Single arm, centrifugal, water turbine for low head and low flow application : Part 1 – Theory and Design

Abstract

Many parts of sub-Saharan Africa have small streams and rivers that have a potential to produce hydropower on small scale for rural and off-grid applications. However, the high cost of commercially designed micro-hydro turbines limits the exploitation of the available hydropower. Thus any efforts to improve the understanding of the fundamental principles involved in the design, manufacture, and operation of simple micro-hydro turbines that could be constructed from readily available low cost materials and construction methods would be invaluable. This paper presents the fundamental theory and the methodology for design of a single arm centrifugal reaction water turbine that would allow efficient extraction of hydro-power. Continuum mechanics approach was adopted where the design of the turbine was derived from a mathematical model that was based on the balance equations formulated in a rotating control volume. The model showed that the theoretical power output is equivalent to the product of the following: density of water, volume flow rate, angular velocity of the turbine, radial length of the turbine arm and the absolute velocity of water as they exit the turbine. Further, the analysis showed that the theoretical efficiency of the turbine is directly proportional to the ratio of angular acceleration to the gravitational acceleration. The experimental test results of the model turbine are presented in our subsequent work (Part 2).