Effect of semi vertex angle on stability derivatives for an oscillating cone for constant value of specific heat ratio

Abstract

In this work we estimate stiffness derivatives for an oscillating non-slender axi-symmetric cone in pitch at Mach number greater than five. Results indicate that there is continous decrease in the stiffness derivative with the rise in the semi vertex angle for all the Mach number. The variation in the stiffness derivative is only visible for Mach numbers in the range from 5 to 7 for specific heat ratio of 1.67. For Mach number greater than 9 the stiffness derivative becomes independent of the geometrical parameter of the cone. The stiffness derivative becomes independent with the semi vertex angle for Mach 9 and above. Only at Mach 5 the variation of the stiffness derivative is distinct as at this Mach number the flow is in the transition zone from supersonic to hypersonic. The damping derivatives for h = 0, 0.2, 0.4, and 0.6 have similar trends, where the magnitude of the damping derivatives is decreasing with Mach number as well as with the semi vertex angle. However, the damping derivatives behave differently for h = 0.8 and 1.0 there is non-linear decrement in the magnitude of the damping derivatives, achieves minima, then again there sudden increase in the magnitude. Although this study is for sharp edged cone with attached shock wave case, once theory is developed it can easily extended for most practical cases with detached cases where nose bluntness will play an important role to tackle the aerodynamic heating.