Flow in a planar convergent–divergent nozzle

Abstract

Flow in a convergent–divergent nozzle is studied for pressure ratios (NPR) of 1–11 and exit-to-throat area ratios of 1.2 to 2.0. The unsteady compressible Navier–Stokes equations along with the Spalart–Allmaras turbulence model are solved using a stabilized finite element method in two dimensions. Asymmetric flow is observed at moderate NPR. The side loads due to the flow asymmetry increase with increases in NPR and area ratio. Various flow regimes that are possible in the entire parameter space are identified. The introduction of boundary layer bleed results in steady and symmetric flow conditions at all NPR. Consequently, the nozzle does not experience a lateral force for any NPR. Application of bleed leads to a significant downstream shift in the shock location at low to moderate NPR. Compared to no-bleed, the nozzle experiences a loss of thrust in this regime. The thrust performance for $$\text {NPR} > 6$$ is, however, unaffected by bleed. The effect of nozzle geometry on the flow at various NPR is studied. Four different geometries with the same area ratio and nozzle length are considered. These geometries differ from each other in terms of the nozzle surface profile, including the discontinuity in slope of the surface. Barring some minor differences at low to moderate NPR, the flow is similar for all the geometries considered.