Hydraulic power of slow-rotating waterwheels: a novel analytical approximation

Abstract

Slow-rotating waterwheels are mechanical devices of great historical relevance since they provided power to ancient communities for shifting from a subsistence to a market-oriented economy. Technical studies of these antecessors of hydraulic turbines mainly rely on basic principles that do not take into account the blade-to-blade distance and, therefore, the loss of energy from spillage (parts of the jet flow that do not interact with the moving blades). These effects are included in this article in a novel analytical approximation based on a sequential frame methodology. We apply this extended analytical expression to the analysis of three different sets of parameters referred to a laboratory-scale horizontal waterwheel. Results are compared with those obtained experimentally and, also, with computational fluid dynamics simulations. In contrast to the classical expression that clearly fails to explain the waterwheel behaviour when few blades are employed, our new analytical approximation remarkably agrees with both simulations and experimental data.