This paper proposes an original approach to investigate the influence of the geometry of Francis turbines draft tube on pressure fluctuations and energy losses in off-design conditions. It is based on Design of Experiments (DOE) of the draft tube geometry and steady/unsteady Computational Fluid Dynamics (CFD) simulations of the draft tube internal flow. The test case is a Francis turbine unit of specific speed Ns=120 m-kW which is required to operate continuously in off-design conditions, either with 45% (part-load) or 110% (full-load) of the design flow rate. Nine different draft tube geometries featuring a different set of geometrical parameters are first defined by an orthogonal array-based DOE approach. For each of them, unsteady and steady CFD simulations of the internal flow from guide vane to draft tube outlet are performed at part-load and full-load conditions, respectively. The influence of each geometrical parameter on both the flow instability and resulting pressure pulsations, as well as on energy losses in the draft tube, are investigated by applying an Analysis of Means (ANOM) to the numerical results. The whole methodology enables the identification of a set of geometrical parameters minimizing the pressure fluctuations occurring in part-load conditions as well as the energy losses in both full-load and part-load conditions while maintaining the requested pressure recovery. Finally, the results of the CFD simulations with the final draft tube geometry are compared with the results estimated by the ANOM, which demonstrates that the proposed methodology also enables a rough preliminary estimation of the draft tube losses and pressure fluctuations amplitude.
Numerical investigation of inter‐blade cavitation vortex for a Francis turbine at part load conditions