### Computational and Analytical Investigation of Aerodynamic Derivatives of Similitude Delta Wing Model at Hypersonic Speeds

*Musavir Bashir, S. A. Khan, Qummare Azam, Ayub Ahmed Janvekar*

**Abstract**: This research paper presents a computational and analytical investigation

of aerodynamic derivatives in an oscillating wedge. Unsteady hypersonic

similitude has been apprehended for an oscillating wedge with an attached bow

shock at a large incidence angle. The problems of instability and shock waves

are generally associated with hypersonic flow and, therefore, it is imperative

to evaluate aerodynamic models that can solve these problems. Lighthill’s

piston theory is an unsteady aerodynamic model that is valid for an oscillating

wedge with an attached shock wave. The analytical solution verifies that both

the stiffness and the damping derivatives attain high values when the

semi-vertex angle of the wedge is increased, while both derivatives assume

lower values at increasing Mach numbers. Similarly, the pressure distribution

over the wedge is evaluated to determine the details of how the developing flow

cause the instabilities. Our study presents the contour plots of pressure,

temperature, density, and Mach number that unravels the positions of flow

separations in an oscillating wedge model.

**Keywords**: Damping derivatives; Hypersonic flow; Piston theory; Stiffness derivatives; Wedge model

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