On the Kutta Condition in Potential Flow over Airfoil

This paper proposes a novel method to implement the Kutta condition in irrotational, inviscid, incompressible flow (potential flow) over an airfoil. In contrast to common practice, this method is not based on the panel method. It is based on a finite difference scheme formulated on a boundary-fitted grid using an O-type elliptic grid generation technique. The proposed algorithm uses a novel and fast procedure to implement the Kutta condition by calculating the stream function over the airfoil surface through the derived expression for the airfoils with both finite trailing edge angle and cusped trailing edge. The results obtained show the excellent agreement with the results from analytical and panel methods thereby confirming the accuracy and correctness of the proposed method. 1. Introduction The advent of high speed digital computers has revolutionized the numerical treatment of fluid dynamics problems. Numerical methods, nowadays, have become a routine tool to investigate fluid flows over the bodies such as airfoil. Amongst such fluid flows, incompressible potential flows are of crucial importance in studying the low-speed aerodynamics problems. The limitations associated with the exact (analytical) solutions with complex variables methods (conformal mapping) motivated fluid dynamicists to develop numerical techniques to solve incompressible potential flow problems (the Laplace’s equation) over an airfoil. Since the late 1960s, the panel methods have become the standard aerodynamic tools to numerically treat such flows [1]. Panel methods are applicable to any fluid-dynamic problem governed by Laplace’s equation. In these methods, the airfoil surface is divided into piecewise straight line segments or panels and singularities such as source, doublet, and vortex of unknown strength are distributed on each panel. Panel method used for the simulation of an incompressible potential flow past an airfoil is concerned with the vortex panel strength and circulation quantities and the evaluation of such quantities results in the calculation of the velocity distribution over the airfoil surface and hence the determination of the pressure coefficients. These methods have been extensively investigated in the aerodynamics literature [2–6], so these will not be discussed any further here. The interested reader can refer to the above references for further information. However, dealing with the panels and their attributes is numerically much more complex than the method proposed in this paper and of high programming effort. The Kutta condition should be introduced