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

The modification of the transonic flow structure around a NACA0012 aerofoil at free-stream Mach number 0.85 and at zero angle of incidence is studied as a function of Reynolds number in the range (500, 10,000) by solving the time-dependent Navier-Stokes equations as described in part I. At the selected value of the Mach number, the flow is subjected only to the von Karman-instability mode developed downstream of the trailing edge shock, as has been studied in part I. By using the time-dependent amplitude evolution versus the period of the fundamental mode, the coefficients of the Stuart-Landau global oscillator model have been evaluated, yielding the linear and non-linear parts of the instability process. The supercritical nature of mode I instability as well as the critical Reynolds number of this instability (Re = 2070) have been determined for the transonic regime. The spatial growth and decay of mode I instability are evaluated in the near wake by means of a detailed spectral analysis of the time-dependent signals. The variation law for the location of the maximum amplification of this near wake mode as a function of Reynolds number has been established and found to scale as: X-max similar to Re-0.2. (C) 2002 Elsevier Science Ltd. All rights reserved.