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Some recent work on the existence of vibrational de-excitation shocks (δ-shocks) in expanding non-equilibrium nozzle flows is extended to include situations in which an adiabatic shock (δ-shocks) may be embedded within the de-excitation shock. A discussion of some further properties of the shock solution is given and some examples are worked out. Numerical solutions of the full equations are also presented. These solutions confirm the existence of the δ-shocks but bring to light certain anomalies in the simple approximate solution. The modifications necessary to remove these discrepancies are outlined, and the implications of the numerical results are briefly discussed. Finally, some comments on the nature of the asymptotic solution for an arbitrary rate process are made.

Direct numerical simulation (DNS) of jets in cross-flow (JICF) has been carried out in this study, aiming for the investigation of vortex structure formation and evolution process associated with JICF. A recently developed DNS code is used, which solves three-dimensional (3D) compressible unsteady Navier–Stokes (NS) equations using high-order finite differences and multi-block structure grid treatment for complex geometry. Jet flow from a square duct, perpendicular to the mainstream flow, is introduced and the flow Reynolds number is 100 based on the jet duct diameter (D) and free-stream quantities. Two-dimensional (2D) calculations using various jet to free-stream velocity ratio (R = V jet/V free) reveals different vortex patterns and a further 3D study continues focusing on a velocity ratio of R = 2, for which complex vortex structure is produced. It is found from the 3D simulation that a counter-rotating vortex pair (CRVP) forms immediately after the jet exits, as observed from the experimental test and reproduced by other numerical simulations. The CRVP originates from the near wall viscous layer and its core position moves away from the wall as it evolves downstream. For the condition simulated, the CRVP is finally weakened (due to viscous diffusion) at about 1.6D downstream from the centre of the jet exit. No asymmetric CRVP has been observed, which was reported by other researchers for high-Reynolds number simulations

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