Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil: Part I: Mach number effect

The identification of successive stages in the transition of unsteady viscous transonic flow around an aerofoil is carried out by solving the time-dependent Navier-Stokes equations for a compressible fluid in two-dimensional approach. The numerical simulation is carried out at the Mach number range (0.2-0.98). At a fixed Reynolds number (Re=10,000), it is found that this flow undergoes the following four transition steps: It remains steady up to the Mach number values (0.2-0.35) and afterwards it develops spontaneously, without any imposed artificial perturbation, an inherent unsteadiness corresponding to a near-wake von Kármán instability, in the Mach number range (0.35-0.9). It is found that there exists a critical Mach number between the values (0.90-0.95) for which the flow returns to a steady-state. Furthermore, the flow is found to be governed by two instability processes in the Mach number range (0.75-0.8), where, apart from the von Kármán mode (mode I), a lower frequency mode II appears, due to the formation of weakly supersonic alternating zones in the region upstream of the aerofoil, related to the buffeting phenomenon. A triple role played by the increasing compressibility effects to trigger the instability processes, to maintain and to inhibit them in the transonic flow regime is therefore analysed in detail.