Approach to determine the circulation and vorticity around supersonic airfoil with spoiler

Abstract

This paper investigates the circulation, vorticity, and oblique shock waves generated by the airfoil with a spoiler. In this regard, the effects of the geometric parameters of the airfoils, such as the attack angle, shock wave angle, and Mach number etc., are studied first. We have introduced the conformal mapping technique, which has helped transform the flow past a circular cylinder to an airfoil shape. Based on the Kutta conditions, we have solved the unsteady flow in the region of an airfoil. The results show that the flow patterns form a strong vortex after the spoiler when the attack angle of the airfoil changes from 0° to 10° at a spoiler angle of 85°. Furthermore, we have used the shock wave expansion method, and the deflection angle has been found to increase with increasing the shock wave angle for a certain Mach number. A higher shock wave angle is obtained for a lower Mach number at any deflection angle. In addition, it is also found that the post Mach number is decreased with the increasing shock wave angle for fixed pre Mach number.