Analytically-derived Aerodynamic Force and Moment Coefficients of Resident Space Objects in Free-Molecular Flow

Abstract

Fast, high-fidelity trajectory propagation of objects in near-Earth orbits is a key capability for space situational awareness and mitigating probability of collisions on orbit. This high-fidelity analysis requires accurate aerodynamics prediction for objects in the freemolecular regime of flight, but most tools for aerodynamic prediction for this regime either are found using assumptions or are computationally intensive. Symbolic manipulation software can be used to analytically integrate expressions for pressure and shear pressure coefficients acting on a general body in free-molecular regime to derive aerodynamic force and moment expressions. The analytical aerodynamics prediction method is described and relations have been developed for the sphere, cylinder, panel, and rectangular prism. The NASA-developed Direct Simulation Monte Carlo Analysis Code is used to validate the analytical expressions and it is shown that expressions are accurate within 0.38%. These generalized analytic expressions in terms of angle of attack, sideslip angle, freestream conditions, wall temperature, and accommodation coefficients allow near-instantaneous computation of the rarefied aerodynamics and enables space situation awareness analysis.

Analytical Aerodynamic Force and Moment Coefficients of Axisymmetric Objects in Rarefied Flow

“…Unfortunately, after the u-integration of Eqs. (8) and (9), the v-integrals do not have closed-form solutions. Another issue with this definition of the shadow boundary arise when the shadow boundary intersects the natural bound on the cylinder.…”

“…7) and (10)-(13) provide explicit definitions for the aerodynamic force and moment integrals described in Eqs. (8) and (9). A more thorough derivation is available in the literature.…”

“…A more thorough derivation is available in the literature. 8 For analytic geometries, this formulation provides exact aerodynamic characterization within the limits of the governing equations (Eqs. (2) and (3)), providing accurate sensitivity information and a rapid solution capability while eliminating the numerical error that is part of any numerical paneling tool.…”

“…(7), results in the general integral definitions for aerodynamic force and moment coefficients given in Eqs. (8) and (9). The domain of integeration defined in Eq.…”

“…5 Hence, the incident flow is entirely undisturbed by the presence of the body. 6 Though much of the literature rests on this assumption, [5][6][7][8] there have been investigations into cases where reemitted particles collide with the surface of the body more than once. 9,10 The similarity parameter that is generally used to define the interfaces between continuum flow, rarefied flow, and the regime between them known as transition flow, is the Knudsen Number (Kn) of the flow.…”