Blade shape optimization of centrifugal pump
impeller with adjoint method
Zhang Renhui1,2, Guo Miao1, Yang Junhu1,2, Liu Yi1,2
1.School of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou, Gansu 730050, China; 2.Key Laboratory of Fluid Machinery and Systems, Gansu Province, Lanzhou, Gansu 730050, China
Abstract:To prevent some drawbacks in hydrodynamics optimization procedure of hydraulic machinery, such as a huge timeconsuming and the difficulty in blade shape control and update etc, an adjoint method is proposed to optimize the blade shape of centrifugal pump impellers. At first, the camber line of impeller blade of a low specific centrifugal pump is expressed as a polynomial in terms of dimensionless radius. Secondly, the governing equations of ideal fluid flow in the centrifugal pump impeller are considered as the constraints of the optimization problem; then the constrained optimization problem is transformed into an unconstrained one by introducing four adjoint variables. Finally, the variation formulas of objective function, the adjoint equations and the boundary conditions of the computational domain for the adjoint variables are deduced. The gradients of the objective function with respect to the control variables are calculated. Accordingly the blade shape is updated continually against the direction of the gradients starting with straight blade until a minimized objective function is achieved. Because the variation of flow variables is not included in the variation of objective function, the flow filed and adjoint variable field need to be simulated once only in one optimization cycle, causing a greatly reduced computing time for the optimization. The results of the case study indicate that the proposed adjoint method is feasible for blade shape optimization of centrifugal impellers.