Transient accompanying-based radiator flow channel topological optimization method and system

Abstract

The invention discloses a radiator flow channel topological optimization method and system based on transient accompanying, and the method comprises the steps: carrying out the optimization of an optimization problem of a radiator flow channel; constructing and solving a transient NS equation on the basis of an optimization column formula, solving the transient NS equation by taking design variable distribution, boundary conditions and initial conditions as inputs and taking a PIMPLE algorithm in OpenFOAM as a discrete method, and performing stepping on forward time to obtain physical fields under different time steps; solving an adjoint differential equation of the transient NS equation by using a PIMPILE algorithm to obtain adjoint variable information and sensitivity information under different time steps; performing optimization solution by applying a moving asymptote method MMA to obtain new design variable distribution and a target function; and carrying out residual calculation on the new design variable distribution and the target function and a previous calculation result, comparing with a convergence index to judge whether a convergence condition is reached, and if the convergence condition is reached, ending optimization.

Description

Technical Field

[0001] The present invention belongs to the technical field of heat dissipation and cooling, and in particular to a method and system for topological optimization of a radiator flow channel based on transient adjointness. Background Art

[0002] With the development of additive manufacturing technology, topology optimization has moved from theoretical feasibility to practical application, and has become a research hotspot in the field of heat sink design due to its high design freedom and significant optimization effect. Traditional heat sink design methods are mainly based on the analysis and understanding of CFD (Computational Fluid Dynamics) simulation results and experimental results by heat sink designers, which are mainly reflected in the variable parameter analysis of heat sink size parameters and even the attempt to change the overall shape. These two optimization methods correspond to parameter optimization and shape optimization respectively. Topology optimization as a whole is based on parameter optimization and shape optimization. It includes the optimization of material distribution parameters in each area or the descriptive parameters of the overall material interface, and at the same time optimizes the shape of the material distribution or the shape of the material interface. On this basis, changes in the overall topological morphology that cannot appear in the previous two methods can be introduced, such as introducing bifurcations in the microfluidic structure distribution, or introducing cavities in the material to reduce the overall weight of the material. The number of bifurcations and cavities is calculated by the optimization algorithm. Researchers cannot know the optimized morphology from the beginning, and results with very different morphologies may appear under different constraints. These optimization results greatly increase the researchers' selectivity and reflect the superiority of topological optimization in the field of heat sink design.

[0003] The topology optimization of the radiator is an optimization that considers the distribution of multiple materials to achieve the best heat transfer effect or a better temperature index. The difference from the topology optimization in the traditional mechanics field is that its constraints are more complex. The constraints of the heat conduction equation need to be considered in the radiator that mainly relies on heat conduction, and the radiator that mainly relies on convection heat transfer needs to consider the NS equations (Navier-Stokes equations) to achieve a more complex optimization design. There are many mature and efficient topology optimization methods for steady-state problems. However, there is currently no complete optimization method and optimization system for the topology optimization problem of heat exchanger design with obvious transient effects and variable heat sources.

[0004] The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention proposes a radiator flow channel topology optimization method and system based on transient accompaniment, implements the topology structure optimization method of the transient variable heat source radiator, and at the same time, based on the OpenFOAM open source environment, realizes the efficient parallel solution of the topology optimization problem.

[0006] The purpose of the present invention is achieved through the following technical solutions. The radiator flow channel topology optimization method based on transient adjointness includes the following steps:

[0007] Step 1, the optimization problem of the radiator flow channel is optimized and converted into a mathematical description, and the design variables, objective functions, and constraint boundary conditions and initial conditions are determined at the same time;

[0008] Step 2: Based on the optimization formula, the transient NS equations are constructed and solved. Based on the design variable distribution, boundary conditions and initial conditions as input, the PIMPLE algorithm in OpenFOAM is used as a discrete method to solve the transient NS equations. The solution is stepped in the forward time to obtain the physical field at different time steps.

[0009] Step 3, the physical field and design variable distribution, boundary conditions and initial conditions at different time steps are used as input, and the adjoint differential equation of the transient NS equation is solved by the PIMPILE algorithm to obtain the adjoint variable information and sensitivity information at different time steps;

[0010] Step 4, using the concomitant variable information and sensitivity information as input, using the moving asymptote method MMA to perform optimization and solve to obtain a new design variable distribution and objective function;

[0011] Step 5, calculate the residuals of the new design variable distribution and objective function with the previously calculated results, and compare them with the convergence index to determine whether the convergence conditions are met. If the convergence conditions are met, the optimization ends. If the convergence conditions are not met, the current design variable distribution and objective function are used as initial inputs to repeat step 2 until the convergence conditions are met and the optimization ends.

[0012] In the method described, the optimization column is expressed as:

[0013]

[0014] Where γ is the optimized design variable, which represents the interpolation function of the material distribution in this transient topology optimization problem. When it is 0, the material is the solid material of the heat sink, and when it is 1, it is the fluid material of the heat sink. The subscript n represents the overall grid node. φ is the objective function of this optimization problem, which is expressed as a function of temperature T, and in this example, it is the average temperature It should be noted that the objective function in the optimization problem can be any continuous differentiable function. u, p, and T are all state variables of the optimization problem. u is the velocity variable, p is the pressure, T is the temperature, and t is the time variable of the optimization process. t0 represents the starting time value, and t1 represents the ending time value. R1 and R2 are the constraints of this optimization problem. R1 represents the left side of the control equation, and R2 represents the left side of the boundary conditions and initial conditions for solving the control equation. Λ is the energy dissipation of the heat exchanger with flow channel, Λ0 is the pump work constraint value set for the optimization problem, and the volume constraint V st =0.4.

[0015] In the method described, the boundary conditions of the constraints are:

[0016]

[0017] Where Γ a is the entrance boundary, Γ b is the adiabatic wall boundary, Γ c is the outlet boundary. It should be noted that any type of first, second or third boundary condition can meet the requirements. In the method described, the objective function is the average temperature Φ in time and space:

[0018]

[0019] Wherein Δt=t0-t1 is the time difference between the optimization start time t0 and the end time t1.

[0020] In the method described, the transient NS equation and the adjoint transient NS equation are:

[0021]

[0022]

[0023] Where R′1 represents the left side of the adjoint equation in the adjoint optimization, and the right side value of the adjoint equation is Φ p , Φ u and Φ T represents the partial derivative of the objective function Φ with respect to the state variables velocity u, pressure p, and temperature T. In R′1, u′, p′, and T′ are the accompanying velocity, accompanying pressure, and accompanying temperature variables introduced by the accompanying optimization method. α represents the mushy zone resistance coefficient used to distinguish between solid and fluid regions, ρ represents the density, and c p is the specific heat capacity, λ is the thermal conductivity, and Q is the heat source term.

[0024] In the method described, in step 3, the distribution of physical fields and design variables at different time steps, boundary conditions and initial conditions are used as input, and the adjoint differential equation of the transient NS equation is solved in reverse time using the PIMPILE algorithm.

[0025] In the method described, in step 3, the control equation for solving the adjoint differential equation of the transient NS equation is obtained by the KKT condition of the dual problem of the transient NS equation solution problem.

[0026] In the method described, step 4, the implementation of the moving asymptote method MMA is based on Petsc's portable and extensible toolkit for scientific computing and the OpenFOAM platform to achieve parallel solution of optimization problems.

[0027] An optimization system for implementing a heat sink flow channel topology optimization method based on transient adjoint includes:

[0028] The optimization start module optimizes the optimization problem of the radiator flow channel and constructs and solves the transient NS equation based on the optimization formula, while determining the design variables, objective functions, and constraint boundary conditions and initial conditions;

[0029] A transient NS equation solving module is connected to the optimization start module. The transient NS equation solving module uses the distribution of design variables, boundary conditions and initial conditions as inputs, uses the PIMPLE algorithm in OpenFOAM as a discrete method to solve the transient NS equations, and steps the solution in forward time to obtain the physical field at different time steps;

[0030] A transient adjoint equation solving module is connected to the optimization start module and the transient NS equation solving module. The transient adjoint equation solving module takes the distribution of the physical field and design variables at different time steps, boundary conditions and initial conditions as inputs, solves the adjoint differential equation of the transient NS equation with the PIMPILE algorithm, and obtains the adjoint variable information and sensitivity information at different time steps;

[0031] An optimization and solution design variable module, which is connected to the transient adjoint equation solution module, takes the adjoint variable information and sensitivity information as input, and uses the moving asymptote method MMA to optimize and solve to obtain a new design variable distribution and objective function;

[0032] The optimization end module connects the optimization solution design variable module, the transient adjoint equation solution module and the transient NS equation solution module. The optimization end module calculates the residual between the new design variable distribution and the objective function and the previously calculated results, and compares them with the convergence index to determine whether the convergence conditions are met. If the convergence conditions are met, the optimization ends. If the convergence conditions are not met, the current design variable distribution and objective function are used as the initial input to solve the transient adjoint equation module until the convergence conditions are met and the optimization ends.

[0033] In the optimization system, the module for solving the transient NS equations includes a first processing unit integrating the PIMPLE algorithm in OpenFOAM, the module for optimizing and solving the design variables includes a second processing unit integrating the moving asymptote method MMA, and the optimization end module includes a third processing unit for residual calculation.

[0034] Compared with the prior art, the present invention has the following advantages: based on the open source CFD solver OpenFOAM, the overall system framework is written in C++, which can realize the underlying C++ code calculation, and the calculation is efficient and can be parallelized; the PIMPLE algorithm in OpenFOAM is used to solve the transient NS equation and the adjoint differential equation of the transient NS equation, and the algorithm can achieve stable calculation of a large time step. The present invention can realize the optimization design of the topological structure under transient and variable heat source conditions, and can efficiently realize the design of radiators under different spatial sizes and different time spans under given pump power and given weight constraints, solving the problem of obvious transient effects and topological optimization of heat exchanger design under variable heat source conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] By reading the detailed description of the preferred specific embodiments below, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The drawings in the specification are only for the purpose of illustrating the preferred embodiments and are not considered to be limitations of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0036] In the attached picture:

[0037] Figure 1 It is a flow chart of the method for optimizing the topology of the radiator flow channel based on transient adjoint;

[0038] Figure 2 It is a schematic diagram of boundary conditions for an example of a method for optimizing the topology of a heat sink channel based on transient adjoint;

[0039] Figure 3 It is a schematic diagram of variable heat source conditions for an example of a heat sink flow channel topology optimization method based on transient adjoint;

[0040] Figure 4 It is a schematic diagram of the topology optimization results of an example of the radiator flow channel topology optimization method based on transient adjoint;

[0041] Figure 5 It is a schematic diagram of the temperature field results of the topology optimization structure of the heat sink flow channel based on transient adjoint topology optimization method;

[0042] Figure 6 It is a schematic diagram of the velocity field results of the topology optimization structure of the radiator channel topology structure optimization method based on transient adjoint.

[0043] The present invention is further explained below in conjunction with the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0044] The specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to enable the scope of the present invention to be fully communicated to those skilled in the art.

[0045] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the present invention. The scope of protection of the present invention shall be determined by the attached claims.

[0046] To facilitate understanding of the embodiments of the present invention, further explanation will be given below by taking specific embodiments as examples in conjunction with the accompanying drawings, and each of the accompanying drawings does not constitute a limitation on the embodiments of the present invention.

[0047] For better understanding, in one embodiment, Figures 1 to 6 As shown in Figure 2, the radiator flow channel topology optimization method based on transient adjoint includes the following steps:

[0048] Step 1, the optimization problem of the radiator flow channel is optimized and converted into a mathematical description, and the design variables, objective functions, and constraint boundary conditions and initial conditions are determined at the same time;

[0049] Step 2: Based on the optimization formula, the transient NS equations are constructed and solved. Based on the design variable distribution, boundary conditions and initial conditions as input, the PIMPLE algorithm in OpenFOAM is used as a discrete method to solve the transient NS equations. The solution is stepped in the forward time to obtain the physical field at different time steps.

[0050] Step 3, the physical field and design variable distribution, boundary conditions and initial conditions at different time steps are used as input, and the adjoint differential equation of the transient NS equation is solved by the PIMPILE algorithm to obtain the adjoint variable information and sensitivity information at different time steps;

[0051] Step 4, using the concomitant variable information and sensitivity information as input, using the moving asymptote method MMA to perform optimization and solve to obtain a new design variable distribution and objective function;

[0052] Step 5, calculate the residuals of the new design variable distribution and objective function with the previously calculated results, and compare them with the convergence index to determine whether the convergence conditions are met. If the convergence conditions are met, the optimization ends. If the convergence conditions are not met, the current design variable distribution and objective function are used as initial inputs to repeat step 2 until the convergence conditions are met and the optimization ends.

[0053] In a preferred embodiment of the method, the optimization formula is expressed as:

[0054]

[0055] Where γ is the optimized design variable, which represents the interpolation function of the material distribution in this transient topology optimization problem. When it is 0, the material is the solid material of the heat sink, and when it is 1, it is the fluid material of the heat sink. The subscript n represents the overall grid node. φ is the objective function of this optimization problem, which is expressed as a function of temperature T, and in this example, it is the average temperature It should be noted that the objective function in the optimization problem can be any continuous differentiable function. u, p, and T are all state variables of the optimization problem. u is the velocity variable, p is the pressure, T is the temperature, and t is the time variable of the optimization process. t0 represents the starting time value, and t1 represents the ending time value. R1 and R2 are the constraints of this optimization problem. R1 represents the left side of the control equation, and R2 represents the left side of the boundary conditions and initial conditions for solving the control equation. Λ is the energy dissipation of the heat exchanger with flow channel, Λ0 is the pump work constraint value set for the optimization problem, and the volume constraint V st =0.4.

[0056] In a preferred embodiment of the method, the boundary conditions of the constraints are:

[0057]

[0058] Where Γ a is the entrance boundary, Γ b is the adiabatic wall boundary, Γ c For the exit boundary, it should be noted that any form of first-class, second-class, or third-class boundary conditions can meet the requirements.

[0059] In a preferred embodiment of the method, the objective function is the average temperature Φ in time and space:

[0060]

[0061] Wherein Δt=t0-t1 is the time difference between the optimization start time t0 and the end time t1.

[0062] In a preferred embodiment of the method, the transient NS equation and the adjoint transient NS equation are:

[0063]

[0064]

[0065] Where R′1 represents the left side of the adjoint equation in the adjoint optimization, and the right side value of the adjoint equation is Φ p , Φ u and Φ T represents the partial derivative of the objective function Φ with respect to the state variables velocity u, pressure p, and temperature T. In R′1, u′, p′, and T′ are the accompanying velocity, accompanying pressure, and accompanying temperature variables introduced by the accompanying optimization method. α represents the mushy zone resistance coefficient used to distinguish between solid and fluid regions, ρ represents the density, and c p is the specific heat capacity, λ is the thermal conductivity, and Q is the heat source term.

[0066] In a preferred embodiment of the method, in step 3, the distribution of physical fields and design variables at different time steps, boundary conditions and initial conditions are used as input to solve the adjoint differential equation of the transient NS equation in reverse time using the PIMPILE algorithm.

[0067] In a preferred embodiment of the method, in step 3, the control equation for solving the adjoint differential equation of the transient NS equation is obtained by the KKT condition of the dual problem of the transient NS equation solution problem.

[0068] In a preferred embodiment of the method, step 4, the implementation of the moving asymptote method MMA is based on Petsc's portable and extensible toolkit for scientific computing and the OpenFOAM platform to achieve parallel solution of optimization problems.

[0069] In one embodiment, a heat sink flow channel topology optimization method based on transient adjoint includes the following steps:

[0070] Step 1, starting from the optimization start module 10, the optimization problem is optimized and formulated, converted into a mathematical description, and the design variables, objective function, and constraint boundary conditions and initial conditions can be determined at the same time.

[0071] Step 2, based on the design variable distribution, boundary conditions and initial conditions 111 as input, the transient NS equations are solved 112 using the PIMPLE algorithm 113, and the solution is stepped in forward time to obtain the physical field 114 distribution at different time steps.

[0072] Step 3, using the distribution of the physical field 114 at different time steps obtained in step 2 and the distribution of the design variables, boundary conditions and initial conditions 111 as input, the adjoint differential equation of the transient NS equation is solved 121 using the PIMPILE algorithm 113 to obtain the adjoint variable information and sensitivity information 122 at different time steps.

[0073] Step 4, using the accompanying variable information and sensitivity information 122 obtained in step 3 as input, use the moving asymptote method MMA131 to optimize and solve to obtain a new design variable distribution and objective function 132.

[0074] Step 5, calculate the residual of the design variable distribution and objective function 132 obtained in step 4 and the previously calculated results, and compare them with the convergence index to determine whether the convergence condition is met. If the convergence condition is met, enter the optimization end module 14. If the convergence condition is not met, repeat step 2 with the currently obtained design variable as the initial input until the optimization end module 14 is started.

[0075] In one embodiment, the present example starts with the optimization start module 10, the optimization problem is optimized and formulated, converted into a mathematical description, and the design variables, objective function, and boundary conditions and initial conditions of the constraints can be determined at the same time.

[0076] Based on the proposed optimization system algorithm, the boundary conditions and description of this example are as follows Figure 2 As shown, it can be expressed as:

[0077]

[0078] Where Γ a is the entrance boundary, Γ b is the adiabatic wall boundary, Γ c is the export boundary, such as Figure 2 shown.

[0079] Figure 2 Where l = 0.01 m, l0 = 0.001 m, as shown in formula (1), the wall refers to the wall boundary condition, which specifically refers to the no-slip condition of velocity and the adiabatic boundary condition of temperature; the inlet refers to the inlet boundary condition, which specifically refers to the inlet velocity u in The inlet temperature is T inconditions; the outlet refers to the outlet boundary conditions, which specifically refers to the conditions that the outlet static pressure is 0 and the temperature is adiabatic; symmetry refers to the symmetric boundary conditions. Here, since the calculation domain is axisymmetric and the control equations and boundary conditions can be treated symmetrically, this symmetry axis is used as the symmetry boundary.

[0080] In this example, the constraints of the fluid control equation are:

[0081]

[0082] ρ is the density, c p is the specific heat capacity, λ is the thermal conductivity, u is the velocity, p is the pressure, and T is the temperature. α is the mushy zone resistance coefficient used to distinguish between solid and fluid regions

[0083] In this example, the heat source is a variable heat source, such as Figure 3 As shown, the variable heat source is a sinusoidal wave heat source, whose period is time T and the maximum amplitude remains unchanged at Q0.

[0084] In this example, the optimized objective function is the average temperature Φ in time and space:

[0085]

[0086] Wherein Δt=t0-t1 is the time difference between the optimization start time t0 and the end time t1.

[0087] In this example, the instantaneous dissipation of energy is Λ:

[0088]

[0089] In this example, the overall optimization formula can be expressed as:

[0090]

[0091] In formula (5), the volume constraint V st =0.4.

[0092] In this example, the adjoint transient NS equation can be expressed as:

[0093]

[0094] Where R′1 represents the left side of the adjoint equation in the adjoint optimization, and the right side value of the adjoint equation is Φ p , Φ u and Φ T represents the partial derivative of the objective function Φ with respect to the state variables velocity u, pressure p, and temperature T. In R′1, u′, p′, and T′ are the accompanying velocity, accompanying pressure, and accompanying temperature variables introduced by the accompanying optimization method. α represents the mushy zone resistance coefficient used to distinguish between solid and fluid regions.

[0095] Implement step 2, based on the design variable distribution, boundary conditions and initial conditions 111 as input, solve 112 the transient NS equations using the PIMPLE algorithm 113, and step the solution in forward time to obtain the physical field 114 distribution at different time steps.

[0096] Implement step 3, using the distribution of the physical field 114 and the distribution of the design variables, boundary conditions and initial conditions 111 at different time steps obtained in implementing step 2 as input, and use the PIMPILE algorithm 113 to solve 121 the adjoint differential equation of the transient NS equation to obtain the adjoint variable information and sensitivity information 122 at different time steps.

[0097] Implement step 4, use the accompanying variable information and sensitivity information 122 obtained in step 3 as input, and use the moving asymptote method MMA131 to optimize and solve to obtain a new design variable distribution and objective function 132.

[0098] In step 5, the residuals of the design variable distribution and the objective function 132 obtained in step 4 and the previously calculated results are calculated, and compared with the convergence index to determine whether the convergence conditions are met. If the convergence conditions are met, the optimization end module 14 is entered. If the convergence conditions are not met, the currently obtained design variables are used as the initial input and step 2 is repeated until the optimization end module 14 is started.

[0099] After module 14 is started, the optimization result is obtained after 450 iterations, as shown in Figure 4 As shown in the figure, the white area is the area where the design variable material distribution interpolation function γ is close to 1, that is, the fluid area, and the black area is the area where the design variable material distribution interpolation function γ is close to 0, that is, the solid area. The temperature field results are as follows: Figure 5 As shown in the figure, the white area is the high temperature area, the black area is the low temperature area, and the right side contains a scale bar containing the temperature distribution. The right side of the scale bar is the name of the physical quantity T, which refers to the size of the temperature. The unit is the international standard unit K. The time of the cloud map is half of the heating process, that is, t = 0.5t0 + 0.5t1. Under this heating time, the highest temperature reaches 305.5K and the lowest temperature is 298.10K. The velocity field results are as follows Figure 6 As shown, the white area is the area with larger velocity values, the black area is the area with lower velocity values, and the right side contains a scale bar containing the velocity value distribution. On the right side of the scale bar is the name of the physical quantity U Magnitude, which refers to the magnitude of the velocity vector. The unit is the international standard unit m / s. The time of the cloud map is half of the heating process, that is, t=0.5t0+0.5t1. At this time, the maximum velocity is 0.07m / s and the minimum velocity is 0m / s.

[0100] An optimization system for implementing a heat sink flow channel topology optimization method based on transient adjoint includes:

[0101] The optimization start module optimizes the optimization problem of the radiator flow channel and constructs and solves the transient NS equation based on the optimization formula, while determining the design variables, objective functions, and constraint boundary conditions and initial conditions;

[0102] A transient NS equation solving module is connected to the optimization start module. The transient NS equation solving module uses the distribution of design variables, boundary conditions and initial conditions as inputs, uses the PIMPLE algorithm in OpenFOAM as a discrete method to solve the transient NS equations, and steps the solution in forward time to obtain the physical field at different time steps;

[0103] A transient adjoint equation solving module is connected to the optimization start module and the transient NS equation solving module. The transient adjoint equation solving module takes the distribution of the physical field and design variables at different time steps, boundary conditions and initial conditions as inputs, solves the adjoint differential equation of the transient NS equation with the PIMPILE algorithm, and obtains the adjoint variable information and sensitivity information at different time steps;

[0104] An optimization and solution design variable module, which is connected to the transient adjoint equation solution module, takes the adjoint variable information and sensitivity information as input, and uses the moving asymptote method MMA to optimize and solve to obtain a new design variable distribution and objective function;

[0105] The optimization end module connects the optimization solution design variable module, the transient adjoint equation solution module and the transient NS equation solution module. The optimization end module calculates the residual between the new design variable distribution and the objective function and the previously calculated results, and compares them with the convergence index to determine whether the convergence conditions are met. If the convergence conditions are met, the optimization ends. If the convergence conditions are not met, the current design variable distribution and objective function are used as the initial input to solve the transient adjoint equation module until the convergence conditions are met and the optimization ends.

[0106] In a preferred embodiment of the optimization system, the module for solving the transient NS equations includes a first processing unit integrating the PIMPLE algorithm in OpenFOAM, the module for optimizing and solving the design variables includes a second processing unit integrating the moving asymptote method MMA, and the optimization end module includes a third processing unit for residual calculation.

[0107] In one embodiment, the radiator flow channel topology structure optimization system based on transient adjoint includes an optimization start module 10, a Navier-Stokes NS equation solving module 11, a transient adjoint equation solving module 12, an optimization solving design variable module 13 and an optimization end module 14.

[0108] In one embodiment, the starting module 10 of the radiator flow channel topology optimization system based on transient adjoint is the start of the topology optimization system; the NS equation solving module 11 includes a transient NS equation solving 112 based on the design variable distribution, boundary conditions and initial conditions 111 as input to obtain the physical field 114 at different time steps, wherein the transient NS equation solving 112 uses the PIMPLE algorithm 113 in OpenFOAM as a discrete method; the transient adjoint equation solving module 12 uses the physical field 114 at different time steps obtained by solving the transient NS equation module 11 as its parameter input, and at the same time uses the design variable distribution, boundary conditions and initial conditions 111 as input to solve the NS equation The adjoint differential equation is solved in reverse time 121, and the discrete method for solving is also the PIMPLE algorithm 113. Through numerical solution after discretization, the information of its adjoint variables and sensitivity information 122 are obtained; the optimization solution of the design variables 13 is to solve the adjoint equation 12 to obtain the adjoint variable information and sensitivity information 122 as input, and the new design variable distribution and objective function 132 are calculated by the moving asymptote MMA 131 method. After the calculation is completed, it is determined whether the residual of the design variable distribution and the residual change of the objective function are determined. If there is no convergence, the currently calculated design variables are imported as input into the NS equation solution module 11 to introduce them into the input part based on the design variable distribution, boundary conditions and initial conditions 111. If the convergence standard is reached, the optimization end module 14 is entered to complete the entire optimization process.

[0109] In one embodiment, a module 11 for solving transient NS equations based on a transient radiator flow channel topology optimization system is composed of a design variable distribution, boundary conditions and initial conditions 111 as input, and a transient NS equation solution (forward time solution) 112 as a calculation step, and obtains a physical field 114 at different time steps as an output step.

[0110] In one embodiment, the process of solving the transient NS equation module 11 based on the transient accompaniment heat sink flow channel topology structure optimization system is based on the design variable distribution, boundary conditions and initial conditions 111 as input, and the input of the design variable distribution is the starting module 10 or the optimization solution design variable module 13, depending on whether the optimization process starts from the beginning or is an iterative process. If it starts from the starting module 10, the input of the design variable distribution is the starting module 10. If the convergence standard is not reached during the iterative process, the input of the design variable distribution is obtained from the optimization solution design variable module 13. After obtaining the design variable input, it is input into the transient NS equation solution module 112 together with the boundary conditions and initial conditions.

[0111] In one embodiment, based on the process of solving the transient NS equation module 11 of the radiator flow channel topology optimization system accompanied by transient state, after obtaining the design variable distribution, boundary conditions and initial conditions 111 as input, the transient NS equation is forward solved 112, OpenFOAM is used as the solution platform, and the PIMPLE algorithm 113 of the transient solution in OpenFOAM is used as the discretization method, and finally the physical field results 114 at different time steps are obtained.

[0112] In one embodiment, the PIMPLE algorithm 113 for transient solution in OpenFOAM is used as a discretization method in the forward time solution 112 of the transient NS equation. In a single time step, the PIMPLE algorithm 113 is equivalent to adding an outer loop similar to the SIMPLE algorithm to the outer layer on the basis of the PISO algorithm to reconstruct the momentum equation. Each time the momentum equation is updated, the originally lagging flux is updated, so that the PIMPLE algorithm can better handle transient calculations under large time steps.

[0113] The radiator flow channel topology structure optimization system based on transient adjoint, the module for solving transient adjoint equations 12, takes the physical fields 114 at different time steps obtained by solving the transient NS equation module 11 and the distribution of design variables, boundary conditions and initial conditions 111 as inputs, the adjoint equation solution (reverse time solution) 121 of the transient NS equation as a calculation step, and obtains the adjoint variable information and sensitivity information 122 as an output step.

[0114] In one embodiment, the module 12 for solving the transient adjoint equations uses the physical fields 114 at different time steps obtained by solving the transient NS equations module 11 and the design variable distribution, boundary conditions and initial conditions 111 as inputs, and is characterized in that it is necessary to store the physical field results of solving the transient NS equations module 11 at different times, and at the same time, combine the design variable distribution and the boundary conditions and initial conditions of the adjoint differential equations as a prerequisite for solving the transient NS equations adjoint differential equation solution 121.

[0115] In one embodiment, the transient adjoint equation solving module 12 and the adjoint differential equation solving module 121 of the transient NS equation use the PIMPLE algorithm 113 in the OpenFOAM solver as a discretization method to obtain the adjoint variable information and sensitivity information 122.

[0116] In one embodiment, the control equation of the transient adjoint equation solving module 12 and the adjoint differential equation solving module 121 of the transient NS equation is obtained by the KKT (Karush-Kuhn-Tucker) condition of the dual problem of the transient NS equation solving problem 112 of the transient NS equation solving module 11.

[0117] The optimization and solution design variable module 13 of the radiator flow channel topology structure optimization system based on transient adjoint uses the adjoint variable information and sensitivity information 122 obtained by solving the transient adjoint equation module 12 as the solution input, and uses the moving asymptote method MMA131 to obtain a new design variable distribution and objective function 132, and at the same time, subtracts the design variables and objective functions of the previous iteration step of the optimization process to obtain their residuals, and then judges whether the iteration process converges 133. If the iteration converges, the optimization process enters the optimization end module 14. If the iteration does not converge, the result is used as a new design variable, and as a new design variable, it is input into the transient NS equation solution module 11 based on its distribution, boundary conditions and initial conditions 111.

[0118] In one of the embodiments, the design variable module 13 is optimized and solved, wherein the implementation of the moving asymptote method MMA131 method is based on Petscthe Portable, Extensible Toolkit for Scientific Computation and the OpenFOAM platform, which can realize parallel solution of large-scale optimization problems.

[0119] The optimization end module 14 of the radiator flow channel topology structure optimization system based on transient accompaniment is that when the new design variable distribution calculated by the optimization solution design variable module 13 and the solution obtained by the objective function module 132 converge, the optimization process proceeds to the optimization end module 14 and obtains the final design variable distribution and objective function.

[0120] This system is guided by solving the adjoint differential equation of transient Navier-Stokes (NS) equation to obtain sensitivity information, and constructs a topology optimization system for flow heat transfer and fluid-solid conjugate heat transfer in transient processes. The overall transient topology optimization system is divided into three modules, namely: (1) forward time solution of the transient NS equation based on initial conditions and boundary conditions to obtain the physical field at different times; (2) reverse time solution of the adjoint equation of the transient NS equation based on the physical field at different times and the boundary conditions and initial conditions of the adjoint equation to obtain the distribution of the adjoint variable field at different times; (3) based on the adjoint variables at different times and the time-related optimization objective function, obtain the sensitivity information of the objective function with respect to the design variables, and solve the distribution of the design variables based on the sensitivity information.

[0121] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and instructive, rather than restrictive. A person of ordinary skill in the art can also make many forms under the guidance of this specification and without departing from the scope of protection of the claims of the present invention, all of which belong to the protection of the present invention.

Claims

1. A radiator flow channel topology optimization method based on transient adjoint, characterized in that: It includes the following steps, Step 1, the optimization problem of the radiator flow channel is optimized and converted into a mathematical description, and the design variables, objective functions, and constraint boundary conditions and initial conditions are determined at the same time; Step 2: Based on the optimization formula, the transient NS equations are constructed and solved. Based on the design variable distribution, boundary conditions and initial conditions as input, the PIMPLE algorithm in OpenFOAM is used as a discrete method to solve the transient NS equations. The solution is stepped in the forward time to obtain the physical field at different time steps. Step 3, the physical field and design variable distribution, boundary conditions and initial conditions at different time steps are used as input, and the adjoint differential equation of the transient NS equation is solved by the PIMPILE algorithm to obtain the adjoint variable information and sensitivity information at different time steps; Step 4, using the concomitant variable information and sensitivity information as input, using the moving asymptote method MMA to perform optimization and solve to obtain a new design variable distribution and objective function; Step 5, calculate the residuals of the new design variable distribution and objective function with the previously calculated results, and compare them with the convergence index to determine whether the convergence conditions are met. If the convergence conditions are met, the optimization ends. If the convergence conditions are not met, the current design variable distribution and objective function are used as initial inputs to repeat step 2 until the convergence conditions are met and the optimization ends.

2. The method according to claim 1, characterized in that Preferably, the optimized column form is expressed as: Where γ is the optimized design variable, which represents the interpolation function of material distribution in transient topology optimization problem. When γ is 0, the material is the solid material of the heat sink, and when γ is 1, the material is the fluid material of the heat sink. The subscript n represents the overall grid node, and φ is the objective function of this optimization problem, which is expressed as a function of temperature T. The average temperature u, p, and T are all state variables of the optimization problem. u is the velocity variable, p is the pressure, and T is the temperature. t is the time variable of the optimization process. t0 represents the starting time value, and t1 represents the ending time value. R1 and R2 are the constraints of this optimization problem. R1 represents the left side term of the control equation, and R2 represents the left side term of the boundary conditions and initial conditions for solving the control equation. Λ is the energy dissipation of the heat exchanger with flow channel, Λ0 is the pump work constraint value set for the optimization problem, and the volume constraint V st =0.

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3. The method according to claim 2, characterized in that The boundary conditions of the constraints are: Where Γ a is the entrance boundary, Γ b is the adiabatic wall boundary, Γ c is the export boundary.

4. The method according to claim 2, characterized in that The objective function is the average temperature Φ in time and space: Where Δt=t0-t1 is the time difference from the start to the end of optimization.

5. The method according to claim 2, characterized in that The transient NS equation and the adjoint transient NS equation are: Where R1′ represents the left side of the adjoint equation in the adjoint optimization, and the right side value of the adjoint equation is Φ p , Φ u and Φ T represents the partial derivative of the objective function Φ with respect to the state variables velocity u, pressure p, and temperature T. In R1′, u′, p′, and T′ are the accompanying velocity, accompanying pressure, and accompanying temperature variables introduced by the accompanying optimization method. α represents the mushy zone resistance coefficient used to distinguish between solid and fluid regions. ρ represents the density. c p is the specific heat capacity, λ is the thermal conductivity, and Q is the heat source term.

6. The method according to claim 1, characterized in that Step 3: The distribution of physical fields and design variables at different time steps, boundary conditions and initial conditions are used as inputs to solve the adjoint differential equation of the transient NS equations in reverse time using the PIMPILE algorithm.

7. The method according to claim 1, characterized in that Step 3, the control equation for solving the adjoint differential equation of the transient NS equation is obtained from the KKT conditions of the dual problem of the transient NS equation solution problem.

8. The method according to claim 1, characterized in that Step 4, the implementation of the moving asymptote method (MMA) is based on the Petsc portable and extensible toolkit for scientific computing and the OpenFOAM platform to achieve parallel solution of optimization problems.

9. An optimization system for implementing the heat sink flow channel topology optimization method based on transient adjointment according to any one of claims 1 to 8, characterized in that: These include, The optimization start module optimizes the optimization problem of the radiator flow channel and constructs and solves the transient NS equation based on the optimization formula, while determining the design variables, objective functions, and constraint boundary conditions and initial conditions; A transient NS equation solving module is connected to the optimization start module. The transient NS equation solving module uses the distribution of design variables, boundary conditions and initial conditions as inputs, uses the PIMPLE algorithm in OpenFOAM as a discrete method to solve the transient NS equations, and steps the solution in forward time to obtain the physical field at different time steps; A transient adjoint equation solving module is connected to the optimization start module and the transient NS equation solving module. The transient adjoint equation solving module takes the distribution of the physical field and design variables at different time steps, boundary conditions and initial conditions as inputs, solves the adjoint differential equation of the transient NS equation with the PIMPILE algorithm, and obtains the adjoint variable information and sensitivity information at different time steps; An optimization and solution design variable module, which is connected to the transient adjoint equation solution module, takes the adjoint variable information and sensitivity information as input, and uses the moving asymptote method MMA to optimize and solve to obtain a new design variable distribution and objective function; The optimization end module connects the optimization solution design variable module, the transient adjoint equation solution module and the transient NS equation solution module. The optimization end module calculates the residual between the new design variable distribution and the objective function and the previously calculated results, and compares them with the convergence index to determine whether the convergence conditions are met. If the convergence conditions are met, the optimization ends. If the convergence conditions are not met, the current design variable distribution and objective function are used as the initial input to solve the transient adjoint equation module until the convergence conditions are met and the optimization ends.

10. The optimization system according to claim 9, characterized in that: The module for solving transient NS equations includes a first processing unit integrating the PIMPLE algorithm in OpenFOAM, the module for optimizing and solving design variables includes a second processing unit integrating the moving asymptote method MMA, and the optimization end module includes a third processing unit for residual calculation.

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