Dynamic instability modeling on phase plane for thin aeroshell capsule with pitching motion at transonic speed

Abstract

For sample return missions from deep space, a thin aeroshell capsule was proposed aimed at mitigating the aerodynamic heating during its reentry into the earth's atmosphere. The functional requirements of the capsule mandate that it aerodynamically decelerate sufficiently and land in the appropriate attitude without a parachute. To evaluate its motion attitude during transonic conditions in a wind tunnel, we employed the 1-degree of freedom (1-DOF) oscillation method. Furthermore, to predict its motion during an actual flight based on the wind tunnel test results, we examined the impact of the moment of inertia (MOI) on the motion. In all the MOI cases investigated, the limit cycle oscillation (LCO) was observed with a constant amplitude of angle. The variations in the MOI resulted in differences in the amplitude of the angle and time to reach the LCO. This study focused on the growth phase until the LCO and evaluated the characteristics on the phase plane. Consequently, a gradual approach to acceleration attributed to the static moment was observed in the growth history. A new modeling approach, centered on the nullcline during the growth phase, was adopted. Here, an approximation using a third-order function of angular velocity was applied to reproduce the nullcline obtained from the experiment. Upon non-dimensionalization of this model equation using the motion period, it was confirmed that the non-dimensional parameters were affected by the motion period, while this model focused solely on the growth phase. Furthermore, upon parameter tuning to replicate the amplitude of the angle and time to reach the LCO, and using these parameters, we predicted the impact of the MOI. The predicted results qualitatively reproduced larger MOI leading to larger amplitudes of angle and longer times to reach the LCO, which was consistent with the experimental results.

Keywords

• dynamic stability
• reentry capsule
• wind tunnel
• phase plane
• model equation