Condensation shocks in nozzle flows

Abstract

Supersonic nozzle flows of a condensable vapour are considered in the high activation limit for homogeneous nucleation. Conditions are determined under which the final collapse of the supersaturated state is described by a condensation shock. It is shown that the shock zone is associated with droplet growth: droplet production occurs in a thin layer upstream of the growth region. Some new scaling laws are obtained for the structure of the production layer.

The mathematical theory of thermal choking in nozzle flows

“…This model can be approximately realized for flows where 0 < dA/dx ,~ 1 for x > xk. In fact it can be shown that this model is precisely what is achieved in the differently scaled droplet growth zones of the asymptotic theories of Blythe and Shih (1976) and Clarke and Delale (1986). In this case the function A, denoted herein by A3(g', x), and the critical amount of heat q*, denoted herein by * ' q3 (g, x), are given by R(g', x) is strictly increasing, thereby q*(g', x) and q* (g', x) j = 2, 3, 4 are strictly increasing whereas q*(g', x) is a constant.…”

“…In spite of this fact Hill (1966) has carried out a detailed analysis of the physical mechanisms underlying the nature of the rate processes required for the construction of the nonequilibrium condensation rate equation. Asymptotic theories of the nonequilibrium condensation rate equation for nozzle flows (with different ordering of the double-limit process corresponding to large nucleation time followed by small droplet growth time) that yield the structure of condensation zones are already available from the work of Blythe and Shih (1976) and Clarke and Delale (1986). Results of experiments conducted in nozzle flows during the expansion of moist air and pure steam which reveal some general features about the physics of nonequilibrium condensation can also be found in the work of Wegener and Mack (1958), Pouring (1965), Barschdorff (1967), Wegener (1969, The system of equations (1)-(4) can then be solved for the flow velocity u in functional form as…”

“…Before proceeding any further, we first discuss the nature of flow in the interval Xs < x <-Xk. From the asymptotic theories of condensation [Blythe and Shih (1976) and Clarke and Delale (1986)], one can easily show that in the interval x~ <-x < Xk the condensate mass fraction g' is exponentially small everywhere except for a thin zone near Xk. In both theories in the interval Xs < x < Xk the nearly frozen…”

Analysis of Constant-Rate Aerosol Reactors

“…It is noted that there have been previous asymptotic studies of homogeneous nucleation for other situations. For example, Blythe and Shih (1976) studied condensation shocks in nozzle flows, whereas Feder et al (1966) examined nucleation and growth of droplets in an expansion chamber. The constant-rate aerosol reactor appears not to have been analyzed in this manner.…”

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

“…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.…”