A method for generating a turbulent boundary of a complex spatial surface

Abstract

The application discloses a method for generating a turbulent boundary of a spatial complex curved surface, and relates to the technical field of turbulent boundary generation. The method comprises the following steps: acquiring a spatial curved surface grid of a free flow boundary, and preprocessing the spatial curved surface grid to obtain data information of the spatial curved surface grid and data information of a cuboid spatial grid; calculating a theoretical fluctuation velocity based on a preset free flow turbulence degree and a free flow velocity; calculating a spatial fluctuation velocity vector field based on the data information of the cuboid spatial grid and a von Kármán-Pao turbulent energy spectrum model; the turbulent energy spectrum model comprises the theoretical fluctuation velocity; and performing data interpolation on a face center point of each face grid block in the spatial curved surface grid based on the spatial fluctuation velocity vector field by using a nearest neighbor spatial interpolation method to determine a turbulent boundary suitable for the spatial complex curved surface and meeting a real turbulent energy spectrum relationship.

Description

Technical Field

[0001] This application relates to the field of turbulent boundary generation technology, and in particular to a method for generating turbulent boundaries on spatially complex curved surfaces. Background Technology

[0002] In the field of high-fidelity numerical simulation research in computational fluid dynamics, the transition of object surfaces and the turbulent boundary layer are highly sensitive to free-flow conditions. Reasonable and accurate turbulent boundary settings directly affect 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 simulation, LES, and direct numerical simulation. This is because the pulsation information at the turbulent inlet is unknown and highly random. High-fidelity numerical simulations require artificially setting turbulent boundaries containing certain pulsation information. Whether this pulsation information can accurately reflect the real turbulence and reproduce the true turbulent evolution process downstream is crucial to achieving high-fidelity numerical simulation.

[0003] Currently, methods for generating turbulence are mainly divided into two categories: pre-simulation and artificial synthesis. Pre-simulation typically requires solving two computational domains. First, a stable flow field needs to be simulated in an auxiliary computational domain. 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 the target turbulent characteristics. It requires multiple adjustments and repeated calculations, resulting in low efficiency and high cost. Artificial synthesis, on the other hand, directly generates turbulent conditions by simulating stochastic processes to provide the corresponding turbulent fluctuation information. While this method is relatively simple, it has significant shortcomings. Artificial synthesis methods based on white noise, Gaussian white noise, etc., suffer from significant differences in turbulence compared to reality due to the incompatibility of their noise components with the Navier-Stokes (NS) equations. The turbulence obtained differs greatly from the actual situation and decays rapidly, failing to effectively reproduce the true turbulence decay process.

[0004] Meanwhile, for some complex shapes, especially hypersonic complex shapes, when drawing computational meshes suitable for high-fidelity numerical simulations, it is necessary to ensure both the effective utilization of the mesh and the accurate capture of the shock wave structure. Therefore, the generated computational meshes usually have complex three-dimensional spatial curved surface flow boundaries, and traditional two-dimensional planar turbulence generation methods are difficult to apply to the generation of turbulent boundaries for 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. This method can easily and conveniently generate turbulent boundaries that are applicable to complex spatial surfaces and satisfy the real turbulent energy spectrum relationship. This provides technical support for high-fidelity numerical simulation studies of complex three-dimensional aircraft in terms of boundary layer transition and turbulent development and evolution.

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

[0007] Firstly, this application provides a method for generating turbulent boundaries on spatially complex curved surfaces, including:

[0008] A spatial surface mesh of the free-flow boundary is obtained, and a spatial Cartesian coordinate system is constructed and preprocessed on the spatial surface mesh to obtain the data information of the spatial surface mesh and the data information of the cuboid spatial mesh. The spatial surface mesh is composed of multiple face mesh blocks. The data information of the spatial surface mesh includes the coordinates of the vertices of each face mesh block and the coordinates of the center point of each face mesh block. The cuboid spatial mesh is composed of multiple volume mesh blocks, and the cuboid spatial mesh can enclose the spatial surface mesh. The volume mesh blocks are obtained based on mesh node division. The data information of the cuboid spatial mesh includes the scale information of the cuboid spatial 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 turbulence intensity and free incoming velocity, the theoretical pulsating velocity is calculated;

[0010] Based on the data information of the cuboid spatial grid and the von Kármán-Pao turbulent energy spectrum model, the spatial fluctuating velocity vector field is calculated; the von Kármán-Pao turbulent energy spectrum model includes the theoretical fluctuating velocity; the spatial fluctuating velocity vector field includes the fluctuating velocity of the body center point of each volume grid block;

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

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

[0013] This application provides a method for generating turbulent boundaries on complex spatial surfaces. First, the spatial surface mesh of the free-flow boundary is preprocessed and converted into a cuboid spatial mesh, providing structured and regularized mesh data for turbulent boundary calculation. This effectively reduces the difficulty of numerical computation for complex surface meshes and simplifies subsequent calculations without sacrificing accuracy. Second, the von Kármán-Pao turbulent energy spectrum model is used for calculation, combined with theoretical fluctuating velocity parameters, to obtain a spatial fluctuating velocity vector field. The fluctuating velocity field generated by this model accurately describes the turbulent characteristics in the flow field, making the generation process of the turbulent boundary more closely resemble actual fluid dynamics phenomena. After obtaining the spatial fluctuating velocity vector field, the nearest neighbor spatial interpolation method can be used to obtain a turbulent boundary suitable for complex spatial surfaces. Therefore, this application can easily and conveniently generate turbulent boundaries suitable for complex spatial surfaces that satisfy realistic turbulent energy spectrum relationships, providing technical support for high-fidelity numerical simulation research on boundary layer transition and turbulent evolution of complex three-dimensional aircraft. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 A flowchart illustrating a method for generating turbulent boundaries on complex spatial surfaces, provided in an embodiment of this application;

[0016] Figure 2 A schematic diagram of the computational mesh for the shape of a wing-body assembly provided in another embodiment of this application;

[0017] Figure 3 A schematic diagram of spatial surface mesh A and spatial surface mesh B obtained by topologically partitioning the free flow boundary of the wing-body combination shape for another embodiment of this application;

[0018] Figure 4 A flowchart illustrating a method for generating turbulent boundaries on complex spatial surfaces, provided in another embodiment of this application;

[0019] Figure 5 This application provides another embodiment of a cuboid spatial mesh A obtained by preprocessing a spatial curved surface mesh A. T A schematic diagram;

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

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

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

[0023] Figure 7a A schematic diagram of the fluctuating velocity in the x-direction of a turbulent boundary generated on a spatial curved surface mesh A, provided for another embodiment of this application;

[0024] Figure 7b A schematic diagram of the fluctuating velocity in the y direction of a turbulent boundary generated on a spatial curved surface mesh A, provided for another embodiment of this application;

[0025] Figure 7c A schematic diagram of the fluctuating velocity in the z-direction of a turbulent boundary generated on a spatial curved surface mesh A, provided for another embodiment of this application;

[0026] Figure 8 This application provides another embodiment of a cuboid spatial mesh B obtained by preprocessing a spatial curved surface mesh B. T A schematic diagram;

[0027] Figure 9a Another embodiment of this application provides a cuboid space grid B T A schematic diagram of the pulsating velocity generated in the x-direction;

[0028] Figure 9b Another embodiment of this application provides a cuboid space grid B T A schematic diagram of the pulsating velocity generated in the y-direction;

[0029] Figure 9c Another embodiment of this application provides a cuboid space grid B T A schematic diagram of the pulsating velocity generated in the z-direction;

[0030] Figure 10a A schematic diagram of the fluctuating velocity in the x-direction of a turbulent boundary generated on a spatial curved surface mesh B, provided for another embodiment of this application;

[0031] Figure 10b A schematic diagram of the fluctuating velocity in the y direction of a turbulent boundary generated on a spatial curved surface mesh B, provided for another embodiment of this application;

[0032] Figure 10c This is a schematic diagram of the fluctuating velocity in the z-direction of a turbulent boundary generated on a spatial curved mesh B, provided as another embodiment of this application. Detailed Implementation

[0033] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0034] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] In one exemplary embodiment, such as Figure 1 As shown, a method for generating turbulent boundaries on complex spatial surfaces is provided, including steps 101 to 104. Wherein:

[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 to obtain the data information of the spatial surface mesh and the data information of the cuboid spatial mesh. The spatial surface mesh consists of multiple face mesh blocks. The data information of the spatial surface mesh includes the coordinates of the vertices of each face mesh block and the coordinates of the center point of each face mesh block. The cuboid spatial mesh consists of multiple volume mesh blocks, and the cuboid spatial mesh can enclose the spatial surface mesh. The volume mesh blocks are obtained based on the mesh nodes. The data information of the cuboid spatial mesh includes the scale information of the cuboid spatial 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 turbulence intensity and free incoming velocity.

[0038] Step 103: Based on the data information of the cuboid space grid and the von Kármán-Pao turbulent energy spectrum model, calculate the spatial fluctuating velocity vector field; the von Kármán-Pao turbulent energy spectrum model includes the theoretical fluctuating velocity; the spatial fluctuating velocity vector field includes the fluctuating velocity of the body center point of each volume grid block.

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

[0040] Further, in step 101, the spatial surface mesh of the free-flow boundary is read in, and a spatial Cartesian coordinate system is constructed and preprocessed on the spatial surface mesh to obtain the data information of the spatial surface mesh. A cuboid spatial mesh that can enclose it is also generated, along with its data information, to prepare for the subsequent random generation of the spatial pulsating velocity vector field. Specifically, this includes the following steps:

[0041] Step 1011: Based on the read-in and stored spatial surface mesh data, 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 (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 face 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 curved surface mesh is actually composed of many planar quadrilateral mesh blocks, in order to obtain the coordinates of the center point of each mesh block, it is first necessary to establish the corresponding diagonal intersection parameterized 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 curved 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] Here, t and s represent the parametric coordinates of the face center point. t and s can be obtained by simultaneously solving any two of the above equations.

[0048] Then, the coordinates (x, y) of the face center can be obtained using the following parametric equation. 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 satisfying {x∈[x... min ,x max ],y∈[y min ,y max ],z∈[z min ,z max The cuboid spatial mesh is used to enclose the spatial curved surface mesh, and the number of mesh nodes (N) in the three directions of the cuboid spatial mesh can be manually specified. x N y N z The system stores the distribution information and scale information (L) of the cuboid spatial grid, as well as the scale information of the cuboid spatial grid. x ,L y ,L z ).

[0053] Step 1014: Calculate the coordinates of the body center of all volume mesh blocks in the cuboid space mesh and store them as (x... t y t , z t Since the eight grid nodes of an arbitrary volume mesh block are strictly distributed according to a Cartesian coordinate system, the coordinates of the volume center point can be obtained using 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 formulas represent the coordinate data of the eight vertices of the volume mesh block, namely N1(x1, y1, z1) to N8(x8, y8, z8).

[0058] Further, step 102: Calculate the theoretical pulsating velocity based on the given incoming turbulence intensity and free incoming velocity.

[0059] Based on the input inflow turbulence Tu ∞ and free flow velocity U ∞ Calculate the theoretical pulsation velocity U rms The calculation formula is as follows:

[0060] U rms =Tu ∞ ×U ∞ (10);

[0061] Further, step 103: Based on the von Kármán-Pao turbulent energy spectrum model, generate a discrete, divergence-free fluctuating velocity vector field at each centroid of the cuboid space grid.

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

[0063]

[0064] in, Let be the pulsation velocity in the x-direction. Let be the pulsation velocity in the y-direction. The pulse velocity is in the z-direction, M is the preset total wavenumber, and a m Let k be the amplitude of the m-th wavenumber. m For the m-th wave number, The first unit direction vector, The relative displacement vector is related to the coordinates of the body center of the current volume mesh block, and φ is the phase angle randomly distributed in the interval [-π / 2, π / 2]. This 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 m-th wave number k m The calculation process is as follows:

[0067] First, determine the minimum wave number k. min and 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] Where Δk is the change between two adjacent wavenumbers.

[0075] Step 1032: Calculate the amplitude a of the m-th wavenumber based on the von Kármán-Pao turbulent energy spectrum model E(k). m The calculation process is as follows:

[0076]

[0077] Where α is a scaling factor, and for isotropic turbulence, α = 1.453, U rms The theoretical pulsation velocity, k, is calculated in step 102. e It is the wavenumber associated with the maximum energy E(k0), for conventional flow k0 = 40, k η It is the Kolmogorov wavenumber, f(k m ) is the wave number k m With wave number k η The relevant scaling terms are ν, where 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 m-th wavenumber. and the body center N(x) t y t , z t The 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: Calculation and Vertical second unit direction vector

[0083] First, auxiliary vectors need to be constructed. The corresponding f can be obtained using the same calculation method as formula (23). xm ,f ym ,f zm .

[0084] Then, in order to construct a divergence-free velocity field on a discrete volume mesh, a modified wavenumber direction vector can be used. The calculation formula is as follows:

[0085]

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

[0087] Finally, the unit direction vector is obtained by using the vector cross product.

[0088]

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

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

[0091] Specifically, it includes the following steps:

[0092] Step 1041: For a specific face center point M(x) of a face mesh block c y c , z cIn a cuboid space grid, a nearest neighbor search is performed to determine the four nearest centroids to point M, labeled T1, T2, T3, and T4, respectively. The distances from point M to these four points are recorded and labeled d1, d2, d3, and d4. Then, the pulsation velocity data of point M is interpolated based on a distance-weighted method, as follows:

[0093]

[0094] Where ω1 to ω4 are the reciprocals of the distance, representing the corresponding weight coefficients. These represent points T obtained in step 103, respectively. i The pulsation velocity of (i = 1, 2, 3, 4) This indicates the pulsation velocity of point M obtained after interpolation.

[0095] Step 1042: Traverse every face 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 turbulent energy spectrum relation.

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

[0097] according to Figure 4The flowchart shown illustrates the specific process of generating the turbulent boundaries of the wing-body assembly in this embodiment. Since the free flow boundary of the wing-body assembly is divided into two parts, the corresponding turbulent boundaries need to be generated separately for each part. Firstly, for… Figure 3 Generating turbulent boundaries using spatial curved surface mesh A:

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

[0099] Step 1.1: Based on the mesh data of the spatial curved 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 point of all face 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 parameter equations based on the four vertices A(x1, y1, z1), B(x2, y2, z2), C(x3, y3, z3), and D(x4, y4, z4) of a 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] Here, t and s represent the parametric coordinates of the face center point. t and s can be obtained by simultaneously solving any two of the above equations.

[0106] Then, the coordinates (x, y) of the face center can be obtained using the following parametric equation. 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 ​​in the x, y, and z directions obtained in Step 1.1, establish a cuboid spatial mesh with a distribution range satisfying {x∈[-36.2,-19.7], y∈[-34.8,-0.2], z∈[-36.6,36.6]} (unit: mm) to enclose the spatial curved surface mesh A. Specify that the grid points of this cuboid spatial mesh are uniformly distributed in the three directions and satisfy {N... x =50,N y =80,N z =80}, and simultaneously store the scale information {L} of the cuboid spatial mesh. x =16.5mm,L y =34.6mm,L z =73.2mm}. Figure 5 This embodiment describes the cuboid spatial mesh A obtained after preprocessing the spatial curved surface mesh A. T .

[0111] Step 1.4: Calculate the cuboid space mesh A T The volume 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 formulas 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 pulsating velocity based on the given incoming turbulence intensity and free incoming velocity.

[0117] Based on the input inflow turbulence Tu ∞ and free flow velocity U ∞ Calculate the theoretical pulsation velocity U rms The results are as follows:

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

[0119] Step 3: Based on the von Kármán-Pao turbulent energy spectrum model, in the cuboid space grid A T Each body center point generates a discrete, divergence-free pulsating velocity vector field.

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

[0121]

[0122] in, Let be the pulsation velocity in the x-direction. Let be the pulsation velocity in the y-direction. The pulse velocity is in the z-direction, M is the preset total wavenumber, and a m Let k be the amplitude of the m-th wavenumber. m For the m-th wave number, The first unit direction vector, The relative displacement vector is related to the coordinates of the body center of the current volume mesh block, and φ is the phase angle randomly distributed in the interval [-π / 2, π / 2]. This 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 m-th wave number k m The calculation process is as follows:

[0125] First, determine the minimum wave number k. min and 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] Where Δk is the change between two adjacent wavenumbers.

[0132] Step 3.2: Calculate the amplitude a of the m-th wavenumber based on the von Kármán-Pao turbulent energy spectrum model E(k). m The calculation process is as follows:

[0133]

[0134] Where α is a scaling factor, and for isotropic turbulence, α = 1.453, U rms The theoretical pulsation velocity, k, is calculated from step 2. e It is the wavenumber associated with the maximum energy E(k0), for conventional flow k0 = 40, k η It is the Kolmogorov wavenumber, f(k m ) is the wave number k m With wave number k η The relevant scaling terms are ν, where 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 m-th wavenumber. and the body center N(x) t y t , z t The 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: Calculation and Vertical unit direction vector

[0140] First, auxiliary vectors need to be constructed. The corresponding f can be obtained using the same calculation method as formula (23). xm ,f ym ,f zm .

[0141] Then, in order to construct a divergence-free velocity field on a discrete volume mesh, a modified wavenumber direction vector can be used. The calculation formula is as follows:

[0142]

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

[0144] Finally, the unit direction vector is obtained by using the vector cross product.

[0145]

[0146] Step 3.5: Traverse each center point of the volume mesh, repeat steps 3.1-3.4, and substitute the calculated parameters into formulas (11)-(13) to obtain a complete spatial pulsating velocity vector field. Figures 6a-6c In this embodiment, the rectangular space grid A is... T A discrete, divergence-free fluctuating velocity vector field is generated above, specifically, Figure 6a Let be the pulsation velocity in the x-direction. Figure 6b Let be the pulsation velocity in the y-direction. Figure 6c Let be the pulsation velocity in the z-direction.

[0147] Step 4: Based on the nearest neighbor spatial interpolation method, perform data interpolation on the center points 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 center point M(x) of a face mesh block c y c, z c In a cuboid space grid, a nearest neighbor search is performed to determine the four nearest centroids to point M, labeled T1, T2, T3, and T4 respectively. The distances from point M to these four points are recorded and labeled d1, d2, d3, and d4. Then, the pulsating velocity data of point M is interpolated based on a distance-weighted method, as follows:

[0149]

[0150] Where ω1 to ω4 are the reciprocals of the distance, representing the corresponding weight coefficients. These represent points T obtained in step 3. i The pulsation velocity of (i = 1, 2, 3, 4) This indicates the pulsation velocity of point M obtained after interpolation.

[0151] Step 4.2: Traverse every face center point of the spatial surface mesh A and repeat step 4.1 to obtain a turbulent boundary that is applicable to complex spatial surfaces and satisfies the von Kármán-Pao turbulent energy spectrum relation. Figures 7a-7c This embodiment generates a turbulent boundary on a spatial curved surface mesh A. Specifically, Figure 7a Let be the pulsation velocity in the x-direction. Figure 7b Let be the pulsation velocity in the y-direction. Figure 7c Let be the pulsation velocity in the z-direction.

[0152] When generating turbulent boundaries for the spatial curved surface mesh B, in addition to the cuboid spatial mesh B T The number of grid points is set to {N} x =500,N y =150,N z =150}, the process is completely consistent with the turbulent boundary generation process of spatial curved surface mesh A. The details are as follows:

[0153] Step 1: Read in the spatial curved surface mesh B and perform mesh preprocessing to generate a cuboid spatial mesh B that can enclose it. T . Figure 8 This embodiment describes the cuboid spatial mesh B obtained after preprocessing the spatial curved surface mesh B. T .

[0154] Step 2: Calculate the theoretical pulsating velocity based on the given incoming turbulence intensity and free incoming velocity.

[0155] Based on the input inflow turbulence Tu ∞ and free flow velocity U ∞ Calculate the theoretical pulsation velocity U rms The results are as follows:

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

[0157] Step 3: Based on the von Kármán-Pao turbulent energy spectrum model, in the cuboid space grid B T Each body center point generates a discrete, divergence-free pulsating velocity vector field. Figures 9a-9c In this embodiment, the cuboid space grid B... T A discrete, divergence-free fluctuating velocity vector field is generated above, specifically, Figure 9a Let be the pulsation velocity in the x-direction. Figure 9b Let be the pulsation velocity in the y-direction. Figure 9c Let be the pulsation velocity in the z-direction.

[0158] Step 4: Based on the nearest neighbor spatial interpolation method, perform data interpolation on each face center point of each face grid block in the spatial surface grid B to obtain the corresponding turbulent boundary. Figures 10a-10c This embodiment generates a turbulent boundary on the spatial curved surface mesh B. Specifically, Figure 10a Let be the pulsation velocity in the x-direction. Figure 10b Let be the pulsation velocity in the y-direction. Figure 10c Let be the pulsation velocity in the z-direction.

[0159] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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 descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for generating turbulent boundaries on complex spatial curved surfaces, characterized in that, The method for generating turbulent boundaries on complex spatial curved surfaces includes: A spatial surface mesh of the free-flow boundary is obtained, and a spatial Cartesian coordinate system is constructed and preprocessed on the spatial surface mesh to obtain the data information of the spatial surface mesh and the data information of the cuboid spatial mesh. The spatial surface mesh is composed of multiple face mesh blocks. The data information of the spatial surface mesh includes the coordinates of the vertices of each face mesh block and the coordinates of the center point of each face mesh block. The cuboid spatial mesh is composed of multiple volume mesh blocks, and the cuboid spatial mesh can enclose the spatial surface mesh. The volume mesh blocks are obtained based on mesh node division. The data information of the cuboid spatial mesh includes the scale information of the cuboid spatial 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 turbulence intensity and free incoming velocity, the theoretical pulsating velocity is calculated; Based on the data information of the cuboid spatial grid and the von Kármán–Pao turbulent energy spectrum model, the spatial fluctuating velocity vector field is calculated; the von Kármán–Pao turbulent energy spectrum model includes the theoretical fluctuating velocity; the spatial fluctuating velocity vector field includes the fluctuating velocity of the body center point of each volume grid block; Based on the spatial pulsating velocity vector field, the nearest neighbor spatial interpolation method is used to interpolate the data of the face center point of each surface grid block in the spatial curved surface grid to determine the turbulent boundary. Specifically, based on the data information of the cuboid spatial grid and the von Kármán–Pao turbulent energy spectrum model, the spatial fluctuating velocity vector field is calculated, including: Based on the obtained preset total wavenumber, the number of grid nodes in the cuboid space grid, and the scale information of the cuboid space grid, the m-th wavenumber is calculated. The amplitude of the m-th wavenumber is calculated based on the m-th wavenumber and the von Kármán–Pao turbulent energy spectrum model. Based on the m-th wavenumber, calculate the first unit direction vector associated with the m-th wavenumber, and based on the first unit direction vector, calculate the second unit direction vector perpendicular to the first unit direction vector; Perform a first operation on the center point of each volume grid block in the cuboid space grid to obtain the pulsation velocity corresponding to the center point of each volume grid block; The spatial pulsating velocity vector field is obtained by summing the pulsating velocities corresponding to the center points of all volume mesh blocks. The first operation is as follows: Based on the coordinates of the center point of the current volume mesh block, the relative displacement vector related to the coordinates of the center point of the current volume mesh block is calculated; the current volume mesh block is any volume mesh block in the cuboid space mesh. The pulsation velocity corresponding to the center point of the current volume mesh is calculated based on the relative displacement vector related to the m-th wavenumber, the amplitude of the m-th wavenumber, the first unit direction vector, the second unit direction vector, and the coordinates of the center point of the current volume mesh.

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

3. The method for generating turbulent boundaries on complex spatial curved surfaces according to claim 1, characterized in that, Based on the preset incoming turbulence intensity and free incoming velocity, the theoretical fluctuating velocity is calculated. The specific process is as follows: According to the formula The theoretical pulsation velocity was calculated. in, The theoretical pulsation velocity, The preset inflow turbulence intensity, The preset free flow speed.

4. The method for generating turbulent boundaries on complex spatial curved surfaces according to claim 1, characterized in that, Based on the m-th wavenumber, the amplitude of the m-th wavenumber, the first unit direction vector, the second unit direction vector, and the relative displacement vector related to the coordinates of the center point of the current volume mesh block, the pulsation velocity corresponding to the current center point is calculated, specifically including: The pulsation velocity corresponding to the center point of the current volume mesh block is calculated using the following formula; ； ； ； in, for x pulsation velocity in the direction, for y pulsation velocity in the direction, for z pulsation velocity in the direction, The preset total wavenumber, Let m be the amplitude of the m-th wavenumber. For the m-th wave number, The first unit direction vector, The relative displacement vector related to the coordinates of the center point of the current volume mesh block. For in the interval Randomly distributed phase angles This is the second unit direction vector.

5. The method for generating turbulent boundaries on complex spatial curved surfaces according to claim 1, characterized in that, The expression for the von Kármán–Pao turbulent energy spectrum model is as follows: ； in, It is a scaling factor, which is applicable to isotropic turbulence. ; It is the theoretical pulsation velocity; It is related to maximum energy The relevant wavenumber has the following effect on conventional flows. =40; Wavenumber k m With Kolmogorov wavenumber k η Related scaling items.

6. The method for generating turbulent boundaries on complex spatial curved surfaces according to claim 1, characterized in that, Based on the spatial pulsating velocity vector field, the center point of each surface grid block in the spatial curved surface grid is interpolated using the nearest neighbor spatial interpolation method to determine the turbulent boundary, specifically including: Perform a second operation on the center point of each face grid block in the spatial curved surface mesh to obtain the pulsating velocity of the center point of each face grid block after interpolation. The pulsating velocities after interpolation of the center points of all surface mesh blocks are summarized to determine the turbulent boundary. The second operation is as follows: Based on the face center point of the current face grid block, perform a nearest neighbor search in the cuboid space grid to determine the four body center points that are closest to the face center point of the current face grid block, and calculate the distance from the face center point of the current face grid block to the four body center points respectively. Based on the distance from the face center point of the current face grid block to the four body center points and the pulsation velocity corresponding to the four body center points, the pulsation velocity data of the face center point of the current face grid block is interpolated using the distance weight method to obtain the interpolated pulsation velocity of the face center point of the current face grid block.

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