Study On Fluid Topology Optimization Method Based On Variable Density Method And Experimental Analysis

Fluid topology optimization has been a popular research topic in recent years,but it is still in the initial stage of development in China.Most of the existing studies aim at the fluid topology optimization design of simple channel structure,while the fluid topology optimization for complex engineering problems is very few.Therefore,it is very important to establish a reliable numerical model of fluid topology optimization for the practical engineering problems and to carry out experimental verification analysis.The fluid topology optimization based on the polygonal meshes method breaks through the problem for the mesh division of the complex channel structure.Comparing to the traditional mesh generation method,the polygonal meshes method has less dependence on the structure,stronger adaptability and higher calculation precision.Therefore,the fluid topology optimization of the finite element method and the polygonal meshes method based on the variable density method are studied respectively in this paper.The feasibility and superiority of the polygonal meshes method for the fluid topology optimization have been verified integrating experimental analysis with numerical simulation.The main research contents include:(1)The governing equation of steady flow problem for incompressible fluid is discretized by using FEM(Finite Element Method),EFG(Element-free Galerkin)method and polygonal meshes method,and then he flow field analysis and comparison verification of several practical examples were carried out by programming.The results show that the velocity of polygonal meshes method is in good agreement with that of the EFG method and the FEM method,but the polygonal meshes method only needs a set of meshes to obtain the same precision compared to the two sets of nodes are needed to deal with the pressure shock problem in the EFG method.(2)The mathematical model of the finite element method for the fluid topology optimization for the flow channel structure is established by using the rational approximate model of material properties(RAMP)in the variable density method,and the minimum energy dissipation is chosen as the objective function.The fluid topology optimization of the flow channel structure is finished to make the objective function performance of the channel structure optimal under the specified boundaries and constraints.The effect of the volume fraction,Reynolds number and interpolating function parameter q on the optimal topological structure of flow channel is compared and analyzed.The influence of the above parameters on the objective function is further discussed,and the reasonable range of these parameters is provided.(3)The mathematical model of the polygonal meshes method for fluid topology optimization based on the variable density method is established,and the relative density of the polygonal element is chosen as the design variable and the minimum energy dissipation is selected as the objective function.The fluid topology optimization of several numerical examples is carried out to verify the above established fluid topology optimization model.The comparison analysis shows that the penalty factor,the inlet velocity and the volume fraction have great influence on the optimal topology structure of the flow channel,including the flow direction,diffluence or confluence of the channel.The effect of volume fraction on the flow channel structure will change to a secondary factor,especially when the inlet velocity is increased to a certain value in a certain range,and then the topology structure of the channel is basically unchanged even if the volume fraction is increased.Meanwhile,a clear topology boundary of flow channel can be obtained by selecting the appropriate penalty factor.(4)The optimized flow channel structure was manufactured by using 3D printing technology based on the fluid topology optimization results.The flow characteristics of the optimal channel structure under different parameters and the non optimized channel structure were compared and analyzed by experimental tests.The results show that the flow performance parameters of the optimized channel were superior to the non optimized channel,and then the reliability and correctness of the fluid topology optimization model is verified.In this paper,the fluid topology optimization based on the variable density method is studied by using the finite element method and the polygonal meshes method respectively.The corresponding mathematical models of the fluid topology optimization are established,and then the fluid topology optimization of several practical examples are performed and compared with the experimental test.The selection range of some important parameters in the fluid topology optimization method is obtained.The results show that the polygonal meshes method fluid topology optimization based on the variable density method has better applicability and superiority,and it has better theoretical research and engineering application value.