Abstract
The behavior of an unsteady shock associated with the surface of the forebody of a hypersonic vehicle is modeled analytically. The present study develops a simple engineering model, based on the nonlinear oscillator theory, to perform a dynamic analysis on nonuniform e ow over two-dimensional hypersonic forebodies. The emphasis is on exploring the e uid physics while avoiding time-intensive computational techniques for unsteady calculations. Closed-form solutions of the shock motion are derived and any coupling phenomena between the boundary layer and the shock are studied by including viscous effects in the analysis. The response of the shock to different freestream Mach numbers, frequencies, and amplitudes of perturbation is examined. A quasisteady approach and piston analogy have been incorporated. It is shown that the amplie cation factor of the inviscid shock relative to the surface matches with the computational results within 10% accuracy under similar conditions.
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