Research On Adjoint Sensitivity Method For Topology Optimization Of Pump Flow Channel

Centrifugal pump is a kind of general-purpose fluid machinery that is even more widely used,and it is also a huge energy-consuming device.At present,most of domestic centrifugal pumps are still in low efficiency,and there are great opportunities for improvement.The research on optimization design method for centrifugal pumps has been carried out.However,most of these methods are not easy to carry out due to complex optimization model and large amount of calculation.Therefore,deeply studying the law of pump internal flow and developing a rapid and convenient method for centrifugal pump optimization design are of great importance.This paper mainly studies a concomitant sensitivity method for topology optimization of centrifugal pump flow channels.Firstly,on the basis of topology optimization for fluid in pipe,we extend it to the flow channel optimization for rotating machine by combining with Multiple Reference Frames(MRF).In this method,the design domain is described by porous media.The movement of the fluid is described by the N-S equation with Darcy's law.The blades and flow channel of the centrifugal pump are divided into the same computational domain which is discretized through the grid.A continuous material density was introduced as a design variable for each cell,and the material density 0 and 1 indicated for solid and fluid regions,respectively.We derived the N-S equation containing the Darcy's law in a rotating coordinate system,then the solver was programmed to solve the flow analysis of the porous media model of the centrifugal pump.Its solution accuracy under different permeability coefficients was compared and analyzed.For the solution of the topology optimization sensitivity of the centrifugal pump flow channel.We derived the general adjoint equation corresponding to the N-S equation containing the Darcy's law in a rotating coordinate system,and the difference method was used to verify the sensitivity calculation results with specific objective function.The adjoint method greatly reduces the computational complexity of the gradient solution and provides an efficient sensitivity calculation method for the topology optimization of the pump flow channel.