Unsteady Shock Wave: Turbulent Boundary Layer Interaction in the Laval Nozzle

The flow in transonic diffusers and supersonic air intakes often becomes unsteady due to shock wave-boundary layer interaction. Oscillations may be induced by natural separation unsteadiness or forced by boundary conditions. Significant improvements of CFD tools, increased computer resources and the development of experimental methods have again drawn the attention of researchers to this topic. Forced oscillations of a transonic turbulent flow in an asymmetric two-dimensional Laval nozzle have been considered to investigate the problem. A viscous, perfect gas flow was numerically simulated using SPARC, a Reynolds-averaged compressible Navier-Stokes solver, employing a two-equation, eddy viscosity, turbulence closure in the URANS approach. For time-dependent and stationary flow simulations, Mach numbers upstream of the shock between 1.2 and 1.4 were considered. Comparison of computed and experimental data for steady states generally gave acceptable agreement. In the case of forced oscillations, a harmonic pressure variation was prescribed at the exit plane resulting in shock wave motion. Excitation frequencies between 0Hz and 1024Hz were investigated at a constant pressure amplitude. The main result of the work is the relation between the amplitude of shock wave motion and the excitation frequency in the investigated range. Increasing excitation frequency resulted in decreasing amplitude of the shock movement. At high frequencies, a natural mode of shock oscillation (of small amplitude) was observed, which was insensitive to forced excitement.