ESTIMATION OF AERODYNAMIC DERIVATIVES IN PITCH OF A WEDGE IN HYPERSONIC FLOW
ABSTRACT In the present paper a theory for 2-D slender bodies at high angles of attack in hypersonic flow has been developed. This 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. Results show that the stiffness and damping derivatives increase with the increase in the semi vertex angle. The present method includes the thin wedge case as well, which was covered by…show more content… Equivalence of a steady hypersonic flow on a slender body with an unsteady flow in one fewer space dimensions was pointed out by Hayes [2]. Unsteady supersonic flow has been well studied by using the potential theory. Unsteady hypersonic flow has been studied by many researchers using unsteady analogues of either the shock expansion theory or the tangent wedge approximation [3,4].
For an oscillating wedge, more theoretical studies have been made, such a theory of oscillating aero foils at high Mach number is developed by Lighthill [6].Here the pitching oscillation is taken into consideration. Lighthill uses Hayes [3,4] results that to a good approximation, any plane slab of fluid ,initially perpendicular to the undisturbed flow, remains so as it is swept downstream and moves in its own plane under the laws of one dimensional unsteady motion?. A parameter is introduced,whose purpose will be to serve as a measure of the maximum inclination angle of Mach waves in the flow field.Here it is assumed that and is of the order of maximum deflection of a stream line. So in the flow past an aerofoil at high Mach number, the perturbations and gradients are much larger in the lateral direction than those in the axial…show more content… So a condition that the piston velocity should be less than or equal to free stream sound velocity is imposed to satisfy isentropic assumption. This is consistent with hypersonic small disturbance theory on which Lighthil?s piston analogy is based. Then the Pressure ratio can be written as
+ (2)
Where, A = B =
The nose down moment,
(3)
Of the load distribution about the axis . is the pressure on the windward surface.The pressure on the leeward surface is taken to be zero..
Thus the aerodynamic stiffness derivative is,
] (4)
And the aerodynamic damping derivative is,