Modélisation quasi-tridimensionnelle des écoulements dans les turbomachines hydrauliques

Quasi three-dimensinal flows in hydraulic turbomachines

Société Neyrpic, Grenoble

Abstract

In this paper the three-dimensional flow of a perfect, incompressible fluid through the rotor of a turbomachine is studied with a method using two-dimensional flows: * meridional flow * blade-to-blade flow We first mention the equations for the three-dimensional case. We then explain the assumptions required to establish the equations of two two-dimensional flows. (In order to be two-dimensional the meridional flow must be axisymetrical). Meridional flow : In order to obtain an evolution of the fluid energy level inside the rotor, it is necessary to introduce a non-conservative field of force F, normal to W. The orthogonalit of F to W ensures conservation of the relative energy Erel in the rotor along the path of a particle. Finally, the meridonal flow equations become: [see formula (a) in PDF] [see formula (b) in PDF] were t is a blokage factor. It is to be noted that these equations are written in an orthognal curvilinear system (v, s, u). Blade-to-blade flow. The base flow equations on a surface of revolution are made out from the irrotationality of the flow on this surface and from continuity: [see formula (c) in PDF] [see formula (d) in PDF] Db Iterative resolution technique Equation (b) shows that the calculation of meridional flow necessitates knowledge of the distribution of rV0 over the whole field inside the meridian contour studied. This distribution is given by the blade-to-blade calculation. Similarly, the blade cascade ca1culation requires knowledge of the axisymetrical surface and the fonction Db. These data are the result of the meridional calculation. The iterative process is stopped when two successive flows are deemed to be sufficiently close. Conclusion Figure 4 (or 7) gives as example the result of a meridional flow ca1culation which allows for the presence of the distributeur and the runner. Probe tests (figure 5, 8) may be compared to the theorical ca1culation. Actually good results are obtained with this flow model.