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Rotating compressible flows with internal sources and sinks

An analysis is presented that describes a model of the flow field of a rotating compressible fluid in a cylinder with internal sources or sinks of mass, momentum or energy, A solution of the mathematical model is obtained using an expansion in eigenfunctions of the corresponding homogeneous equation. The internal sources or sinks produce countercurrent flows analogous to flows generated by boundary conditions in the classical analysis of the problem. The application of this model to the flow driven by a feed stream or a scoop is discussed. Some sample calculations are presented that illustrate the countercurrent flow produced by sources of mass, the three components of momentum, energy and a mass source/sink combination. Calculations simulating feed introduction and a tails-removal scoop have been performed and the fluid-dynamics solutions have been used to calculate the optimum separative performance of the example centrifuge.