Calcul aux éléments finis de l'écoulement aube à aube dans les pompes

Finite-element calculation of blade-to-blade flow in pumps

Istituto di Energetica, Florence

Abstract

Inviscid flow numerical calculations offer a valid tool for the analysis and design of turbomachines : usually, the coupling of two sets of bidimensional calculations, a first one on the meridional surface (S2) and a second one on the blade-toblade (S1) surface, is used to obtain a quasi-three-dimensional simulation of the flow in the turbomachine. The second type of calculation (S1 surface) is particularly important, as it gives important informations of the velocity and pressure field inside the bladed channel, and it can lead, through the use of an adequate closure condition, to a satisfactory calculation of the outlet angle (which is actually determined by the true, viscous flow). The numerical difficulties which are encountered in such a calculation range from the generation of a satisfactory mesh to the treatment of periodic flow boundaries and to the non-linearity of the flow equations : this last is particularly relevant if the flow surface is three-dimensional, i.e. in mixed or radial flow impellers of the type common in pumps. The proposed numerical analysis is based on the solution of the flow equations on an axisimmetric S1 surface in the coordinates m (meridional abscissa)-θ (tangential angular abscissa), thus obtaining a relevant uniformity of approach with respect to the most widespread codes (Katsanis etc.). The discretization of the flow surface is done by means of three node Finite Elements, after a quasi-variational reformulation of the problem. The input is simplified by a generalized use of spline extrapolation techniques, which allow satisfactory discretizations to be obtained starting by a limited set of impeller geometric data. The results of the calculation are presented for two testcases a first one, proposed by SHF, on which experimental data will be avaiIable within a short time, and a second one, whose results in terms of theoretical calculations and experiments are available in the literature.