Analytical method for frictional flows in a Pelton turbine

Abstract

The frictional flow in the rotating buckets of a Pelton turbine has been considered analytically for two special cases: the lateral flow along the path of constant circumferential velocity and the longitudinal flow with varying circumferential velocity. For the first flow form, the additional concept regarding the flow losses and dissipation in the flow has been accounted for to complete the existing flow friction theorem. For the longitudinal flow in the rotating buckets, detailed analyses have been performed to confirm the influences of centrifugal, Coriolis, frictional, and inertia forces on the power exchange between water and rotating buckets. Because the flow of this form along the bucket surface could not be integrated mathematically, the calculation algorithm by means of the spreadsheet method has been presented. For both flow forms, the flow friction has again been confirmed to be most effective in affecting the hydraulic efficiency. Because the flow mechanism in the rotating buckets of a Pelton turbine has been extensively worked out, direct calculations of combined flows of other forms become highly available, for instance in using the spreadsheet, and can be considered at least as a best available alternative to the computational fluid dynamics.