Effect of the nozzle shape on its off-design performance in the presence of shock wave and boundary layer separation

In this paper, compressible flows inside converging-diverging nozzles with different shapes at off-design conditions are investigated. Shock waves and boundary layer separation are present in the flows. The area ratio (outlet to the throat) and the total combustion chamber pressure are constant while the nozzle shape and its length are variable. Compressible Reynolds averaged Navier Stokes equations were solved using the finite volume method. By comparing the results with available experimental data, the Spalaret-Almars model has been selected for simulations. Axisymmetric, unsteady and viscous flow is considered in all simulations. The characteristics method is used to design the nozzle shape and important parameters such as Mach number, wall shear stress, Thrust efficiency, wall pressure, axial pressure and boundary layer separation due to shock wave are studied in detail. By comparing the results for four shapes of the nozzles (i.e. perfect nozzles, 15° conical nozzle, 30° conical nozzle, and minimum length nozzle) it is concluded that at design condition, perfect nozzle gives higher thrust (7889 N). However, at off-design conditions (when the shock wave and boundary layer separation occurs), the conical nozzle gives higher thrust (9700 N).