Radiator flow channel topology optimization method and system based on transient concomitance

Abstract

A heat sink flow channel topology optimization method and system based on transient concomitant, in the method, the optimization problem of the heat sink flow channel is optimized; the transient NS equation is constructed and solved based on the optimization formula, the design variable distribution, the boundary condition and the initial condition are taken as the input, the PIMPLE algorithm in OpenFOAM is taken as the discrete method to solve the transient NS equation, the solution is stepped forward in time, and the physical field at different time steps is obtained; the concomitant differential equation of the transient NS equation is solved by the PIMPLE algorithm, and the concomitant variable information and the sensitivity information at different time steps are obtained; the moving asymptote method (MMA) is used for optimization and solution to obtain new design variable distribution and objective function; the residual error of the new design variable distribution and the objective function and the calculated results before is calculated, and compared with the convergence index to determine whether the convergence condition is reached, if the convergence condition is reached, the optimization is ended.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of heat dissipation cooling, and in particular to a heat sink flow channel topology optimization method and system based on transient concomitance. BACKGROUND

[0002] Topology optimization has developed from the previous theoretical feasibility to the actual application with the development of additive manufacturing technology, and has become a research hotspot in the field of heat sink design due to its high design freedom and significant optimization effect. The traditional heat sink design method is mainly based on the analysis and understanding of CFD (Computational Fluid Dynamics) simulation results and experimental results by heat sink designers, mainly reflected in the parametric analysis of heat sink size parameters and even the change of overall shape. These two optimization methods correspond to parameter optimization and shape optimization. Topology optimization is above parameter optimization and shape optimization, which not only contains the description of material distribution parameters or overall material interface optimization, but also optimizes the shape of material distribution or material interface. On this basis, the overall topological morphology change that cannot be achieved by the previous two methods can be introduced, such as introducing bifurcation in micro-channel structure distribution or introducing cavity in material to reduce the overall weight of the material. The number of bifurcations and cavities is calculated by optimization algorithm, and researchers cannot know the optimized morphology from the beginning. Under different constraint conditions, the results may be very different. These optimization results greatly increase the selectivity of researchers, which reflects the superiority of topology optimization in the field of heat sink design.

[0003] Topology optimization of heat sink is an optimization that considers multiple material distributions to achieve the best heat exchange effect or better temperature index. Unlike traditional topology optimization in the field of mechanics, the constraints are more complex. In the heat sink dominated by heat conduction, the constraint of heat conduction equation needs to be considered. In the heat sink dominated by convective heat transfer, N-S equation (Navier-Stokes equations) needs to be considered to achieve more complex optimization design. For topology optimization methods for steady-state problems, there are many mature and efficient methods. However, for topology optimization problems of heat exchangers designed under variable heat source conditions with obvious transient effects, there is no perfect optimization method and optimization system.

[0004] The above information disclosed in the background section is only used to enhance the understanding of the background of the present application, and therefore can contain information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] In view of the problems in the prior art, the application provides a heat sink flow channel topology optimization method and system based on transient adjoint, which realizes the topology structure optimization method of a transient variable heat source heat sink, and realizes efficient parallel solution of the topology optimization problem based on an OpenFOAM open source environment.

[0006] The application aims to realize the following technical scheme, a heat sink flow channel topology optimization method based on transient adjoint comprises the following steps,

[0007] Step 1, the optimization problem of the heat sink flow channel is optimized and expressed, which is converted into mathematical description, and the design variables, the objective function, and the boundary conditions and initial conditions of the constraint are determined;

[0008] Step 2, the transient NS equation is constructed and solved based on the optimization expression, the design variable distribution, the boundary conditions and the initial conditions are taken as input, the PIMPLE algorithm in OpenFOAM is taken as a discrete method to solve the transient NS equation, the solution is stepped forward in the positive time, and the physical field at different time steps is obtained;

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

[0010] Step 4, the adjoint variable information and the sensitivity information are taken as input, and the moving asymptote method (MMA) is used to optimize and solve to obtain a new design variable distribution and an objective function;

[0011] Step 5, the residual error of the new design variable distribution and the objective function and the result calculated before is calculated, and the convergence index is compared to determine whether the convergence condition is reached, if the convergence condition is reached, the optimization is ended, and if the convergence condition is not reached, the design variable distribution and the objective function obtained at present are taken as initial input to repeat step 2 until the convergence condition is reached and the optimization is ended.

[0012] In the method, the optimization expression is:

[0013]

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

[0015] In the method, the boundary condition of the constraint is:

[0016]

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

[0018]

[0019] In the formula, Δt = t0-t1, which is the time difference from the optimization starting time t0 to the ending time t1.

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

[0021]

[0022]

[0023] In the formula, R'1 represents the left side of the adjoint equation in the adjoint optimization, and the right side of the adjoint equation is Φ p , Φ u and Φ T represent the partial derivatives of the objective function Φ with respect to the state variables velocity u, pressure p and temperature T. u', p', T' in R'1 are the adjoint velocity, adjoint pressure and adjoint temperature variables introduced by the adjoint optimization method. α represents the paste area resistance coefficient used to distinguish the solid and fluid areas, ρ represents the density, c p is the specific heat capacity, λ is the thermal conductivity, and Q is the heat source term.

[0024] In the method, in step 3, the distribution of the physical field and the design variable at different time steps, the boundary condition and the initial condition are input, and the PIMPILE algorithm is used to solve the adjoint differential equation of the transient NS equation in reverse time.

[0025] In the method, in step 3, a control equation for solving the adjoint differential equation of the transient NS equation is obtained from KKT conditions of a dual problem of the transient NS equation solving problem.

[0026] In the method, in step 4, implementation of the moving asymptote method (MMA) is based on a portable extensible toolkit for scientific computing (Petsc) and an OpenFOAM platform to realize parallel solving of the optimization problem.

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

[0028] An optimization starting module optimizes an optimization problem of a heat sink flow channel, and constructs and solves a transient NS equation based on the optimization problem, while determining boundary conditions and initial conditions of design variables, an objective function and constraints;

[0029] A transient NS equation solving module connected to the optimization starting module solves the transient NS equation based on distribution of the design variables, the boundary conditions and the initial conditions as inputs, and solves the transient NS equation by using a PIMPLE algorithm in OpenFOAM as a discrete method, and steps forward in a forward time to obtain physical fields at different time steps;

[0030] A transient adjoint equation solving module connected to the optimization starting module and the transient NS equation solving module inputs the physical fields at different time steps and the distribution of the design variables, the boundary conditions and the initial conditions as inputs, and solves an adjoint differential equation of the transient NS equation by using the PIMPLE algorithm to obtain adjoint variable information and sensitivity information at different time steps;

[0031] An optimization design variable solving module connected to the transient adjoint equation solving module inputs the adjoint variable information and the sensitivity information as inputs, and uses a moving asymptote method (MMA) to obtain a new design variable distribution and an objective function by optimization solving;

[0032] An optimization ending module connected to the optimization design variable solving module, the transient adjoint equation solving module and the transient NS equation solving module calculates a residual error of the new design variable distribution and the objective function and a previously calculated result, and compares the residual error with a convergence index to determine whether a convergence condition is reached, and if the convergence condition is reached, the optimization ends, and if the convergence condition is not reached, the design variable distribution and the objective function obtained at present are used as initial inputs to solve the transient adjoint equation module until the convergence condition is reached and the optimization ends.

[0033] The solving transient NS equation module comprises a first processing unit integrating a PIMPLE algorithm in OpenFOAM, the optimization solving design variable module comprises a second processing unit integrating a moving asymptote method (MMA), and the optimization ending module comprises a third processing unit for residual error calculation.

[0034] Compared with the prior art, the application has the following advantages: based on the open source CFD solver OpenFOAM, the overall system framework part is written in C++, the underlying C++ code calculation can be realized, the calculation is efficient and parallelization can be realized; the PIMPLE algorithm in OpenFOAM is used to solve the transient NS equation and the solving of the accompanying differential equation of the transient NS equation, and the algorithm can realize stable calculation of a larger time step. The application can realize the topological structure optimization design under the condition of transient and variable heat source, and can efficiently realize the radiator design under different spatial sizes and different time spans under the condition of given pump power and given weight constraint, and solve the topological optimization of the heat exchanger design under the condition of obvious transient effect and variable heat source. BRIEF DESCRIPTION OF DRAWINGS

[0035] Various other advantages and benefits of the present application will become apparent to those of ordinary skill in the art, upon reading the following detailed description of the preferred embodiment. The accompanying drawings are intended to only illustrate preferred embodiments of the application, and are not intended to limit the application thereto. Obviously, other drawings than those shown below can be derived from the drawings shown below by those of ordinary skill in the art without any creative effort, and the drawings shown below are only some embodiments of the application. Moreover, the same reference numerals are used to denote the same components throughout the drawings.

[0036] In the drawings:

[0037] Figure 1 Flow chart of the heat radiator flow channel topological structure optimization method based on transient concomitant;

[0038] Figure 2 Boundary condition schematic diagram of the heat radiator flow channel topological structure optimization method based on transient concomitant;

[0039] Figure 3 Variable heat source condition schematic diagram of the heat radiator flow channel topological structure optimization method based on transient concomitant;

[0040] Figure 4 Topological structure optimization result schematic diagram of the heat radiator flow channel topological structure optimization method based on transient concomitant;

[0041] Figure 5 Topological optimization structure temperature field result schematic diagram of the heat radiator flow channel topological structure optimization method based on transient concomitant;

[0042] Figure 6 Fig. 3 is a schematic diagram of a topological optimization structure velocity field result of a heat sink flow channel topology optimization method example based on transient concomitant.

[0043] The application will be further explained with reference to the drawings and embodiments. DETAILED DESCRIPTION

[0044] Embodiments of the application will be described in more detail with reference to the drawings. Although specific embodiments of the application are shown in the drawings, it should be understood that the application can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thoroughly and completely understood, and so that the scope of the application will be completely conveyed to those skilled in the art.

[0045] It should be noted that certain terms have been used in the specification and claims to refer to certain components. Those skilled in the art will appreciate that the same component can be referred to by different names and that the name given to such component in this specification and claims should not be treated as limiting. The specification and claims should not be construed as indicating that the components referred to therein should be essential to the application. As used throughout this specification and in the claims, "comprise" or "comprising" means "comprising but not limited to", and should not be interpreted as indicating that the components listed after such term are essential to the application. The description that follows is the best mode contemplated by the inventors of carrying out this application. It should be understood that every maximum embodiment of the application includes every minimum embodiment of the application. The scope of the application should be defined by the appended claims and equivalents thereof.

[0046] In order to facilitate the understanding of the embodiments of the application, the following will be further explained and described with specific examples in conjunction with the drawings, and each drawing does not constitute a limitation on the embodiments of the application.

[0047] For better understanding, in one embodiment, as shown in Figures 1 to 6 the heat sink flow channel topology optimization method based on transient concomitant includes the following steps,

[0048] Step 1, the optimization problem of the heat sink flow channel is optimized to form an optimization equation, which is converted into a mathematical description, and the design variables, objective function, and boundary conditions and initial conditions of the constraints are determined;

[0049] Step 2, based on the optimization equation, the transient NS equation is constructed and solved, the design variable distribution, boundary conditions and initial conditions are taken as input, the PIMPLE algorithm in OpenFOAM is taken as the discrete method to solve the transient NS equation, the solution is stepped forward in time, and the physical field at different time steps is obtained;

[0050] Step 3, the physical field and design variable distribution, boundary condition and initial condition at different time steps are inputted to solve the adjoint differential equation of transient NS equation by PIMPILE algorithm to obtain the adjoint variable information and sensitivity information at different time steps;

[0051] Step 4, the adjoint variable information and sensitivity information are inputted to solve the new design variable distribution and objective function by using moving asymptote method (MMA) for optimization;

[0052] Step 5, the residual error of the new design variable distribution and objective function and the previous calculation result is calculated, and compared with the convergence index to determine whether the convergence condition is reached, if the convergence condition is reached, the optimization is ended, if the convergence condition is not reached, the design variable distribution and objective function obtained at present are taken as initial input to repeat step 2 until the convergence condition is reached and the optimization is ended.

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

[0054]

[0055] In the formula, γ is the design variable of optimization, in the present transient topology optimization problem, it represents the interpolation function of material distribution, when it is 0, the material is solid material of heat sink, when it is 1, it is fluid material of heat sink, and its subscript n represents the whole grid node. φ is the objective function of the present optimization problem, which is represented as the function of temperature T, in the present example, it is the average temperature It should be noted that the objective function in the optimization problem can be any continuous derivable function. u, p and T are state variables of the optimization problem, u is velocity variable, p is pressure, T is temperature, t is time variable of optimization process, t0 represents the starting time value, t1 represents the ending time value. R1 and R2 are constraints of the present optimization problem, R1 represents the left side item of control equation, R2 represents the left side item of boundary condition and initial condition of control equation solution. Λ is the energy dissipation of the heat exchanger with flow channel, Λ0 is the pump work constraint value set in the optimization problem, and the volume constraint V st = 0.4.

[0056] In the preferred embodiment of the method, the constraint boundary condition is:

[0057]

[0058] In the formula, Γ a is the inlet boundary, Γ b is the adiabatic wall boundary, Γ c is the outlet boundary, it should be noted that any form of first, second or third boundary condition 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] where Δt = t0-t1 is the time difference from the start time t0 to the end time t1.

[0062] In a preferred embodiment of the method, the adjoint NS equation is given by:

[0063]

[0064]

[0065] where R'1 represents the left-hand side of the adjoint equation, and the right-hand side value Φ p , Φ u and Φ T denote the partial derivatives of the objective function Φ with respect to the state variables velocity u, pressure p, and temperature T. u', p', and T' in R'1 are the adjoint velocity, adjoint pressure, and adjoint temperature variables introduced by the adjoint optimization method. α represents the mushy zone resistance coefficient used to distinguish the solid and fluid regions, ρ represents the density, c p is the specific heat capacity, and λ is the thermal conductivity. Q is the heat source term.

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

[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 derived from the KKT conditions of the dual problem of the transient NS equation solving problem.

[0068] In a preferred embodiment of the method, in step 4, the implementation of the moving asymptotes method (MMA) is based on the portable extensible toolkit for scientific computing (Petsc) and the open source field operation and manipulation (OpenFOAM) platform to achieve parallel solving of the optimization problem.

[0069] In one embodiment, the transient-adjoint-based heat sink flow channel topology optimization method comprises the following steps,

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

[0071] Step 2, based on the distribution of design variables, boundary conditions and initial conditions 111 as input, the PIMPLE algorithm 113 is used to solve the transient NS equation 112, and the solution is stepped forward in time to obtain the physical field 114 distribution at different time steps.

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

[0073] Step 4, taking the adjoint variable information and sensitivity information 122 obtained in step 3 as input, the moving asymptote method MMA 131 is used to optimize the solution to obtain the new design variable distribution and objective function 132.

[0074] Step 5, the design variable distribution and objective function 132 obtained in step 4 are compared with the previously calculated results to calculate the residual, and the convergence index is compared to determine whether the convergence condition is reached. If the convergence condition is reached, the optimization ends module 14 is entered, and if the convergence condition is not reached, the current design variable is taken as the initial input to repeat step 2 until the optimization ends module 14 is started.

[0075] In one embodiment, the optimization problem is optimized in this example by the optimization start module 10, which is converted into a mathematical description, and the design variables, objective function and constraint boundary conditions and initial conditions are determined.

[0076] Based on the proposed optimization system algorithm, the boundary conditions and description in this example are as shown in Figure 2 , which can be represented as:

[0077]

[0078] In the formula, Γ a is the inlet boundary, Γ b is the adiabatic wall boundary, Γ c is the outlet boundary, as shown in Figure 2 .

[0079] Figure 2 In the formula (1), l = 0.01 m, l0= 0.001 m, as shown in the formula (1), the wall refers to the wall boundary condition, here specifically refers to the velocity no-slip condition and the temperature adiabatic boundary condition; the inlet refers to the inlet boundary condition, here specifically refers to the inlet velocity u in and the inlet temperature T ininlet means the inlet boundary condition, here specifically means the inlet static pressure is 0 and the temperature is adiabatic condition; outlet means the outlet boundary condition, here specifically means the outlet static pressure is 0 and the temperature is adiabatic condition; symmetry means the symmetry boundary condition, here because the computational domain is axisymmetric type, and the control equation and boundary condition can be processed symmetrically, therefore the symmetry axis is taken as the symmetry boundary.

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

[0081]

[0082] ρ represents 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 represents the paste region resistance coefficient used to distinguish the solid and fluid regions

[0083] In this example, the heat source is a variable heat source, as shown in Figure 3 , which is a sinusoidal heat source with a period of time T and a constant maximum amplitude of Q0.

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

[0085]

[0086] In the formula, Δt = t0-t1 is the time difference from the optimization start time t0 to the end time t1.

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

[0088]

[0089] In this example, the overall optimization expression 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] In the formula, R'1 represents the left side term 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 represent the partial derivatives of the objective function Φ with respect to the state variables velocity u, pressure p, and temperature T. u', p', and T' in R'1 are the adjoint velocity, adjoint pressure, and adjoint temperature variables introduced by the adjoint optimization method. α represents the paste region resistance coefficient used to distinguish the solid and fluid regions.

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

[0096] Step 3 is implemented to solve the adjoint differential equation of the transient NS equation 121 using the PIMPLE algorithm 113, based on the physical field 114 distribution at different time steps obtained in Step 2 and the design variable distribution, boundary conditions and initial conditions 111 as input, to obtain the adjoint variable information and sensitivity information 122 at different time steps.

[0097] Step 4 is implemented to obtain the new design variable distribution and objective function 132 by using the moving asymptote method MMA 131 for optimization solution, based on the adjoint variable information and sensitivity information 122 obtained in Step 3 as input.

[0098] Step 5 is implemented to calculate the residual of the design variable distribution and objective function 132 obtained in Step 4 and the previously calculated results, and compare it with the convergence index to determine whether the convergence condition is reached. If the convergence condition is reached, it enters the optimization end module 14. If the convergence condition is not reached, the current design variable is taken as the initial input to repeat Step 2 until the optimization end module 14 is started.

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

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

[0101] An optimization start module that optimizes an optimization problem of a heat sink flow channel, and constructs and solves a transient NS equation based on the optimization problem, while determining a design variable, an objective function, and boundary conditions and initial conditions of a constraint;

[0102] A transient NS equation solving module connected to the optimization start module, the transient NS equation solving module solving the transient NS equation based on a distribution of the design variable, the boundary conditions and the initial conditions as inputs, using a PIMPLE algorithm in OpenFOAM as a discrete method to solve the transient NS equation, and solving in a forward time step to obtain physical fields at different time steps;

[0103] A transient adjoint equation solving module connected to the optimization start module and the transient NS equation solving module, the transient adjoint equation solving module inputting the physical fields at different time steps and the distribution of the design variable, the boundary conditions and the initial conditions, and using the PIMPLE algorithm to solve an adjoint differential equation of the transient NS equation to obtain adjoint variable information and sensitivity information at different time steps;

[0104] An optimization design variable solving module connected to the transient adjoint equation solving module, the optimization design variable solving module inputting the adjoint variable information and the sensitivity information, and using a moving asymptote method (MMA) to obtain a new design variable distribution and an objective function;

[0105] An optimization end module connected to the optimization design variable solving module, the transient adjoint equation solving module and the transient NS equation solving module, the optimization end module calculating a residual error of the new design variable distribution and the objective function with a previously calculated result, and comparing the residual error with a convergence index to determine whether a convergence condition is reached, and if the convergence condition is reached, the optimization ends, and if the convergence condition is not reached, the design variable distribution and the objective function obtained at present are used as initial inputs to solve the transient adjoint equation module until the convergence condition is reached and the optimization ends.

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

[0107] In one embodiment, a heat sink flow channel topology 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 design variable solving module 13, and an optimization end module 14.

[0108] In one embodiment, the start module 10 of the heat sink flow channel topology optimization system based on transient adjoint is the start of the topology optimization system; the NS equation solving module 11 includes transient NS equation solving 112 based on the design variable distribution, boundary conditions and initial conditions 111 as input, and obtains physical fields 114 at different time steps, wherein the transient NS equation solving 112 uses the PIMPLE algorithm 113 in OpenFOAM as the discretization method; the transient adjoint equation solving module 12 uses the physical fields 114 at different time steps obtained by the NS equation solving module 11 as its parameter input, and simultaneously inputs the design variable distribution, boundary conditions and initial conditions 111 as input, and performs reverse time solving 121 on the adjoint differential equation of the NS equation, and the discretization method is also the PIMPLE algorithm 113, and the information of the adjoint variable and the sensitivity information 122 are obtained by numerical solving after discretization; the optimization solving design variable module 13 inputs the adjoint variable information and the sensitivity information 122 obtained by solving the adjoint equation 12 as input, calculates a new design variable distribution and an objective function 132 by the moving asymptote MMA 131 method, and determines whether to converge by judging the residual of the design variable distribution and the residual change of the objective function after the calculation is completed. If it does not converge, the currently calculated design variable is input into the NS equation solving module 11 and introduced 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, and the entire optimization process is completed.

[0109] In one embodiment, the NS equation solving module 11 of the heat sink flow channel topology optimization system based on transient adjoint inputs the design variable distribution, boundary conditions and initial conditions 111 as input, and the transient NS equation solving (forward time solving) 112 as a calculation step, and obtains physical fields 114 at different time steps as an output step.

[0110] In one embodiment, the process of the NS equation solving module 11 of the heat sink flow channel topology optimization system based on transient adjoint inputs the design variable distribution, boundary conditions and initial conditions 111 as input, and the input of the design variable distribution is the start module 10 or the optimization solving design variable module 13, depending on whether the optimization process is performed from the beginning or in an iterative process. If it is performed from the beginning, the input of the design variable distribution is the start module 10, and if it is in an iterative process and the convergence standard is not reached, the input of the design variable distribution is obtained from the optimization solving design variable module 13. After the design variable input is obtained, it is input to the transient NS equation solving module 112 together with the boundary conditions and the initial conditions.

[0111] In one of the embodiments, the process of the solving transient NS equation module 11 of the heat sink flow channel topology optimization system based on transient concomitant is that, after obtaining the design variable distribution, boundary conditions and initial conditions 111 as inputs, the transient NS equation is solved in forward time 112, OpenFOAM is used as the solving platform, the PIMPLE algorithm 113 for transient solving in OpenFOAM is used as the discrete method, and finally the physical field results 114 at different time steps are obtained.

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

[0113] The heat sink flow channel topology optimization system based on transient concomitant, the solving transient concomitant equation module 12, the physical field 114 at different time steps obtained by the solving transient NS equation module 11 and the design variable distribution, boundary conditions and initial conditions 111 are used as inputs, the concomitant equation solving (backward time solving) 121 of the transient NS equation is used as the calculation step, and the concomitant variable information and sensitivity information 122 are obtained as the output step.

[0114] In one of the embodiments, the solving transient concomitant equation module 12 uses the physical field results 114 at different time steps obtained by the solving transient NS equation module 11 and the design variable distribution, boundary conditions and initial conditions 111 as inputs, and is characterized in that the physical field results 114 at different time steps obtained by the solving transient NS equation module 11 are stored, and the design variable distribution and the boundary conditions and initial conditions of the concomitant differential equation are combined to serve as the premise for solving the concomitant differential equation of the transient NS equation 121.

[0115] In one of the embodiments, the solving transient concomitant equation module 12, the concomitant differential equation solving module 121 of the transient NS equation uses the PIMPLE algorithm 113 in the OpenFOAM solver as the discrete method to obtain the concomitant variable information and sensitivity information 122.

[0116] In one of the embodiments, the solving transient concomitant equation module 12, the control equation of the concomitant differential equation solving module 121 of the transient NS equation is derived from the KKT (Karush-Kuhn-Tucker) condition of the dual problem of the transient NS equation solving 112 of the solving transient NS equation module 11.

[0117] The optimization solving design variable module 13 of the heat sink flow channel topology optimization system based on transient adjoint obtains the adjoint variable information and sensitivity information 122 obtained by the solving transient adjoint equation module 12 as a solving input, simultaneously uses the moving asymptote method MMA 131, obtains a new design variable distribution and a target function 132, simultaneously subtracts the design variable and the target function of the last iteration step of the optimization process, obtains a residual, and further judges whether the iteration process converges 133. If the iteration converges, the optimization process enters the optimization end module 14, and if the iteration does not converge, the result is taken as a new design variable, which is input into the solving transient NS equation module 11 based on the distribution, boundary conditions and initial conditions 111 of the new design variable.

[0118] In one embodiment, the optimization solving design variable module 13, in which the implementation of the moving asymptote method MMA 131 is based on the Petscthe Portable, Extensible Toolkit for Scientific Computation (a portable, extensible toolkit for scientific computation) and the OpenFOAM platform, can realize parallel solving of large-scale optimization problems.

[0119] The optimization end module 14 of the heat sink flow channel topology optimization system based on transient adjoint is used when the solution obtained by the optimization solving design variable module 13 of the new design variable distribution and the target function module 132 converges, the optimization process proceeds to the optimization end module 14, and the final design variable distribution and the target function are obtained.

[0120] The system obtains sensitivity information from the adjoint differential equation of the transient Navier-Stokes (NS) equation, and constructs a topology optimization system for flow heat exchange and fluid-solid conjugate heat transfer in a transient process. The overall transient topology optimization system is divided into three modules, which are: (1) based on the initial conditions and boundary conditions, the forward time solving of the transient NS equation is used to obtain the physical field at different times; (2) based on the physical field at different times and the boundary conditions and initial conditions of the adjoint equation, the reverse time solving of the transient NS equation adjoint equation is used to obtain the adjoint variable field distribution at different times; (3) based on the adjoint variable at different times and the time-dependent optimization target function, the sensitivity information of the target function with respect to the design variable is obtained, and the distribution of the design variable is solved according to the sensitivity information.

[0121] Although the embodiments of the present application have been described above with reference to the accompanying drawings, the present application is not limited to the above-described specific embodiments and areas of application, and the above-described specific embodiments are merely illustrative and instructive, but are not restrictive. Many modifications can be made by those skilled in the art under the teachings of the present specification and without departing from the scope of the present application as defined by the claims.

Claims

1. A heat sink flow channel topology optimization method based on transient adjoint states, characterized in that, It includes the following steps, Step 1: Optimize the heat sink flow channel problem by formulating an optimization equation and converting it into a mathematical description. At the same time, determine the design variables, objective function, and boundary conditions and initial conditions of the constraints. Step 2: Construct and solve the transient NS equations based on the optimized formulas. Using the design variable distribution, boundary conditions and initial conditions as inputs, the PIMPLE algorithm in OpenFOAM is used as the discrete method to solve the transient NS equations. The solution is performed in forward time steps to obtain the physical field at different time steps. Step 3: Using the physical field and design variable distributions, boundary conditions and initial conditions at different time steps as inputs, the adjoint differential equations of the transient NS equations are solved using the PIMPILE algorithm to obtain the adjoint variable information and sensitivity information at different time steps. Step 4: Using the accompanying variable information and sensitivity information as input, the Moving Asymptote Method (MMA) is used to optimize and solve for the new design variable distribution and objective function. Step 5: Calculate the residuals between the new design variable distribution and objective function and the previously calculated results, and compare them with the convergence index to determine whether the convergence condition has been met. If the convergence condition is met, the optimization ends. If the convergence condition is not met, the current design variable distribution and objective function are used as the initial input to repeat Step 2 until the convergence condition is met and the optimization ends.

2. The method as described in claim 1, characterized in that, The preferred, optimized formula is as follows: In the formula, γ is the design variable for optimization, representing the interpolation function of material distribution in transient topology optimization problems. A value of 0 indicates the material is solid material in the radiator, and a value of 1 indicates fluid material in the radiator. The subscript n represents the global mesh node. φ is the objective function of this optimization problem, expressed as a function of temperature T, where the average temperature is... u, p, and T are all state variables in the optimization problem, where u is the velocity variable, p is the pressure, and T is the temperature. t is the time variable of the optimization process, with t0 representing the start time and t1 representing the end time. R1 and R2 are constraints in this optimization problem; R1 represents the left-hand side of the governing equation, and R2 represents the left-hand side of the boundary and initial conditions for solving the governing equation. Λ represents the energy dissipation of the heat exchanger with the flow channel, Λ0 is the pump work constraint value set for the optimization problem, and V is the volume constraint. st =0.

4.

3. The method as described in claim 2, characterized in that, The boundary conditions for the constraints are: In the formula Γ a Γ is the entrance boundary. b For the boundary of the adiabatic wall, Γ c This is the export boundary.

4. The method as described in claim 2, characterized in that, The objective function is the average temperature Φ in both time and space: In the formula, Δt = t0 - t1 is the time difference between the start and end of the optimization.

5. The method as described in claim 2, characterized in that, The transient Navier-Stokes equations and the adjoint transient Navier-Stokes equations are as follows: In the formula, R1′ represents the left-hand side of the adjoint equation in the adjoint optimization, and Φ represents the right-hand side value of the adjoint equation. p Φ u and Φ T R1′ represents the partial derivatives 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 associated velocity, pressure, and temperature variables introduced by the adjoint optimization method. α represents the drag coefficient of the mushy region used to distinguish between solid and fluid regions, ρ represents density, and c... p λ is the specific heat capacity, λ is the thermal conductivity, and Q is the heat source term.

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

7. The method as described in claim 1, characterized in that, Step 3: The governing equations for solving the adjoint differential equations of the transient Navier-Stokes equations are derived from the KKT conditions of the dual problem of the transient Navier-Stokes equations solution problem.

8. The method as described in claim 1, characterized in that, Step 4: The Moving Asymptote Method (MMA) is implemented based on Petsc's Portable and Scalable Toolkit for Scientific Computing and the OpenFOAM platform to achieve parallel solution of optimization problems.

9. An optimization system implementing any one of claims 1-8 based on the transient adjoint radiator flow channel topology optimization method, characterized in that, It includes, The optimization start module optimizes the heat sink flow channel optimization problem by formulating the optimization formula and constructing and solving the transient Navier-Stokes equations based on the optimization formula, while determining the design variables, objective function, and boundary conditions and initial conditions of the constraints. The transient NS equation solving module is connected to the optimization start module. The transient NS equation solving module takes the distribution of design variables, boundary conditions and initial conditions as input, and uses the PIMPLE algorithm in OpenFOAM as the discrete method to solve the transient NS equation. The solution is performed in positive time step to obtain the physical field at different time steps. The transient adjoint equation solving module connects the optimization start module and the transient NS equation solving module. The transient adjoint equation solving module takes the distribution of physical fields and design variables, boundary conditions and initial conditions at different time steps as input, and uses the PIMPILE algorithm to solve the adjoint differential equation of the transient NS equation to obtain the adjoint variable information and sensitivity information at different time steps. The module for optimizing the solution of design variables is connected to the module for solving transient adjoint equations. The module for optimizing the solution of design variables takes the adjoint variable information and sensitivity information as inputs and uses the moving asymptote method (MMA) to optimize the solution and obtain a new distribution of design variables and objective function. The optimization termination module connects the optimization solution module for design variables, the solution module for transient adjoint equations, and the solution module for transient Navier-Stokes equations. The optimization termination module performs residual calculations on the new design variable distribution and objective function with the previously calculated results, and compares them with the convergence index to determine whether the convergence condition has been met. If the convergence condition is met, the optimization ends. If the convergence condition is not met, the currently obtained design variable distribution and objective function are used as the initial input to solve the transient adjoint equations module until the convergence condition is met and the optimization ends.

10. The optimization system as described in claim 9, characterized in that, The module for solving the transient Navier-Stokes equations includes a first processing unit that integrates the PIMPLE algorithm from OpenFOAM; the module for optimizing the solution of design variables includes a second processing unit that integrates the Moving Asymptote Method (MMA); and the optimization termination module includes a third processing unit for residual calculation.

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