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

摘要

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, 1000) 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 downream 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{sub}(max) ～ Re{sup}(-0.2).