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.
Highlights
The flow past conical bodies has been studied for many different cases
Perturbation method is widely applied to studies of flow on conical bodies
Using Fourier series a relation between and the shape of the cross section of the body is obtained for each case
Summary
The flow past conical bodies has been studied for many different cases. A supersonic compressible three dimensional solution is useful in design of supersonic aircrafts, missiles, rockets and etc. Perturbation method is widely applied to studies of flow on conical bodies. Stone [2, 3] applied the power series expansion for a small angle of attack and obtained a solution via perturbation method. The flow is sought as a small perturbation from some basic circular cone flow which is basically an ellipse. In these studies only pressure has been obtained for the elliptic cone and there is no calculation and comparisons of the lift to drag coefficient with the basic circular cone. In [7] the geometry of the cone cross sections and surface velocities are expanded in Fourier series, using the supersonic linearized conical flow theory, the flow over slender pointed cones are calculated
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