest neighbor spatial interpolation method. It can be seen that the present application can simply and conveniently generate turbulent boundaries suitable for complex spatial surfaces and satisfying the real turbulent energy spectrum relationship, providing certain technical support for high-fidelity numerical simulation research on complex three-dimensional aircraft in terms of boundary layer transition and turbulence development and evolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0015] Figure 1 A schematic diagram of a flow chart of a method for generating turbulent boundaries on a spatially complex curved surface provided in one embodiment of the present application;

[0016] Figure 2 A schematic diagram of a calculation grid for the shape of a wing-body assembly provided in another embodiment of the present application;

[0017] Figure 3 A schematic diagram of a spatial curved surface mesh A and a spatial curved surface mesh B obtained by topologically partitioning the free flow boundary of the wing-body assembly shape according to another embodiment of the present application;

[0018] Figure 4 A schematic flow chart of a method for generating turbulent boundaries on a spatially complex curved surface provided in another embodiment of the present application;

[0019] Figure 5 The rectangular space grid A obtained by mesh preprocessing the space surface grid A provided in another embodiment of the present application is T Schematic diagram of;

[0020] Figure 6a Another embodiment of the present application provides a rectangular space grid AT Schematic diagram of the pulsating velocity generated in the x-direction;

[0021] Figure 6b Another embodiment of the present application provides a rectangular space grid A T Schematic diagram of the pulsating velocity generated in the y direction;

[0022] Figure 6c Another embodiment of the present application provides a rectangular space grid A T Schematic diagram of the pulsating velocity generated in the z direction;

[0023] Figure 7a A schematic diagram of the pulsating velocity in the x-direction of a turbulent boundary generated on a spatial curved surface grid A provided in another embodiment of the present application;

[0024] Figure 7b A schematic diagram of the pulsating velocity in the y direction of a turbulent boundary generated on a spatial curved surface grid A provided in another embodiment of the present application;

[0025] Figure 7c A schematic diagram of the pulsating velocity in the z direction of a turbulent boundary generated on a spatial curved surface grid A provided in another embodiment of the present application;

[0026] Figure 8 The rectangular space grid B obtained by mesh preprocessing the space surface grid B provided in another embodiment of the present application is T Schematic diagram of;

[0027] Figure 9a Another embodiment of the present application provides a rectangular space grid B T Schematic diagram of the pulsating velocity generated in the x-direction;

[0028] Figure 9b Another embodiment of the present application provides a rectangular space grid B T Schematic diagram of the pulsating velocity generated in the y direction;

[0029] Figure 9c Another embodiment of the present application provides a rectangular space grid B T Schematic diagram of the pulsating velocity generated in the z direction;

[0030] Figure 10a A schematic diagram of the pulsating velocity in the x-direction of a turbulent boundary generated on a spatial curved surface grid B provided in another embodiment of the present application;

[0031] Figure 10b A schematic diagram of the pulsating velocity in the y direction of a turbulent boundary generated on a spatial curved surface grid B provided in another embodiment of the present application;

[0032] Figure 10c A schematic diagram of the pulsating velocity in the z direction of a turbulent boundary generated on a spatial curved surface grid B provided in another embodiment of the present application. DETAILED DESCRIPTION

[0033] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0034] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0035] In an exemplary embodiment, Figure 1 As shown, a method for generating turbulent boundaries on a spatial complex curved surface is provided, comprising the following steps 101 to 104. In which:

[0036] Step 101, obtain the spatial surface mesh of the free flow boundary, construct a spatial Cartesian coordinate system for the spatial surface mesh and perform preprocessing operations on the spatial surface mesh to obtain data information of the spatial surface mesh and data information of the rectangular space mesh; the spatial surface mesh is composed of multiple surface mesh blocks; the data information of the spatial surface mesh includes the coordinates of the vertices of each surface mesh block and the coordinates of the center point of each surface mesh block; the rectangular space mesh is composed of multiple volume mesh blocks, and the rectangular space mesh can surround the spatial surface mesh; the volume mesh blocks are obtained based on the division of mesh nodes; the data information of the rectangular space mesh includes the scale information of the rectangular space mesh, the coordinates of the vertices of each volume mesh block and the coordinates of the center point of each volume mesh block.

[0037] Step 102: Calculate the theoretical pulsating velocity based on the preset incoming flow turbulence and free incoming flow velocity.

[0038] Step 103 , based on the data information of the rectangular space grid and the von Kármán-Pao turbulence energy spectrum model, a spatial pulsating velocity vector field is calculated; the von Kármán-Pao turbulence energy spectrum model includes a theoretical pulsating velocity; and the spatial pulsating velocity vector field includes the pulsating velocity of the body center point of each volume grid block.

[0039] Step 104 : Based on the spatial pulsating velocity vector field, a nearest neighbor spatial interpolation method is used to perform data interpolation on the surface center point of each surface grid block in the spatial surface grid to determine the turbulent boundary.

[0040] Furthermore, step 101 reads in the spatial surface mesh of the free flow boundary, constructs a spatial Cartesian coordinate system for the spatial surface mesh, and performs preprocessing operations on the spatial surface mesh to obtain data information of the spatial surface mesh. A rectangular spatial mesh that can enclose the spatial surface mesh is then generated, and the data information of the rectangular spatial mesh is obtained to prepare for the subsequent random generation of the spatial pulsating velocity vector field. Specifically, the following steps are included:

[0041] Step 1011: Based on the read and stored spatial surface mesh data, determine the coordinate position (x, y, z) of each mesh node in the spatial surface mesh data in the spatial Cartesian coordinate system, and obtain the maximum and minimum values ​​of all mesh nodes in three directions (i.e., x-axis, y-axis, and z-axis), including x max 、x min 、y max 、y min 、z max and z min .

[0042] Step 1012: Calculate the coordinates of the center points of all surface grid blocks based on the coordinate positions of the above grid nodes and store them as (x c ,y c , z c The specific calculation process is as follows:

[0043] Considering that the spatial surface mesh is actually composed of many planar quadrilateral mesh blocks, in order to obtain the coordinates of the surface center point of the mesh block, it is first necessary to establish the corresponding diagonal intersection parameterization equation based on the four vertices A(x1, y1, z1), B(x2, y2, z2), C(x3, y3, z3), and D(x4, y4, z4) of each mesh block in the spatial surface mesh:

[0044] x1+t(x3-x1)=x2+s(x4-x2)(1);

[0045] y1+t(y3-y1)=y2+s(y4-y2)(2);

[0046] z1+t(z3-z1)=z2+s(z4-z2)(3);

[0047] Where t and s represent the parameterized coordinates of the surface center point. By solving any two of the above equations simultaneously, we can obtain t and s.

[0048] Then, the coordinates of the center point (x c ,y c , z c ):

[0049] x c=x1+t(x3-x1)(4);

[0050] y c =y1+t(y3-y1)(5);

[0051] z c =z1+t(z3-z1)(6);

[0052] Step 1013: Based on the maximum and minimum values ​​in the x, y, and z directions obtained in step 1011, establish a distribution range that satisfies {x∈[x min ,x max ],y∈[y min ,y max ],z∈[z min ,z max The cuboid space grid is used to enclose the space surface grid, and the number of grid nodes in the three directions of the cuboid space grid can be manually specified (N x ,N y ,N z ) and distribution, and also stores the scale information of the cuboid space grid (L x ,L y ,L z ).

[0053] Step 1014: Calculate the coordinates of the center points of all volume grid blocks of the cuboid space grid and store them as (x t ,y t , z t Since the eight grid nodes of any volume grid block are strictly distributed according to the rectangular coordinate system, the coordinates of the body center point can be obtained by the following calculation method:

[0054] x t =0.125(x1+x2+x3+x4+x5+x6+x7+x8)(7);

[0055] y t =0.125(y1+y2+y3+y4+y5+y6+y7+y8)(8);

[0056] z t =0.125(z1+z2+z3+z4+z5+z6+z7+z8)(9);

[0057] The parameters involved in the above formula represent the coordinate data of the eight vertices of the volume mesh block, namely N1 (x1, y1, z1) to N8 (x8, y8, z8).

[0058] Furthermore, step 102: calculating the theoretical pulsating velocity based on the given incoming flow turbulence and free incoming flow velocity.

[0059] According to the input flow turbulence Tu ∞ and free flow velocity U ∞ , calculate the theoretical pulsation speed U rms , the calculation formula is as follows:

[0060] U rms =Tu ∞ ×U ∞ (10);

[0061] Furthermore, step 103: generating a discrete divergence-free pulsating velocity vector field at each center point of the rectangular space grid according to the von Kármán-Pao turbulence energy spectrum model.

[0062] For a specific body center point N(x t ,y t , z t ), the following theoretical formula is used to generate the pulsating velocity:

[0063]

[0064] in, is the pulsating velocity in the x direction, is the pulsating velocity in the y direction, is the pulsating speed in the z direction, M is the total number of preset waves, a m is the amplitude of the mth wave number, k m is the mth wave number, is the first unit direction vector, is the relative displacement vector related to the coordinates of the center point of the current volume grid block, φ is the phase angle randomly distributed in the interval [-π / 2,π / 2], is the second unit direction vector.

[0065] Specifically, the generation process includes the following steps:

[0066] Step 1031: Based on the read or stored M, (N x ,N y ,N z ) and (L x ,L y ,L z ), calculate the mth wave number k m , the calculation process is as follows:

[0067] First determine the minimum wave number k min and the maximum wave number k max :

[0068]

[0069]

[0070] in,

[0071] Then, based on M,k min and k max Calculate k m :

[0072] k m =k min +Δk(m-1) (16);

[0073]

[0074] Among them, Δk is the change value between two adjacent wave numbers.

[0075] Step 1032: Calculate the amplitude a of the mth wave number according to the von Kármán-Pao turbulence energy spectrum model E(k) m , the calculation process is as follows:

[0076]

[0077] Where α is a scale factor, for isotropic turbulence α=1.453, U rms is the theoretical pulsation velocity calculated in step 102, k e is the wave number associated with the maximum energy E(k0), for normal flow k0 = 40, k η is the Kolmogorov wave number, f(k m ) is the wave number k m and wave number k η , ν is the kinematic viscosity of the fluid, ε is the dissipation rate, and

[0078] Step 1033: Calculate the first unit direction vector associated with the mth wave number and the body center point N(x t ,y t , z t ) related relative displacement vector

[0079] l xm =sin(θ)cos(σ); l ym =sin(θ)sin(σ); l zm = cos(θ)(23);

[0080] x e =x t -x min ;ye =y t -y min ;z e =z t -z min (twenty four);

[0081] Where θ and σ are random numbers distributed in the interval [0, 2π].

[0082] Step 1034: Calculate and Perpendicular second unit direction vector

[0083] First, we need to construct the auxiliary vector The corresponding f can be obtained by the same calculation method as formula (23) xm ,f ym ,f zm .

[0084] Then, to construct a divergence-free velocity field on the discretized volume grid, the modified wavenumber direction vector The calculation formula is as follows:

[0085]

[0086] Among them, the involved Δx, Δy, and Δz are consistent with formula (15).

[0087] Finally, the vector cross product is used to obtain the unit direction vector

[0088]

[0089] Step 1035: Traverse each center point of the volume grid, repeat steps 1033-1034, and substitute the calculated corresponding parameters into formulas (11)-(13), thereby obtaining a complete spatial pulsating velocity vector field.

[0090] Furthermore, step 104: based on the spatial pulsating velocity vector field, the nearest neighbor spatial interpolation method is used to perform data interpolation on the surface center point of each surface grid block in the spatial surface grid to determine the turbulent boundary.

[0091] Specifically, the method includes the following steps:

[0092] Step 1041: For a specific surface mesh block, the center point M(x c ,y c , z c), perform nearest neighbor search in the cuboid space grid, determine the four centroid points closest to point M, mark them as T1, T2, T3, and T4 respectively, and record the distances from point M to these four points, mark them as d1, d2, d3, and d4 respectively. Then, interpolate the pulsating velocity data of point M based on the distance weight method, as follows:

[0093]

[0094] Among them, ω1~ω4 are the inverse of the distance and represent the corresponding weight coefficients. They represent the point T obtained based on step 103 respectively i The pulsation speed of (i=1,2,3,4) It represents the pulsation speed of point M obtained after interpolation processing.

[0095] Step 1042: Traverse each center point of the spatial surface mesh and repeat step 1041 to obtain a turbulent boundary that is applicable to complex spatial surfaces and satisfies the von Kármán-Pao turbulence energy spectrum relationship.

[0096] In another exemplary embodiment of the present application, a wing-body assembly shape is used as the application scenario of this embodiment. The wing-body assembly shape has a total length of 405.3 mm, a non-axisymmetric circular cross-section at the bottom, a circular cross-section radius of the upper half (upper surface) of 39.5 mm, a circular cross-section radius of the lower half (lower surface) of 58.8 mm, and a model bottom height of 61.2 mm. The model wing is a swept delta wing, the angle between the swept wing and the centerline of the fuselage is 13°, and the swept wing width at the bottom of the model is 190.4 mm. The free flow condition is Ma ∞ =6, T ∞ =52.93K, U ∞ =875.23m / s, and the freeflow turbulence used for testing was set to 2.0%. Due to the symmetrical shape of the wing-body assembly, a half-module multi-zone docking grid was used for the calculation to reduce the computational effort. To ensure the quality of the computational grid, the freeflow boundary of the wing-body assembly's shape required a reasonable topological division. Therefore, the freeflow boundary of the wing-body assembly's shape was divided into two parts: the first part is a spatial surface grid with a very small area at the head, and the remaining spatial surface grids constitute the second part of the freeflow boundary. Figure 2 It is the calculation grid of the wing-body assembly shape in this embodiment. Figure 3 These are the space curved surface mesh A and the space curved surface mesh B obtained by topologically dividing the free flow boundary of the wing-body assembly shape in this embodiment.

[0097] according to Figure 4The flow chart shown in the figure describes the specific process of generating the turbulent boundary of the wing-body assembly shape in this embodiment. Since the free flow boundary of the wing-body assembly shape is divided into two parts, it is necessary to generate the corresponding turbulent boundaries one by one. Figure 3 Generate turbulent boundaries using the spatial surface mesh A in :

[0098] Step 1: Read in the spatial surface mesh A and perform mesh preprocessing to generate a rectangular spatial mesh A that can surround it T Specifically:

[0099] Step 1.1: Based on the mesh data of the spatial surface mesh A, determine the coordinate position (x, y, z) of each mesh node in the spatial Cartesian coordinate system, and obtain the maximum and minimum values ​​of all mesh nodes in the three directions. The result shows x max =-19.7mm, x min =-36.2mm, y max =-0.21mm, y min =-34.8mm, z max =36.6mm and z min =-36.6mm.

[0100] Step 1.2: Calculate the coordinates of the center points of all surface grid blocks based on the coordinate positions of the above grid nodes and store them as (x c ,y c , z c The specific calculation process is as follows:

[0101] First, we need to establish the corresponding diagonal intersection parameterization equation based on the four vertices A(x1, y1, z1), B(x2, y2, z2), C(x3, y3, z3), and D(x4, y4, z4) of a surface mesh block:

[0102] x1+t(x3-x1)=x2+s(x4-x2)(1);

[0103] y1+t(y3-y1)=y2+s(y4-y2)(2);

[0104] z1+t(z3-z1)=z2+s(z4-z2)(3);

[0105] Where t and s represent the parameterized coordinates of the surface center point. By solving any two of the above equations simultaneously, we can obtain t and s.

[0106] Then, the coordinates of the center point (x c ,y c , z c ):

[0107] x c =x1+t(x3-x1)(4);

[0108] y c =y1+t(y3-y1)(5);

[0109] z c =z1+t(z3-z1)(6);

[0110] Step 1.3: Based on the maximum and minimum values ​​of the x, y, and z directions obtained in step 1.1, establish a rectangular space grid with a distribution range of {x∈[-36.2,-19.7], y∈[-34.8,-0.2], z∈[-36.6,36.6]} (unit: mm) to surround the spatial surface grid A. Specify that the grid points of the rectangular space grid are evenly distributed in the three directions and have {N x =50,N y =80,N z = 80}, and store the scale information of the rectangular space grid {L x =16.5mm,L y =34.6mm,L z =73.2mm}. Figure 5 This is the cuboid space mesh A obtained by mesh preprocessing the space surface mesh A in this embodiment. T .

[0111] Step 1.4: Calculate the cuboid space mesh A T The body center coordinates of all volume mesh blocks are stored as (x t ,y t , z t ). The calculation method is as follows:

[0112] x t =0.125(x1+x2+x3+x4+x5+x6+x7+x8)(7);

[0113] y t =0.125(y1+y2+y3+y4+y5+y6+y7+y8)(8);

[0114] z t =0.125(z1+z2+z3+z4+z5+z6+z7+z8)(9);

[0115] The parameters involved in the above formula represent the coordinate data of the eight vertices of the volume mesh block, namely N1 (x1, y1, z1) to N8 (x8, y8, z8).

[0116] Step 2: Calculate the theoretical pulsation velocity based on the given incoming flow turbulence and free stream velocity.

[0117] According to the input flow turbulence Tu ∞ and free flow velocity U ∞ , calculate the theoretical pulsation speed U rms , the results are as follows:

[0118] U rms =Tu ∞ ×U ∞ =2.0%×875.23=17.5m / s(10);

[0119] Step 3: According to the von Kármán-Pao turbulence energy spectrum model, in the rectangular space grid A T A discrete divergence-free pulsating velocity vector field is generated at each body center point of .

[0120] For a specific body center point N(x t ,y t , z t ), the following theoretical formula is used to generate the pulsating velocity:

[0121]

[0122] in, is the pulsating velocity in the x direction, is the pulsating velocity in the y direction, is the pulsating speed in the z direction, M is the total number of preset waves, a m is the amplitude of the mth wave number, k m is the mth wave number, is the first unit direction vector, is the relative displacement vector related to the coordinates of the center point of the current volume grid block, φ is the phase angle randomly distributed in the interval [-π / 2,π / 2], is the second unit direction vector.

[0123] Specifically, the generation process includes the following steps:

[0124] Step 3.1 Based on the read or stored M, (N x ,N y ,N z ) and (L x ,L y ,L z ), calculate the mth wave number k m , the calculation process is as follows:

[0125] First determine the minimum wave number k min and the maximum wave number k max:

[0126]

[0127] in,

[0128] Then, based on M,k min and k max Calculate k m :

[0129] k m =k min +Δk(m-1)(16);

[0130]

[0131] Among them, Δk is the change value between two adjacent wave numbers.

[0132] Step 3.2: Calculate the amplitude a of the mth wave number according to the von Kármán-Pao turbulence energy spectrum model E(k) m , the calculation process is as follows:

[0133]

[0134] Where α is a scale factor, for isotropic turbulence α=1.453, U rms is the theoretical pulsation velocity calculated in step 2, k e is the wave number associated with the maximum energy E(k0), for normal flow k0 = 40, k η is the Kolmogorov wave number, f(k m ) is the wave number k m and wave number k η , ν is the kinematic viscosity of the fluid, ε is the dissipation rate, and

[0135] Step 3.3: Calculate the unit direction vector associated with the mth wave number and the body center point N(x t ,y t , z t ) related relative displacement vector

[0136] l xm =sin(θ)cos(σ); l ym =sin(θ)sin(σ); l zm = cos(θ)(23);

[0137] x e =x t -x min;y e =y t -y min ;z e =z t -z min (twenty four);

[0138] Where θ and σ are random numbers distributed in the interval [0, 2π].

[0139] Step 3.4: Calculate and vertical unit direction vector

[0140] First, we need to construct the auxiliary vector The corresponding f can be obtained by the same calculation method as formula (23) xm ,f ym ,f zm .

[0141] Then, to construct a divergence-free velocity field on the discretized volume grid, the modified wavenumber direction vector The calculation formula is as follows:

[0142]

[0143] Among them, the involved Δx, Δy, and Δz are consistent with formula (15).

[0144] Finally, the vector cross product is used to obtain the unit direction vector

[0145]

[0146] Step 3.5: Traverse each center point of the volume grid, repeat steps 3.1-3.4, and substitute the calculated corresponding parameters into formulas (11)-(13), thereby obtaining a complete spatial pulsating velocity vector field. Figure 6a-6c This embodiment is in the rectangular space grid A T A discrete divergence-free pulsating velocity vector field is generated on the surface. Specifically, Figure 6a is the pulsating velocity in the x direction, Figure 6b is the pulsating velocity in the y direction, Figure 6c is the pulsating velocity in the z direction.

[0147] Step 4: Based on the nearest neighbor spatial interpolation method, perform data interpolation on the center point of each surface grid block in the spatial surface grid A to obtain the corresponding pulsating velocity vector field. Specifically:

[0148] Step 4.1: For a specific face mesh block’s face center point M(x c ,y c, z c ), perform a nearest neighbor search in the cuboid space grid to determine the four centroid points closest to point M, marked as T1, T2, T3, and T4 respectively, and record the distances from point M to these four points, marked as d1, d2, d3, and d4 respectively. Then, interpolate the pulsating velocity data of point M based on the distance weight method, as follows:

[0149]

[0150] Among them, ω1~ω4 are the inverse of the distance and represent the corresponding weight coefficients. Represent the point T obtained based on step 3 i The pulsation speed of (i=1,2,3,4) It represents the pulsation speed of point M obtained after interpolation processing.

[0151] Step 4.2: Traverse each center point of the spatial surface mesh A and repeat step 4.1 to obtain a turbulent boundary that is suitable for complex spatial surfaces and satisfies the von Kármán-Pao turbulence energy spectrum relationship. Figure 7a-7c is the turbulent boundary generated on the spatial surface mesh A in this embodiment. Specifically, Figure 7a is the pulsating velocity in the x direction, Figure 7b is the pulsating velocity in the y direction, Figure 7c is the pulsating velocity in the z direction.

[0152] When generating turbulence boundary for space surface mesh B, in addition to the cuboid space mesh B T The number of grid points is set to {N x =500,N y =150,N z =150}, the process is exactly the same as the turbulence boundary generation process of the spatial surface mesh A. It is described as follows:

[0153] Step 1: Read in the spatial surface mesh B and perform mesh preprocessing to generate a rectangular spatial mesh B that can surround it T . Figure 8 The cuboid space mesh B is obtained by pre-processing the space surface mesh B in this embodiment. T .

[0154] Step 2: Calculate the theoretical pulsation velocity based on the given incoming flow turbulence and free stream velocity.

[0155] According to the input flow turbulence Tu ∞ and free flow velocity U ∞ , calculate the theoretical pulsation speed U rms , the results are as follows:

[0156] U rms =Tu ∞ ×U ∞ =2.0%×875.23=17.5m / s(10);

[0157] Step 3: According to the von Kármán-Pao turbulence energy spectrum model, in the rectangular space grid B T A discrete divergence-free pulsating velocity vector field is generated at each body center point of . Figure 9a-9c This embodiment is in the rectangular space grid B T A discrete divergence-free pulsating velocity vector field is generated on the surface. Specifically, Figure 9a is the pulsating velocity in the x direction, Figure 9b is the pulsating velocity in the y direction, Figure 9c is the pulsating velocity in the z direction.

[0158] Step 4: Based on the nearest neighbor spatial interpolation method, data interpolation is performed on each surface center point of each surface grid block in the spatial surface grid B to obtain the corresponding turbulent boundary. Figure 10a-Figure 10c is the turbulent boundary generated on the spatial surface mesh B in this embodiment. Specifically, Figure 10a is the pulsating velocity in the x direction, Figure 10b is the pulsating velocity in the y direction, Figure 10c is the pulsating velocity in the z direction.

[0159] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0160] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for generating turbulent boundaries on complex spatial surfaces, characterized in that: The method for generating turbulent boundaries on a spatial complex curved surface comprises: Acquire a spatial surface mesh of a free flow boundary, construct a spatial Cartesian coordinate system for the spatial surface mesh, and perform preprocessing operations on the spatial surface mesh to obtain data information of the spatial surface mesh and data information of a rectangular space mesh; the spatial surface mesh is composed of a plurality of surface mesh blocks; the data information of the spatial surface mesh includes the coordinates of the vertices of each surface mesh block and the coordinates of the center point of each surface mesh block; the rectangular space mesh is composed of a plurality of volume mesh blocks, and the rectangular space mesh can surround the spatial surface mesh; the volume mesh blocks are obtained based on mesh node division; the data information of the rectangular space mesh includes the scale information of the rectangular space mesh, the coordinates of the vertices of each volume mesh block, and the coordinates of the center point of each volume mesh block; Based on the preset incoming flow turbulence and free incoming flow velocity, the theoretical pulsation velocity is calculated; A spatial pulsating velocity vector field is calculated based on the data information of the rectangular space grid and the von Kármán-Pao turbulence energy spectrum model; the von Kármán-Pao turbulence energy spectrum model includes the theoretical pulsating velocity; the spatial pulsating velocity vector field includes the pulsating velocity of the body center point of each volume grid block; Based on the spatial pulsating velocity vector field, a nearest neighbor spatial interpolation method is used to perform data interpolation on the surface center point of each surface grid block in the spatial curved surface grid to determine a turbulent boundary.

2. The method for generating turbulent boundaries on spatial complex curved surfaces according to claim 1, characterized in that: Constructing a spatial Cartesian rectangular coordinate system for the spatial curved surface mesh and performing preprocessing operations to obtain data information of the spatial curved surface mesh and data information of the cuboid spatial mesh, specifically including: Constructing a spatial Cartesian coordinate system for the spatial curved surface grid, determining the coordinate position of each grid node in the spatial curved surface grid and the maximum and minimum values ​​of the spatial curved surface grid on the x-axis, y-axis, and z-axis, respectively; the x-axis is horizontal, the z-axis is vertical, and the y-axis is perpendicular to the x-axis and the z-axis; The coordinates of the center point of each surface mesh block are calculated based on the coordinates of the four vertices of each surface mesh block in the spatial curved surface mesh; wherein the coordinates of the four vertices are the coordinate positions of the four mesh nodes constituting the surface mesh block in a spatial Cartesian coordinate system; Constructing a cuboid space grid according to the maximum and minimum values ​​of the space surface grid on the x-axis, y-axis and z-axis; According to the number of grid nodes in the preset cuboid space grid and the scale information of the cuboid space grid obtained by the preprocessing operation, the cuboid space grid is divided to obtain a plurality of volume grid blocks; The coordinates of the body center point of each volume grid block are calculated based on the coordinates of the eight vertices of each volume grid block in the rectangular space grid; wherein the eight vertex coordinates are the coordinate positions of the eight grid nodes constituting the volume grid block in the spatial Cartesian rectangular coordinate system.

3. The method for generating turbulent boundaries on spatial complex curved surfaces according to claim 1, characterized in that: Based on the preset incoming flow turbulence and free flow velocity, the theoretical pulsation velocity is calculated. The specific process is as follows: According to the formula U rms =Tu ∞ ×U ∞ The theoretical pulsation velocity is calculated; Among them, U rms is the theoretical pulsation velocity, Tu ∞ is the preset incoming flow turbulence, U ∞ is the preset free flow velocity.

4. The method for generating turbulent boundaries on spatial complex curved surfaces according to claim 1, characterized in that: According to the data information of the rectangular space grid and the von Kármán-Pao turbulence energy spectrum model, the spatial pulsating velocity vector field is calculated, specifically including: Calculating the mth wave number according to the obtained preset total wave number, the number of grid nodes in the rectangular parallelepiped space grid, and scale information of the rectangular parallelepiped space grid; The amplitude of the mth wave number is calculated according to the mth wave number and the von Kármán-Pao turbulence energy spectrum model; Based on the m-th wave number, calculating a first unit direction vector associated with the m-th wave number, and based on the first unit direction vector, calculating a second unit direction vector perpendicular to the first unit direction vector; Performing a first operation on the body center point of each volume grid block in the rectangular parallelepiped space grid to obtain a pulsating velocity corresponding to the body center point of each volume grid block; Summarize the pulsating velocities corresponding to the body center points of all volume grid blocks to obtain the spatial pulsating velocity vector field; The first operation is: Based on the coordinates of the body center point of the current volume grid block, a relative displacement vector related to the coordinates of the body center point of the current volume grid block is calculated; the current volume grid block is any volume grid block in the rectangular parallelepiped space grid; The pulsating velocity corresponding to the body center point of the current body grid block is calculated based on the mth wave number, the amplitude of the mth wave number, the first unit direction vector, the second unit direction vector and the relative displacement vector related to the coordinates of the body center point of the current body grid block.

5. The method for generating turbulent boundaries on spatial complex curved surfaces according to claim 4, characterized in that: Calculating the pulsating velocity corresponding to the current body center point according to the mth wave number, the amplitude of the mth wave number, the first unit direction vector, the second unit direction vector, and the relative displacement vector associated with the body center point coordinates of the current volume grid block specifically includes: The pulsating velocity corresponding to the center point of the current volume grid block is calculated according to the following formula; in, is the pulsating velocity in the x direction, is the pulsating velocity in the y direction, is the pulsating speed in the z direction, M is the total number of preset waves, a m is the amplitude of the mth wave number, k m is the mth wave number, is the first unit direction vector, is the relative displacement vector related to the coordinates of the center point of the current volume grid block, φ is the phase angle randomly distributed in the interval [-π / 2,π / 2], is the second unit direction vector.

6. The method for generating turbulent boundaries of spatial complex curved surfaces according to claim 4, characterized in that: The expression of the von Kármán-Pao turbulence energy spectrum model is: Where α is a scale factor, and for isotropic turbulence α=1.453; U rms is the theoretical pulsation speed; k e is the wave number associated with the maximum energy E(k0), for normal flow k0 = 40; f(k m ) is the wave number k m and Kolmogorov wave number k η .

7. The method for generating turbulent boundaries of spatial complex curved surfaces according to claim 4, characterized in that: Based on the spatial pulsating velocity vector field, a nearest neighbor spatial interpolation method is used to interpolate data of the surface center point of each surface grid block in the spatial curved surface grid to determine the turbulent boundary, specifically including: Performing a second operation on the surface center point of each surface mesh block in the spatial curved surface mesh to obtain a pulsating velocity after interpolation processing of the surface center point of each surface mesh block; Summarize the pulsating velocities after interpolation of the center points of all surface grid blocks to determine the turbulent boundary; The second operation is: Based on the center point of the current surface grid block, a nearest neighbor search is performed in the cuboid space grid to determine the four body center points closest to the center point of the current surface grid block, and the distances from the center point of the current surface grid block to the four body center points are calculated respectively; Based on the distances from the center point of the current surface grid block to the four body centers and the pulsating velocities corresponding to the four body centers, the pulsating velocity data of the center point of the current surface grid block is interpolated using the distance weight method to obtain the pulsating velocity after interpolation of the center point of the current surface grid block.

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