Unsteady operation of the Francis turbine

Increasing interconnection of individual power systems into major grids has imposed more stringent quality assurance requirements on the modelling of hydroelectric generating plant. This has provided the impetus for the present study in which existing industry models used to predict the transient behaviour of the Francis-turbine plants are reviewed. Quasi-steady flow models for single- and multiple-turbine plants developed in MATLAB Simulink are validated against field test results collected at Hydro Tasmania's Mackintosh and Trevallyn power stations. Nonlinear representation of the Francis-turbine characteristics, detailed calculation of the hydraulic model parameters, and inclusion of the hydraulic coupling effects for multiple-machine station are found to significantly improve the accuracy of predictions for transient operation. However, there remains a noticeable phase lag between measured and simulated power outputs that increases in magnitude with guide vane oscillation frequency. The convective lag effect in flow establishment through the Francis-turbine draft tube is suspected as a major contributor to this discrepancy, which is likely to be more important for hydro power stations with low operating head and short waterway conduits. To further investigate these effects, the steady flow in a typical Francis-turbine draft tube without swirl is analysed computationally using the commercial finite volume code ANSYS CFX. Experimental studies of a scale model draft tube using air as the working medium are conducted to validate and optimise the numerical simulation. Surprisingly, numerical simulations with a standard k-˜í¬µ turbulence model are found to better match experimental results than the steady-flow predictions of more advanced turbulence models. The streamwise pressure force on the draft tube is identified as a quantity not properly accounted for in current industry models of hydro power plant operation. Transient flow effects in the model draft tube following a sudden change in discharge are studied computationally using the grid resolution and turbulence model chosen for the steady-flow analysis. Results are compared with unsteady pressure and thermal anemometry measurements. The three-dimensional numerical analysis is shown to predict a longer response time than the one-dimensional hydraulic model currently used as the power industry standard. Convective lag effects and fluctuations in the draft tube pressure loss coefficient are shown to largely explain the remaining discrepancies in current quasi-steady predictions of transient hydro power plant operation.