Causation of Supersonic Limit Cycle Oscillations in Atmospheric Entry Vehicles

Abstract

A successful atmospheric entry vehicle (AEV) design demonstrates manageable aerodynamic heating, bearable structural load, smooth deceleration, and intended trajectory during a descent into the atmosphere. Interestingly, the supersonic regime of the AEV manifests limit cycle oscillations (LCO) that restrict the maneuver potential and deployment of the drag chute. In this paper, efforts are made numerically and analytically to link the causation of LCO with external geometric variables of AEV. Computational fluid dynamics is used to calculate damping derivatives. The numerical results are validated with the Orion Crew Exploration Vehicle. The multiple time scales method, which belongs to the class of perturbation methods, is explored to develop an approximate closed-form solution of the nonlinear dynamic behavior of AEV. The analytical solution identifies that higher-order nonlinearities associated with pitch damping and static lift govern the onset of LCO. Finally, a parametric interaction study is carried out to determine the effect of two design variables, apex angle and length, on the vehicle’s dynamic stability. The mean data values from the main geometric effects plot show the condition of finite-amplitude oscillations. The results indicate that variation in these two parameters significantly impacts the magnitude of identified higher-order nonlinearities.