A Fast Viscous Correction Method for Unsteady Transonic Flow About Airfoils

Abstract

This study modified the inviscid, small-disturbances, unsteady, transonic code, LTRAN2, so that the viscous effect could be considered for the purpose of improving the code's accuracy without substantially increasing the computational time. By using a conventional integral boundary layer method to determine the displacement thickness and an empirical model of viscous wedge to simulate the suddenly thickened boundary layer behind a shock, it resulted in better agreement with experimental data for both the shock position and the pressure coefficient. Aerodynamic performances were calculated for two supercritical airfoils. When the unsteady procedure was used to obtain steady state results as the initial condition, the unsteady viscous solution for the RAE 2822 airfoil required 100.5% of the computational time of the inviscid solution. When an iterative scheme was used to obtain the steady state results as the initial condition, the unsteady viscous solution for the NLR 7301 airfoil required 88% of the computational time of the inviscid solution.