Fluid-structure interaction heat transfer simulation method, device and medium based on compressible ghost point immersion boundary method

Abstract

The invention discloses a fluid-solid coupling heat transfer simulation method and device based on a compressible ghost point immersion boundary method and a medium. The method comprises the following steps: acquiring a flow field and a solid temperature field in the (st-1) th step; obtaining the position and the speed of the mass center of the solid and the angular speed of the solid in the (st-1) th step; determining the attributes of grid nodes; if a new fluid node exists, calculating a fluid variable value at the new fluid node; calculating a solid centroid acceleration, a solid angular acceleration and a solid speed at a grid node in the solid; calculating a flow field ghost point variable value; if a new solid node appears, calculating the temperature value of the solid at the new solid node; calculating a solid temperature ghost point value; updating a solid temperature field and a flow field; and when the simulation step number is reached, ending the whole simulation process. The fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersion boundary method is suitable for solving the problem of coupling heat transfer between a static or moving object and a compressible flow.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of fluid mechanics, and particularly relates to a fluid-solid coupling heat transfer simulation method, device and medium based on a compressible ghost point immersed boundary method. BACKGROUND

[0002] Compressible flow problems involving moving boundaries are widely present in high-speed motion fields, such as spacecraft landing on Mars and bomb explosion. In order to solve such problems, various methods have been developed, including body-fitted grid methods and non-body-fitted grid methods commonly known as immersed boundary methods. Compared with body-fitted grid methods, immersed boundary methods are simpler and more effective because they can use fixed Cartesian grids, unlike body-fitted grid methods that require moving grids or even regridding. There are various compressible immersed boundary methods, such as compressible cut-cell methods and compressible ghost point immersed boundary methods. Compressible flow problems involving moving boundaries often involve complex fluid-solid coupling heat transfer phenomena. Existing research on compressible immersed boundary methods has mostly focused on the handling of pure fluid dynamics problems. There are few studies on using compressible immersed boundary methods to solve fluid-solid coupling heat transfer problems. Recently, a numerical simulation method for fluid-solid coupling heat transfer based on a compressible ghost point immersed boundary method has been proposed [1] . This method is designed for stationary objects in compressible flow. For coupling heat transfer problems between moving objects and compressible fluids, this method cannot handle them. This seriously restricts the application of this method in high-speed motion practical problems.

[0003] [1] T. Wang, D. Zhang, Z. Yu, A ghost-point immersed boundary method for compressible flows with moving body and conjugate heat transfer, International Journal of Heat and Mass Transfer 241 (2025) 126689. SUMMARY

[0004] To overcome the shortcomings of the existing numerical simulation method for fluid-solid coupling heat transfer based on the compressible ghost point immersed boundary method, which cannot handle the coupling heat transfer problem between moving objects and compressible fluids, the application provides a numerical simulation method for fluid-solid coupling heat transfer based on the compressible ghost point immersed boundary method suitable for moving objects, device and medium.

[0005] To achieve the above technical purposes, the application adopts the following technical solutions:

[0006] In a first aspect, the embodiments of the present application provide a fluid-solid coupling heat transfer simulation method based on compressible ghost cell immersed boundary method, and the method comprises the following steps:

[0007] obtaining the flow field and the solid temperature field of the st-1th step;

[0008] obtaining the position, velocity and solid angular velocity of the centroid of the solid of the st-1th step;

[0009] determining the grid node attribute based on the position of the centroid of the solid and the radius of the solid according to the ghost cell immersed boundary method for solving the solid temperature field and the compressible ghost cell immersed boundary method for solving the flow field;

[0010] if a new fluid node appears, determining the immersed boundary condition according to the velocity and acceleration of the centroid of the solid, the solid angular velocity and angular acceleration and the solid temperature field, calculating the fluid variable values of the new fluid node, including the density value, the velocity value and the temperature value, by using the immersed boundary condition and the fluid variable values of other grid nodes;

[0011] calculating the solid centroid acceleration and the solid angular acceleration of the st-1th step by using the immersed boundary condition and the flow field of the st-1th step, and calculating the velocity at the grid node in the solid of the st-1th step by using the velocity and the solid angular velocity of the centroid of the solid of the st-1th step;

[0012] determining the immersed boundary condition according to the velocity and acceleration of the centroid of the solid, the solid angular velocity and angular acceleration and the solid temperature field, and calculating the flow field ghost cell value, including the density value, the velocity value and the temperature value, by using the immersed boundary condition and the flow field;

[0013] if a new solid node appears, determining the solid temperature boundary condition according to the fluid temperature field of the st-1th step and the fluid temperature field ghost cell value, and calculating the solid temperature value of the new solid node according to the solid temperature boundary condition and the solid temperature values of other grid nodes;

[0014] calculating the solid temperature ghost cell value according to the solid temperature boundary condition and the solid temperature field of the st-1th step;

[0015] updating the solid temperature field of the st-1th step as the solid temperature field of the stth step by using the ghost cell immersed boundary method combined with the solid temperature ghost cell value, and updating the flow field of the st-1th step as the flow field of the stth step by using the compressible ghost cell immersed boundary method combined with the flow field ghost cell value;

[0016] completing the stth step;

[0017] iterating for N steps to complete the fluid-solid coupling heat transfer simulation.

[0018] In a second aspect, an electronic device is provided, comprising a memory and a processor, the memory being coupled to the processor; wherein the memory is configured to store program data, and the processor is configured to execute the program data to implement the compressible ghost point immersed boundary method based fluid-structure coupling heat transfer simulation method described above.

[0019] In a third aspect, a computer readable storage medium is provided, having stored thereon a computer program, the program being executable by a processor to implement the compressible ghost point immersed boundary method based fluid-structure coupling heat transfer simulation method described above.

[0020] In a fourth aspect, a computer program product is provided, comprising computer programs / instructions, the computer programs / instructions being executable by a processor to implement the compressible ghost point immersed boundary method based fluid-structure coupling heat transfer simulation method described above.

[0021] Compared with the prior art, the present application has the following beneficial effects:

[0022] The compressible ghost point immersed boundary method based fluid-structure coupling heat transfer numerical simulation method for moving objects provided by the present application can solve the fluid-structure coupling heat transfer problem of moving objects, compared with the original compressible ghost point immersed boundary method based fluid-structure coupling heat transfer numerical simulation method, and thus can be applied to the solution of more high-speed motion actual problems. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0024] Figure 1 is a flow chart of the compressible ghost point immersed boundary method based fluid-structure coupling heat transfer numerical simulation method for moving objects of the present application;

[0025] Figure 2 is the type of grid nodes near the immersed boundary in the compressible ghost point immersed boundary method;

[0026] Figure 3 is the extrapolation of the type of grid nodes near the immersed boundary and the ghost point value in the ghost point immersed boundary method for solving the temperature field of the solid;

[0027] Figure 4 The four nodes around the point include Figure 4 (a) a newly appearing fluid point in and Figure 4interpolation stencil of fluid variable values at the newly emerged fluid point when there is (a) one ghost point in the

[0028] Figure 5 extrapolation of ghost fluid variable values in the compressible ghost fluid immersed boundary method;

[0029] Figure 6 interpolation stencil of image point values when there are (a) one ghost point in the Figure 6 Figure 6

[0030] Figure 7 interpolation stencil of image point values when there are (a) one ghost point in the Figure 7 Figure 7 Figure 7 interpolation stencil of solid temperature values at the newly emerged solid point when there are (a) one newly emerged solid point in the

[0031] Figure 8 schematic of the computational setup for the shock impinging on a cylinder example;

[0032] Figure 9 is grid near the cylinder, grid spacing Δx and Δy are D / 100 in the uniform grid region, only one grid line is shown for every four grid lines for display purpose;

[0033] Figure 10 evolution of the drag coefficient C D for the cylinder;

[0034] Figure 11 evolution of the surface averaged temperature for the cylinder;

[0035] Figure 12 schematic of the computational setup for the shock impinging on a sphere example;

[0036] Figure 13 evolution of the drag coefficient C D for the sphere;

[0037] Figure 14 evolution of the surface averaged temperature for the sphere;

[0038] Figure 15 is a schematic of an electronic device. DETAILED DESCRIPTION

[0039] ​​​​The application will be further described below in connection with the embodiments. The following description of the embodiments is only to help understand the application. It should be noted that for those skilled in the art, some improvements and modifications can be made to the application without departing from the principles of the application, and these improvements and modifications also fall within the protection scope of the claims of the application.

[0040] In addition, the technical solutions of each embodiment can be combined with each other, but it must be based on the fact that a person skilled in the art can realize it. When the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist and is not within the protection scope required by the present application.

[0041] The operation steps of the fluid-solid coupling heat transfer numerical simulation method based on the compressible ghost point immersed boundary method suitable for moving objects provided by the application are as shown in Figure 1 .

[0042] Step 1: Obtain the flow field and solid temperature field of the previous step, i.e., the st-1 step.

[0043] If the current step st = 1, initialize the flow field and solid temperature field. If the current step st ≥ 2, obtain the flow field and solid temperature field of the st-1 step, i.e., the st-1 step.

[0044] Step 2: Obtain the position, velocity and angular velocity of the center of mass of the solid of the st-1 step.

[0045] The control equation set of the solid motion is:

[0046]

[0047] In the formula, d / dt represents the solid time derivative, x s is the position vector of the center of mass of the solid, v s is the velocity of the center of mass, a s is the acceleration of the center of mass, ω s is the angular velocity of the solid rotating around its center of mass, Ω s is the angular acceleration of the solid rotating around its center of mass.

[0048] It should be noted that in the present example, only two-dimensional circular solid or three-dimensional spherical solid is concerned, so the angular orientation of the solid is not important, and therefore is not solved. The above quantities are dimensionless quantities, which are dimensionless by reference length L*, reference velocity u* and reference time L* / u*. The time derivative term in the control equation set of the solid motion is discretized by the explicit third-order total variation diminishing Runge-Kutta method. In the explicit third-order total variation diminishing Runge-Kutta method, three steps of sub-cycle calculation are required for each time step.

[0049] At the first step, i.e. st=1, the position, velocity and solid angular velocity of the centroid of the solid are initialized; or, according to equation (1), the position and velocity of the centroid of the solid at the st-1 step are calculated based on the velocity and acceleration of the centroid of the solid at the st-2 step, and the angular velocity of the solid at the st-1 step is calculated based on the angular acceleration of the solid at the st-2 step.

[0050] At the st-1 step, the position, velocity and solid angular velocity of the centroid of the solid corresponding to the st-1 step flow field are not calculated, as described above, they are calculated at step 2 of this step. The acceleration of the centroid of the solid and the angular acceleration of the solid corresponding to the st-1 step flow field are also not calculated at the st-1 step, they will be calculated at step 5 of this step.

[0051] Step 3: Based on the position of the centroid of the solid and its radius, the grid node properties are determined according to the ghost point immersed boundary method for solving the solid temperature field and the compressible ghost point immersed boundary method for solving the flow field.

[0052] In the compressible ghost point immersed boundary method, the grid points are divided into fluid points (grid points located in the fluid domain) and solid points (grid points located in the solid). The values of the flow field variables need to be defined at some solid points for the flow field solving calculation. These solid points are called ghost points. The values of the fluid variables at these ghost points are extrapolated from the boundary conditions at the immersed boundary and the values of the fluid variables at the fluid points. It is these values of the fluid variables at the ghost points that reflect the existence of the immersed boundary in the flow field calculation.

[0053] In the method proposed in the present application, the governing equation of the flow is the compressible Navier-Stoke equation. It is specifically described as follows. The dimensionless form of the equation is:

[0054]

[0055] In the formula, x, y and z are Cartesian coordinates, U is a conservative variable vector, F1, F2 and F3 are respectively the inviscid flux vectors in x, y and z directions, and G1, G2 and G3 are respectively the viscous flux vectors in x, y and z directions. The conservative variable vector, the inviscid and viscous flux vectors are defined as:

[0056]

[0057]

[0058] Viscous stress tensor:

[0059]

[0060] In the above equation, ρ is the fluid density, u, v, and w are the fluid velocities in the x, y, and z directions, respectively, p is the fluid thermodynamic pressure, E is the total energy per unit volume of the fluid, k is the fluid thermal conductivity, T is the fluid temperature, γ is the fluid specific heat ratio, that is, the specific heat at constant pressure to the specific heat at constant volume, Ma is the Mach number, Pr is the Prandtl number, Re is the Reynolds number, μ is the dynamic viscosity, u1, u2, and u3 are u, v, and w, respectively, x1, x2, and x3 are x, y, and z, respectively, and δ is the specific heat ratio of the fluid. ij is the Kronecker symbol.

[0061] In the current method, the fluid considered in this example is an ideal gas, so the state equation of the ideal gas is:

[0062]

[0063] is used to close the above equations. The total energy E per unit volume of fluid is defined as:

[0064]

[0065] k and μ are calculated using Sutherland's law, as follows:

[0066]

[0067] Where, T * is the reference temperature.

[0068] The above equation is composed of reference length L*, reference speed u*, reference time L* / u*, reference temperature T*, reference density ρ*, reference pressure ρ*u* 2 , reference dynamic viscosity μ*, and reference thermal conductivity k* are dimensionless. μ* and k* are the dynamic viscosity and thermal conductivity at temperature T*, respectively. Pr, Re, and Ma can be expressed as dimensionless quantities:

[0069]

[0070] is the dimensionless specific heat at constant pressure,

[0071]

[0072] is the dimensionless velocity of sound in the fluid at temperature T*. g is the specific gas constant.

[0073] In this example, the explicit third-order total variation diminishing Runge-Kutta method is used to discretize the time derivative term in the Navier-Stoke equation, the fifth-order weighted essentially non-oscillatory (WENO5) scheme is used to calculate the spatial derivative of inviscous flux vector to capture the shock structure, and the sixth-order central difference scheme is used to calculate the spatial derivative of viscous flux vector. Therefore, in the method proposed in the present application, there are three layers of ghost points for the solution of the flow field, as shown in Figure 2 .

[0074] In the method proposed in the present application, a ghost point immersed boundary method is used to solve the solid temperature field. The ghost point at this time is a fluid point belonging to the finite difference stencil of the derivative of the temperature of the solid point.

[0075] The governing equation of heat conduction in the solid is:

[0076]

[0077] where ρ s is the density of the solid, C ps is the specific heat of the solid, T s is the temperature of the solid, u s is the velocity of a point in the solid, and k s is the thermal conductivity of the solid. These physical quantities are dimensionless quantities, which are dimensionless by using the reference quantities of the fluid variables. The convection term on the left side of equation (12) is discretized by the fifth-order upwind scheme, the diffusion term on the right side is discretized by the sixth-order central difference scheme, and the time term is discretized by the explicit third-order total variation diminishing Runge-Kutta method. Therefore, in the ghost point immersed boundary method for solving the solid temperature field, there are three layers of ghost points, as shown in Figure 3 .

[0078] Step 4: If a new fluid node appears, determine the immersed boundary condition according to the velocity and acceleration of the center of mass of the solid, the angular velocity and angular acceleration of the solid, and the solid temperature field, and calculate the fluid variable values of the new fluid node, including the density value, the velocity value, and the temperature value, by using the immersed boundary condition and the fluid variable values of other grid nodes.

[0079] When the immersed boundary moves, it is necessary to determine the fluid variable values at the newly appeared fluid point. The newly appeared fluid point is inside the solid at the mth time step and outside the solid at the (m+1)th time step. In the compressible ghost point immersed boundary method, a bilinear (trilinear in three dimensions) interpolation method is used to calculate the fluid variable values at the newly appeared fluid point. For the sake of convenience, only the interpolation method in the two-dimensional case is described here. In the bilinear interpolation method, the polynomial is:

[0080] φ(x,y)=C1+C2x+C3y+C4xy (13)

[0081] which is used to approximate the distribution of the general variable φ(x, y) near the newly emerged fluid point, where C i , i = 1,..., 4, are four unknown coefficients. The four unknown coefficients can be obtained using the information of φ(x, y) at the four fluid points or boundary points surrounding the newly emerged fluid point. After the four coefficients are obtained, the value of φ(x, y) at the newly emerged fluid point can be obtained by substituting the coordinates of the newly emerged fluid point into equation (13).

[0082] In order to determine the interpolation template for interpolating the fluid variable value at the newly emerged fluid point, the present example defines an image point (IP) and a body intercept point (BI) for each newly emerged fluid point. The image point IP is located on the outer normal of the immersed boundary intersecting the newly emerged fluid point, and the BI point is the intersection of the above normal and the immersed boundary. The distance between the image point IP and the newly emerged fluid point is 0.2 times the grid spacing. In the simplest case, the interpolation template of the fluid variable value at the newly emerged fluid point is composed of the BI point and three fluid points surrounding the image point, as shown in (a) of FIG. 6. Figure 4 If there are multiple newly emerged fluid points among the four nodes surrounding the image point, the interpolation template is composed of the fluid points and the body intercept points corresponding to the newly emerged fluid points. Figure 4 (b) of FIG. 6 shows the interpolation template in the case where there are two newly emerged fluid points among the four nodes surrounding the image point.

[0083] The information at the body intercept point, i.e. the boundary condition, is needed in interpolation, including the temperature boundary condition, the velocity boundary condition and the pressure boundary condition.

[0084] Physically, the temperature field at the immersed boundary should satisfy the temperature and heat flux continuity conditions:

[0085]

[0086] where IBP is the immersed boundary point, T s represents the solid temperature, T s | IBP i.e. the solid temperature at the immersed boundary point IBP, T represents the fluid temperature, k s represents the solid thermal conductivity, k represents the fluid thermal conductivity, and n is the outer normal coordinate of the immersed boundary IB.

[0087] The present example uses a loose coupling algorithm to handle the temperature coupling problem. In the loose coupling algorithm, the fluid temperature boundary condition applied at the immersed boundary point IBP is the Dirichlet boundary condition:

[0088] T| IBP = T s | IBP . (15)

[0089] The right-hand term of equation (15) is obtained by bilinear interpolation of the temperature field of the solid. The interpolation stencil consists of the four grid nodes surrounding the IBP. The velocity boundary condition of the flow field at the immersed boundary point IBP is

[0090] u| IBP = u B | IBP = v s + ω s x r CIBP , (16)

[0091] where u is the fluid velocity vector, u B is the velocity of the solid boundary, v s is the velocity of the centroid, ω s is the angular velocity of the solid about its centroid, and r CIBP is the position vector of the IBP point from the centroid.

[0092] The pressure boundary condition of the flow field at the immersed boundary point IBP is

[0093]

[0094] D / Dt denotes the material time derivative of the fluid, n is the outward unit normal vector at the IB, p denotes the fluid thermodynamic pressure, p denotes the fluid density, and t denotes time. In the right-hand term of the pressure boundary condition, the density at the boundary point is unknown, so the pressure boundary condition is transformed into

[0095]

[0096] where γ denotes the fluid specific heat ratio and Ma is the Mach number. The temperature in the right-hand term is obtained from the temperature boundary condition, and in addition

[0097]

[0098] where a s is the acceleration of the centroid, and Ω s is the angular acceleration of the solid about its centroid.

[0099] In interpolating the values of the fluid variables at the newly emerged fluid points using the above boundary conditions, the acceleration of the solid boundary point is taken as that of the solid boundary point in the st-1 step, the temperature of the solid boundary point is taken as that of the solid boundary point in the st-1 step, and the velocity of the solid boundary point is taken as that of the solid boundary point in the current step.

[0100] In summary, once the boundary conditions are determined, the fluid temperature value at the non-newly appearing fluid point and the temperature boundary condition at the boundary point (Equation (15)) can be used to obtain the explicit form of Equation (13) when φ is the temperature, from which the fluid temperature value at the newly appearing fluid point can be obtained. The velocity value at the non-newly appearing fluid point and the velocity boundary condition at the boundary point (Equation (16)) can be used to obtain the explicit form of Equation (13) when φ is the velocity, from which the fluid velocity value at the newly appearing fluid point can be obtained. The pressure value at the non-newly appearing fluid point and the pressure boundary conditions at the boundary point (Equations (18) and (19)) can be used to obtain the explicit form of Equation (13) when φ is the pressure, from which the fluid pressure value at the newly appearing fluid point can be obtained. The pressure value and temperature value at the newly appearing fluid point combined with the state equation (6) can be used to obtain the density value at the newly appearing fluid point.

[0101] Step 5: Use the immersed boundary condition and the flow field of step st-1 to calculate the solid center of mass acceleration and solid angular acceleration of step st-1, and use the solid center of mass velocity and solid angular velocity of step st-1 to calculate the velocity at the solid inner mesh node of step st-1.

[0102] The solid center of mass acceleration and the solid angular acceleration are calculated by the following formula:

[0103]

[0104] Where m s is the mass of the solid, a s is the acceleration of the center of mass, F is the force exerted by the fluid on the solid, p is the fluid thermodynamic pressure, n is the external unit normal vector of IB, τ is the viscous stress tensor, J s is the moment of inertia tensor of the solid, Ω s is the angular acceleration of the solid about its center of mass, T is the torque exerted by the fluid on the solid, and r is the position vector of a point on the solid surface relative to the solid's center of mass. When calculating forces and torques, the integral terms at boundary points are computed using bilinear (trilinear in three dimensions) interpolation, using the four mesh nodes surrounding the boundary points as the interpolation template. These four mesh nodes may contain ghost points, so the flow field variables at these ghost points must be calculated before integration.

[0105] In the current compressible ghost point immersed boundary method, the velocity and pressure values ​​at the ghost point are calculated using second-order polynomial extrapolation, while the temperature at the ghost point is calculated using first-order polynomial extrapolation. The first-order polynomial extrapolation method is used to calculate the temperature value to ensure computational stability. Using second-order polynomial extrapolation to calculate the temperature value at the ghost point will result in unreasonable temperature predictions when the immersed boundary encounters a shock wave, leading to computational divergence.

[0106] To calculate the ghost point value, the present example defines two image points, IP1 and IP2, for each ghost point G, which lie on the outward normal to the immersed boundary. The normal passes through the ghost point G and intersects the immersed boundary at a body intersection point, BI, as shown in Figure 5 FIG. 1. One of the two image points is the mirror image of the ghost point, IP2. The IP2 point is the same distance from the BI point as the ghost point G is from the BI point. The other image point is the midpoint of the line segment from the BI point to the mirror image point IP2, IP1.

[0107] In calculating the velocity value and the pressure value at a ghost point, the values at the two image points and the boundary condition at the BI point can be used to obtain a second order polynomial. The ghost point velocity and pressure can then be extrapolated using the second order polynomial. For a general variable φ, when the boundary condition at the immersed boundary is φ(x BI ,y BI ) = φ BI (x BI and y BI are the x and y coordinates of the BI point, respectively), the extrapolation formula for φ G at the ghost point G is:

[0108]

[0109] where φ IP1 and φ IP2 are the values of φ at the image points IP1 and IP2, respectively. When the boundary condition at the immersed boundary is , the extrapolation formula for φ G is:

[0110]

[0111] n is the outward normal coordinate of the immersed boundary IB, 1 is the distance from IP1 to IP2, and α and β are non-zero coefficients.

[0112] In calculating the temperature value at a ghost point, the temperature value at the mirror image point IP2 and the temperature boundary condition at the BI point can be used to obtain a first order polynomial. The ghost point temperature value can then be extrapolated using the first order polynomial. The extrapolation formula for the temperature value T G at the ghost point G is:

[0113]

[0114] T BI and T IP2 are the values of the fluid temperature T at the BI point and the IP2 point, respectively.

[0115] The image point values in the above extrapolation formulas are calculated using bilinear (trilinear in three dimensions) interpolation. Figure 5 and Figure 6The interpolation stencil shows the interpolation of the image point value in three different cases, i.e. four fluid points or boundary points surrounding the image point.

[0116] The boundary conditions at the immersed boundary used in the calculation of the ghost point values have been described in step 4, i.e. the temperature boundary condition (15), the velocity boundary condition (16), the pressure boundary conditions (18) and (19). In using these boundary conditions, the acceleration of the solid boundary point is taken as the acceleration of the solid boundary point in the st-2 step (in the first step, the acceleration of the solid boundary point in the st-2 step is unknown, here an approximate pressure boundary condition is obtained by using the 0 acceleration), the temperature of the solid boundary point is taken as the temperature of the solid boundary point in the st-2 step (in the first step, the temperature of the solid boundary point in the st-2 step is unknown, here the adiabatic boundary condition is used instead of the Dirichlet temperature boundary condition), and the velocity of the solid boundary point is taken as the velocity of the solid boundary point in the st-1 step.

[0117] In summary, when the boundary conditions are determined, the temperature value at the ghost point is calculated by (24) combined with the temperature boundary condition (15), where the image point value in (24) is obtained by using the fluid temperature value at the fluid point, the temperature boundary condition (15) at the boundary point and (13) when φ is the fluid temperature. The velocity value at the ghost point is calculated by (22) combined with the velocity boundary condition (16), where the image point value in (22) is obtained by using the fluid velocity value at the fluid point, the velocity boundary condition (16) at the boundary point and (13) when φ is the fluid velocity. The pressure value at the ghost point is calculated by (23) combined with the pressure boundary conditions (18) and (19), where the image point value in (23) is obtained by using the fluid pressure value at the fluid point, the pressure boundary conditions (18) and (19) at the boundary point and (13) when φ is the fluid pressure. The ghost density value is obtained by using the pressure value and the temperature value at the ghost point combined with the equation of state (6). After the ghost point values are calculated, the solid centroid acceleration and the solid angular acceleration are calculated by using the ghost point values and the flow field information combined with (20) and (21).

[0118] The solid velocity u at the grid node in the solid is calculated by s u = v + ω x r, (25)

[0119] u = v + ω x r, (25) s = v s + ω s x r CSP , (25)

[0120] v s is the velocity of the centroid, ω s is the angular velocity of the solid rotating around its centroid, and r CSP is the position vector of the grid node SP in the solid relative to the centroid.

[0121] Step 6: Determine the immersed boundary conditions according to the velocity and acceleration of the centroid of the solid, the angular velocity and angular acceleration of the solid, and the temperature field of the solid. Use the immersed boundary conditions to calculate the ghost point values of the flow field, including the density value, the velocity value, and the temperature value.

[0122] Determine the boundary conditions at the immersed boundary using the velocity and acceleration of the solid boundary point of the st-1th step and the temperature of the solid boundary point of the st-2th step. In the first step, the temperature of the solid boundary point of the st-2th step is unknown, and here we consider using the adiabatic boundary condition instead of the Dirichlet temperature boundary condition. After the boundary conditions are determined, the temperature value at the ghost point is calculated by equation (24) combined with the temperature boundary condition equation (15), the velocity value at the ghost point is calculated by equation (22) combined with the velocity boundary condition equation (16), and the pressure value at the ghost point is calculated by equation (23) combined with the pressure boundary condition equations (18) and (19). The density value at the ghost point is obtained by using the pressure value and the temperature value at the ghost point combined with the state equation (6).

[0123] Step 7: If a new solid node appears, determine the solid temperature boundary condition according to the st-1th step of the fluid temperature field and the ghost point value of the fluid temperature field, and calculate the solid temperature value of the new solid node according to the solid temperature boundary condition and the solid temperature values of other grid nodes.

[0124] When the immersed boundary moves, new solid points appear when solving the solid temperature field. We use a bilinear (trilinear in three dimensions) interpolation method to calculate the solid temperature value at the newly appeared solid point. In order to determine the interpolation template for interpolating the solid temperature value at the newly appeared solid point, we define an image point (IP) and a body intersection point (BI). The image point is located on the inner normal of the immersed boundary intersecting the newly appeared solid point. The distance between the image point and the newly appeared solid point is 0.2 times the grid spacing. The BI point is the intersection of the above normal and the immersed boundary. In the simplest case, the interpolation template for the solid temperature value at the newly appeared solid point is composed of the BI point and three solid points around the image point, as shown in (a) of FIG. 6. Figure 7 If there are multiple newly appeared solid points or ghost points among the four nodes around the image point, the body intersection points corresponding to the solid points and these newly appeared solid points or ghost points constitute the interpolation template. Figure 7 (b) of FIG. 6 shows the interpolation template in the case where there are two newly appeared solid points among the four nodes around the image point. Figure 7 (c) of FIG. 6 shows the interpolation template in the case where there is one newly appeared solid point and one ghost point among the four nodes around the image point.

[0125] The solid temperature boundary condition at the immersed boundary is needed when interpolating the solid temperature value at the newly emerged solid point. As mentioned in Step 4, the temperature coupling is handled by the loosely coupled algorithm in this example, so the solid temperature boundary condition is the Neumann boundary condition.

[0126]

[0127] The determination of the right hand side term of equation (26) requires the values of k and From equation (8), k is a function of T, and

[0128]

[0129] n x and n y are the x and y components of the outer unit normal vector n at IB, respectively. Therefore, the determination of T and and In this example, the bilinear interpolation of the values of the four nodes around the immersed boundary point is used to calculate the values of T and and

[0130] When interpolating the solid temperature value at the newly emerged solid point using the solid temperature boundary condition at the immersed boundary, the fluid temperature in the boundary condition is taken as the fluid temperature in the st-1 step.

[0131] In summary, after the solid temperature boundary condition is determined, equation (26) can be used to obtain the explicit form of equation (13) when φ is the solid temperature, using the solid temperature values of other grid nodes and the solid temperature boundary condition. From this form, the solid temperature value of the new solid node can be obtained.

[0132] Step 8: Calculate the solid temperature ghost point value according to the solid temperature boundary condition and the solid temperature field in the st-1 step.

[0133] Similar to the calculation of the ghost point value in the compressible ghost fluid immersed boundary method, the solid temperature ghost point value is calculated using the second order polynomial extrapolation method. When calculating the ghost point value, two image points, IP1 and IP2, are defined for each ghost point G, which are located on the inner normal of the immersed boundary. The normal passes through the ghost point G and intersects the immersed boundary at the body intersection point BI, as shown in Figure 3 One of the two image points is the mirror image point of the ghost point, IP2. The distance between the IP2 point and the BI point is the same as the distance between the BI point and the ghost point G. The other image point is the midpoint of the line segment from the BI point to the mirror image point IP2, IP1.

[0134] Using the values of the two image points and the boundary condition at the BI point, a second order polynomial can be obtained. Then the ghost point value can be extrapolated using the second order polynomial:

[0135]

[0136] where T s,G denotes the solid temperature at the ghost point G, denotes the solid temperature at the image point IP2, l is the distance from IP1 to IP2, T s denotes the solid temperature, n is the outward normal coordinate of the immersed boundary IB, denotes the value of the outward normal derivative of the solid temperature at the point BI. The derivative term in the above equation is determined by the solid temperature boundary condition equation (26) described in step 7, and the fluid temperature in the boundary condition is the fluid temperature of the st-1 step.

[0137] In summary, the solid temperature value at the ghost point is calculated by equation (28) combined with the solid temperature boundary condition equation (26), where the image point value in equation (28) is obtained by the solid temperature value at the solid point, the solid temperature boundary condition equation (26) at the boundary point and equation (13) when φ is the solid temperature.

[0138] Step 9: update the solid temperature field and the flow field; thus complete the 1 step calculation; by analogy, after N times of calculation, the fluid-solid coupling heat transfer simulation is completed, and N is the calculation step number.

[0139] Specifically, the ghost point immersed boundary method is combined with the ghost point value of the solid temperature to update the solid temperature field of the st-1 step as the solid temperature field of the st step; the compressible ghost point immersed boundary method is combined with the ghost point value of the flow field to update the flow field of the st-1 step as the flow field of the st step. The specific calculation process of this step is exactly the same as the specific calculation process of updating the solid temperature field and the flow field in the original fluid-solid coupling heat transfer numerical simulation method based on the compressible ghost point immersed boundary method.

[0140] Because in the present application, the explicit third-order total variation diminishing Runge-Kutta method is used to discretize the time derivative term, so the total running time step number is N / 3. The complete information of the flow field and the particle in the last step, that is, in addition to the flow field and the solid temperature field, it also includes the position, velocity, acceleration of the center of mass of the solid, the angular velocity and angular acceleration of the solid, and the ghost point value of the flow field and the ghost point value of the solid temperature field, as described in the previous steps, it also needs to run steps 1 to 8 to obtain.

[0141] Example 1

[0142] For the fluid-solid coupling heat transfer numerical simulation method based on the compressible ghost point immersed boundary method suitable for moving objects provided by the present application, two examples of shock wave impacting a freely moving cylinder and shock wave impacting a freely moving sphere are used to verify its ability to handle the coupling heat transfer problem of moving objects and compressible fluid.

[0143] In the example of shock wave impacting a freely moving cylinder, the computational domain is [0D, 12D] × [0D, 12D], as shown in Figure 8 As shown. D is the diameter of the cylinder. The center of the cylinder is initially located at (3D, 6D). The shock wave is initially located at x = 1.5D and propagates along the positive x direction. At the initial moment, the flow field before and after the shock wave is uniform. The Mach number of the incident shock wave is Ma s =u s / c p0 =1.745 and Reynolds number Re = 181.971. s is the velocity of the incident shock wave, c p0 is the speed of sound in the shock front flow field at the initial state. The Mach number is 1.0. In the current example, the reference length is the diameter of the cylinder and the reference speed is c p0 The other reference quantities are the corresponding physical quantities of the flow field before the shock wave in the initial state. The properties of the fluid after the shock wave in the initial state are determined by the Rankine-Hugo Newton formula. The density of the fluid after the shock wave in the initial state is ρ po0 , velocity u along the x direction po0 and temperature T po0 The Mach number and Reynolds number are calculated based on the physical quantities of the flow field after the shock wave in the initial state, that is, Ma po0 =u po0 / c po0 =0.8 and Re po0 =ρ po0 u po0 D / μ po0 =300. Among them, c po0 and μ po0 are the sound velocity and dynamic viscosity of the fluid after the shock wave in the initial state. Particle density ρ s = 10. The inlet boundary condition is the Dirichlet boundary condition, the outlet boundary condition is the zero gradient boundary condition, and the boundary conditions at the other boundaries of the computational domain are periodic boundary conditions.

[0144] In the current example, two sets of non-uniform grids are used to test the grid convergence. The number of grid nodes in the two sets of grids is 521×328 and 731×428 respectively. The grid spacing is uniformly distributed in the area [2.4D, 6.6D]×[5D, 7D], as shown in the following example: Figure 9 . In this region, the grid spacing Δx and Δy in the x and y directions are identical, with the two meshes having spacings of D / 100 and D / 150, respectively. The simulation time step is 0.0002. Because the mesh is refined only within the [2.4D, 6.6D] × [5D, 7D] region, the calculation stops when the cylinder center reaches (6D, 3D).

[0145] The drag coefficient C of the cylinder D The evolution of the temperature of the cylinder surface is shown in Figure 10 C D = F D / (1 / 2p * u *2 D), F D is the drag of the cylinder. The evolution of the temperature of the cylinder surface is shown in Figure 11 The results of different meshes agree well.

[0146] In the case of a shock wave impacting a freely moving sphere, the computational domain is [0D, 8D] x [0D, 6D] x [0D, 6D], as shown in Figure 12 D is the diameter of the sphere. The center of the sphere is initially located at (3D, 3D, 3D). The shock wave is initially located at x = 1.5D and propagates in the positive x direction. At the initial time, the flow field in front of the shock wave and the flow field behind the shock wave are both uniform flow fields. The Mach number Ma s = 1.745 and the Reynolds number Re = 181.971. The Mach number is 1.0. In the current case, the reference length is the diameter of the sphere, and the reference velocity is c p0 . Other reference quantities are the corresponding physical quantities of the flow field in front of the shock wave at the initial state. The properties of the fluid behind the shock wave at the initial state are determined by the Rankine-Hugoniot relations. The density p po0 , the velocity u po0 in the x direction, and the temperature T po0 of the fluid behind the shock wave at the initial state are 2.2710, 0.9766, and 1.4909, respectively. The Mach number and the Reynolds number based on the physical quantities of the flow field behind the shock wave at the initial state, i.e., Ma po0 = 0.8 and Re po0 = 300. The particle density p s = 10. The inlet boundary condition is the Dirichlet boundary condition, and the outlet boundary condition is the zero gradient boundary condition. The boundary conditions at other boundaries of the computational domain are the periodic boundary conditions.

[0147] In this example, three non-uniform meshes are used to test mesh convergence. The mesh node counts for these three meshes are 291×180×180, 401×240×240, and 519×308×308, respectively. The mesh spacing is uniformly distributed within the region [2.4D, 4.6D]×[2.4D, 3.6D]×[2.4D, 3.6D]. Within this region, the mesh spacings Δx, Δy, and Δz in the x, y, and z directions are identical, with the mesh spacings for the three meshes being D / 100, D / 150, and D / 200, respectively. The simulation time step is 0.0002. Because the mesh is refined only within the region [2.4D, 4.6D]×[2.4D, 3.6D]×[2.4D, 3.6D], the calculation terminates when the center of the sphere reaches (4D, 3D, 3D).

[0148] The drag coefficient of the sphere is C D The evolution of Figure 13 As shown. C D =F D / (1 / 2ρ * u *2 πD 2 / 4), F D is the resistance of the sphere. The average surface temperature of the sphere The evolution of Figure 14 The results of different meshes are basically consistent, especially the results of the two fine meshes.

[0149] The results of the above two examples illustrate that the method provided by the present invention can correctly handle the coupled heat transfer problem between a moving object and a compressible fluid.

[0150] Accordingly, the present application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method as described above. Figure 15 As shown in FIG, a hardware structure diagram of any device with data processing capability in which the fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method provided by the embodiment of the present invention is used, except Figure 15 In addition to the processor, memory, and network interface shown, any device with data processing capabilities in which the apparatus in the embodiment is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0151] Correspondingly, the application further provides a computer readable storage medium, which stores computer instructions, and the instructions are executed by a processor to realize the fluid-solid coupling heat transfer simulation method based on the compressible ghost cell immersed boundary method. The computer readable storage medium can be an internal storage unit of any device with data processing capability, such as a hard disk or a memory. The computer readable storage medium can also be an external storage device, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. Further, the computer readable storage medium can include both the internal storage unit of any device with data processing capability and the external storage device. The computer readable storage medium is used to store the computer program and other programs and data required by the device with data processing capability, and can also be used to temporarily store data that has been output or will be output.

[0152] The above examples are only used to illustrate the design concept and characteristics of the present application, and the purpose is to enable those skilled in the art to understand the present application and implement it, and the protection scope of the present application is not limited to the above examples. Therefore, any equivalent changes or modifications made according to the disclosed principles and design ideas of the present application are within the protection scope of the present application.

Claims

1. A fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method, characterized in that: The method comprises: Obtain the flow field and solid temperature field of the previous step, i.e. step st-1; Get the position, velocity and angular velocity of the center of mass of the solid at step st-1; According to the ghost point immersed boundary method for solving the solid temperature field and the compressible ghost point immersed boundary method for solving the flow field, the mesh node properties are determined based on the position of the solid's center of mass and its radius; If a new fluid node appears, the immersed boundary conditions are determined based on the velocity and acceleration of the solid's center of mass, the solid's angular velocity and angular acceleration, and the solid's temperature field. The fluid variable values ​​of the new fluid node are calculated using the immersed boundary conditions and the fluid variable values ​​of other mesh nodes. Using the immersed boundary conditions and the flow field of step st-1, calculate the center-of-mass acceleration and solid angular acceleration of step st-1; use the center-of-mass velocity and solid angular velocity of step st-1 to calculate the velocity at the mesh node in the solid of step st-1; The immersed boundary conditions are determined according to the velocity and acceleration of the center of mass of the solid, the angular velocity and angular acceleration of the solid, and the solid temperature field, and the ghost point value of the flow field is calculated using the immersed boundary conditions and the flow field; If a new solid node appears, determine the solid temperature boundary condition based on the fluid temperature field and the ghost point value of the fluid temperature field in step st-1, and calculate the solid temperature value of the new solid node based on the solid temperature boundary condition and the solid temperature values ​​of other grid nodes; Calculate the solid temperature ghost point value according to the solid temperature boundary condition and the solid temperature field of step st-1; The ghost point immersed boundary method is used in combination with the solid temperature ghost point value to update the solid temperature field of the st-1 step as the solid temperature field of the st step; the compressible ghost point immersed boundary method is used in combination with the flow field ghost point value to update the flow field of the st-1 step as the flow field of the st step; Complete 1 step; And so on, after N steps of iteration, the fluid-solid coupling heat transfer simulation is completed.

2. The fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method according to claim 1 is characterized in that: The process of obtaining the position, velocity, and angular velocity of the solid mass center at step st-1 includes: If the current step st=1, customize the position, velocity and angular velocity of the solid's center of mass; or, if the current step st≥2, calculate the position and velocity of the solid's center of mass in step st-1 based on the velocity and acceleration of the solid's center of mass in step st-2, and calculate the angular velocity of the solid in step st-1 based on the angular acceleration of the solid in step st-2.

3. The fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method according to claim 1 is characterized in that: If a new fluid node appears, the immersed boundary conditions are determined based on the velocity and acceleration of the solid's center of mass, the solid's angular velocity and angular acceleration, and the solid's temperature field. The immersed boundary conditions and the fluid variable values ​​of other mesh nodes are used to calculate the fluid variable values ​​of the new fluid node. The process includes: The fluid temperature at the new fluid node is calculated using the fluid temperature at the non-newly appeared fluid point and the temperature boundary condition at the boundary point. The temperature boundary condition is expressed as follows: T| IBP =T s | IBP Where, T s | IBP represents the solid temperature at the immersed boundary point IBP, T| IBP represents the fluid temperature at the immersed boundary point IBP; The velocity values ​​at the non-newly appearing fluid points and the velocity boundary conditions at the boundary points are used to calculate the fluid velocity values ​​at the new fluid nodes. The velocity boundary conditions are expressed as follows: u| IBP =u B | IBP =v s +ω s ×r CIBP Where u is the fluid velocity vector, u B is the velocity of the solid boundary, v s is the velocity of the center of mass, ω s is the angular velocity of the solid around its center of mass, r CIBP is the position vector of the IBP point relative to the center of mass; The fluid pressure value of the new fluid node is calculated using the pressure value at the non-newly appeared fluid point and the pressure boundary condition at the boundary point. The expression of the pressure boundary condition is as follows: Where p is the fluid thermodynamic pressure, n is the outer normal coordinate of the immersed boundary IB, γ represents the fluid specific heat ratio, Ma is the Mach number, T is the fluid temperature, D / Dt represents the fluid time derivative, n is the outer unit normal vector of IB, d / dt represents the solid time derivative, and a s is the acceleration of the center of mass, Ω s is the angular acceleration of the solid about its center of mass; The density of the new fluid node is calculated using the ideal gas state equation according to the fluid pressure and temperature of the new fluid node.

4. Fluid-solid coupling heat transfer simulation based on compressible ghost point immersed boundary method according to claim 1 The method is characterized in that The process of calculating the solid center of mass acceleration and solid angular acceleration at step st-1 using the immersed boundary condition and the flow field at step st-1 includes: The solid center of mass acceleration and the solid angular acceleration are calculated by the following formula: Where m s is the mass of the solid, a s is the acceleration of the center of mass, F is the force exerted by the fluid on the solid, p is the thermodynamic pressure of the fluid, n is the external unit normal vector of the immersed boundary IB, τ is the viscous stress tensor, J s is the moment of inertia tensor of the solid, Ω s is the angular acceleration of the solid about its center of mass, T is the torque of the fluid on the solid, and r is the position vector of a point on the surface of the solid relative to the center of mass of the solid.

5. The fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method according to claim 1 is characterized in that: The process of calculating the flow field ghost point value based on the velocity and acceleration of the solid center of mass, the solid angular velocity and angular acceleration, the solid temperature field, the immersed boundary conditions and the flow field includes: Combined with the temperature boundary conditions, the temperature value at the ghost point is calculated, and the expression is as follows: Where, T G is the temperature value at the ghost point G, T BI and T IP2 are the values ​​of fluid temperature T at the body intercept point BI and the image point IP2 respectively; Combined with the velocity boundary conditions, the velocity value at the ghost point is calculated, and the expression is as follows: Where u G is the velocity value at the ghost point G, u BI is the value of velocity u at point BI, u IP1 and u IP2 are the values ​​of velocity u at image points IP1 and IP2 respectively; Combined with the pressure boundary conditions, the pressure value at the ghost point is calculated, and the expression is as follows: In the formula, α, β and are the coefficients in the pressure boundary condition, which can be rewritten by rewriting the pressure boundary condition into Get, x BI and y BI They are the x-coordinate and y-coordinate of point BI respectively. The variable subscript BI refers to the value of the variable at point BI. l is the distance from IP1 to IP2. p G is the pressure value at the ghost point G, p IP1 and p IP2 are the pressure values ​​at image points IP1 and IP2 respectively; According to the fluid pressure and temperature at the ghost point, the density at the ghost point is calculated using the ideal gas state equation.

6. The fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method according to claim 1 is characterized in that: If a new solid node appears, the solid temperature boundary condition is determined based on the fluid temperature field and the ghost point value of the fluid temperature field in step st-1. The solid temperature value of the new solid node is calculated based on the solid temperature boundary condition and the solid temperature values ​​of other grid nodes. The process includes: The expression of the solid temperature boundary condition is as follows: Where, T s represents the solid temperature, T represents the fluid temperature, k s represents the solid thermal conductivity, k represents the fluid thermal conductivity, and n is the external normal coordinate of the immersed boundary IB; Combined with the solid temperature boundary conditions, the solid temperature values ​​of other grid nodes are used to calculate the solid temperature values ​​of the new solid nodes.

7. The fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method according to claim 1 is characterized in that: The process of calculating the solid temperature ghost point value according to the solid temperature boundary condition and the solid temperature field of step st-1 includes: Using the solid temperature boundary condition, calculate the solid temperature value at the ghost point. The expression is as follows: Where, T s,G represents the solid temperature at the ghost point G, represents the solid temperature at the image point IP2, l is the distance from IP1 to IP2, T s represents the solid temperature, n is the outer normal coordinate of the immersed boundary IB, Represents the value of the external normal derivative of the solid temperature at the body intercept point BI.

8. An electronic device comprising a memory and a processor, characterized in that: The memory is coupled to the processor; wherein the memory is used to store program data, and the processor is used to execute the program data to implement the fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method as described in any one of claims 1 to 7 is implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the fluid-solid coupling heat transfer simulation method based on the compressible ghost point immersed boundary method described in any one of claims 1 to 7 is implemented.

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