Topology Optimization For The Layout Of Cooling Channels Of Heat Generating Products And Equipment

Cooling channels are widely used in components and equipment such as CPU,batteries and stamping tools.The circulating coolant inside the cooling device carries heat from the heat source to the outside in a convective way,which is an efficient heat dissipation method.The arrangement of the cooling channel directly affects the heat dissipation performance.Changing the layout of channels,such as inlet and outlet positions and internal channel position,can meet various heat dissipation requirements of industrial applications,such as decreasing the maximum temperature or ensuring uniform temperature in a specific area,etc.How to design the cooling channel,providing a good working temperature is the key to ensuring the normal operation of components or equipment and prolonging their service life.In the design process of the cooling channel,on the one hand,it is necessary to consider the influence of the fluid flow inside the channel on the temperature field.On the other hand,it is necessary to consider the influence of the channel on the structural strength.For example,in the working process of a hot stamping tool with water-cooled channels,on the surface of the stamping tool,there are both thermal load caused by hot blank sheet and mechanical load caused by clamping.Therefore,it is necessary to build a multi-physics coupled model in the design of the cooling channel to describe the velocity field,temperature field and displacement field involved in the working process simultaneously.In addition,due to the constraints of the processing technology and other conditions,it is also necessary to consider the influence of the size constraints of the channel on the layout of the cooling channel.Among the traditional cooling channel design,the size parameter-based design method was usually adopted.By using this method,the optimized result is limited by the parameter range such as size and shape.Hence,the feasible solution space is compressed,which is not suitable for the conception design of the product.Topology optimization is a design method with topology as design variables,which can better overcome the limitations brought by parameter-based method.By the combination of manufacturing technologies such as 3D printing,the results of topology optimization design can be directly applied to the manufacture of products,and the complicated parameter design process can be omitted,hence the design cost is further reduced.This paper proposes several typical topology optimization methods for cooling channel topology optimization design including two-dimensional circular cross-section channel design,two-dimensional cross-section multiple material design,two-dimensional planar layout design and three-dimensional channel layout design.The implementation process of the above optimization method is introduced through specific design examples.The main research works are listed as followings.(1)The thermal mechanical behavior is considered in a two-dimensional channel cross section design.An equivalent model for describing temperature field is established according to the characteristics of the straight circular channel.The turbulent flow velocity field is replaced by the uniform single dimensional fluid velocity field,coupled with the convective heat transfer equation.A design dependent weak form is introduced to describe the temperature boundary condition.A thermo-mechanical coupling model considering thermal stress is established to describe the thermo-mechanical properties of the stamping tool structure.The cross-sectional topology with circular channels is obtained by introducing discrete objects filtering method.The problem of mixing two kinds of filtering projections caused by the discrete method is solved by adding a geometric constraint.The topological optimization formula is constructed by taken the temperature uniformity and displacement uniformity of the surface of stamping tool as the optimization target and constraint,respectively.The feasibility of the method is verified by the cooling channel design examples of a simple flat top tool and a complex top surface U-shaped tool,respectively.(2)In a two-dimensional cross section design with the shape of the cooling channel is not limited to a circular,the effects of three materials of solid,liquid,and gas are considered.Two sets of design variables are introduced to describe three material properties by the interpolation form of their products.The temperature field and displacement field in the design of the cooling channel are described by the equivalent convection heat transfer equation and the thermo-mechanical coupling equation.By introducing geometric constraints,the "unreasonable"design phenomena of liquid-gas contact and liquid-to-design domain boundary contact are overcome.A minimum size constraint is introduced to eliminate tiny structures.The average temperature and the displacement uniformity are taken as the optimization objective function and constraint,respectively.A simple cooling channel design is taken as an example,in which the optimization process and the influence of design material are both discussed.The cross section topology of the cooling channel inside the hot stamping tool with a complex profile is further optimized according to the reasonable optimization process.(3)In the planar layout design problem,the Darcy flow model based on the design-dependent equivalent diffusion coefficient is constructed to be equivalent to the original turbulence flow model.The reliability of equivalent model is verified by comparison of CFD model with different structures and different finite element meshes,respectively.In the optimization process,the average temperature of a specified area is taken as the objective function.In addition,the pressure drop constraint and the minimum length scale constraint are introduced in optimization formula.A simple heat sink cooling layout design is taken as an example,to introduce the various parameter settings and optimization processes in the optimization process.A reasonable optimization parameter setting is hence summarized.Based on the parameter setting,a topology optimization design of a heat sink plate is carried out with two main types of position of inlet and outlet.The optimized forms of the cooling channels under different pressure drop constraints and different Reynolds numbers are discussed in this example.(4)The topology optimization method of Darcy model is extended to 3D topology optimization to overcome the limitations brought by 2D optimization.The parallel computing optimization design program is built based on PETSc(Portable,Extensible Toolkit for Scientific Computation).The finite element equations of each physical field are stored using parallel processed vectors and sparse matrices.The parallel solution of large-scale linear equations is carried out by the Krylov subspace method with precondition method.The turbulent velocity field is described by the Darcy velocity field,and the velocity field is coupled to the convective heat transfer equation for temperature field analysis.Taking the average temperature of a specific area as the objective function,the optimal formulation is further constructed considering the pressure drop constraint and the volume constraint.The sensitivity of the objective function and the constraint function is solved by the adjoint method.A three-dimensional cooling channel design problem is taken as an example.The reliability of the self-developed program is verified by comparing the optimized analysis program based on PETSc with the optimization result of commercial code.Due to limited space,the research content involved in this paper may not cover all the products and equipment of the built-in cooling channels.It did not cover other functions of some products either,such as considering electromagnetic effects.The main focus of this paper is to give a topology optimization method for cooling channel layout considering thermal-mechanical load and light weight requirements.