Boundary Element Method In The AnalysisOf The Hydrodynamic Assymetry At The FlowRound Reversible Axial Cascades

Abstract

In order to obtain superior performances for reversible axial turbomachines, it is important to know the behaviour of the axial profile cascades in direct and reverse flow in different operation conditions. The paper presents an anlysis of the ideal and incompressible fluid motion round these axial cascades in direct and reverse flow, using BEM. The problem solution was obtained by solving in a series of some mixed boundary-value problems for the Laplace equation in the stream function using linear elements for the domain boundary discretization. A special problem was the imposing of the Kutta-Joukovski-Carafoli condition in the trailing edge zone respectively leading edge zone of the profiles and its influence upon the velocity and pressure field on the profile boundary. In the end, the hydrodynamic assymetry was defined and some problems resulting from it were presented. The method was applied to a NACA profile cascade with pump cascade start. INTRODUCTION The solving of the direct problem of the reversible axial profile cascades means the determination of the motion with circulation around those cascades of the ideal and incompressible fluid both for the direct flow and for the reverse flow, the cascade geometry and the cinematic conditions for an accepted section as being an entrance, being given. The determination of these problems requires a supplementary boundary condition the Kutta-Joukovski-Carafoli condition namely the null velocity in the posterior stagnation point from the profile boundary. Transactions on Modelling and Simulation vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X 110 Boundary Elements THE TYPICAL ANALYSIS DOMAIN. THE BOUNDARY VALUE PROBLEM FORMULATION The analysis domain is defined by the boundaries of the two neighbouring profiles disposed at step t, and the boundary conditions on the entrance section, respectively exit section, will be considered at t/2 from the leading front respectively from the trailig front of the cascade; (Fig 1); Anton and Carte 1 1 1 . Fig.l. The analysis domain for a pump axial cascade If 012 is the fundamental plane of the motion, the potential flow condition of the ideal and incompressible fluid leads to the Laplace equation for the stream function and the velocity field is given by # = £..11),. . ijTfj The periodicity of the velocity field imposes for the l|J function Ip (x , %2 + kt) = ip (Xj, x%) + kt k (1) (2) (3) % (Xj, X, + kt) =tp,. (Xj, X,) (4) Thus we have to solve a mixt boundary-value problem with periodicity for equation (1) with the following boundary conditions on the F boundary of the Q domain for the direct flow Transactions on Modelling and Simulation vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X Boundary Elements on GF on O'C ill