2-D transonic flow with energy supply by homogeneous condensation: Onset condition and 2-D structure of steady Laval nozzle flow

Abstract

Abstract.A generalized form of the similarity law for the condensation onset Mach number of water vapor in air in the transonic and supersonic range for water vapor flow in moist air is derived from well known basic approaches for supersonic nozzles. These statements are confirmed by extensive experimental investigations in Laval nozzles, as well as by results of other authors and computations on the basis of the Euler equation linked with the classical theory of nucleation and droplet growth. In this experimental research priority is given to the qualitative description of the twodimensional condensation processes, and their effects in transonic flows in nozzles of different geometrical configuration (e, g. slightly or well curved). A quantitative discussion of 2-D structures in condensation regions requires the introduction of a characteristic angle along streamlines. It is then directly possible to describe the different types of compression disturbances in supersonic flows with heat addition.

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

“…By correlating the results of all of these experiments for the nozzles S2 and G1 by Eq. ͑56͒ and by utilizing the shock Mach number-initial relative humidity correlation of Schnerr 9 together with the condensation model of Schnerr and Dohrmann, 13 we find, to a good approximation, the result cϭ6.0ϫ10 3…”

“…Surveys of such flows are well documented in the literature. [1][2][3][4] Various investigations [5][6][7][8][9][10][11] have been devoted to nonequilibrium flows with homogeneous condensation in converging-diverging nozzles. In this case the flow in the condensation zones remains steady and supersonic as long as the latent heat release to the flow is below a critical value for a given nozzle geometry and reservoir conditions ͑subcritical flows͒.…”

“…Detailed structure of the condensation zones for both subcritical and supercritical flows can be found in Delale et al 10,11 using an asymptotic predictive method given by Blythe and Shih 7 and Clarke and Delale. 8 Two-dimensional numerical simulations of such flows were given by Schnerr 9 and Schnerr and Dohrmann. 13 If the heat addition to the flow is further increased ͑e.g., by increasing the initial relative humidity keeping appropriate reservoir conditions fixed͒, the flow becomes unsteady and different patterns of periodic flow structures with moving shock waves occur ͑e.g., see Adam and Schnerr 14 ͒.…”

Unsteadiness in Condensing Flow: Dynamics of Internal Flows with Phase Transition and Application to Turbomachinery

“…Delale et al [38] recently derived a mathematical theory including a theoretical condition for the limit of stability of a supercritical shock based on asymptotic approach. process, which is controlled by thermodynamics and therefore triggered by iso-lines or iso-surfaces of constant temperature, and stabilize the flow via the so-called subsonic heating fronts to remain in steady state [39]. To demonstrate this effect, the dynamical behaviour of oscillations in nozzles No.…”

Real gas effects in thermally choked nozzle flows

“…for x > xk where xk denotes the onset of condensation (this point can be located either empirically [12], semi-empirically by similarity analysis [13], numerically [14] or by the asymptotic solution of the condensation rate equation [ 11,15]). We herein assume that heat addition to the flow from condensation occurs in the supersonic region of the nozzle so that xk > 0.…”