Existing data on the condensation of steam and moist air in supersonic nozzles are compared with predictions based on nucleation and drop-growth theory. It is concluded that, if the surface tension is assumed independent of curvature, and the classical liquid-drop theory (based on a stationary liquid drop) is used, the theory is in general agreement with the data. The effects of uncertainties in cluster surface energy and also of the large corrections to nucleation theory due to the ‘gasification’ concept are examined. The gasification correction is in accord with experimental data only if the surface tension is considered to rise significantly with curvature. In neither case can the Tolman or Kirkwood–Buff equations be supported. A review of existing data shows that there is some question as to the appropriate value of the condensation coefficient but this is of little consequence as long as the accommodation coefficient for the liquid–vapour surface is taken to be unity. The usefulness of the nozzle experiments for testing the validity of nucleation theory is demonstrated.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112066000284

Condensation of water vapour during supersonic expansion in nozzles

This paper reviews important advances in understanding and predicting the behavior of scramjet combustion systems since the classic article published in this series by Antonio Fed (1973). The review focuses on basic fluid phenomena and is divided into three distinct sections. The first briefly describes progress that has been made in the design and demonstration of practical scramjets around the world, especially in the US, the FSU, France, and Germany. The second provides a contemporary exposition of the aerothermodynamics of the dual-mode ramjetkcramjet combustion system, accounting for the role of the isolator in preventing unstart from either thermal choking or flow separation due to heat release. The third part summarizes the current state of knowledge regarding fuel- air mixing in dual-mode ramjetkcramjet combustors, especially the potential of axial vorticity to increase mixing effectiveness over that of lateral vorticity.

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Fluid Phenomena in Scramjet Combustion Systems

The critical supersaturations for the homogeneous nucleation of ethanol, methanol, hexane, and water were experimentally determined in the temperature range 235° to 295°K using a thermal diffusion cloud chamber. The design, construction, and operation of the chamber are described. A computer solution of the heat and mass flux equations determines the variation of pressure and temperature as a function of chamber height. The determination of the experimental critical supersaturation from chamber conditions is described and a comparison made with the values calculated from the Becker‐Doering, Volmer, Zeldovich equation. Good agreement (usually within 5%) is obtained for ethanol, methanol, and hexane over a 60°K temperature range. Experimental difficulties limited the water data to a temperature range less than 15°K and agreement to within 15%.

Diffusion Cloud‐Chamber Investigation of Homogeneous Nucleation

The temperature variation of the critical supersaturation for water vapor has been measured using a diffusion cloud chamber. By attaching a layer of glass wool to the upper plate of the chamber, the persistent refusal (in previous experiments) of water to wet this plate has been overcome. As a result, for the first time measurements without appreciable scatter have been achieved for water vapor. The resulting temperature dependence agrees reasonably well with that predicted by the classical Becker‐Doering‐Zeldovitch theory, while the experimental curve is shifted by approximately 8% from the classical prediction.

/pdf/investigation-of-the-homogeneous-nucleation-of-water-vapor-g29dai5xv3.pdf

Investigation of the homogeneous nucleation of water vapor using a diffusion cloud chamber

Steady two-dimensional flow of vapor/carrier gas mixtures (moist air) with nonequilibrium condensation is investigated in theory and experiment. Aside from Laval nozzles, transonic flow over airfoils at M<x ^ 1 is considered. The numerical calculation is based on the Euler equation linked with the classical theory of homogeneous nucleation and droplet growth using a new diabatic, time-dependent, explicit, finite volume method. By means of this model, the effects of energy supply in local supersonic flow over airfoils are investigated including a detailed analysis of the two-dimensional structure in the diabatic case. The variation of the pressure drag coefficient due to the heating is the sum of the following connected processes: the reduction of the wave drag in the local supersonic area producing a higher Mach number behind the shock, the shock shifting, and the pressure increase in the rear section of an airfoil due to evaporation. Both airfoil series investigated, circular arc and NACA-0012, show the same tendency concerning the shifting of the normal shock. But the pressure drag coefficients vary in opposite directions with different supply conditions.

Transonic flow around airfoils with relaxation and energy supply by homogeneous condensation

Publisher Summary In an isentropic expansion of a vapor mixture, the entropy of individual components is not necessarily constant In an expansion of moist air, the presence of water vapor may be neglected until condensation occurs The relative humidity of moist air during an expansion in a supersonic nozzle increases rapidly with increasing Mach number Saturation—with respect to equilibrium conditions—is reached for all normal humidities ahead of a nozzle throat The shocklike disturbances and pressure nonuniformities, which are seen near the throat of a supersonic nozzle operated with moist air, are because of the condensation of the water vapor and the attendant heat release in the flow Actual condensation is nearly always observed at supersonic speeds, which demonstrates that before condensing, the water vapor is in a highly supersaturated state Finally, it is apparent that the prediction of condensation effects in nozzles operated with moist air is a subject for kinetic theory However, once the condensation environment is known, thermodynamic and fluid dynamic considerations will be applicable

P.P. Wegener

Papers

Condensation in Supersonic and Hypersonic Wind Tunnels