A fast numerical method for flow analysis and blade design in centrifugal pump impellers

A numerical methodology is developed to simulate the turbulent flow in a 2-dimensional centrifugal pump impeller and to compute the characteristic performance curves of the entire pump. The flow domain is discretized with a polar, Cartesian mesh and the Reynolds-averaged Navier–Stokes (RANS) equations are solved with the control volume approach and the k–ε turbulence model. Advanced numerical techniques for adaptive grid refinement and for treatment of grid cells that do not fit the irregular boundaries are implemented in order to achieve a fully automated grid construction for any impeller design, as well as to produce results of adequate precision and accuracy. After estimating the additional hydraulic losses in the casing and the inlet and outlet sections of the pump, the performance of the pump can be predicted using the numerical results from the impeller section only. The regulation of various energy loss coefficients involved in the model is carried out for a commercial pump, for which there are available measurements. The predicted overall efficiency curve of the pump was found to agree very well with the corresponding experimental data. Finally, a numerical optimization algorithm based on the unconstrained gradient approach is developed and combined with the evaluation software in order to find the impeller geometry that maximizes the pump efficiency, using as free design variables the blade angles at the leading and the trailing edge. The results verified that the optimization process can converge very fast and to reasonable optimal values.