Flow in the Simplified Draft Tube of a Francis Turbine Operating at Partial Load-Part I: Simulation of the Vortex Rope

Numerical simulations and analysis of the vortex rope formation in a simplified draft tube of a model Francis turbine are carried out in this paper, which is the first part of a two-paper series. The emphasis of this part is on the simulation and investigation of flow using different turbulence closure models. Two part-load operating conditions with same head and different flow rates (91% and 70% of the best efficiency point (BEP) flow rate) are considered. Steady and unsteady simulations are carried out for axisymmetric and three-dimensional grid in a simplified axisymmetric geometry, and results are compared with experimental data. It is seen that steady simulations with Reynolds-averaged Navier-Stokes (RANS) models cannot resolve the vortex rope and give identical symmetric results for both the axisymmetric and three-dimensional flow geometries. These RANS simulations underpredict the axial velocity (by at least 14%) and turbulent kinetic energy (by at least 40%) near the center of the draft tube, even quite close to the design condition. Moving farther from the design point, models fail in predicting the correct levels of the axial velocity in the draft tube. Unsteady simulations are performed using unsteady RANS (URANS) and detached eddy simulation (DES) turbulence closure approaches. URANS models cannot capture the self-induced unsteadiness of the vortex rope and give steady solutions while DES model gives sufficient unsteady results. Using the proper unsteady model, i.e., DES, the overall shape of the vortex rope is correctly predicted and the calculated vortex rope frequency differs only 6% from experimental data. It is confirmed that the vortex rope is formed due to the roll-up of the shear layer at the interface between the low-velocity inner region created by the wake of the crown cone and highly swirling outer flow.