Study of Underexpanded Sonic Jets by Numerical Simulation

Abstract

This paper deals with the numerical simulation of sonic underexpanded axi-symmetric jets, issuing from a convergent nozzle, at different nozzle pressure ratios. The simulations have been carried out by solving the unsteady Reynolds Average Navier-Stokes (RANS) equations utilizing the realizable k-ε (epsilon) two equations turbulence model in the commercial software FLUENT (version 6.3.26). The flow is assumed to be axi-symmetric and turbulent. The computational domain included a convergent nozzle of length 50 mm and a rectangular domain of size 25 times the nozzle exit diameter (D) verses 4D, which have been modeled and meshed in GAMBIT (version 2.46). The grid consisted of 81020 cells, while gradient grid adaptions were performed later to pronounce the accuracy of the results and visualize the shock-cell structures. From the simulations, it is inferred that, for correctly expanded jets, the potential core extends upto 6D, where D is the exit diameter of the nozzle. For underexpanded jets, the shock-cell structures in the jet flow field were captured properly. A pattern of ‘shock-diamonds’ or shock-cells were observed in the flow at low NPR. The formation of shock-cell is found to change considerably and also its strength increases with increase in nozzle pressure ratio (NPR). From this study, it is clear that the effect of favorable pressure gradient in the underexpanded jet influences the jet characteristics significantly. At high NPRs, ‘Mach disc’ formation is observed in the flow field. The flow after the Mach disc becomes subsonic and regains energy from the surrounding fluid.