Investigation On The Optimization Of Centrifugal Pump Impeller Based On Adjoint Method

With the development of modern testing technology and computing technology of flow, the flow structure and performance in pump has become a hot issue in hydraulic research. Abundant research results have been achieved. However, mainly due to the complicated implicit relation between the hydraulic performance and the complicated geometry shape of impeller passages, the study of optimization and inverse problem of centrifugal pump moves slowly. The main methods of optimal hydraulic design include the optimization method based on the evolutionary algorithm, the optimization method based on the gradient algorithm, and the optimization method based on the design of experiment and response surface, etc. The cost function has to be estimated on every sample in the case of the optimization method based on the experiment design and response surface. When the dimension of design variables is large, flow field needs to be computed more than once, which results in great amount of calculation. The main difficulty is that the gradient vector for the cost function with respect to the design variables is hard to evaluate in the optimization method based on gradient algorithm, the costs of computation increase by geometric progression by the dimension of the design variables. The adjoint method was widely used in the optimization of flow control with the development of flow theory. The adjoint method was applied to the optimization of aviation airfoil by Antony Jameson. The method can reduce the amount of calculation when solve the gradient vectors for the cost function respect to the design variables. The adjoint method is applied to the optimization of the inverse problem of centrifugal pump, which was proposed in this thesis. The major content was as follows:1. The adjoint method was applied to the study of impeller of centrifugal pump hydraulic inverse design. The corresponding adjoint equations and boundary conditions were derived. At the same time the gradient vectors for the cost function and the numerical algorithm was also derived. RANS equations were used to solve flow field. The adjoint equations were used to solve adjoint variables field, which based on three dimensional Euler equations. The effective optimization inverse design programs for impeller of centrifugal pump are developed by following aspects:grid generation and flow field analysis, solving the adjoint equations and the gradient vector for cost function, the impeller blade shape updated and potent combination of optimal arithmetic.2. The inverse problem of centrifugal pump and mathematical expression of variables under Cartesian was deduced during the optimization process. And the correspondence between coefficients of partial differential equations and coefficients of the adjoint equations were also deduced in Comsol Multiphysics. At the same time the boundary conditions was established.3. The optimization design theory which based on Navier-Stokes equations and adjoint method in Cartesian coordinate system was investigated. The formulation of adjoint equations was derived. The corresponding adjoint equations, boundary conditions and the gradient vector of final variation of cost function were derived by combing the given cost function.4. The adjoint variables field solved by adjoint method was coupling with CFD results of centrifugal pump.The Comsol Multiphysics was applied to calculate flow field and the adjoint variables field, and it was applied to couple results too. At last the blade shape was renewed by MATLAB program. The process is stable and feasible. It also can be used for optimization design of other objective function by appropriate modification.5. Efficiency of pump is regard as target of optimize under the design conditions, which is connected with flow and head of centrifugal pump. For the change of head is extremely small in the optimization process, the moment acting on the blade is considered as the cost function. The initial blade shape is built straight. With the adjoint method, the gradient of the cost function with respect to the control variables will be established easily, and the blade shape can be renewed according to the inverse direction of the gradient vectors. The optimum design will finished when the cost function is minimized. At the same time, head, efficiency and torque of the model are stable, which shows that the algorithm has converged. The calculation case results show that the adjoint method for the optimization of centrifugal pump impeller is rational.