Different Implementations of Diffuse Reflection with Incomplete Accommodation for Drag Coefficient Modeling

Abstract

Diffuse reflection with incomplete accommodation is the favored gas–surface interaction model for calculating the drag coefficient of satellites in low Earth orbit, where drag is the largest source of uncertainty in the orbital trajectory of satellites. Closed-form solutions have incorporated the variation of the energy accommodation coefficient through equating the total energy of the incident and reflected flows; however, this leads to an incorrect reflected velocity distribution for incomplete accommodation. The problem is highlighted by investigating the velocity distribution functions for a gas reflected from a flat plate at zero accommodation. A physically accurate implementation for diffuse reflection with incomplete accommodation based on the Cercignani–Lampis–Lord gas–surface interaction model is compared with the closed-form solutions that equate the incident and reflected energy of the flow. The Cercignani–Lampis–Lord gas–surface interaction model shows the conservation of energy on a molecule-by-molecule basis for zero accommodation, as expected, whereas the closed-form method only conserves energy on average. The macroscopic effect of the different velocity distributions manifests in differences of in the drag coefficient of a flat plate, sphere, and the GRACE satellite at zero accommodation and differences larger than 1% for energy accommodation coefficients less than 0.90.