Navier-Stokes solutions for an axisymmetric nozzle in a supersonic external stream

Numerical solutions of the Navier-Stokes equations are obtained for an axisymmetric nozzle in supersonic external stream (M infinity = 1.94, Mj = 3.0, Re infinity = 2.2 x 10 to the 6th power). Five jet pressure conditions ranging from a highly over-expanded case which exhibits a Mach disc shock formation to a slightly under-expanded case are examined and solved numerically. MacCormack's explicit method is applied as the numerical algorithm. An adaptive grid scheme 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 regions 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 excellent results. The computational solutions of the axisymmetric nozzle accurately reproduced the experimentally observed viscous effects on the nozzle base pressure and shock wave 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 a Mach disc reflection at the appropriate nozzle static pressure ratio.