Laminar Boundary Layer Calculation over Airfoil Surface

Abstract

In the initial stage, the 2 dimensional panel method will be used to determine aerodynamic characteristics of an airfoil. But its results still have a lot of errors, especially the results in high angle of attack region. The significant cause of these errors is that the 2 dimensional panel method considers its incoming flow is inviscid which is different from the real viscous flow. Therefore, in order to obtain better results, the determination of  aerodynamic characteristics of an airfoil must take the effects of viscosity into attention. One method can deal with this is to apply the boundary-layer equations. In this research the boundary-layer equations will be used to approximate variables within laminar boundary layer which is the first boundary layer of inviscid flow over an airfoil starting from airfoil stagnation point till its transition point. At first, solutions of boundary-layer equations are obtained by using finite different method based on second order partial differential equations to construct system of quasi-linear equations and to solve for boundary-layer velocity profiles. Then, boundary-layer variables such as displacement thickness, momentum thickness,  form factor, and skin-friction coefficient will be determined with the assumptions are:  the flow has low Reynolds number passing over NACA 0012 airfoil and using the velocity distributions at the edge of its boundary layer obtained from the 2 dimensional panel method. The obtained results will be compared with the results of the same types obtained from the references and find that they are consistent with each other and have low differences.