Second-Order-Accurate Calculation of Transonic Flow over Turbomachinery Cascades

This paper presents a number of observations made and techniques developed in the process of constructing an accurate finite-difference method for the calculation of transonic flow through a cascade. These techniques can be applied to related problems such as flows over airfoils and inlets. A simple method is given to account for wind-tunnel sidewall effects in transonic flow calculations. A method is then presented which can be utilized to produce more rapid convergence for coupled viscous-inviscid transonic flow relaxation calculations. Finally, a stable set of fully second-order-accurate difference equations for the full-transonic potential flow equation is presented, along with some principles governing its construction and use. Calculations are presented to demonstrate the importance and effectiveness of these new methods.