Entropy generation minimization of a pump running in reverse mode based on surrogate models and NSGA-II

Abstract

Pumps in reverse function are one of the most cost-effective industrial devices to generate power from small hydropower capacities. Due to the fact that the pump components are not inherently designed for the turbine mode, the hydraulic performance of the pump as turbine (PAT) is usually not ideal. One low-cost solution to improve the PAT performance is to redesign the pump Impeller without changing of any other components. In this study a multi-objective optimization process is applied based on the surrogate models with focus on minimizing the entropy generation rate (EGR) at 2 flow rates of the QBEP (best efficiency point) and Q1.3BEP in order to improve the hydraulic performance of the PAT over a wide range of operating points. In the optimization process, the sample space points are determined by the optimal Latin hypercube sampling (OLHS) technique. The values of the objective functions and the constraints at the sample points are specified by numerical solution of the 3D incompressible steady-state RANS equations. Kriging (KRG) surrogate models have been constructed to estimate the objective functions and constraints at the whole sample space. The blade inlet and outlet angles, the blade wrap angle, the runner inlet width and the number of blades are defined as the design variables. Finally, by using non-dominated sorting genetic algorithm II (NSGA-II), in addition to obtaining the Pareto optimal fronts (POFs), the optimal combinations of the design variables are determined. Analysis of the importance level of the design variables has been performed using the RSA surrogate model. Optimization results reveals that the maximum reduction in the EGR occurs in the optimal 8-bladed runner by approximately 50%. The decrease in the entropy production leads to a decrease in irreversible hydraulic losses and an increase in the hydraulic efficiency of the PAT, e.g. 3.8% and 5.72% increase in efficiency at the QBEP and Q1.3BEP, respectively. Flow field analysis demonstrates that the entropy generation minimization causes a reduction in flow disorders within the optimal PATs. As a result, inlet shock, flow deviation at the blade outlet, flow separation at the blade passage, backflow and swirling flow at the draft tube are dramatically reduced or completely eliminated. The optimization of the PAT with the help of surrogate models and evolutionary algorithms (EAs), from the point of view of the second law of thermodynamics, has been successfully investigated in this work and the improvement of hydraulic performance was achieved.