In free molecular flows, occurring at very low gas densities, the interaction between gas molecules is neglected and only the interaction between the gas molecules and the solid surface is taken into account. In Chapter 4 we discussed the flow of highly rarefied gases in the case of ‘internal’ flows which are typically associated with vacuum installations. There is, however, a much more interesting situation which arises with respect to high altitude flights at hypersonic velocities. This situation involves the aerodynamics of high speed rarefied gas flow past submerged bodies.

In this chapter we consider the interaction of solid bodies with rarefied gas flows with Knudsen numbers (the ratio of the molecular mean free path and the characteristic size of the body) larger than unity. This regime, which is called free molecular interaction, is quite different from normal gasdynamic flows around solid bodies and therefore very different mathematical methods must be applied.

Typical mean free path values in the terrestrial upper atmosphere are shown in Figure 7.1 (when calculating the mean free path an average cross section value of σ = 10–19 m2 was used). Inspection of Figure 7.1 reveals that above approximately 150 km the condition Kn ≫ 1 is satisfied (at this altitude λ∽100 m, which is large compared to typical space vehicles). In the h ≥ 150 km region the interaction is free molecular but the number density is still high enough to make macroscopic averages meaningful (the atmospheric density profile is shown in Figure 1.2).