Mass transfer cooling of a flat plate placed in a high velocity laminar boundary layer is studied. The binary gas system considered is that of a nitrogen free stream with the injected gas being carbon dioxide. Thermodynamic and transport properties are assumed to be functions of local temperature and concentration. Two parallel analyses are carried out: one assuming that neither the carbon dioxide nor the nitrogen dissociates but both behave as perfect gases even at extremely high temperatures, and the other and major analysis takes into account the influence of dissociation. In this major analysis, the assumption of thermochemical equilibrium is imposed. For temperature levels less than 5000 deg K, which is assumed to be the maximum temperature in the boundary layer, the dissociation of nitrogen is neglected and the equilibrium composition of CO2 is assumed to be CO2, CO, O2, and O. The mole fractions of these four components depend on local temperature only (the pressure is taken to be 1 atm) and are calculated by White, Johnson and Dantzig’s method. This system is then treated as a modified, binary gas model which consists of injected gas “A” (i.e., CO2, CO, O2, and O) and the free stream gas “B” (i.e., N2). The partial differential equations of continuity, momentum, diffusion, and energy are first transformed into total differential equations, then into integral forms which can be solved numerically on an electronic computer. Both constant wall temperature and recovery temperature cases are studied. The Mach numbers covered are 0, 4, 8, and 12; the free-stream temperature is chosen to be 218 deg K; the dimensionless wall temperature Tw = tw/t∞ considered are 2, 4, 6, 10, 15, and 20. For each combination of the boundary conditions, both dissociation and nondissociation cases are calculated. Typical temperature, concentration, and velocity profiles are determined. For the cases where the dimensionless wall temperature is less than 10, no significant difference was found between dissociation and nondissociation cases in the prediction of heat transfer, skin friction, and recovery temperature. At higher temperatures the effect of dissociation on the boundary-layer profiles was to reduce the gradient at the wall. For example, at Tw = 20, the Stanton number and skin-friction coefficient are reduced up to 25 percent at high blowing rates due to the effect of dissociation. The recovery temperature is also reduced but only by 2 percent for Mach number of 12. In all of the constant wall-temperature cases, increasing any of the following three parameters, free-stream Mach number, wall temperature, or mass blowing rate, results in a decrease in the normalized skin friction Cf/Cf0 and Stanton number St/St0 (here Cf0 and St0 refer to the solid wall values). For the recovery case, increasing Mach number or mass transfer rate results in a decrease in the normalized recovery factor, r/r0. Skin-friction ratios Cf/Cf0, Stanton number ratios St/St0, and recovery factor ratios r/r0 are also presented as a function of the parameter −fwC* where C* is the Chapman-Rubesin constant evaluated at the reference temperature. In this presentation, all of the skin-friction curves lie in a narrow band with a variation of ± 20 percent from the mean value. The Stanton number curves have a similar behavior with a variation of only ± 15 percent from the mean value in its band.
Effect of wall temperature on separation bubble size in laminar hypersonic shock/boundary layer interaction flows