Quantifying the Effects of Rarefaction in High Velocity, Slip-Flow Regime

The present work follows two former papers by the first author where the effects of rarefaction in transitional regime were considered. In the first paper these effects were evaluated on the aerodynamic coefficients of a re-entering sphere-cone capsule. In the second paper, parameters quantifying non-equilibrium (anisotropy and thermodynamic non equilibrium) were proposed. Both studies were carried out changing at the same time velocity and altitude. In the present paper a sensitivity analysis, for identifying the most critical parameter for non-equilibrium, and an evaluation of the influence of non-equilibrium, slip velocity and temperature jump (slip effects) on the drag and heat transfer coefficients are carried out. Parameters quantifying the slip effects are also proposed. Computer simulations are made on a sphere in slip-flow regime by a: i) DSMC code (DS2V) for the sensitivity analysis and for quantifying the influence of non-equilibrium, ii) Navier-Stokes code (FLUENT) for the evaluation of the slip effects. The sensitivity analysis showed that the influence of the free stream velocity on the non-equilibrium parameters is much stronger than the one of the free stream thermodynamic parameters. Therefore the quantification was carried out changing the free stream velocity; in order to point out only the influence of rarefaction, excluding the fluid-dynamic effects, for each variation of the free stream velocity the thermo-dynamic parameters were adapted in such a way to keep the same value of the free stream Mach, Reynolds, Knudsen, Prandtl and Lewis numbers. The results showed that the influence of non-equilibrium and slip on the aerodynamic coefficients is of the order of one percentage unit. A more consistent difference, between the aerodynamic coefficients from DS2V and from FLUENT, is probably due to the failure of the phenomenological equations of Newton, Fourier and Fick.