Advanced analytical model for orbital aerodynamic prediction in LEO

The growing interest in low earth orbit (LEO) applications demands for accurate modeling of orbital aerodynamics. But classical analytical models of aerodynamic coefficients in free molecule flow, such as the Sentman's model, Schamberg's model and Schaaf-Chambre model, were built upon over simplistic gas-surface interaction models, which degrade the fidelity of aerodynamic prediction. This work presents a new analytical model of orbital aerodynamic coefficients based on the state-of-the-art Cercignani–Lampis–Lord (CLL) gas-surface interaction model, where lobular quasi-specular scattering pattern and separate accommodation degree for different velocity components can be well captured. A key component of the new model is a rigorous function approximation solution of the reflected normal momentum flux based on the CLL model which is derived for the first time and is validated within 1% for any hypothermal flow and surface accommodation conditions. Closed-form analytical solutions of aerodynamic coefficients for simple convex geometries are obtained and exhibit high accuracy (within 0.1%) in typical LEO scenarios. The new analytical model surpasses the classical models in some important aspects, such as overcoming the diffuse scattering hypothesis constraint, considering the variation of normal momentum exchange with the surface incidence angle and being applicable in any hypothermal flow situation. In virtue of the advanced CLL model and feasibility of coupling with the panel method technique, the new analytical model is promising to provide more accurate predictions on the orbital aerodynamic coefficients for LEO applications.