Study on the optimum design of cross flow water turbines using RSM with weighted least squares method

Abstract

In this study, an optimum design method using the response surface method (RSM) was applied to a cross-flow water turbine in which a circular cavity was installed. The efficiency obtained by CFD analysis was used as the objective function. A quadratic equation for the shape parameters obtained using the weighted least-squares method was used to the response surface. For optimal nozzle design, three shape parameters were used: the runner opening angle, nozzle wall exit angle, and radius of curvature of the nozzle wall. In the weighted least-squares method, the weights of the residual between the efficiency obtained from CFD analysis and the value from the response surface were defined as inversely proportional to the root mean square of the difference between the efficiency of the calculation point from CFD and that at the highest efficiency point, such that more accurate optimal values could be estimated. The shape derived using this optimum method achieved high efficiency.