An accurate and robust Navier-Stokes procedure to predict the complex flow about an airfoil has been developed. To keep the equations simple and to minimize the errors due to the false diffusion, the computational grid for an arbitrary airfoil shape is generated to be orthogonal and aligned with the inviscid streamlines by using conformal mapping. Further improvement of the method is achieved by employing the QUICK scheme for the convective derivatives and the two-layer κ-ε model for the turbulence closure. Sample calculations for various airfoil sections show that the prediction is improved substantially over those by existing methods. The details of the flow extending to the wake, such as the surface pressure distribution, $C_{lmax}$, the velocity fields, and the Reynolds-stress profiles, are found to be in excellent agreement with the data.
The procedure is then extended for two-dimensional airfoils in unsteady motion. Upon completing the code verification through calculations for the oscillatory flow about a cylinder, the method is applied to solve the flow about an impulsively started airfoil at various angles of attack for Re=1000. After an initial transient period, the flow either approaches to the steady limit or becomes periodic and exhibits the formation and breakaway of many, large and small, vortices, especially on the suction side. At α=25°, the flow is still periodic, but the flow in each cycle is much more complex. These phenomena as well as the observations made on the initial flow behavior and the unsteady separation are discussed in the thesis.
Finally, the unsteady turbulent flow is examined for a NACA 4412 airfoil section in an oscillating freestream at the mean Reynolds number of $1.5×10^6$. Although the calculation is made only for one angle of attack and the frequency, the results clearly exhibit essential features of the unsteady turbulent flow, i.e., the aerodynamic forces and separation.
