Écoulement dans une turbine Kaplan : comparaison entre calcul théorique, mesures de vitesse et observations de cavitation

Flow field analysis in Kaplan turbine: comparison between theoretical calculations, velocity measurments and cavitation observations

¹ Hydroat, Milan
² Istituto di Macchine de l'Université de Gènes

Abstract

Experimental and theoretical results of the flow field analysis in a medium specific speed Kaplan turbine model are presented. The five analysed operating points which have been obtained with the two runner blade openings of maximum efficiency and maximum prototype power are shown in figure 1. The experimental analysis consists of velocity and total pressure measurements by means of bidirectional probes in three sections upstream and one downstream of the runner (Fig. 2), and of observations and photos of the cavitated zones on the blade surfaces and in the blade channels for different values of the σu cavitation coefficient. The quasi-threedimensional analysis of the flow field included between the guide vane inlet and section 4 has been carried out utilizing for the meridional calculation a computer program based on the method of fixed projection lines [3] and for the blade-to-blade calculation a program based on the method of integral equations [4]. The results of the meridional calculation have been compared with the experirnental results of the four measuring sections for the five operating points. As an example, the comparison relevant to point D is reported in figure 3. In the upstream stations, for all operating points, the velocity percentile differences do not reach 10 % and the differences of the β angle are not larger than 60 near the hub and 20 at the tip. In the downstream station the maximum difference of the β angles is less than 2. At point D blade-to-blade calculations have been performed assigning both the theoretical and experimental upstream velocity distributions in order to evidence the effects of the errors of the upstream velocity on the blade pressure distribution (Fig. 4). The downstream tangential absolute velocity (Fig. 5) and total pressure distributions (Fig. 6) indicate that a regular distribution of work extraction along the blade height has been obtained with a downstream tangential velocity distribution which is favourable from the point of view of the outlet kinetic energy losses and of the losses in the draft tube. The computed distribution of the Cp coefficient drawn on the front view of the blade for all the operating points (Fig. 7 to 11), allows to visualize irnmediately the theoretical cavitation zone for each value of σu, In fact, the static pressure coefficient Cp has been defined in such a way (see the definition in the text) that Cp is equal to - σu when the local static pressure reaches the vapour pressure. An exact prediction of the extension of the cavitating regions cannot be obtained because the method does not take into account the effect of the vapour bubbles on the pressure distribution, but a general nearly good agreement of the calculations with the cavitation configurations has been found. Two different types of leading edge cavitation have been observed : a burst type near the hub, characterized by a very strong pressure gradient (Fig. 12, fc = 0.15), and a fixed type connected with a weaker pressure gradient at the tip (Fig. 12, fc = 0.85).