IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN:2319-765X. Volume 10, Issue 2 Ver. VI (Mar-Apr. 2014), PP 15-24 www.iosrjournals.org www.iosrjournals.org 15 | Page Supersonic Similitude for Oscillating Nonplanar Wedge Asha Crasta 1 and S. A. Khan 2 Research Scholar, Department of Mathematics, Jain University, Bangalore, Karnataka, India, Principal, Department of Mechanical Engineering, Bearys Institute of technology, Mangalore, Karnataka, India, Abstract:A similitude has been obtained for a pitching oscillating Nonplanar wedge with attached bow shock at high angle of attack in supersonic flow. A strip theory in which flow at a span wise location is two dimensional and independent of each other is being used. This combines with the similitude to lead to a one- dimensional piston theory. Closed form of simple relations is obtained for stiffness and damping derivatives in pitch. The present theory is valid only when the shock wave is attached with the nose of the wedge. From the theory developed some of the results are obtained for wide range of Mach number and angle of attack with remarkable computational ease. From the results it is found that when convexity is introduced in the non-planar wedge, this results in shifting of the center of pressure towards the leading edge, and the stiffness as well as the damping derivative decreases with the increase in the Mach number for all the values of the semi vertex angles. Keywords: Supersonic Flow, Non Planar wedge, Piston Theory, pitch I. Introduction: High incidence hypersonic similitude ofSychev’s [1] is applicable to a wing provided it has an extremely small span in addition to small thickness. The unsteady infinite span case has been analyzed, but mostly for small flow deflections. The piston theory of Light hill [2] neglects the effects of secondary wave reflection. Appleton [3] and McIntosh [4] have included these effects. Hui’s [5] theory is valid for wedges of arbitrary thickness oscillating with small amplitude provided the bow shock remains attached. Erricsson’s [6] theory covers viscous and elastic effects for airfoils with large flow deflection. Orlik-Ruckemann [7] has included viscous effect and Mandl[8] has addressed small surface curvature effect for oscillating thin wedges. Ghosh’s [9] similitude and piston theory for the infinite span case with large flow deflection is valid for airfoils with planar or non-planar surfaces whereas Hui’s theory[10] is for plane wedges. Ghosh’s piston theory has been applied to non-planar cases, both steady and unsteady. The effect of viscosity and secondary wave reflection has not been included.Crasta and Khan have studied the hypersonic and supersonic similitude for planar wedge([17],[12]), for Delta wing ([11],[13])and for Delta wing with curved leading edges([14],[16]). Crasta and Khan have further extended the similitude tostudy the stability derivatives for Newtonian limit for planar wedge, delta wing[18] and delta wing with curved leading edges[15]. In the present work the similitude of Supersonic planar wedge has been extended for supersonic flows past a non-planar wedge. Analysis: STEADY WEDGE: Fig. A shows the wedge at time t. Fig. A shows that upper half of a steady wedge with attached bow shock in rectilinear flight from right to left in stationary air, at time t. Dimensional analysis indicates that the flow is conical in nature, i.e., at a given instant