A Perturbation Method to Analyze the Effect of Cross Section and Angle of Attack for Some Conical Bodies in Hypersonic Flow

ABSTRACT

An analysis is performed to study the supersonic flow over conical bodies of three different cross sections circular, elliptic and squircle (square with rounded corners) shaped. Perturbation method is applied to find flow variables analytically. In order to find lift and drag forces the pressure force on the body is found, the component along x is drag and the component along z is lift. Three equations are obtained for lift to drag ratio of each cross section. The graphs for L/D show that for a particular cross section an increase in angle of attack, increases L/D. Comparing L/D in the three mentioned cross sections it is obtained that L/D is the greatest in squircle then in ellipse and the least in circle. The results have applications in design of flying objects such as airplanes where many more seats can be arranged in ellipse and or squircle cross section compared to regular circular case.

Keywords:

Supersonic flow, conical bodies, lift to drag ratio, squircle cross-section, Euler', equations, Perturbation techniques.