Nonlinear feedback control of bimodality in the wake of a three-dimensional bluff body

Abstract

The turbulent wake behind a square-back Ahmed body in close proximity to the ground exhibits bi-modal switching. This manifests as the centre of the wake switching between one of two asymmetric positions, either horizontally or vertically. Switches occur over random timescales, with the wake recovering symmetry in the long time-average. The present work employs wall-resolved large eddy simulations to investigate feedback control for suppressing horizontal (lateral) wake bi-modality of a square-back Ahmed body at ReH ∼ 3.3 × 10 4 based on the body height. Base-mounted pressure sensors are used to estimate the position of the wake as an input signal for the controller, while actuation targets the near-wake region via synthetic jets emanating from a gap around the perimeter of the Ahmed body base. A nonlinear feedback controller based on a Langevin model of the wake dynamics is synthesized. This successfully suppresses the wake lateral bi-modal switching. However, this switching is replaced by a time-periodic streamwise motion of the large coherent structure occupying the near-wake region, leading to amplification of the higher frequency dynamical wake modes. The action of feedback control also leads to base pressure recovery and a reduction in pressure drag. Upon varying the controller parameters, a trade-off between the degree of bi-modality suppression and drag reduction is observed. A maximum drag reduction of 7.4% is achieved for a semi-symmetrised wake, with a fully symmetrised wake achieving 2.5% reduction. Bi-modality suppression is proposed to have an indirect link to drag reduction through the effect of the wake state on the separated free shear layers and the upstream boundary layers.

Wake bi-modality: the effect of upstream boundary layer dynamics

“…This appendix shows the details of the mesh used in this study, which is similar to the mesh used in Ahmed & Morgans (2022). An unstructured hexahedral-dominant grid was used to optimise the usage of computational resources.…”

“…For both case-1 and case-3, horizontal bi-modality is suppressed (even if the oscillation bounds of the remaining wake fluctuations differ). Symmetrising the wake horizontally is known to have a favourable effect on base pressure recovery (Haffner et al 2020;Ahmed & Morgans 2022). The link between the mean base pressure recovery and the vertical asymmetry of the wake was previously investigated experimentally by Haffner et al (2020).…”

“…The dynamics of the free shear layers (mixing layers) is found to be related to the instantaneous spatial location of the recirculation region, which is directly linked to wake bi-modality. Vortex roll up at a relatively higher frequency of St H ∼ 1 is reported from one of the parallel shear layers, occurring interchangeably between them in a manner that follows the position of the recirculation region (Haffner et al 2020;Ahmed & Morgans 2022).…”

“…They include Kármán vortex shedding in both cross-flow directions, streamwise bubble pumping, bi-modal wake switching and mixing layer dynamics, as well as more complex interactions between these. Both experimental (Grandemange, Gohlke & Cadot 2013b;Haffner et al 2020) and numerical studies using direct numerical simulation (Podvin et al 2020), large eddy simulations (LES) (Hesse & Morgans 2021;Ahmed & Morgans 2022) and improved delayed detached eddy simulations (IDDES) (Fan et al 2020;Kang et al 2021) capture most of these modes.…”

“…2020) and numerical studies using direct numerical simulation (Podvin et al. 2020), large eddy simulations (LES) (Hesse & Morgans 2021; Ahmed & Morgans 2022) and improved delayed detached eddy simulations (IDDES) (Fan et al. 2020; Kang et al.…”