Application of the Harmonic Balance method for regime change prediction using Francis-99 test case

Abstract

An efficient method for predicting the turbine start-up and shut-down flow parameters is presented in this paper. Due to start-up or shut-down usually lasting a large number of periods, simulations of such processes are highly demanding and long lasting. To alleviate this, a modified Harmonic Balance method is used, thus casting a problem into spectral space and solving start-up and shut-down simultaneously, as a complete period. By doing this, the results are obtained in a fraction of time required by time-accurate simulation. Furthermore, the same approach could be used for any change of regime from operating point OP1 to operating point OP2 and back to OP1. The method is implemented in foam-extend and suitable for solving incompressible turbulent Navier-Stokes equations. Validation is performed on two test cases: a simple 2D pump case for initial validation, followed by a Francis turbine. Francis turbine test case and experimental data are provided by the Francis-99 Workshop. For Francis turbine the power curve is assembled and compared with experiment.