A proposed model is introduced for predicting the performance characteristics of an inward flow hydraulic turbine at design and off-design conditions. The model simulates the flow through the turbine runner based on fundamental principles. The incidence loss at the runner inlet, which commonly exists under off-design conditions is taken into account for both positive and negative incidence angles. The runner internal loss and the draft tube loss, which exist even under design conditions are taken into consideration through the use of simple and reasonable empirical expressions. The model is developed for studying the effect of the operating and the geometric parameters on the turbine performance under design and off-design conditions. The energy losses at the runner entrance due to incidence and that occur at the runner exit are minimized. An alternative optimization method is adopted to obtain the best possible efficiency of the turbine. Moreover, new charts are obtained and can be used for maximizing the efficiency of the radial turbine at different operating conditions. The obtained results from the proposed model show an acceptable agreement with the available published experimental and theoretical data.

A theoretical model is developed for the effect of the operating parameters and the geometric parameters on the Kaplan turbine performance under design and off-design conditions. In the theoretical model, the incidence loss at the runner inlet that exists under off-design conditions for both positive and negative incidence angles is taken into account. The runner internal loss and the draft tube loss, which exist even under design conditions, are also taken into consideration through the use of simple and reasonable empirical expressions. The experimental works were carried out to validate the theoretical results. An optimization technique is adopted to obtain the operating parameters that achieve the best possible efficiency of a Kaplan turbine. A chart is deduced for detecting the suitable values of the operating parameters that achieve efficiency higher than 88% for different geometric parameters of the axial flow turbine, constant runner inlet blade angle. Comparisons of the obtained results with the present experimental and available published works show an acceptable agreement