S. Pavitra ¹, S. Lavanya ², S. A. Khan ³, Asha Crasta ⁴

Affiliations
1 Department of Mathematics, B. I. T, Mangalore - 574153, Karnataka, IN
2 Department of Mathematics, P.A.C.E, Mangalore - 574153, Karnataka, IN
3 Department of Mechanical Engineering, Faculty of Engineering, IIUM, Gombak Campus, Kuala Lumpur, MY
4 Department of Mathematics, MITE, Moodbidre - 574225, Karnataka, IN

Abstract

In the present paper a theory for 2D slender bodies at high angle of attack in hypersonic flow has been developed to determine the aerodynamic derivatives in pitch for different Mach numbers. The present theory has been applied to a sharp thick wedge with attached shock case. Using the theory, a relation for a piston moving in a cylinder at any velocity and relations for stiffness and damping derivatives are obtained for zero incidence of the wedge and it is found to be dependent on flight Mach number and wedge semi vertex angle. The present method includes the thin wedge case as well, which was covered by Lighthill piston theory, and applies only for small amplitude and low reduced frequency case. Effect of viscosity and secondary wave reflections have been neglected. The results are obtained for wedges of different semi vertex angles and Mach numbers. It is observed that the stiffness and Damping derivatives increase with increase in the semi vertex angle and decrease with an increase in Mach number. At very high Mach number the Mach number independence principle holds good.

Keywords

Aerodynamic Derivative, Hypersonic Flow, Mach Number, Semi Vertex Angle, Stability Derivative.

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