Large scale dynamics of a high Reynolds number axisymmetric separating/reattaching flow

Abstract

A numerical study is conducted to unveil the large scale dynamics of a high Reynolds number axisymmetric separating/reattaching flow at M∞ = 0.7. The numerical simulation allows us to acquire a high rate sampled unsteady volumetric dataset. This huge amount of spatial and temporal information is exploited in the Fourier space to visualize for the first time in physical space and at such a high Reynolds number (ReD = 1.2 × 106) the statistical signature of the helical structure related to the antisymmetric mode (m = 1) at StD = 0.18. The main hydrodynamic mechanisms are identified through the spatial distribution of the most energetic frequencies, i.e., StD = 0.18 and StD ≥ 3.0 corresponding to the vortex-shedding and Kelvin-Helmholtz instability phenomena, respectively. In particular, the dynamics related to the dimensionless shedding frequency is shown to become dominant for 0.35 ≤ x/D ≤ 0.75 in the whole radial direction as it passes through the shear layer. The spatial distribution of the coherence function for the most significant modes as well as a three-dimensional Fourier decomposition suggests the global features of the flow mechanisms. More specifically, the novelty of this study lies in the evidence of the flow dynamics through the use of cross-correlation maps plotted with a frequency selection guided by the characteristic Strouhal number formerly identified in a local manner in the flow field or at the wall. Moreover and for the first time, the understanding of the scales at stake is supported both by a Fourier analysis and a dynamic mode decomposition in the complete three-dimensional space surrounding the afterbody zone.