Predição teórica das características hidrodinâmicas de turbinas Francis

Abstract

This work presents a methodology for the performance prediction of Francis turbine based on mean streamline analysis. The performance prediction takes into account only the overall dimensions of the Francis turbine and also the losses correlations for each main component of the turbine. There is no necessity of take into account any operation parameter in the maximum efficiency point to accomplish such prediction. The performance prediction is realized for a wide range of normal operation of the Francis turbine and not only for the design point. Various empirical losses correlations that are reported in the technical literature are presented. The analysis of the losses takes into account different roughnesses of spiral case, stay vane, wicket gate, runner, draft tube, labyrinths and side rooms between the runner and fixed components of the turbine. Some empirical correlations refer to a same type of loss, which are tested and evaluated. From the comparison among these correlations, it is verified that they can improve substantially the performance prediction, not only at the design point as at the off-design point. The methodology also allows predict the effect of the roughness as well as of the Reynolds number on the different efficiencies of the Francis turbine. A computational routine was developed by means of modules and functions allowing its modification and the inclusion of new losses correlations. In the initial calculations, some operation parameters are not known or they depend on parameters that should still be calculated in posterior calculations. A procedure is presented to illustrate all sequences of calculations made by the computational routine to obtain the point of maximum efficiency vi and all necessary parameters for the performance prediction in a wide range of Francis turbine operation. Several theoretical results are presented for some models of losses and for different roughnesses of the Francis turbine components. These results allow evaluate the gain in the efficiency of the Francis turbine when the surface roughness is reduced and which components the efforts should be concentrated for the improvement of the superficial finish. This effect is expected to be dependent of the specific rotation of the Francis turbine. The theoretical results are compared with the experimental results obtained for a Francis turbine with nqA = 266 . A good agreement was observed between measured and calculated values for a wide range of Francis turbine operation.