J.F. Quaatz, M. Giglmaier, S. Hickel, N.A. Adams (2014) 
International Journal of Heat and Fluid Flow 49: 108-115. doi: 10.1016/j.ijheatfluidflow.2014.05.006

Well-resolved Large-Eddy Simulations (LES) of a pseudo-shock system in the divergent part of a Laval nozzle with rectangular cross section are conducted and compared with experimental results. The LES matches the parameter set of a reference experiment. Details of the experiment, such as planar side walls, are taken into account, all wall boundary layers are well-resolved and no wall model is used.

The Adaptive Local Deconvolution Method (ALDM) with shock sensor is employed for subgrid-scale turbulence modeling and shock capturing. The LES results are validated against experimental wall-pressure measurements and schlieren pictures. A detailed discussion of the complex flow phenomena of three-dimensional shock-wave–boundary-layer interaction, including corner vortices and recirculation zones, is presented. Limitations of RANS approaches are discussed with reference to the LES results.


Comparison of experiment obtained by Gawehn et al. (2010) and simulation by means of schlieren pictures. Compressions appear dark and expansions light. (a) Experimental schlieren photography through the parallel side walls. (b) Instantaneous snapshot of the LES spatially averaged along the z-direction showing the axial density gradient. (c) Instantaneous snapshot of the LES spatially averaged along the z-direction showing the transversal density gradient. Details of the primary shock for (d) Experiment and (e) LES show.


Numerically obtained 3-D shape of the pseudo-shock system. Yellow iso-surfaces indicate Mach number Ma=1. One quarter of the channel is cut out to allow for a view into the supersonic flow region, which is colored by the Mach number, blue iso-surfaces enclose reverse-flow. (a) Time averaged LES result; (b) RANS EARSM simulation.