Numerical simulation of shock wave patterns in supersonic divergent symmetric nozzles

This paper presents the results of numerical simulations of supersonic flows with shock waves in a divergent symmetric nozzle of an opening angle ranging from 2 degrees to 6 degrees. At certain Mach number values the shock pattern becomes asymmetric. This asymmetry is analysed here for different values of velocity upstream of the shock wave and for different nozzle divergence angles. Only the divergent part of the nozzle is considered. Supersonic conditions at the nozzle inlet were prescribed with a chosen Mach number value Ma>1. The inlet velocity profile included a turbulent boundary layer profile on side walls. The steady flow simulation was applied for nozzle opening angles, α , of 1.877 degrees, 2.5 degrees and 3 degrees, whereas the unsteady approach was necessary for a nozzle of the divergence angle α =6.54 degrees to obtain a converged solution. The asymmetry of the shock structure is visible in the unevenness of the heights of both λ-feet. It happens at the same Mach number, at the same boundary layer and with the same geometrical constraints. This is in contradiction with our current understanding of the parameters affecting λ-foot size. The paper provides an explanation of this problem.