On the stability of stationary shock waves in nozzle flows with homogeneous condensation

C.F. Delale, G. Lamanna, M.E.H. Dongen, van

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    Abstract

    The stability limit of stationary normal shock waves in supercritical nozzle flows with homogeneous condensation is investigated by the singularity theory of the quasi-one-dimensional steady-state differential equations of motion. In this case it is shown that a catastrophic change in the phase portraits of the flow variables, where the spiral point turns into a nodal point, occurs when the initial relative humidity exceeds a critical value, resulting in the alteration of the quasi-one-dimensional steady-state condensation structures. In particular, a criterion for the limit of stability, based on the break-up of structural stability of the steady equations of motion in the quasi-one-dimensional approximation, is established by variational analysis and a correlation for the critical initial relative humidity is derived for fixed nozzle geometry keeping appropriate reservoir conditions fixed in the same approximation. A comparison of the values of the critical initial relative humidity, calculated by this correlation, shows excellent agreement with those of experiments and/or numerical simulations for moist air expansions in various slender nozzles under different reservoir conditions.
    Original languageEnglish
    Pages (from-to)2706-2719
    JournalPhysics of Fluids
    Volume13
    Issue number9
    DOIs
    Publication statusPublished - 2001

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