Numerical calculation method of bidirectional fluid-structure interaction FVM considering radiation

Abstract

This paper provides a numerical calculation method for bidirectional fluid-structure coupling (FVM) with radiation considerations. The method establishes a numerical model for radiation transfer in heterogeneous participating media based on CCFVM, a CCFVM numerical model for heat transfer that considers radiation-induced fluid-structure coupling, and a CVFVM numerical model for bidirectional fluid-structure coupling stress. This method constructs a numerical framework for bidirectional fluid-structure coupling with radiation considerations and develops a solver. This method leverages the advantages of CCFVM in flow field calculations and CVFVM in structural field calculations, and employs a unified grid model to avoid errors caused by data mapping between different numerical methods.

Description

Technical Field

[0001] The present invention relates to a multi-physical field coupling numerical calculation technology, specifically a bidirectional fluid-solid coupling numerical calculation method based on a unified finite volume method and considering radiation. Background Art

[0002] Fluid-structure interaction is an interdisciplinary subject of fluid-solid interaction and a multi-physics coupling problem. Common numerical methods for multi-physics coupling problems include unified methods and hybrid methods.

[0003] The hybrid method uses two or more numerical methods to simulate different regions or physical fields. For example, the Monte Carlo method is used to solve the radiation intensity field, while the Boltzmann method is used to solve the flow field. Since the hybrid method uses different numerical methods for different physical fields, the data transfer at the coupling point requires approximation or difference processing, which will lead to the generation of calculation errors and increase the possibility of calculation divergence. The unified method uses the same numerical method for different physical fields and establishes a unified numerical framework for multi-physical field coupling. For example, FVM is used to solve the radiation intensity field, flow field and solid field at the same time. Since the unified method uses a unified numerical method for different physical fields, it can be calculated based on the same grid, and the coupling surface does not require special processing. The generation of coupling surface processing errors is avoided, and the calculation is not prone to divergence.

[0004] This paper establishes a numerical model for radiation heat transfer in heterogeneous participating media based on CCFVM, a numerical model for fluid-solid coupling heat transfer that considers radiation based on CCFVM, and a numerical model for fluid-solid coupling stress based on CVFVM. Leveraging the differences between the CCFVM and CVFVM numerical models, a unified numerical framework is established based on the same grid. Dynamic mesh technology is introduced to establish a finite volume numerical model for bidirectional fluid-solid coupling that considers radiation based on the unified finite volume method. A complete computational program for this bidirectional fluid-solid coupling numerical model based on the unified finite volume method is developed using the C++ language.

[0005] The symbols used in this application mean: FVM: finite volume method, CVFVM: grid-type finite volume method, CCFVM: grid-centred finite volume method. Summary of the Invention

[0006] Aiming at the problems of incomplete consideration of coupling effect in existing fluid-solid coupled heat transfer and additional errors introduced by coupling surface data processing, the present invention proposes a bidirectional fluid-solid coupled FVM numerical calculation method considering radiation.

[0007] In the first step, the radiation source term and the wall radiation heat flux density obtained by calculating the radiation intensity field in the numerical model of non-uniform participatory medium radiation transfer based on CCFVM are first brought into the fluid-solid coupling heat transfer numerical model established based on CCFVM; then, the temperature field calculated by the fluid-solid coupling heat transfer numerical model established based on CCFVM is used to update the radiation physical properties of the non-uniform participatory medium in the radiation intensity field; finally, the radiation physical properties of the non-uniform participatory medium in the radiation transmission numerical model of non-uniform participatory medium based on CCFVM are used to update the radiation intensity field, and finally the establishment of the CCFVM numerical model considering radiation fluid-solid coupling heat transfer is realized;

[0008] In the second step, the solid structure field temperature and fluid force on the fluid-solid coupling surface calculated by the CCFVM numerical model considering radiation fluid-solid coupling heat transfer are first brought into the solid structure field stress calculation based on the fluid-solid coupling stress numerical model established based on CVFVM, and a flow-induced vibration numerical model and a thermo-solid coupling numerical model based on CVFVM are established. Then, the flow-induced vibration numerical model and the thermo-solid coupling numerical model based on CVFVM are used to solve the thermal stress and stress distribution of the structural field, and a one-way fluid-solid coupling numerical calculation considering radiation based on CVFVM is established.

[0009] In the third step, the coupling surface displacement obtained by numerical calculation of the one-way fluid-solid coupling based on CVFVM considering radiation is transferred to the flow field grid of the CCFVM numerical model considering radiation fluid-solid coupling heat transfer, and the dynamic mesh technology is introduced to establish the CVFVM numerical model of bidirectional fluid-solid coupling stress.

[0010] The fourth step is to establish a numerical calculation method for the bidirectional fluid-solid coupling FVM considering radiation based on the CCFVM numerical model considering radiation fluid-solid coupling heat transfer established in the first step and the CVFVM numerical model of bidirectional fluid-solid coupling stress established in the third step, and develop the numerical calculation program for the bidirectional fluid-solid coupling FVM considering radiation using C++ language.

[0011] (1) Establishment of a numerical model of radiation transfer in inhomogeneous participating media based on CCFVM

[0012] For scenarios involving radiative heat transfer in non-uniform participating media, where the medium inhomogeneity manifests itself as spatiotemporal variations in the absorption coefficient, scattering coefficient, and refractive index with temperature, and where changes in the medium's radiative physical properties can affect heat transfer, the following steps are used to establish a numerical model for radiative transfer in non-uniform participating media based on CCFVM.

[0013] The first step is to calculate thermal radiation based on CCFVM.

[0014] In the second step, based on the CCFVM discretized radiation transfer equation, the radiation physical parameters are stored in the unit center, the solid angle is discretized through CCFVM, the solid angle correlation coefficient and the surface unit coefficient are calculated, and the change of radiation physical parameters is introduced in the discretization process to realize the calculation of radiation heat transfer based on the CCFVM discretized spatial solid angle and control equation.

[0015] In the third step, the unit radiation source term and the wall radiation heat flux density are calculated and the calculation results are stored at the unit center.

[0016] (2) Establishment of a CCFVM numerical model considering radiation fluid-solid coupling heat transfer

[0017] The following steps are used to establish the calculation method of the CCFVM numerical model considering radiation fluid-solid coupling heat transfer.

[0018] The first step is to build a fluid-solid coupled heat transfer numerical model based on CCFVM. When the temperature is high, radiation heat transfer calculation needs to be included.

[0019] In the second step, the CCFVM numerical model considering radiation fluid-solid coupling heat transfer is calculated.

[0020] In the third step, the heat conduction equation and energy equation are separated by using the fluid-solid coupled heat transfer numerical model established based on CCFVM, the material physical properties are defined at the center of the grid, and the surface unit coefficients in the discrete equations are calculated.

[0021] The fourth step is to form a calculation coefficient matrix, add the radiation source term calculated in the third step of the numerical model of radiation transfer in non-uniform participatory media based on CCFVM to the control equation, use a unified discretization method for the fluid subdomain and the solid subdomain, store the coefficients of the two domains in the same matrix, and form a unified set of algebraic equations.

[0022] In the fifth step, the synchronous iterative solution method is combined with the implicit algorithm to establish a CCFVM numerical model calculation method for fluid-solid coupled heat transfer considering radiation, and the solution program is compiled using C++ language.

[0023] (3) Establishment of the CVFVM numerical model of bidirectional fluid-solid coupling stress

[0024] The calculation method of the fluid-solid coupling stress CVFVM numerical model is established using the following steps.

[0025] The first step is to establish a numerical model of fluid-solid coupling stress based on CVFVM, including the solid structural stress caused by the pulsating pressure of the flow field and the solid structural thermal stress caused by the temperature field. The solid structural field temperature and fluid force on the fluid-solid coupling surface calculated using the CCFVM numerical model considering radiation fluid-solid coupling heat transfer are incorporated into the solid structural field stress calculation based on the CVFVM fluid-solid coupling stress numerical model, thus establishing a flow-induced vibration numerical model and a thermal-solid coupling numerical model based on CVFVM.

[0026] In the second step, based on the CVFVM discrete thermoelastic equation, the variables to be solved are stored at the cell nodes, and the physical parameters are stored at the cell center. The pulsating pressure of the fluid-structure coupling boundary flow field and the cell center temperature of the solid structure field, calculated using the CCFVM numerical model for fluid-structure coupling heat transfer with radiation, are then extracted.

[0027] The third step is to form the coefficient matrix;

[0028] In the fourth step, an iterative solution method is used to solve the flow-induced vibration numerical model based on CVFVM, and a direct solution method is used to solve the thermal-solid coupling numerical model based on CVFVM. The above models are then used to solve the thermal stress and stress distribution of the structural field, and a one-way fluid-solid coupling numerical model based on CVFVM considering radiation is established.

[0029] In the fifth step, the coupling surface displacement obtained by numerical calculation of the one-way fluid-solid coupling based on CVFVM considering radiation is transferred to the flow field grid of the CCFVM numerical model considering radiation fluid-solid coupling heat transfer, and feedback is loaded to the flow field boundary. The dynamic mesh technology is introduced to update the flow field mesh, and the dynamic mesh technology is introduced to establish the CVFVM numerical model of bidirectional fluid-solid coupling stress.

[0030] The technical problem solved by this invention is to establish a numerical model for bidirectional fluid-structure interaction (FVM) that considers radiation, thereby avoiding data mapping errors caused by different numerical methods solving different physics problems. Using this numerical model, the radiation intensity field, flow field, temperature field, and solid structure field can be calculated using the same grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Technology Roadmap

[0032] Figure 2 Schematic diagram of the numerical model of bidirectional fluid-structure interaction FVM considering radiation

[0033] Figure 3 Schematic diagram of the FVM control volume (taking a two-dimensional grid as an example, the thick solid line is the grid boundary, the solid dots are the grid nodes, and the hollow dots are the grid centers)

[0034] Figure 4Schematic diagram of a heat exchanger, where (a) is the solid subdomain and (b) is the fluid subdomain.

[0035] Figure 5 Schematic diagram of heat exchanger mesh division

[0036] Figure 6 Heat exchanger temperature spatial distribution diagram DETAILED DESCRIPTION

[0037] The numerical calculation method for bidirectional fluid-structure interaction (FVM) with radiation considerations is applicable to single or coupled solutions of one or more physical fields, including radiation intensity, flow, temperature, and structural stress. The following uses a numerical model of bidirectional fluid-structure interaction (FVM) with radiation considerations within a simple gas-to-gas heat exchanger as a specific example for illustration.

[0038] The simple gas-gas heat exchanger includes a solid subdomain 1 composed of an outer shell 101, and a fluid subdomain 2 composed of a low-temperature gas 201 and a high-temperature gas 202. Due to the different materials of the solid subdomain 1 and the fluid subdomain 2, the effects of radiation heat transfer on their heat transfer processes are also different. For the solid subdomain 1, its absorption coefficient is relatively large, and the radiation energy is absorbed after propagating a very short distance, so it is called an opaque medium; for the low-temperature gas 201 and the high-temperature gas 202 in the fluid subdomain 2, their absorption coefficient and scattering coefficient are very small, and they neither absorb nor scatter the radiation energy, so they are called transparent media. For this reason, when solving the fluid-solid coupled heat transfer, it is first determined whether each domain needs to consider radiation heat transfer. The low-temperature gas 201 and the high-temperature gas 202 in the fluid subdomain 2 are participating media, and the influence of radiation heat transfer needs to be considered. The heat exchanger shell 101 in the solid subdomain 1 is an opaque medium, and the influence of radiation heat transfer does not need to be considered. Based on CCFVM, a numerical model of radiation transfer of non-uniform participating media is established, and the grid is used as the control body to discrete equations (such as Figure 3 The grid is formed by the grid nodes ABCD). When the spatial solid angle of the grid cells is discretized, the number of solid angle discretizations is stored in advance, and the coefficients related to the solid angle in the equation are calculated and stored at each cell center. The physical parameters are stored at the center of the grid cells. The physical parameters of the grid surface are required in the discrete control equations, and the parameters of the grid surface are obtained by differentiating the values ​​at the centers of adjacent cells. This takes into account the spatial distribution of the participating medium and implements CCFVM's treatment of the radiation transfer problem of non-uniform participating media. CCFVM is also used to establish the radiation intensity field in the numerical model of radiation transfer of non-uniform participating media to calculate the radiation source term and wall radiation heat flux density at each cell center for subsequent calculations based on the CCFVM fluid-solid coupling heat transfer numerical model.

[0039] When calculating a fluid-solid coupled heat transfer numerical model based on CCFVM, the material properties and initial temperature are stored at the cell centers because the CCFVM-based model needs to discretize the heat conduction and energy equations. This approach is consistent with the discretization of the CCFVM-based numerical model for radiation transfer in inhomogeneous participating media, where the physical properties on the grid surface are obtained by differencing the values ​​at the grid centers. The SIMPLE algorithm is used to solve the continuity and momentum equations, and an appropriate turbulence model is employed to determine the velocity and pressure within the entire fluid subdomain 2. The need to consider the influence of radiation heat transfer in each subdomain is then determined. For subdomains that require consideration, the previously calculated cell center radiation source terms are extracted and added to the corresponding coefficient matrix. The coefficients for each subdomain are stored in a unified coefficient matrix. A set of energy equations accounting for radiation is constructed, encompassing both solid subdomain 1 and fluid subdomain 2. The cell center temperatures within each subdomain are simultaneously solved, completing the calculation of the CCFVM numerical model for fluid-solid coupled heat transfer considering radiation.

[0040] The calculation of the CVFVM-based fluid-structure coupling stress numerical model includes the thermal stress distribution in the solid structure field caused by the spatiotemporal temperature distribution and the stress distribution in the solid structure field caused by the flow field pressure. Because the CVFVM-based fluid-structure coupling stress numerical model requires the extraction of the cell center temperature using the CVFVM discrete thermoelastic equation, this temperature coincides with the cell center temperature obtained by solving the CCFVM numerical model considering fluid-structure coupling heat transfer with radiation, thus avoiding errors caused by data mapping. Solving the thermoelastic equations yields the displacement field of solid subdomain 1, which is comprised of the shell 101. The constitutive equations are then solved to obtain the thermal stress field. The cell center temperature (solid structure field temperature) and the fluid-structure coupling surface fluid force obtained from the CCFVM numerical model considering radiation are applied to the solid structure field. The CVFVM-based fluid-structure coupling stress numerical model is then solved to obtain the thermal and stress fields of solid subdomain 1.

[0041] Finally, the coupling surface displacement obtained from the numerical calculation of the one-way fluid-solid coupling based on CVFVM considering radiation is mapped to the flow field grid as the flow field boundary calculation condition. The dynamic mesh technology is introduced to update the mesh of fluid subdomain 2, and the flow field is recalculated to complete the calculation of the CVFVM numerical model of bidirectional fluid-solid coupling stress.

[0042] The numerical calculation method for bidirectional fluid-structure coupling FVM with radiation considerations involves establishing a numerical model for radiation transfer in heterogeneous participating media based on CCFVM, a numerical model for heat transfer in fluid-structure coupling with radiation, and a numerical model for stress in bidirectional fluid-structure coupling with CVFVM. This method constructs a numerical framework for bidirectional fluid-structure coupling FVM with radiation considerations and develops a solver. This method leverages the advantages of CCFVM in flow field calculations and CVFVM in structural field calculations, and employs a unified grid model to avoid errors caused by data mapping between different numerical methods.

Claims

1. A numerical calculation method for bidirectional fluid-structure interaction (FVM) considering radiation, characterized by: In the first step, the radiation source term and the wall radiation heat flux density calculated from the radiation intensity field in the CCFVM-based numerical model of inhomogeneous participating media radiation transfer are introduced into the fluid-solid coupling heat transfer numerical model established based on CCFVM. Then, the temperature field calculated by the fluid-solid coupling heat transfer numerical model established based on CCFVM is used to update the radiation intensity field and the radiation physical property parameters of the heterogeneous participating medium. Finally, the radiation intensity field of the non-homogeneous participating medium radiation physical property parameters will be used to update the radiation intensity field in the non-homogeneous participating medium radiation transmission numerical model based on CCFVM, and finally the establishment of the CCFVM numerical model considering radiation fluid-solid coupling heat transfer is realized; In the second step, the solid structure field temperature and fluid force on the fluid-solid coupling surface calculated by the CCFVM numerical model considering radiation fluid-solid coupling heat transfer are first brought into the solid structure field stress calculation based on the fluid-solid coupling stress numerical model established based on CVFVM, and a flow-induced vibration numerical model and a thermo-solid coupling numerical model based on CVFVM are established. Then, the flow-induced vibration numerical model and the thermo-solid coupling numerical model based on CVFVM are used to solve the thermal stress and stress distribution of the structural field, and a one-way fluid-solid coupling numerical calculation considering radiation based on CVFVM is established. In the third step, the coupling surface displacement calculated based on the unidirectional fluid-structure coupling numerical calculation of the CVFVM considering radiation is transferred to the flow field grid of the CCFVM numerical model considering radiation fluid-structure coupling heat transfer, and the dynamic mesh technology is introduced to establish the CVFVM numerical model of bidirectional fluid-structure coupling stress. The fourth step is to establish a numerical calculation method for the bidirectional fluid-solid coupling FVM considering radiation based on the CCFVM numerical model considering radiation fluid-solid coupling heat transfer established in the first step and the CVFVM numerical model of bidirectional fluid-solid coupling stress established in the third step, and develop the numerical calculation program for the bidirectional fluid-solid coupling FVM considering radiation using C++ language.

2. The method for numerical calculation of bidirectional fluid-structure interaction (FVM) considering radiation according to claim 1 is characterized by: For scenarios involving radiative heat transfer in non-uniform participating media, where the medium inhomogeneity manifests as spatiotemporal variations in the absorption coefficient, scattering coefficient, and refractive index with temperature, and where changes in the medium's radiative physical properties affect heat transfer, the following steps are used to establish a numerical model for radiative transfer in non-uniform participating media based on CCFVM. The first step is to calculate thermal radiation based on CCFVM; In the second step, based on the CCFVM discretized radiation transfer equation, the radiation physical property parameters are stored in the unit center, the solid angle is discretized through CCFVM, the solid angle correlation coefficient and the surface unit coefficient are calculated, and the change of the radiation physical property parameters is introduced in the discretization process to realize the calculation of radiation heat transfer based on the CCFVM discretized spatial solid angle and the control equation; In the third step, the unit radiation source term and the wall radiation heat flux density are calculated and the calculation results are stored at the unit center.

3. The method for numerical calculation of bidirectional fluid-structure coupling FVM considering radiation according to claim 2 is characterized in that: The calculation method of the CCFVM numerical model considering radiation fluid-solid coupling heat transfer is established using the following steps: The first step is to build a fluid-solid coupled heat transfer numerical model based on CCFVM. When the temperature is high, the radiation heat transfer calculation needs to be included; The second step is to calculate the CCFVM numerical model considering radiation fluid-solid coupling heat transfer; The third step is to use the fluid-solid coupled heat transfer numerical model established based on CCFVM to separate the heat conduction equation and energy equation, define the material physical properties at the center of the grid, and calculate the surface element coefficients in the discrete equations; The fourth step is to form a calculation coefficient matrix and append the calculated radiation source term to the control equation. A unified discretization method is used for the fluid subdomain and the solid subdomain, and the coefficients of the two domains are stored in the same matrix to form a unified algebraic equation system. In the fifth step, the synchronous iterative solution method is combined with the implicit algorithm to establish a CCFVM numerical model calculation method for fluid-solid coupled heat transfer considering radiation, and the solution program is compiled using C++ language.

4. The method for numerical calculation of bidirectional fluid-structure coupling (FVM) considering radiation according to claim 1 is characterized in that: The calculation method of the fluid-solid coupling stress CVFVM numerical model is established using the following steps: The first step is to establish a numerical model of fluid-solid coupling stress calculation based on CVFVM, including the solid structure stress caused by the pulsating pressure of the flow field and the solid structure thermal stress caused by the temperature field; The solid structure field temperature and fluid-solid coupling surface fluid force calculated by the CCFVM numerical model considering radiation fluid-solid coupling heat transfer are introduced into the solid structure field stress calculation of the fluid-solid coupling stress numerical model based on CVFVM, and the flow-induced vibration numerical model and thermal-solid coupling numerical model based on CVFVM are established. In the second step, based on the CVFVM discrete thermoelastic equation, the variables to be solved are stored at the unit nodes, and the physical parameters are stored at the unit center. The pulsating pressure of the fluid-solid coupling boundary flow field and the unit center temperature of the solid structure field calculated by the CCFVM numerical model of fluid-solid coupling heat transfer considering radiation are extracted. The third step is to form the coefficient matrix; In the fourth step, an iterative solution method is used to solve the flow-induced vibration numerical model based on CVFVM, and a direct solution method is used to solve the thermal-solid coupling numerical model based on CVFVM. The above models are then used to solve the thermal stress and stress distribution of the structural field, and a one-way fluid-solid coupling numerical model based on CVFVM considering radiation is established; In the fifth step, the coupling surface displacement obtained by numerical calculation of the one-way fluid-solid coupling based on CVFVM considering radiation is transferred to the flow field grid of the CCFVM numerical model considering radiation fluid-solid coupling heat transfer, and feedback is loaded to the flow field boundary. The dynamic mesh technology is introduced to update the flow field mesh, and the dynamic mesh technology is introduced to establish the CVFVM numerical model of bidirectional fluid-solid coupling stress.

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