A simulation analysis method and system based on fluid-solid coupling

Abstract

The present invention relates to a simulation analysis method and system based on fluid-solid coupling, which belongs to the field of simulation analysis technology, and solves the problem that the existing fluid-solid coupling has low computational efficiency and slow convergence speed, resulting in the inability to quickly obtain accurate analysis results. The method includes importing a structural geometry model of an element, generating a fluid geometry model, and performing discretized grid division; calculating the first transfer matrix of physical quantities from the flow field coupling interface to the structural field coupling interface according to boundary conditions; constructing a fluid-solid direct coupling system equation and transforming it into three sub-equations; performing fluid-solid coupling analysis, and updating the unknown quantities of the flow field and structural field, as well as the Lagrange multipliers, in each iteration of each time step by using an iterative calculation method based on the three sub-equations using any one of the flow field solvers and the structural field solver, until they are all less than their respective convergence tolerances and all time steps are completed; and extracting the analysis results from the output result file. Efficient and accurate fluid-solid coupling simulation analysis is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of simulation analysis, and in particular to a simulation analysis method and system based on fluid-solid coupling. Background Art

[0002] Fluid-structure interaction is very important in many engineering and natural systems, such as aerospace, marine engineering, biomedicine, chemical equipment, etc. In these systems, the flow of fluid may cause the deformation of the structure, and the deformation of the structure in turn affects the flow of the fluid.

[0003] Currently, the main methods used are direct coupling method and iterative coupling method. The direct coupling method solves the equations of fluid and solid as a whole at the same time, which is suitable for strong coupling scenarios; the iterative coupling method does not have the system equations for the coupling of fluid and structure, and solves the equations of fluid and structure separately through iteration until the convergence conditions are met; the amount of calculation in each iteration is small, but more iterations may be required to converge, and it is not suitable for strong coupling scenarios.

[0004] The existing direct coupling method can construct the fluid-solid coupling system equation only when the flow field and the structural field adopt the same method, and can only be used to solve simple application problems; but the actual engineering application is relatively complex. The structural field calculation usually adopts the finite element method, while the flow field usually adopts the finite volume method, and the finite element method is rarely used. Therefore, these engineering problems cannot use the direct coupling method to calculate the analysis results; moreover, due to the objective differences in the mechanical properties of the flow field and the structural field, the fluid-solid coupling system equation obtained is a typical nonlinear equation with poor preconditions or even pathological conditions. It is difficult to converge using the existing direct coupling method and iterative coupling method, resulting in low calculation efficiency, inaccurate extracted simulation analysis results, and sometimes even the inability to extract simulation analysis results. Summary of the invention

[0005] In view of the above analysis, an embodiment of the present invention aims to provide a simulation analysis method and system based on fluid-structure coupling, so as to solve the problem that the existing fluid-structure coupling has low computational efficiency and slow convergence speed, resulting in the inability to quickly obtain accurate analysis results.

[0006] On the one hand, an embodiment of the present invention provides a simulation analysis method based on fluid-solid coupling, comprising the following steps:

[0007] Import the structural geometry model of the component, generate the fluid geometry model by extracting the fluid domain from the structural geometry model, and perform discretization meshing on the structural and fluid geometry models respectively;

[0008] The first transfer matrix of physical quantities from the flow field coupling interface to the structural field coupling interface is calculated according to the boundary conditions; the fluid-solid direct coupling system equation is constructed according to the first transfer matrix, Lagrange multipliers, flow field unknowns and structural field unknowns, and transformed into three sub-equations;

[0009] Perform fluid-structure interaction analysis, and update the flow field unknowns using any flow field solver based on the three sub-equations, update the structural field unknowns using any structural field solver, and update the Lagrange multiplier in each iteration of each time step through iterative calculation, until the relative residuals of the flow field unknowns, structural field unknowns, and Lagrange multipliers are all less than their respective convergence tolerances and all time steps are completed;

[0010] Extract analysis results from the result files output by the flow field solver and the structural field solver.

[0011] Based on the further improvement of the above method, according to the first transfer matrix, Lagrange multipliers, flow field unknowns and structural field unknowns, the fluid-solid direct coupling system equation is constructed by the following formula:

[0012] ,

[0013] in, , and They represent the coefficient matrix of the discrete equations of the flow field, the unknown quantities of the flow field to be solved, and the external force vector of the flow field respectively; , and They represent the coefficient matrix of the discrete equations of the structural field, the unknown quantities of the structural field to be solved, and the external force vector of the structural field respectively; represents the time step; represents the Lagrange multiplier; The first transfer matrix representing the physical quantity from the flow field coupling interface to the structure field coupling interface; The external force vector of the entire domain corresponding to the motion of the flow field coupled interface; The external force vector of the entire domain corresponding to the change of the structure-field coupling interface flow field force; The second transfer matrix representing the flow field physical quantity from the entire domain to the flow field coupling interface; The third transfer matrix representing the structural field quantities from the entire domain to the structural field coupling interface.

[0014] Based on the further improvement of the above method, the three sub-equations include: flow field sub-equation, structure field sub-equation and correlation sub-equation; the three sub-equations are expressed by the following formulas:

[0015] ,

[0016] in, and represent the displacement vector of the flow field coupling interface and the displacement vector of the structure field coupling interface respectively; and represent the flow field coupling interface force vector and the structure field coupling interface force vector respectively; and represent the flow field coupling interface velocity vector and the structural field coupling interface velocity vector respectively.

[0017] Based on the further improvement of the above method, before the iterative calculation, it also includes calculating the iteration initial value for the first iteration; the calculation of the iteration initial value is by setting the Lagrange multiplier to 0, calculating the initial value of the unknown quantity of the flow field and the initial value of the unknown quantity of the structural field according to the three sub-equations, and updating the Lagrange multiplier to obtain the initial value of the Lagrange multiplier.

[0018] Based on the further improvement of the above method, the flow field unknowns, structural field unknowns and Lagrange multipliers are updated according to three sub-equations in each iteration, including:

[0019] Based on the flow field sub-equation, any flow field solver is used to solve, update the unknown quantity of the flow field, and extract the flow field coupling interface force vector;

[0020] After the first transfer matrix transformation, the flow field coupling interface force vector is transformed into the structural field coupling interface force vector and fed back to the structural field solver to generate the external force vector of the entire domain of the structural field;

[0021] According to the structural field sub-equation, any structural field solver is used to solve, update the structural field unknowns, and extract the structural field coupling interface displacement vector;

[0022] After the first transfer matrix transformation, the structural field coupling interface displacement vector is converted into the flow field coupling interface displacement vector and fed back to the flow field solver to generate the external force vector of the entire flow field domain;

[0023] Based on the correlation sub-equation, the Lagrange multiplier is updated using the imbalance of the velocity vector at the interface of the flow field and the structural field coupling.

[0024] Based on further improvement of the above method, the structure-field coupling interface force vector is obtained by multiplying the first transfer matrix with the flow-field coupling interface force vector; the flow-field coupling interface displacement vector is obtained by multiplying the transposed matrix of the first transfer matrix with the structure-field coupling interface displacement vector.

[0025] Based on the further improvement of the above method, the Lagrange multiplier is updated by the following formula:

[0026] ,

[0027] in, Indicates the current iteration number. , represents the maximum number of iterations, , and Respectively represent The updated Lagrange multipliers, flow field unknowns and structural field unknowns in the iterations are: Indicates taking the L2 norm, Indicates The time step length is , Indicates the maximum number of time steps.

[0028] Based on the further improvement of the above method, the following formula is used to express that the relative residuals of the unknown flow field, the unknown structural field and the Lagrange multiplier are all less than their respective convergence tolerances:

[0029] ,

[0030] in, , and They represent the convergence tolerance of flow field physical quantities, structural field physical quantities and Lagrange multipliers respectively. Indicates taking the L2 norm, , and Respectively represent The unknown flow field, unknown structural field and Lagrange multipliers at the beginning of the iteration are: , and Respectively represent The updated flow field unknowns, structural field unknowns and Lagrange multipliers in the iteration.

[0031] Based on the further improvement of the above method, the first transfer matrix of the physical quantity from the flow field coupling interface to the structure field coupling interface is calculated according to the boundary conditions, including:

[0032] Obtain the surface and node information on the flow field coupling interface and the structural field coupling interface; take a node on the flow field coupling interface as the current node, and obtain its projection point on the structural field coupling interface according to the surface normal of the surface where the current node is located; obtain the mapping node according to the projection point and calculate the weight of each mapping node, and set the weight of the non-mapped node on the structural field coupling interface to 0; use the weight as the influence weight coefficient of the physical quantity at each node of the flow field coupling interface on the physical quantity at each node of the structural coupling interface, and store it in matrix form to obtain the first transfer matrix.

[0033] On the other hand, an embodiment of the present invention provides a simulation analysis system based on fluid-solid coupling, comprising:

[0034] Model pre-processing module, used to import the structural geometry model of the component, generate the fluid geometry model by extracting the fluid domain from the structural geometry model, and perform discretization meshing on the structural and fluid geometry models respectively;

[0035] A coupling equation construction module is used to calculate the first transfer matrix of physical quantities from the flow field coupling interface to the structural field coupling interface according to boundary conditions; construct the fluid-solid direct coupling system equation according to the first transfer matrix, Lagrange multipliers, flow field unknowns and structural field unknowns, and transform it into three sub-equations;

[0036] The fluid-structure coupling analysis module is used to perform fluid-structure coupling analysis. It uses iterative calculation to update the flow field unknowns based on the three sub-equations using any flow field solver, update the structural field unknowns using any structural field solver, and update the Lagrange multiplier in each iteration of each time step until the relative residuals of the flow field unknowns, structural field unknowns, and Lagrange multipliers are all less than their respective convergence tolerances and all time steps are completed.

[0037] The analysis result acquisition module is used to extract the analysis results from the result files output by the flow field solver and the structural field solver.

[0038] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0039] 1. Improve the system equations of the direct coupling method, introduce Lagrange multipliers, and solve the flow field and structural field in an iterative manner. It does not limit the calculation method used by the solver of the flow field and structural field, nor the solution order of the flow field and structural field. It has strong robustness and controllability, increases application flexibility, and has broad application prospects and practical value.

[0040] 2. By constructing clear fluid-solid coupling system equations for solving, all unknown quantities in the flow field and structural field can be calculated in each iteration. The calculation ability is strong, which improves the solution efficiency and accuracy of engineering applications.

[0041] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components;

[0043] Figure 1 This is a flow chart of a simulation analysis method based on fluid-solid coupling in Example 1 of the present invention;

[0044] Figure 2 Schematic diagram of the 1 / 2 symmetrical structural geometric model of the liquid-resistance composite shock-absorbing element in Example 1 of the present invention;

[0045] Figure 3 Schematic diagram of the structure of a simulation analysis system based on fluid-solid coupling in Example 2 of the present invention. DETAILED DESCRIPTION

[0046] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0047] Fluid-structure interaction analysis has very important significance and application prospects in many fields, including aerospace, shipbuilding and marine engineering, vehicle engineering, nuclear energy, general machinery and biomechanics. For example, in the vehicle industry, high-speed rail bogies use a large number of different types of shock absorbers such as air springs, liquid springs, and liquid-resistance composite shock absorbers to block the mutual movement and vibration between components; in the nuclear energy industry, the flow-induced vibration phenomenon of slender carbon rods caused by the movement of bubbles due to fluid flow and evaporation; in the biological field, the mutual influence of cardiovascular and cerebrovascular and pulsating blood flow; in the aerospace field, the aerodynamic deformation and heating of spacecraft structures during high Mach number flight; in the field of general machinery, the interaction between various pumps, valves, compressors and other equipment and their internal fluid media, the corresponding numerical analysis can all be classified as fluid-structure interaction analysis.

[0048] Example 1

[0049] A specific embodiment of the present invention discloses a simulation analysis method based on fluid-solid coupling, such as Figure 1 As shown, the following steps are included:

[0050] S1. Import the structural geometry model of the component, generate the fluid geometry model by extracting the fluid domain from the structural geometry model, and perform discretized mesh division on the structural and fluid geometry models respectively.

[0051] It should be noted that designers usually design the structural geometry model of the object to be analyzed in CAD software, import it into CAE software, and perform some processing, such as repairing geometric errors, eliminating unnecessary features or details, etc.

[0052] The fluid domain is the area where the fluid can flow. The fluid domain is extracted using the built-in functions of the CAE software, or after the fluid domain is created using geometric Boolean operations, a fluid geometric model is generated based on the fluid domain.

[0053] For example, the liquid-resistance composite shock-absorbing element used on the bogie of the high-speed railway is taken as the object to be analyzed. The element is connected to the bogie through two different parts, the inner and outer metals. The inner and outer metals are fixedly connected with rubber vulcanization to form a cavity, which contains compressible silicone-based hydraulic oil. There is a throttle hole with a very small diameter between the two cavities, which allows the hydraulic oil to flow when the volume of the two cavities changes. When the two parts connected inside and outside move relative to each other, this element will provide motion resistance (and damping) called load force. The load force is the resultant force of structural deformation and fluid pressure distribution in different directions. When the fluid-solid coupling analysis is completed, the load force of this element under different working conditions is obtained from the structural field result file output by the structural field solver. Different working conditions refer to different period and amplitude values ​​in the periodic motion of the inner and outer metals. Figure 2 It is the 1 / 2 symmetrical structural geometric model of the element. The flow field space is two cylinders of equal volume, connected by a throttling channel in the middle.

[0054] Furthermore, the structural geometric model and the fluid geometric model are meshed to generate a structural mesh model suitable for structural mechanics analysis and a flow field mesh model suitable for fluid mechanics analysis, respectively.

[0055] The material properties are defined based on the component material and the type of liquid in it. For the liquid-resistance composite shock-absorbing component, the material properties of the structure include metal and rubber materials. The metal material parameters include: density, elastic modulus and Poisson's ratio; the rubber material parameters adopt the third-order Ogden model, and its main parameters include density and Ogden parameters. The material properties of the fluid include: density, viscosity, bulk modulus, and the parameters of the SST turbulence model used. The above parameters all adopt the metal, rubber and hydraulic oil parameters commonly used in engineering.

[0056] Furthermore, boundary conditions, periodic motion conditions and constraint conditions are set for the grid model. Boundary conditions define the fluid-solid coupling interface and the physical quantities on the interface, such as velocity and pressure, to simulate the working state of the component in the real environment; periodic motion conditions are used to simulate the periodic motion of the component; constraint conditions are used to simulate the fixing method of the component structure in actual application, such as fixed support, hinge, sliding connection, etc., to prevent unnecessary rigid body motion of the structural model and ensure the stability of the structure.

[0057] For example, the structural grid model of the liquid-resistance composite damping element mainly includes three types of conditions: a fixed constraint is imposed on the metal outer boundary in the middle, a displacement boundary condition of periodic motion is imposed on the metal outer boundaries on both sides, and all inner surfaces of the structural cavity are fluid-solid coupling boundary conditions. During the fluid-solid coupling analysis, the changing pressure of the fluid at these boundaries will act on the structural model in the form of an external force vector.

[0058] There is only one type of boundary condition in the flow field grid model, that is, the surface of the entire flow field grid model is a fluid-solid coupling boundary condition. In the fluid-solid coupling analysis, the structural deformation at these boundaries will be transmitted to the flow field, causing the flow field spatial configuration to change continuously.

[0059] S2. Calculate the first transfer matrix of physical quantities from the flow field coupling interface to the structural field coupling interface according to the boundary conditions; construct the fluid-solid direct coupling system equation according to the first transfer matrix, Lagrange multipliers, flow field unknowns and structural field unknowns, and transform it into three sub-equations.

[0060] It should be noted that the first transfer matrix comes from the coupling interface between the flow field and the structural field set in the boundary conditions, and is obtained through the following steps:

[0061] The surface and node information on the flow field coupling interface and the structural field coupling interface are extracted, a node on the flow field coupling interface is taken as the current node, and its projection point on the structural field coupling interface is obtained according to the surface normal of the surface where the current node is located; the mapping node is obtained according to the projection point and the weight of each mapping node is calculated, and the weight of the non-mapped node on the structural field coupling interface is set to 0; the weight is used as the influence weight coefficient of the physical quantity at each node of the flow field coupling interface on the physical quantity at each node of the structural coupling interface, and is stored in a matrix form to obtain the first transfer matrix .

[0062] Specifically, the face and node information of each flow field coupling interface is obtained from the flow field grid model. The node is the grid point, which constitutes the face grid of the flow field coupling interface in space. ; Similarly, the surface mesh of each structure-field coupling interface is obtained from the structure-field mesh model .

[0063] Opposite grid For each node of each face, project along the face normal to obtain its position in the face mesh The projection point on the image; obtain the mapping node according to the projection point and calculate the weight of each mapping node, including:

[0064] If the projection point is a surface mesh If there is a node in , then this node is used as the mapping node of the flow field node, and the weight of the mapping node is set to 1;

[0065] If the projection point is on the surface mesh On an edge in , the two nodes of the edge are used as mapping nodes of the flow field node, and the ratio of the length from the projection point to each mapping node to the length of the edge is calculated to obtain the weight of each mapping node;

[0066] If the projection point is on the surface mesh In one of the faces, the vertex of the face is used as the mapping node of the flow field node. The projection point and each mapping node are sequentially combined to form a triangular face. The proportion of the area of ​​each triangular face to the total area is calculated to obtain the area weights. The area weights of the triangular faces where each mapping node is located are accumulated to obtain the weight of each mapping node.

[0067] Setting up the surface mesh for the structural field coupling interface The weight of the non-mapped node is 0; the weight is used as the influence weight coefficient of the physical quantity at each node of the flow field coupling interface on the physical quantity at each node of the structure coupling interface, and is stored in the form of a matrix to obtain the first transfer matrix The physical quantity of each node on the flow field coupling interface is transferred to the nodes of the structure field coupling interface through the influence weight coefficient in the first transfer matrix.

[0068] Set the number of flow field coupling interface nodes to , the number of structure-field coupling interface nodes is , then the first transfer matrix for The matrix can be expressed as:

[0069] (1)

[0070] Each element in the matrix Indicates the flow field coupling interface The physical quantity at the node is related to the structural coupling interface The influence weight coefficient of the physical quantity at each node.

[0071] It should be noted that the direct coupling method in the prior art couples the fluid-solid control equation into the same equation for solution through the following formula:

[0072] (2)

[0073] in, , and They represent the coefficient matrix of the discrete equations of the flow field, the unknown quantities of the flow field to be solved, and the external force vector of the flow field respectively; , and They represent the coefficient matrix of the discrete equations of the structural field, the unknown quantities of the structural field to be solved, and the external force vector of the structural field respectively; represents the influence of flow field on structural field, Represents the influence of the structural field on the flow field. The mutual influence between the flow field and the structural field is expressed by and Matrix transfer.

[0074] This scheme transforms the existing direct-coupled system equations and introduces the Lagrange multiplier , the constructed fluid-solid direct coupling system equation is as follows:

[0075] (3)

[0076] in, represents the time step, The external force vector of the entire domain corresponding to the motion of the flow field coupled interface; The external force vector of the entire domain corresponding to the change of the structure-field coupling interface flow field force; The second transfer matrix representing the flow field physical quantity from the entire domain to the flow field coupling interface; The third transfer matrix represents the physical quantity of the structural field from the entire domain to the structural field coupling interface; the mutual influence between the flow field and the structural field is expressed by , and Matrix transfer.

[0077] It should be noted that the coefficient matrix of the discrete equations of the flow field is In fluid mechanics, it refers to the coefficient matrix of the algebraic equations obtained by discretizing the fluid control equations.

[0078] Exemplarily, the fluid control equations generally include the mass equation represented by equation (4) and the momentum equation represented by equation (5):

[0079] (4)

[0080] in, represents the fluid density, Indicates time, Represents the velocity vector.

[0081] (5)

[0082] in, Indicates viscosity, Represents the external force vector.

[0083] When the flow field solver uses the finite volume method, the control volume of the flow field is integrated and assembled: by dividing the calculation area into grids, and making each grid point have a non-repeating control volume around it or directly using the discrete grid as the control volume, and then integrating the conservation equations in each control volume, the discrete equations of the control volume are assembled. The unknowns of the equations are the physical quantities of the control volume, such as velocity, pressure, and temperature.

[0084] Coefficient matrix of the discrete equations of the structural field In structural mechanics, it refers to the coefficient matrix of the algebraic equations obtained by discretizing the solid governing equations.

[0085] For example, the governing equation for a solid is usually the momentum equation:

[0086] (6)

[0087] in, represents the density of the solid, represents the displacement vector, represents the stress tensor, Represents the external force vector.

[0088] When the solver uses the finite element method, the solid control equations are integrated and assembled to obtain: By dividing the structural field into a finite number of units, the solid control equations are integrated using shape functions to obtain the local stiffness matrix of each unit, and the discrete equations of all units are assembled. The unknown quantity of the equation system is the displacement of the node.

[0089] For example, for the liquid resistance composite damping element, without considering the thermal factor, the unknown quantity of the flow field is Including velocity vector, pressure, turbulent kinetic energy and energy dissipation rate, structural field unknowns is the displacement vector.

[0090] It should be noted that is the external force vector caused by the coupled boundary motion. When solving any flow field using any flow field solver, The influence on each physical quantity is determined by solving the flow field equations; the flow field model is with Matrices of the same rank. It is the second transfer matrix of the physical quantity from the entire domain to the flow field coupling interface during the flow field solution process. If the number of nodes in the flow field grid model is , the number of flow field coupling interface nodes is , for Matrix of order.

[0091] Similarly, is the external force vector caused by the coupled boundary flow field pressure. When solving any structural field using any structural field solver, The influence on each physical quantity is determined by solving the structural field equations; the structural field model is with Matrices of the same rank. It is the third transfer matrix of the physical quantity from the entire domain to the structural field coupling interface during the solution process of the structural field. If the number of nodes in the structural mesh model is , the number of structure-field coupling interface nodes is , for Matrix of order.

[0092] Above , , and The four matrices are determined by their respective solvers during the calculation process, that is, each field control equation can receive the external force vector brought by the other field through the coupling interface, and after solving the equation, the updated physical quantity at the coupling interface of the flow field and the structural field is extracted. , , and .

[0093] The external force vector represents the external force acting on the fluid and structure. The flow field external force vector and the structural field external force vector need to be determined based on specific physical problems and engineering requirements.

[0094] Furthermore, the above system equation is transformed into the following three sub-equations:

[0095] (7)

[0096] in, and represent the displacement vector of the flow field coupling interface and the displacement vector of the structure field coupling interface respectively; and represent the flow field coupling interface force vector and the structure field coupling interface force vector respectively; and represent the flow field coupling interface velocity vector and the structural field coupling interface velocity vector respectively.

[0097] The above three sub-equations: the first is the flow field sub-equation, the second is the structural field sub-equation, and the third is the associated sub-equation of the flow field and the structural field, and is related to the velocity vector of the coupling interface between the flow field and the structural field. Therefore, this embodiment constructs a clear fluid-solid coupling system equation, uses an iterative calculation method to continuously update the flow field unknowns, structural field unknowns and Lagrange multipliers during the iteration, and uses Lagrange multipliers to accelerate the efficiency of iterative approximation to the true solution, so that the displacement, force and velocity of the fluid-solid coupling interface are close to equilibrium, has strong computing power, and improves the solution efficiency and accuracy of engineering applications.

[0098] S3. Perform fluid-structure coupling analysis. In each iteration of each time step, based on the three sub-equations, any flow field solver is used to update the flow field unknowns, any structural field solver is used to update the structural field unknowns, and the Lagrange multiplier is updated, until the relative residuals of the flow field unknowns, structural field unknowns and Lagrange multipliers are all less than their respective convergence tolerances and all time steps are completed.

[0099] S30, calculating the initial value of the iteration.

[0100] It should be noted that, in order to improve the accuracy of the calculation results and accelerate the convergence speed when performing iterative calculations in this embodiment, the initial value is not directly preset, but the iterative initial value is first calculated through this step and used in the first iteration, that is: by setting the Lagrange multiplier to 0, the initial value of the unknown quantity of the flow field and the initial value of the unknown quantity of the structural field are calculated in turn according to the three sub-equations, and the Lagrange multiplier is updated to obtain the initial value of the Lagrange multiplier.

[0101] Specifically, the Lagrange multiplier is set to 0, and the superscript (0) is used to indicate before the iterative calculation, that is, , then the flow field equation is equivalent to:

[0102] (8).

[0103] Use any flow field solver to perform Iterative calculations are performed to extract the attempted solutions of all unknown quantities in the flow field. , the superscript (1) indicates the first iteration in the subsequent iterative calculation of the entire dynamic coupling.

[0104] It should be noted that the number of iterations of the flow field solver Determined based on the accuracy and efficiency required.

[0105] Further, based on the current attempt to solve , the flow field coupling interface force vector is extracted by the flow field solver , after the first transfer matrix transformation, is converted into Converted into structure-field coupling interface force vector (i.e. dynamic load) :

[0106] (9).

[0107] Structural field coupling interface force vector As boundary conditions, it is fed back to the structural field solver to update the structural field and generate the external force vector of the entire domain of the structural field, which is expressed as: , substituting it into the structural field equation, we get:

[0108] (10)

[0109] because , then the above equation is equivalent to:

[0110] (11).

[0111] Use any structural field solver to solve and obtain accurate solutions for all unknown quantities in the structural field .

[0112] Furthermore, based on the current accurate solution , the structural field coupling interface displacement vector is extracted by the structural field solver , after the first transfer matrix transformation, is converted into Converted into flow field coupling interface displacement vector (i.e. motion load) :

[0113] (12)

[0114] in, The transfer matrix representing the physical quantity from the structure-field coupling interface to the flow-field coupling interface can be obtained by reverse calculation according to the method of calculating the first transfer matrix.

[0115] Force vector at the flow field coupling interface As boundary conditions, it is fed back to the flow field solver to update the spatial shape of the flow field. The change in the spatial shape of the flow field generates an external force vector for the entire domain of the flow field, which is expressed as .

[0116] Since the constraint condition satisfied by the third correlation sub-equation is the balance of the velocity vector at the interface of the flow field and the structural field coupling, the Lagrange multiplier is updated based on the correlation sub-equation using the imbalance of the velocity vector at the interface of the flow field and the structural field coupling, so that the two velocity vectors are close to balance. The update formula is as follows:

[0117] (13)

[0118] in, represents the updated Lagrange multiplier, as the initial value of the Lagrange multiplier, Indicates taking the L2 norm, Represents the time step.

[0119] So far, the initial values ​​of all unknown quantities in the flow field and structural field and the initial values ​​of the Lagrange multipliers have been obtained.

[0120] S31. Perform iterative calculation of dynamic coupling.

[0121] According to the actual problem needs, specify the control parameters to perform iterative calculation of the entire dynamic coupling process, where the control parameters include: the convergence tolerance of the flow field physical quantities in the coupling iterative calculation , Convergence tolerance of structural field physical quantities and the convergence tolerance of the Lagrange multipliers , the current number of iterations and the maximum number of iterations , , the current time step and the maximum number of time steps , . Execute at each time step Iterations.

[0122] Specifically, for each time step In the iteration, the formula corresponding to the flow field sub-equation is as follows:

[0123] (14).

[0124] Based on the Lagrange multiplier in the current iteration, use any flow field solver to perform multiple iterations, update all unknown quantities in the flow field, and obtain the updated trial solution. .

[0125] Further, based on the current attempt to solve , the flow field coupling interface force vector is extracted by the flow field solver , after the first transfer matrix transformation, is converted into Transformed into structural field coupling interface force vector , and is fed back to the structural field solver as a boundary condition to update the structural field and generate the external force vector of the entire domain of the structural field , substituting it into the structural field equation, we get:

[0126] (15).

[0127] Use any structural field solver to solve, update all unknown variables in the structural field, and obtain the updated accurate solution. .

[0128] Furthermore, based on the current accurate solution , the structural field coupling interface displacement vector is extracted by the structural field solver , after the first transfer matrix transformation, is converted into Transformed into flow field coupling interface displacement vector , and is fed back to the flow field solver as a boundary condition to update the flow field spatial morphology. The change in the flow field spatial morphology generates an external force vector for the entire flow field domain. .

[0129] Furthermore, based on the correlation sub-equation, the unbalanced velocity vector of the interface coupling between the flow field and the structural field is used to update the Lagrange multipliers in the iteration , and obtain the updated Lagrange multiplier , so that the two velocity vectors approach equilibrium, the update formula is as follows:

[0130] (16)

[0131] in, Indicates The length of the time step.

[0132] Furthermore, it is necessary to identify whether the relative residuals of the flow field unknowns, structural field unknowns and Lagrange multipliers are all less than their respective convergence tolerances. The formula is as follows:

[0133] (17)

[0134] in, , and They represent the convergence tolerance of flow field physical quantities, structural field physical quantities and Lagrange multipliers respectively. , and Respectively represent The unknown flow field, unknown structural field and Lagrange multipliers at the beginning of the iteration are: , and Respectively represent The updated flow field unknowns, structural field unknowns and Lagrange multipliers in the iteration.

[0135] When the relative residuals of the unknown flow field, unknown structural field and Lagrange multiplier are all less than their respective convergence tolerances, it means that the current time step calculation is completed and converged, the iterative calculation of the current time step is completed, and the current time step number is determined. Has the maximum number of time steps been reached? , if not reached, then the current time step Increment by 1, number of iterations Reset to 1 and start iterative calculation of the new time step according to step S31 until the maximum number of time steps is reached, prompting the completion of the fluid-solid coupling analysis.

[0136] When any of the relative residuals of the flow field unknowns, structural field unknowns, and Lagrange multipliers is not less than the corresponding convergence tolerance, if the number of iterations is less than the maximum number of iterations, the number of iterations increases by 1 and the current time step is entered. Iterations are performed until the three relative residuals are all less than their respective convergence tolerances. The current time step Increment by 1, and start the iterative calculation of the new time step according to step S31 until the maximum number of time steps is reached, and the fluid-structure coupling analysis is completed; if the number of iterations reaches the maximum number of iterations, and there is still a relative residual of the unknown quantity that is not less than the convergence tolerance, the iterative calculation is exited and an error message is prompted that the fluid-structure coupling analysis has failed to converge.

[0137] It can be seen from the above steps that this embodiment does not limit the calculation method adopted by the solver of the flow field and the structural field, and there is no order restriction for the flow field sub-equation and the structural field sub-equation. The above is solved in the order of flow field first and then structural field, and can also be solved in the order of structural field first and then flow field. It has strong robustness and controllability and is suitable for any transient dynamic fluid-solid coupling analysis.

[0138] S4. Extract the analysis results from the result files output by the flow field solver and the structural field solver.

[0139] It should be noted that the analysis results of fluid-structure interaction are in the flow field result files and structural field result files output by the flow field solver and structural field solver.

[0140] Specifically, the flow field result file includes but is not limited to: the spatial distribution of flow field velocity, curl, pressure, shear force, and the mass and flow rate of the fluid at each inlet and outlet. Since the structural response includes the fluid coupling effect, and there is an intuitive correspondence between the structural model and the product model, the results closely related to product design are generally included in the structural field result file, from which the physical response values ​​of each position or part can be obtained and the analysis results can be extracted.

[0141] For example, the fluid-solid coupling simulation analysis of the liquid-resistance composite shock-absorbing element is carried out to analyze whether the load force of the element meets the requirements under different working conditions. In the iterative calculation process of dynamic coupling, the structural field solver calculates the support reaction force value of the constrained metal parts according to the unknown structural field quantities solved at each time step, and writes it into the structural field result file. This support reaction force is composed of the structural force deformation and fluid resistance, which is the load force of the shock-absorbing element.

[0142] The spherical closed tank flange is usually installed on a host in a vibrating environment, and the tank is filled with liquid medium but not filled. The fluid-solid coupling simulation analysis method of this embodiment is used to analyze the interaction between the tank and the internal fluid under random vibration conditions, and the analysis result obtained is the structural strength of the dangerous area of ​​the tank.

[0143] The working principle of the diaphragm gas compressor is to use a diaphragm to divide the fluid medium working chamber into an air chamber and an oil chamber. The air chamber is connected to the intake valve and the exhaust valve; the oil chamber is connected to the piston connecting rod mechanism. During the reciprocating motion of the piston, the change in the oil chamber pressure drives the diaphragm to move and deform, and the volume of the air chamber is thus continuously reduced and expanded. When the volume of the air chamber is reduced, the air pressure rises and eventually the exhaust valve opens to discharge high-pressure gas. When the volume expands, the air pressure decreases and the intake valve opens to inhale low-pressure gas. The fluid-solid coupling simulation analysis method of this embodiment is used to simulate the working process of the entire compressor.

[0144] Compared with the prior art, the simulation analysis method based on fluid-solid coupling provided in this embodiment improves the system equation of the direct coupling method, introduces Lagrange multipliers, and solves the flow field and structural field in an iterative manner. It does not limit the calculation method used by the solver of the flow field and structural field, and the order of solving the flow field and structural field. It has strong robustness and controllability, increases application flexibility, and has broad application prospects and practical value. By constructing a clear fluid-solid coupling system equation for solution, all unknown quantities of the flow field and structural field can be calculated in each iteration, with strong computing power, which improves the solution efficiency and accuracy of engineering applications.

[0145] Example 2

[0146] Another embodiment of the present invention discloses a simulation analysis system based on fluid-solid coupling, thereby realizing the simulation analysis method based on fluid-solid coupling in embodiment 1. The specific implementation of each module refers to the corresponding description in embodiment 1. Figure 3 As shown, the system includes:

[0147] The model pre-processing module 101 is used to import the structural geometry model of the component, generate the fluid geometry model by extracting the fluid domain from the structural geometry model, and perform discretization meshing on the structural and fluid geometry models respectively;

[0148] A coupling equation construction module 102 is used to calculate the first transfer matrix of physical quantities from the flow field coupling interface to the structure field coupling interface according to the boundary conditions; construct the fluid-solid direct coupling system equation according to the first transfer matrix, Lagrange multipliers, flow field unknowns and structure field unknowns, and transform it into three sub-equations;

[0149] The fluid-structure coupling analysis module 103 is used to perform fluid-structure coupling analysis, and in each iteration of each time step, based on the three sub-equations, any one of the flow field solvers is used to update the flow field unknowns, any one of the structural field solvers is used to update the structural field unknowns, and the Lagrange multipliers are updated, until the relative residuals of the flow field unknowns, the structural field unknowns, and the Lagrange multipliers are all less than their respective convergence tolerances and all time steps are completed;

[0150] The analysis result acquisition module 104 is used to extract the analysis results from the result files output by the flow field solver and the structural field solver.

[0151] Since the simulation analysis system based on fluid-solid coupling of this embodiment and the simulation analysis method based on fluid-solid coupling described above can be mutually referenced, it is a repeated description here, so it will not be repeated here. Since the principle of this system embodiment is the same as that of the above method embodiment, this system embodiment also has the corresponding technical effects of the above method embodiment.

[0152] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0153] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A simulation analysis method based on fluid-solid coupling, characterized in that: The following steps are involved: Import the structural geometry model of the component, generate the fluid geometry model by extracting the fluid domain from the structural geometry model, and perform discretization meshing on the structural and fluid geometry models respectively; Calculate the first transfer matrix of physical quantity from the flow field coupling interface to the structure field coupling interface according to the boundary conditions; According to the first transfer matrix, Lagrange multipliers, flow field unknowns and structural field unknowns, the fluid-solid direct coupling system equation is constructed and transformed into three sub-equations; Perform fluid-structure interaction analysis, and update the flow field unknowns using any flow field solver based on the three sub-equations, update the structural field unknowns using any structural field solver, and update the Lagrange multiplier in each iteration of each time step through iterative calculation, until the relative residuals of the flow field unknowns, structural field unknowns, and Lagrange multipliers are all less than their respective convergence tolerances and all time steps are completed; Extract analysis results from the result files output by the flow field solver and the structural field solver; According to the first transfer matrix, Lagrange multipliers, flow field unknowns and structural field unknowns, the fluid-solid direct coupling system equation is constructed by the following formula: ， in, , and They represent the coefficient matrix of the discrete equations of the flow field, the unknown quantities of the flow field to be solved, and the external force vector of the flow field respectively; , and They represent the coefficient matrix of the discrete equations of the structural field, the unknown quantities of the structural field to be solved, and the external force vector of the structural field respectively; represents the time step; represents the Lagrange multiplier; The first transfer matrix representing the physical quantity from the flow field coupling interface to the structure field coupling interface; The external force vector of the entire domain corresponding to the motion of the flow field coupled interface; The external force vector of the entire domain corresponding to the change of the structure-field coupling interface flow field force; The second transfer matrix representing the flow field physical quantity from the entire domain to the flow field coupling interface; The third transfer matrix representing the physical quantity of the structural field from the entire domain to the structural field coupling interface; The three sub-equations include: flow field sub-equation, structure field sub-equation and correlation sub-equation; the three sub-equations are expressed by the following formula: ， in, and represent the displacement vector of the flow field coupling interface and the displacement vector of the structure field coupling interface respectively; and represent the flow field coupling interface force vector and the structure field coupling interface force vector respectively; and represent the flow field coupling interface velocity vector and the structural field coupling interface velocity vector respectively.

2. The simulation analysis method based on fluid-solid coupling according to claim 1 is characterized in that: Before the iterative calculation, it also includes calculating the initial value of the iteration for the first iteration; the initial value of the iteration is calculated by setting the Lagrange multiplier to 0, calculating the initial value of the unknown quantity of the flow field and the initial value of the unknown quantity of the structural field according to the three sub-equations, and updating the Lagrange multiplier to obtain the initial value of the Lagrange multiplier.

3. The simulation analysis method based on fluid-solid coupling according to claim 2 is characterized in that: In each iteration, the flow field unknowns, structural field unknowns and Lagrange multipliers are updated according to three sub-equations, including: Based on the flow field sub-equation, any flow field solver is used to solve, update the unknown quantity of the flow field, and extract the flow field coupling interface force vector; After the first transfer matrix transformation, the flow field coupling interface force vector is transformed into the structural field coupling interface force vector and fed back to the structural field solver to generate the external force vector of the entire domain of the structural field; According to the structural field sub-equation, any structural field solver is used to solve, update the structural field unknowns, and extract the structural field coupling interface displacement vector; After the first transfer matrix transformation, the structural field coupling interface displacement vector is converted into the flow field coupling interface displacement vector and fed back to the flow field solver to generate the external force vector of the entire flow field domain; Based on the correlation sub-equation, the Lagrange multiplier is updated using the imbalance of the velocity vector at the interface of the flow field and the structural field coupling.

4. The simulation analysis method based on fluid-solid coupling according to claim 3 is characterized in that: The structure-field coupling interface force vector is obtained by multiplying the first transfer matrix and the flow-field coupling interface force vector; The flow field coupling interface displacement vector is obtained by multiplying the transposed matrix of the first transfer matrix by the structure field coupling interface displacement vector.

5. The simulation analysis method based on fluid-solid coupling according to claim 3 is characterized in that: The Lagrange multiplier is updated by the following formula: ， in, Indicates the current iteration number. , represents the maximum number of iterations, , and Respectively represent The updated Lagrange multipliers, flow field unknowns and structural field unknowns in the iterations are: Indicates taking the L2 norm, Indicates The time step length , Indicates the maximum number of time steps.

6. The simulation analysis method based on fluid-solid coupling according to claim 1 is characterized in that: The following formula indicates that the relative residuals of the flow field unknowns, structural field unknowns, and Lagrange multipliers are all less than their respective convergence tolerances: ， in, , and They represent the convergence tolerance of flow field physical quantities, structural field physical quantities and Lagrange multipliers respectively. Indicates taking the L2 norm, , and Respectively represent The unknown flow field, unknown structural field and Lagrange multipliers at the beginning of the iteration are: , and Respectively represent The updated flow field unknowns, structural field unknowns and Lagrange multipliers in the iteration.

7. The simulation analysis method based on fluid-solid coupling according to claim 1 is characterized in that: The first transfer matrix of calculating the physical quantity from the flow field coupling interface to the structure field coupling interface according to the boundary conditions includes: Obtain the surface and node information on the flow field coupling interface and the structural field coupling interface; take a node on the flow field coupling interface as the current node, and obtain its projection point on the structural field coupling interface according to the surface normal of the surface where the current node is located; obtain the mapping node according to the projection point and calculate the weight of each mapping node, and set the weight of the non-mapped node on the structural field coupling interface to 0; use the weight as the influence weight coefficient of the physical quantity at each node of the flow field coupling interface on the physical quantity at each node of the structural coupling interface, and store it in matrix form to obtain the first transfer matrix.

8. A simulation analysis system based on fluid-solid coupling, characterized in that: include: Model pre-processing module, used to import the structural geometry model of the component, generate the fluid geometry model by extracting the fluid domain from the structural geometry model, and perform discretization meshing on the structural and fluid geometry models respectively; A coupling equation building module is used to calculate the first transfer matrix of physical quantities from the flow field coupling interface to the structure field coupling interface according to boundary conditions; According to the first transfer matrix, Lagrange multipliers, flow field unknowns and structural field unknowns, the fluid-solid direct coupling system equation is constructed and transformed into three sub-equations; The fluid-structure coupling analysis module is used to perform fluid-structure coupling analysis. It uses iterative calculation to update the flow field unknowns based on the three sub-equations using any flow field solver, update the structural field unknowns using any structural field solver, and update the Lagrange multiplier in each iteration of each time step until the relative residuals of the flow field unknowns, structural field unknowns, and Lagrange multipliers are all less than their respective convergence tolerances and all time steps are completed. An analysis result acquisition module is used to extract analysis results from the result files output by the flow field solver and the structural field solver; In the coupling equation construction module, according to the first transfer matrix, Lagrange multipliers, flow field unknowns and structural field unknowns, the fluid-solid direct coupling system equation is constructed by the following formula: ， in, , and They represent the coefficient matrix of the discrete equations of the flow field, the unknown quantities of the flow field to be solved, and the external force vector of the flow field respectively; , and They represent the coefficient matrix of the discrete equations of the structural field, the unknown quantities of the structural field to be solved, and the external force vector of the structural field respectively; represents the time step; represents the Lagrange multiplier; The first transfer matrix representing the physical quantity from the flow field coupling interface to the structure field coupling interface; The external force vector of the entire domain corresponding to the motion of the flow field coupled interface; The external force vector of the entire domain corresponding to the change of the structure-field coupling interface flow field force; The second transfer matrix representing the flow field physical quantity from the entire domain to the flow field coupling interface; The third transfer matrix representing the physical quantity of the structural field from the entire domain to the structural field coupling interface; The three sub-equations include: flow field sub-equation, structure field sub-equation and correlation sub-equation; the three sub-equations are expressed by the following formula: ， in, and represent the displacement vector of the flow field coupling interface and the displacement vector of the structure field coupling interface respectively; and represent the flow field coupling interface force vector and the structure field coupling interface force vector respectively; and represent the flow field coupling interface velocity vector and the structural field coupling interface velocity vector respectively.

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