Boundary Layer Calculations for Cryogenic Wind Tunnel Flows

Abstract

In order to estimate theoretically the simulation accuracy in planned cryogenic wind tunnels some turbulent boundary calculations have been carried out taking into account real gas effects and heat transfer. Cebeci’s finite difference method has been used including real gas equations of state for representation of the gas behaviour close to its liquefaction boundary and the assumption of isothermal walls for simulation of not correctly cooled down model surfaces. From thermodynamics and boundary layer assumptions a special formulation for the Prandtl number in real gas boundary layers has been derived which shows this number to be a function of the actual position within the boundary layer. But the results achieved with different constant Prandtl numbers indicate that the influence of this Prandtl number variation through the boundary layer is negligible compared with the direct effects introduced by use of the real gas equations of state. In general, the calculated results confirm some fundamental viscous effects predicted earlier by Navier-Stokes calculations for supersonic shock wave-laminar boundary layer interaction in real nitrogen. Although systematic deviations in skin friction always occur as a consequence of real gas effects and small temperature steps, the influence of these differences on the separation behaviour are found to be small under cryogenic wind tunnel conditions.