Real gas effects on receptivity to kinetic fluctuations: I. Mean flow effect

Receptivity of high-speed boundary layers to kinetic fluctuations is considered within the framework of fluctuating hydrodynamics. In this framework, stochastic forcing is introduced into the Navier-Stokes equations through fluctuating shear stress and heat flux terms. The forcing generates unstable modes that are amplified downstream and may lead to transition. Examples of high to moderate-enthalpy (5:60 - 16:53MJ=kg) boundary layers at relatively low wall temperatures (T_ω = 1000K and 2000K), free stream temperature (T_e = 278 - 834K), and low pressure (0:0433 atm) are considered. The real gas effects are manifested in the mean flow profiles through the dependence of the specific heat on temperature, however, for the cases considered here, dissociation is still insignificant. The stability and receptivity analyses are carried out using a solver for calorically perfect gas with an effective Prandtl number and an effective specific heats ratio. We compare receptivity and stability using two mean flow models: a calorically perfect gas model and a real gas model (5-species model for air). Receptivity is seen to be about the same in both cases due to the strong dependence on the edge flow parameters for the high Mach number cases considered. However, the real gas model results in larger downstream amplitudes for the wave packets generated by kinetic fluctuations. It was found that spectra in both cases include unstable supersonic 2nd Mack modes in spite of the temperature ratio T_ω=T_e > 1.