A Hypersonic Vehicle Model Developed With Piston Theory (Preprint)
AIR FORCE RESEARCH LAB WRIGHT-PATTERSON AFB OH AIR VEHICLES DIRECTORATE
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For high Mach number flows, M greater or equal to 4, piston theory has been used to calculate the pressures on the surfaces of a vehicle. In a two-dimensional 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 surfaces motion. The advantage of piston theory over other techniques, such as Prandtl-Meyer flow or Newtonian impact theory, is that unsteady aerodynamic effects can be included in the model. The unsteady effects, considered in this work, include perturbations in the linear velocities and angular rate. This provides a more accurate model that agrees more closely with models derived using computational fluid dynamics or those derived by solving Euler equations. Additionally, 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.
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