Transonic shock oscillations calculated with a new interactive boundary layer coupling method

A new viscous-inviscid interactive coupling method is described with the aim of allowing time-accurate computation of unsteady transonic flows involving separation and reattachment. A lag-entrainment integral boundary layer method is used in conjunction with a transonic small disturbance potential code. The solutions are coupled with a novel variable gain, integral control method for the boundary layer displacement thickness. Efficient and robust computations of steady and unsteady separated flows, including steady separation bubbles and self-excited shock-induced oscillations, are presented. The buffet onset boundary for the NACA 0012 airfoil is accurately predicted and shown computationally to be a Hopf bifurcation. Shock-induced oscillations are also presented for the 18 percent thick circular arc airfoil. The oscillation onset boundaries and frequencies are accurately predicted, as is the experimentally observed hysteresis of the oscillations with Mach number; this latter stability boundary is identified as a jump phenomenon.