Navier-Stokes Solutions for a Supersonic Coflowing Axisymetric Nozzle with a Thick Base Annulus

摘要

Numerical solutions of the Navier-Stokes equations are obtained for a supersonic coflowing axisymmetric nozzle (Infinity) = 2,200,000. Five jet pressure ratio conditions ranging from a highly overexpanded case which exhibits a Mach disc shock formation to a slightly underexpanded case are examined and solved numerically. MacCormack's explicit method is applied as the numerical algorithm. An adaptive grid is utilized in the nozzle wake to allow the fine mesh region of the computational grid to remain in areas containing relatively high flow gradients. Locally dependent eddy viscosity modelling is applied in the form of a Cebeci-Smith two layer model in the boundary layer region on the nozzle walls, and a form of the Prandtl mixing length model in the nozzle wake. A two-dimensional wedge-flat plate validation case was computed using these models with good results. The computational results for the coflowing nozzle accurately reproduced the experimentally observed viscous effects on the nozzle base pressure and shock locations that are caused by the thick nozzle base annulus. Correct transition was achieved numerically from regularly reflected shock waves at the line of symmetry in the jet core to the Mach disc reflection at the appropriate nozzle pressure ratio. (Author)