Analyse théorique-expérimentale de l'écoulement réel dans les pompes assoradiales

Abstract

The paper presents a numerical method for non-isoentropic through flow calculation in centrifugal and mixed-flow pump impellers. The analysis of incompressible fluid motion is done following Wu's general theory on 82 type surface. In particular, one of the motion equations is substituted by the geometrical condition for the flow to follow the prescribed 82 surface. Besides the flow is assumed to take place in presence of a dissipative force field locally opposite to the relative velocity vector and tangent to the stream line. Combining the basic equations of continuity, entropy production, energy and motion, defining the local geometry of the stream surface S2 (angles lambda and mu) and the stream function ψ it is possible to derive the final flow equation of the type δ2ψ/δr2 + δ2ψ/δz2 = q1 +qE ) (7) where q1 depends on velocity components and on S2 geometry and qE depends on the entropy production inside the fluid flow. The equation of stream surface is obtained starting from the blade geometry and considering its distortion due to the slip effect. For the expression of entropy gradient a local loss coefficient n ψ is defined as a ratio between the rise of total pressure in the real flow conditions and the rise of total pressure in isoentropic flow. In this way it is possible to evaluate the therm qE if a preceding isoentropic flow calculation is available. The computer numerical model for the through flow calculation perforrns the following steps : a) defmition of 82 geometry starting from the impeller geometric data and considering the slip effect. b) Iterative solution of equation (7) in the isoentropic case (qE = 0) c) Evaluation of entropy field. d) Iterative solution of equation (7) in its complete form. In the step a) three-dimensional parametric splines are used for surface representation. The discretization of the problem is done using finite element technique with isoparametric, rectangular elements (8 nodes). The solution of non-linear equation (7) is performed using Galerkin's weighted residual method. The paper finally shows an example of through flow calculation in a mixed-flow pump for the design conditions and for two off-design working points. The computed results are compared with experimental measurements.