Effect of a carrier gas on homogeneous condensation in a supersonic nozzle

Abstract

The classical liquid drop theory for condensation was used in a computer solution to determine the effects of a carrier gas on homogeneous condensation. Zinc was used as the condensing vapor with helium, argon, or xenon as carrier gas in a nominal Mach 5 nozzle. It was found that the rate of accumulation of condensate is strongly dependent on the amount of carrier gas and can be rapidly increased by either increasing the mass fraction of carrier gas of low molecular weight or by decreasing the molecular weight of the carrier gas (for a given mass fraction). It was also found that for a change in nozzle angle of a factor of two, the area ratio at which the onset of condensation occurred changed very little. This was also true for a change in nozzle size (throat diameter) for a factor of two. Nomenclature A = nozzle area Cp = specific heat of mixture in the stagnation chamber g = mass fraction of condensed liquid / = nucleation rate k = Boltzman's constant L = latent heat ra = mass rate of flow NA = Advogadro's number p = pressure of the mixture PD = pressure at drop surface pv = partial pressure of the vapor PVS = saturation pressure of the vapor corresponding to T pZo = partial pressure of the vapor in the stagnation chamber pz = partial pressure of the zinc in the expanding mixture p0 = pressure of the mixture in the stagnation chamber r = radius of a liquid drop r* — critical drop radius r' = the integrated value of dr/dx from the saturation point Ru = universal gas constant R* = radius of the throat of the nozzle S = the sum in the equation for gr; denned in Eq. (24) T = the gas temperature TD = the temperature of the droplet Ts = saturation temperature corresponding to pv To = gas temperature in the stagnation chamber u = gas velocity x = distance downstream from the throat Ax = increment in x used in S y = initial mass fraction of the vapor in the stagnation chamber dc = thermal accommodation coefficient of the carrier gas <xv = thermal accommodation coefficient of the vapor 5 = constant in Tolman's equation for cr [Eq. (13)] lie — molecular weight of the carrier gas (Av — molecular weight of the vapor p = total density of the mixture PL = density of the liquid or = surface tension <rm = surface tension of a flat surface d = nozzle half angle £ = a variable defining the point in the nozzle where a given drop was formed