Unsteady Aerodynamic Modeling of Atmospheric Entry Vehicles in Subsonic and Incompressible Flow: A Frequency Response Approach

The determination of time-varying lift force and pitch moment generated by a purely pitching Earth-entry capsule is investigated. Experiments were conducted in the 12-foot Low-Speed Tunnel at NASA Langley Research Center, testing a range of oscillation frequencies at a zero-mean angle of attack with a pitching amplitude of 10 degrees. In light of these measurements, a closed-form set of analytically derived equations for lift and moment was used to develop a semi-empirical formulation, incorporating empirically determined values from the experimental runs. The equations are grounded in potential flow theory, Theodorsen's classical theory of unsteady aerodynamics, and the Joukowski theorem of conformal mapping. The unsteady aerodynamics generated by the oscillating body are then modeled by constructing frequency response functions, with quasi-steady forces and moments serving as inputs and unsteady forces and moments as outputs. The experimentally determined gain and phase variations characterize the unsteady nature of the flow and the system's response and flow time-lag to input flow parameters for a blunt-body entry vehicle. The final semi-empirical model is validated with a set of parameters beyond the initial test matrix.