Different implementations of diffuse reflection with incomplete accommodation for drag coefficient modeling

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.Aphysically 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 ∼1.8-2.5% 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.