Calculation of the Mixed-Out State in Turbomachine Flows

A systematic and rational methodology for the calculation of an equilibrium state from an initial nonuniform flow field, is presented with particular emphasis on the underlying assumptions and their attendant justifications. The imposed conservation criteria that are used to define a final state from the initial one depend on the coordinate system and flow configuration being analyzed. The imposition of these criteria for flow in parallel-walled annular ducts defines a state of complete (mechanical and thermal) equilibrium, for which radial profiles of the velocity components, static pressure and temperature assume a specific form for a perfect gas. A robust method for solving the system of equations that define the state of complete equilibrium (or mixed-out state) is presented using an efficient algorithm. The procedure is applied to the swirling flow exiting an isolated transonic compressor, and comparisons are made with other available methods of averaging flow fields.