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

Abstract

Recent developments in symbolic mathematics allow for analytic modeling of rarefied hypersonic aerodynamic coefficients of nontrivial geometries. These analytic models enable rapid trajectory propagation and sensitivity analysis for objects in low-Earth orbit. High fidelity modeling can be accomplished by generating an aerodynamic database via Direct Simulation Monte Carlo, however this process is computationally intractable considering the 13,000 pieces of debris in orbit. Analytic modeling provides a rapid alternative to DSMC with little loss of fidelity. In this investigation, the Schaaf & Chambré model is applied to geometries composed of conical frustums and cylindrical hulls, validated against DSMC results, and extended to arbitrary geometries of revolution with errors less than 5% relative to traditional numerical simulation.

Aerodynamics of the RANGE Nanosatellites from Direct Flowfield Simulation

“…The free molecular flow theory is constrained to convex geometries because it cannot model self-reflection. 16 This is the case with the RANGE nanosatellite geometry because it has deployable solar panels, so direction simulation Monte Carlo (DSMC) is used to model the flow instead. In DSMC, molecules are grouped together into simulated particles to decrease computational cost, but otherwise the fundamental conservation laws of mass, momentum, and energy are preserved.…”

“…Analytic models provide a basis of comparison for the simulation results, since the two have produced results within 10-15% difference in previous investigations. 11,16 In these cases, DSMC is more accurate because the analytic model is based on several assumptions of the flow and the geometry. An analytic model of the aerodynamics was developed for validation using the hyperthermal pressure and shear coefficients in Eq.…”

A review of gas-surface interaction models for orbital aerodynamics applications

“…T is the vector of the roll, pitch and yaw momentum coefficients and r PO is the position vector defining the distance between the aerodynamic centre of pressure and the centre of mass. The magnitude of the aerodynamic forces and coefficients has been estimated in literature for bodies of different shapes making use of both analytical [41,[48][49][50][51] and numerical techniques [52,53]. Both approaches have benefits and drawbacks and, ideally, the most advantageous strategy would be to adopt them in synergy, when permitted.…”