Calcul du champ d'écoulement dans une turbine Kaplan et calcul des contraintes dans les pales

Calculation of the flow field in a Kaplan turbine and of the stresses in the blades

E.D.F. - D.E.R. Chatou

Abstract

It was planned to study two aspects of a KAPLAN-type hydraulic turbine: - a hydrodynamic study to determine the characteristics of the flow, - a mechanical study to check blade strength. The flow calculation was made by a quasi-three-dimensional method. (1) The fluid was incompressible and non-viscous ; the flow was stationary ; the calculation surfaces were axisymetrical. Matrix methods based on diagrams of finite differences were used both on the meridian surface and on the blade-toblade surfaces. The coupling was initiated by a meridian calculation and after the ca1culations on five blade-to-blade surfaces the average current lines permited the definition of a new meridian surface. The theoretical and experimental values for the flow characteristics matched well, in the middle of the water-vein, for the axial and tangential velocities upstream of the runner. Downstream of the runner, the axial-velocity curves matched in the middle of the water-vein but the tangential velocity curves differed slightly though they had the same pattern. Differences appeared at the hub and the casing both upstream and downstream because the viscosity effects were not taken into account in the calculation. The distributions of static pressure on the blade systems were introduced into the calculation of stresses. This calculation was made using a finite-elements code, the material being assumed to be homogeneous and elastic in this case. The forces taken into account were : the pressure load, the centrifugal force, and the weight of the blade itse1f. The results of these calcu1ations were compared with the experimental values obtained by the Hydraulic Production Department firstly on a blade under actual operating conditions and secondly on a real blade subjected to forces produced by three jacks. Comparison of the theoretical and experirnental results shows a good match for the distribution of radial stresses. However a difference appears between the experirnental and theoretical distributions of circumferential stresses. This difference is probably associated with that found for the circumferential velocities. The results obtained from this study are eneouraging : they show that it is possible to couple up calculation of the flow and ca1culation of the stresses in present-day hydraulic machinery. The comparison between calculation and experirnental concerning the flow characteristics however emphasies the need to take account of the boundary layers and losses in the calculation.