A comparison of nucleation theories by the asymptotic solution of condensing nozzle flows

The classical and Dillmann-Meier nucleation rates are compared in transonic nozzle flows of moist air under atmospheric supply conditions using the asymptotic solution of Delale, Schnerr and Zierep. The comparison is made in slender nozzles using two distinct expressions for the poorly known surface tension, one fitted to the experiments of Peters and Paikert by the classical theory and the other extrapolated from room temperatures to the range of temperatures investigated. The droplet growth law is fixed by the Hertz-Knudsen formula. It is shown that the Dillmann-Meier theory predicts higher nucleation rates than the classical theory together with a delay of the onset of condensation when either of the surface tension expressions is employed

Prandtl-Meyer flows with homogeneous condensation. Part 1. Subcritical flows

Prandtl-Meyer flows with heat addition from homogeneous condensation not exceeding a critical value (subcritical hows) are investigated by an asymptotic method in the double limit of a large nucleation time followed by a small droplet growth time. The physically distinct condensation zones, with detailed analytical structure, are displayed along streamlines and the flow field in each zone is determined utilizing the asymptotic solution of the rate equation along streamlines. In particular the nucleation wave front, which corresponds to states of maximum nucleation along streamlines, is accurately located independently of the particular condensation model employed. Results obtained using the classical nucleation equation together with the Hertz-Knudsen droplet growth law show, despite qualitative agreement, considerable differences between the nucleation wave fronts and measured onset conditions for the experiments of Smith (1971), because of intersecting characteristics in the heat addition zones. This shows the necessity of including an embedded oblique shock wave in the expansion fan of corner expansion flows for the cases investigated

A bubble fission model for collapsing cavitation bubbles

A bubble fission model that takes into account energy dissipation during violent collapses of cavitation bubbles is introduced by assuming volume conservation and continuity of the gas pressure during instantaneous breakup, invoking either Rayleigh-Taylor instability or high speed microjet formation. In particular, a modified Rayleigh-Plesset equation is derived for the volumetric motion of the fission fragments in rebound. Results obtained under a pressure signal typical for cavitation bubbles confirm the scaling law of Brennen [C. E. Brennen, "Fission of collapsing cavitation bubbles," J. Fluid Mech. 472, 153 (2002)] and the observations in experiments. (C) 2004 American Institute of Physics

Theory of embedded shock formation in rarefaction waves by homogeneous condensation

A theory of embedded shock formation by homogeneous condensation in the centered rarefaction wave of a shock tube is presented. The necessary and sufficient conditions for the existence of such embedded shock waves are exhibited in a parabolic approximation to the family of intersecting characteristics. In particular the coordinates of the embedded shock origin are derived explicitly by the construction of the envelope of the family. Predictions of the theory, including an estimate for the average embedded shock speed, are substantiated by comparison of the results obtained employing the classical nucleation theory and Hertz-Knudsen droplet growth law for the condensation model with those of typical experiments showing visualized shocks formed by homogeneous condensation during the expansion of water vapor in nitrogen (or air)

Asymptotic solution and numerical simulation of homogeneous condensation in expansion cloud chambers

Asymptotic solution of homogeneous condensation in expansion cloud chambers in different droplett growth regimes Is presented. In particular an exactly solvable droplet growth model ranging between the Hertz-Knudsen and continuum droplet growth laws is introduced. The distinct condensation zones in each droplet growth regime are identified by the asymptotic solution of the condensation rate equation and the results are compared with those of direct numerical simulations using the classical nucleation theory. Excellent qualitative agreement is reached despite some minor quantitative differences in some of the condensation zones arising from the nature of the asymptotic solution in these zones. (C) 1996 American Institute of Physics

Condensation Discontinuities and Condensation Induced Shock Waves

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