Analysis of the Aerodynamics of Tumbling Spacecraft During Orbital Decay and Reentry

Abstract

Space debris present many potential problems, such as collisions with functional spacecraft and safety hazards. As more satellites are launched every year, the population of space debris is growing faster than satellites and space objects are reentering the Earth's atmosphere. With little data on the reentry and breakup of space debris, there is a need for high-fidelity modeling of various space objects experiencing orbital decay and reentry. Accurate prediction of aerodynamic forces on high altitude orbiting and reentering space objects is necessary for understanding reentry trajectories. Much of low Earth orbit (LEO) consists of free-molecular flow regimes in which the molecules in the very rarefied atmosphere never collide with one another. Reentry takes objects from free-molecular through transitional and finally into the continuum regime that is dominated by inter-molecular collisions. These flow regimes (free-molecular, transitional, and continuum) can be classified by the Knudsen number, a non-dimensional ratio of gas molecules' mean free path, or average distance between collisions, and a characteristic length, usually a maximum length or diameter of a body submerged in the gas flow. An analytical modeling approach for evaluating forces and moments in three dimensions in the free-molecular flow regime is presented. The free-molecular approach is compared with a Direct Simulation Monte Carlo (DSMC) modeling approach. DSMC is a well-verified numerical particle-based probabilistic simulation that emulates the Boltzmann equation for non-equilibrium flows, which include rarefied flows. In this work, DSMC post-processing in three dimensions is extended to yield aerodynamic forces and moments dependent on the body orientation. DSMC is considered to be the most accurate method to analyze flowfields in rarefied regimes, however, the free-molecular method is preferable to the DSMC method due to computational cost, so long as it is sufficiently accurate. The free-molecular method can save computational time when compared with a DSMC simulation by a factor of up to 7,500. Three bodies are used to compare the free-molecular and DSMC modeling approaches: a CubeSat (TBEx), a reentry capsule (REBR), and a rocket motor (Star48B). The bodies are chosen due to their relevance to the current and future space environment. There are over 4,000 pieces of space debris associated with rocket bodies in LEO as of 2020. The differences between the DSMC and free-molecular results on all three bodies are discussed at length. An orbital decay model is presented in order to determine how differing modes of modeling aerodynamic coefficients affects orbital lifetime predictions. Tumbling approximations of the bodies are found to change the orbital lifetime predictions non-negligibly. The developed free-molecular analytical model provides good agreement for all three bodies at Knudsen numbers of 10 and above. At this condition, free-molecular drag results match DSMC drag results within 3%. Agreement wanes as Knudsen number decreases, and for Knudsen numbers of 0.1 or lower, the free-molecular model gives errors in aerodynamic forces as high as 28% leading to errors in time-to-reenter of 25%. The exact Knudsen number at which the free-molecular analysis becomes unacceptable varies by shape, indicating that for specific shapes, individual analysis must be done to quantify where the free-molecular modeling technique fails. This level of disagreement matches expectations for less rarefied flow. The free-molecular method developed saves computational cost when compared to DSMC by a factor of over 7000, and is recommended for use throughout the majority of LEO.