A Flexible Hypersonic Vehicle Model Developed with Piston Theory

Abstract

For high Mach number flows, M ≥ 4, piston theory has been used to calculate the pressures on the surfaces of a vehicle. In a two-dimensional inviscid flow, a perpendicular column of fluid stays intact as it passes over a solid surface. Thus, the pressure at the surface can be calculated assuming the surface were a piston moving into a column of fluid. In this work, first-order piston theory is used to calculate the forces, moments, and stability derivatives for longitudinal motion of a hypersonic vehicle. Piston theory predicts a relationship between the local pressure on a surface and the normal component of fluid velocity produced by the surface’s motion. The advantage of piston theory over other techniques, such as Prandtl-Meyer flow, oblique shock, or Newtonian impact theory, is that unsteady aerodynamic effects can be included in the model. Prandtl-Meyer flow and oblique shock theory are utilized to provide flow properties over the surfaces of the vehicle. These flow properties are used to determine the steady forces and moments and are also included in the unsteady flow calculations. Thus, this work utilizes a combination of Prandtl-Meyer flow, oblique shock, and piston theory to calculate forces and moments. The unsteady effects include perturbations in the linear velocities and angular rates, due to rigid body motion. A flexible vehicle model is developed to take into account the aeroelastic behavior of the vehicle. The vehicle forebody and aftbody are modelled as cantilever beams fixed at the center-of-gravity. Piston theory is used to account for the changes in the forces and moments due to the flexing of the vehicle. Piston theory yields an analytical model for the longitudinal motion of the vehicle, thus allowing design trade studies to be performed while still providing insight into the physics of the problem.