Numerical investigation of turbulent supersonic axisymmetric wakes

Abstract

AbstractNumerical experiments are conducted of turbulent supersonic axisymmetric wakes at Mach number $M= 2. 46$ and Reynolds number, based on free-stream velocity and base diameter, ${\mathit{Re}}_{D} = 1\ensuremath{\times} 1{0}^{5} $. Direct numerical simulations (DNS) are used to study the effect of approach flow conditions, and of specific azimuthal modes, on the near-wake behaviour. To that end, DNS are performed with laminar and turbulent approach boundary layers, and additional turbulent approach flow DNS with reduced circumferential size are conducted to deliberately eliminate certain azimuthal/helical modes. DNS with turbulent approach flow show an increased turning angle and increased growth of the separating shear layer, leading to a shorter recirculation region, a stronger recompression shock system, and ultimately good agreement with experimental data at considerably higher Reynolds number. A similar wake structure is found for laminar and turbulent inflow conditions, giving further evidence of the wake structure being a consequence of the global near-wake instabilities and not a result of upstream conditions. Stability analyses of two-dimensional basic states are carried out by computing the temporal pulse response using forced Navier–Stokes simulations to investigate which azimuthal modes are dominant for fully turbulent wakes and how the stability behaviour is influenced by the choice of basic state. Using the time- and azimuthally averaged data from three-dimensional DNS with turbulent inflow as basic state, an absolute instability of the axisymmetric mode was found and helical modes $m= 4, 5, 6$ were found to be linearly most unstable, in contrast to results obtained earlier using an axisymmetric flow solution as the basic state. The addition of a turbulence viscosity in the forced DNS retains most of the stability characteristics but reduces the wavenumber of the linearly most-amplified modes.