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

The stability limit of stationary normal shock waves in supercritical nozzl e flows with homogeneous condensation is investigated by the singularity th eory of the quasi-one-dimensional steady-state differential equations of mo tion. In this case it is shown that a catastrophic change in the phase port raits of the flow variables, where the spiral point turns into a nodal poin t, occurs when the initial relative humidity exceeds a critical value, resu lting in the alteration of the quasi-one-dimensional steady-state condensat ion structures. In particular, a criterion for the limit of stability, base d 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 de rived for fixed nozzle geometry keeping appropriate reservoir conditions fi xed in the same approximation. A comparison of the values of the critical i nitial relative humidity, calculated by this correlation, shows excellent a greement with those of experiments and/or numerical simulations for moist a ir expansions in various slender nozzles under different reservoir conditio ns. (C) 2001 American Institute of Physics.