The purpose of this research is to study the behavior of a slender two dionensional body placed in a simple linear shear stream, potential or viscous.
The method taken in this report is based upon coordinate transformation to natccral nonorthogonal curvilinear coordinate system to fit bodies of arbitrary cross-section shape, following Thames, et. al. Automatic numerical grid generation and clustering of meshes toward the solid boundary is carried using simple algebraic method. This technique improves the concputational resolution of foundary layer region and presents the capability of solving higher Reynolds number flow than before.
The transformed Navier-Stokes equation, in the form of equations of vorticity transport function and stream function, are solved numerically using successive over-relaxation method for the airfoil NACA64A010 at zero angle of attack. For the inviscid flow case, equations are simpler due to the conservation of free stream vorticity as stateu by Helmhdtz theorem. For the viscous flow various Reynolds numbers from 100 to 5,000 are taken and in all cases it is found that the leading stagnation point falls upon the inviscid case. Also a very interesting pair of seperated recirculating bubbles are found near the leading edge of the acifoil, which merges into one as Reynolds number is increased. He results such as field velocity vectors near airfoil, pressecre distributions on the airfoil are computer-plotterd and the force coefficient variation with the Reynolds number is presented.
Despite the very reasonable results of the computation, their validity will have to be confironed by experiment because there is no published theory or experimental data for direct comparison.