Multi-fidelity CFD for obtaining the runner blade profile parameters of a Francis turbine for optimum hydrodynamic performance

The high fidelity Navier Stokes equations based CFD codes precisely take care of the turbulent and viscous effects of complex flows passing through the hydraulic turbines. However, for preliminary design synthesis and analysis purposes, this full 3D flow can be assumed as a combination of two 2D flows (meridional axi-symmetric flow and blade-to-blade or cascade flow) which is the basis of low fidelity potential flow theory for hydraulic turbines. This paper presents the utilities of high as well as low fidelity CFD analyses for obtaining a runner blade design which yields an optimum hydrodynamic performance of a prototype Francis Turbine. The complete flow domain of the Francis turbine has been considered for the high-fidelity analysis which is carried out by using ANSYS CFX 16.0 for different operating conditions. Whereas, for the low fidelity investigations, full three-dimensional flow domains of different blade rows (i.e., stay vanes, guide vanes and runner) of the Francis turbine is divided into two 2D flow domains (i.e., an axisymmetric annulus of the turbine space for meridional flow analysis and cascades at different sections from hub to shroud for blade-to-blade analysis). By using the low fidelity analysis, runner blade design parameters have been adequately varied in order to obtain a population of different promising runner blade designs. Performances of these promising designs are evaluated, and the obtained results are thoroughly analysed through the response surface analysis. An optimized hydrodynamic performance design of the runner is obtained for the target values of responses (here, swirl velocity at trailing edge of the runner (Cu2) and stagnation pressure at trailing edge of the runner (P02/rho)) at different sections from hub to shroud by determining the design parameters of blade profiles at different sections. The adopted multi-fidelity CFD approach is found very effective and has the potential to yield reasonably accurate hydraulic designs of the Francis turbine in considerably lesser time and cost.