Application du concept d'echelles multiples a l'ecoulement dans une turbomachine axiale

An asymptotic theory to the flow in an axial compressor is presented with the aim of devising a coupling process between the so-called meridian through flow and the flow around cascades. The small parameter ? is the inverse of the (supposed ? 1) number of blades per row and/or number of stages. As a matter of fact, the cascade flow is treated as a small perturbation of the through flow and has to be computed, locally, as the two dimensional unsteady flow around an array of couples of cascades alternately fixed and in motion. The array is constructed by developing on a plane the section of the compressor by a circular cylinder, and continuing by periodicity, the couple of cascades, so obtained, at each location. The coupling between through flow and cascade flow is part of the analysis. It occurs by the way that the equations of through flow are obtained through an averaging process, completed on a domain of periodicity of the array of cascades, while the through flow appears, locally, as an unperturbed flow for the linearized problem defining the cascade flow. The tridimensional nature of the complete flow is built in by the coupling itself, as is visualized by the occurence of source terms in each of the two sets of equations describing through flow and cascade flow. This paper is aimed at giving a preliminary answer to the question of how to devise an, as rational as possible, way of inscribing the familiar scheme of cascade flow within the computation of a mean through flow. The main output is that the concept of cascade flow should be revisited and reassessed as one of unsteady flow around an array of cascades.