Component Losses in Kaplan Turbines and the Prediction of Efficiency from Model Tests

Abstract

This paper has been written in an attempt to provide an improved scale formula for Kaplan turbines, which has theoretical justification as well as offering reasonable results in practice. A survey is made of all the important water turbine scale formulae since 1909 and their merits are compared. The Ackeret formula is one of the most interesting because it considers the kinetic and friction losses separately, and it is widely used on the Continent. By means of a simplified theory the formula was made to apply to both Francis and Kaplan turbines. It is now shown that the theoretical basis can be improved if the argument is restricted to the Kaplan turbine. A more comprehensive analysis suggests a modified formula offering better agreement with full-scale results and, moreover, a useful guide to efficiency away from the optimum. At optimum efficiency it is suggested that about 70 per cent of the losses are frictional, and therefore affected by Reynolds number, instead of 50 per cent as in the original Ackeret formula. The actual proportion will depend on the design and operating conditions of the machine, but the need for dividing the losses into frictional and kinetic parts and the method of calculating their proportions is demonstrated. The theory also shows that between 0.5 and 1.5 times the normal flow the proportion of runner to total losses may decrease from 90 to 50 per cent, and due allowance should be made for this when scaling-up performance away from the optimum. The value of the theory and the formula can be assessed only after comparison with reliable experimental data, but in the light of the limited evidence quoted here it seems worthy of further examination.