Unsteady Computation of over-Expanded flow in a convergent divergent nozzle

The classical one-dimensional inviscid theory does not\ud reveal the complex flow features in an over-expanded nozzle\ud accurately. The code Fluent has been used to simulate the\ud transient flow passing through a 2-D Convergent-Divergent (CD) nozzle (Ae/At=l.7, ae=3.03', Symmetric about centerline) for nozzle pressure ratios (NPR) corresponding to over-expanded flow. The transient RANS equation with Shear Stress Transport k-o (SSTKW) turbulence model has been simulated. Both inviscid and viscous flows have been simulated. Both the first order and second order upwind scheme has been used for all the conservation equations.\ud The inviscid solutions predicted steady results for both first and second order simulations after a certain time. There is no significant unsteadiness in the first order\ud viscous solutions too. Shock structure is also symmetric in the first order viscous predictions for all NPRs. However, second order viscous predictions captured unsteadiness, lambda shock, aftershock and flow separation (FSS and RSS) depending upon NPRs. The lambda shock becomes asymmetric after a certain time for NPR>/1.41. The flow unsteadiness is significant with asymmetric lambda shock. The shock oscillates with the asymmetry. The number of aftershock increases and the size of Mach stem reduces with increase in NPR. The computed solutions differ from the simple theory as far as shock location, shock structure, normal shock strength and aftershocks are concerned. However, the 2nd order viscous predicted results (shock structure, shock location, size of normal shock, aftershock, and asymmetric lambda shocks) are close to the experiments in most of the cases