Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability

Abstract

The flow around the three-dimensional blunt geometry presented in the work of Ahmed, Ramm & Faitin (Tech. Rep., 1984) is investigated experimentally at $\mathit{Re}= {U}_{0} H/ \nu = 9. 2\times 1{0}^{4} $ (where ${U}_{0} $ is free-stream velocity, $H$ the height of the body and $\nu $ viscosity). The very large recirculation on the base responsible for the dominant part of the drag is characterized. The analyses of the coherent dynamics of the wake reveal the presence of two very distinctive time scales. At long time scales ${T}_{l} \sim 1{0}^{3} H/ {U}_{0} $, the recirculation region shifts between two preferred reflectional-symmetry-breaking positions leading to a statistically symmetric wake; the sequence of these asymmetric states is random. This bi-stable behaviour is independent of the Reynolds number but occurs only above a critical value of ground clearance. At short time scales ${T}_{s} \sim 5H/ {U}_{0} $, the wake presents weak coherent oscillations in the vertical and lateral directions. They are respectively associated with the interaction of the top/bottom and lateral shear layers; when normalized by the height and width of the body, the Strouhal numbers are close to 0.17. These results suggest an alternate shedding associated with the vertical oscillation and a one-sided vortex shedding in the lateral direction with an orientation linked to the current asymmetric position. Finally, the impact of these coherent wake motions on the base pressure is discussed to motivate further drag reduction strategies.

Low-dimensional dynamics of a turbulent axisymmetric wake

“…In the spectrum of the angular component, a power-law with an exponent close to -2 is obtained at very low frequencies (VLF). This is analogous to the results of Grandemange et al (2013), and consistent with Brownian dynamics (Brown & Ahlers 2006). Hence the VLF oscillation is a random rotation of the CoP in the azimuthal direction around the axis of the body.…”

High-frequency forcing of a turbulent axisymmetric wake

“…Monkewitz (1988) conducted a linear stability analysis for a family of axisymmetric wake (parallel flow) profiles: he showed that this asymmetric mode is absolutely unstable, and in agreement with experimental observation by Taneda (1978), he noted that it is most clearly observed somewhat downstream of the body. Grandemange et al (2013) show that these characteristics are consistent with those of a wake from a threedimensional body of rectilinear geometry. Ho & Huerre (1984) have identified the boundarylayer momentum thickness, θ, as the appropriate length scale.…”

Low-frequency behavior of the turbulent axisymmetric near-wake

“…Such low-frequency variations result in the axial symmetry being achieved only by very long-term averaging. An analogous instability has been observed in the wake behind spheres 9 as well as rectilinear bodies (e.g., Ahmed bodies), 10 whereby in the latter case it occurs as an irregular shift of the recirculation bubble between two preferred anti-symmetric states. Furthermore, this phenomenon shows similarity with the precession motion experienced by the stagnation point in the wake of turbulent annular jets, 11 featuring a comparable characteristic frequency (St D ≈ 0.0025, D being the jet diameter).…”

“…The existence of such a backflow low-frequency unsteadiness has previously been linked to the persistence in the turbulent regime of the symmetry-breaking mode, 10,11 with the prescribed symmetry plane continuously changing its orientation in view of its sensitivity to external perturbations. 12,13 Asymmetries in the near-wake flows of axisymmetric bodies have been documented in the literature for subsonic conditions [14][15][16] as well as in the transonic 17 and supersonic regime 18 and are mainly ascribed to boundary condition effects such as misalignments between wind-tunnel model and free-stream flow.…”

“…The influence of the recirculating flow unsteadiness on the mean, instantaneous, and fluctuating flow field has been reported for three-dimensional 10 and axisymmetric configurations. 8,9 However, the correlation between backflow precession and the shedding phenomenon requires further clarification, both being m = 1 modes, but occurring at significantly different time scales.…”