Investigation of Vscous/Inviscid Interaction in Transonic Flow Over Airfoils With Suction

The viscous/inviscid interaction over transonic airfoils with and without suction is studied. The streamline angle at the edge of the boundary layer is used to couple the viscous and inviscid flows. The potential flow equations are solved for the inviscid flow field. In the shock region the Euler equations are solved using the method of integral relations. For this the potential flow solution is used as the initial and boundary conditions. An integral method is used to solve the laminar boundary-layer equations. Since both methods are integral methods, a continuous interaction is allowed between the outer inviscid flow region and the inner viscous flow region. To avoid the Goldstein singularity near the separation point the laminar boundary-layer equations are derived in an inverse form to obtain solutions for the flows with small separations. The displacement thickness distribution is specified instead of the usual pressure distribution to solve the boundary-layer equations. The Euler equations are solved for the inviscid flow using finite volume technique and the coupling is achieved by surface transpiration model. A method is developed to apply a minimum amount of suction that is required to have an attached flow on the airfoil. The suction parameter is varied based on the velocity profile parameter and the suction distribution obtained is considered to be close to the optimum value. The turbulent boundary layer equations are derived using the bi-logarithmic wall law for mass transfer. The solution method is similar to the laminar inverse boundary-layer approach. The results are found to be in good agreement with available experimental data and with the results of other computational methods.