Numerical Study and Theoretical Comparison of Outlet Hole Geometry for a Gravitational Vortex Turbine

The gravitational water vortex turbine is an alternative to renewable energies, it transforms the hydrokinetic energy of the rivers into electric energy and it does not require a reservoir. According to studies carried out, the hydraulic efficiency can increase or decrease according to the turbine geometrical configuration. This paper presents a numerical (CFD) and analytical comparison between conical and cylindrical designs for the outlet. The results show a higher performance for conical geometry than the cylindrical tank. The fluid behavior in CFD and analytical studies presents a tangential velocity increase near to air core and outlet hole (similar behavior). The maximum theoretical power generated was 167 W and 150 W for conical and cylindrical design respectively. The differences between geometries of the outlet holes using CFD and analytical models were 11 and 7%, respectively. However, the closest results to the CFD model had different values of 31 and 29% for conical and cylindrical design, respectively. The furthest result regarding the CFD study was 55%. The principal difference is due to tank geometry, the change in discharge zone, as well as the ratio of diameter tank and outlet hole can increase or decrease the tangential velocity and make a stronger and more stable vortex formation. The theoretical power generated is a good parameter to select the height to place the rotor.