Research On Topology Optimization Design Method For Volutes Of Centrifugal Pumps

As the general-purpose fluid machines,centrifugal pumps play an important role in various industries.Improving the performance of centrifugal pumps has always been the focus of researchers at home and abroad.The volute is one of the important overcurrent components of the centrifugal pump.Therefore,the optimization design of the volute has an important influence on the overall performance of the centrifugal pump.At the same time,since the topology optimization method has been extended from the field of solid mechanics to the field of fluid dynamics,many scholars have made in-depth research on topology optimization method for fluid,which makes the method gradually developed and used.Moreover,some scholars apply it to the design of the centrifugal impellers.The advantage of the topology optimization method is that it not only can easily obtain very novel and complex shapes without the help of the previous experience,but also can be not limited to the initial structures.Therefore,this paper used the topology optimization method for fluid to design the volutes of centrifugal pumps.Based on the topology optimization method for fluid,we consider the initial design domain as the porous medium model,and the Darcy's resistance term is introduced in the Navier-Stokes equations.Taking the density of every cell as the design variable,the minimized total pressure loss is the optimization target,and the constraint function is the fraction of fluid volume.The sensitivity required for optimization is solved by the continuous adjoint method to reduce the computational cost when the number of design variables is large.Nonlinear density filtering is added to the optimization process to prevent the checkerboard patterns from appearing in the optimization results and to reduce the generation of gray cells.The main contents of this paper are:(1)The mathematical formula of the volute optimization problem is given.The continuous adjoint equations and their boundary conditions for solving the sensitivity are deduced in detail.In the open source software OpenFOAM,the program for nonlinear filter of design variable density is implemented,and after solving the primal equations and the adjoint equations,the solution of sensitivity and objective function is realized.(2)The whole process of volute optimization is given and implemented in the program.A linker between the optimization program and the OpenFOAM solver is written to enable control the solver for the computational analysis and the data transmission.The optimization problem is optimized using the MMA algorithm and the program is tested with typical examples to demonstrate its usability.(3)Two-dimensional and three-dimensional volutes are obtained through topology optimization.Using the two-dimensional initial design domain for topology optimization,the volute structure of the two-dimensional is obtained,and the optimization results are re-modeled for calculation and comparative analysis with the volute designed by traditional method.Moreover,this paper changes the single outlet of the design domain into two outlets,so the result turns to double volute structure.At the same time,the height of the exit position is changed,and a two-dimensional volute of different shapes are obtained.Then the 3D design domain is optimized,and the three-dimensional volute is obtained.Then the optimization results are post-processed and analyzed.