On the recirculating flow of three-dimensional asymmetric bluff bodies
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LETTER
On the recirculating flow of three‑dimensional asymmetric bluff bodies Antoine Legeai1 · Olivier Cadot1 Received: 24 June 2020 / Revised: 13 October 2020 / Accepted: 19 October 2020 © The Author(s) 2020
Abstract The paper investigates the role of geometrical asymmetric modifications of a rectangular flat-backed body on the properties of the recirculating flow at a Reynolds number Re = 1.8 × 105 . The reference model has two reflectional symmetries denoted sy and sz in both spanwise directions. The flow is subjected to the static instability that leads to two mirrored wake states breaking the symmetry sy . Two families of geometrical variation of the fore-body and after-body are studied, each breaking one of the reflectional symmetries of the reference model. Geometrical modifications that preserve sy evidence possibilities of bistable dynamics suppression although the static instability persists. Geometrical modifications that do not preserve sy produces a large unbalance of both wake states in accordance to recent observations on real cars (Bonnavion et al. in J Wind Eng Ind Aerodyn 184:77–89, 2019). Results offer perspectives for potential drag reduction induced by appropriate coupling of bluff body geometry and wake state selection. Graphic abstract
1 Introduction Flat-backed three-dimensional bluff bodies are known to develop a static instability responsible for a permanent symmetry breaking or deviation of the wake. For Reynolds * Olivier Cadot [email protected] 1
University of Liverpool, Liverpool, UK
numbers beyond the laminar regime where turbulence restores symmetries, very long time dynamics are observed. They are associated with random rotations of the deviated wake for circular base bodies (see Rigas et al. 2014, 2015 for seminal papers) and random switching of two opposite wake deviations (bistability) for rectangular base bodies (see Grandemange et al. 2012, 2013b for seminal papers). In the later case, the wake deviations are observed in the major direction of the rectangular base (Grandemange et al. 2013a;
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Bonnavion and Cadot 2018). Two cases need to be distinguished whether the deviations are in a perpendicular or parallel direction to the ground, respectively, referring to as the z and y-instability following (Grandemange et al. 2013a). The z-instability has first been reported by Grandemange et al. (2013a). For sufficiently high ground clearance (larger than only 7% of the body width), it produces two possible wake states globally deviated towards the top or the ground, with a positive (P state) or negative (N state) vertical base pressure gradient, respectively. This instability has been studied in several academic experiments in a Reynolds number range based on the body height H, of Re ≈ 4.5 × 104 –6.7 × 105 in Grandemange et al. (2013a), Schmidt et al. (2018) and Bonnavion and Cadot (2018), and numerically at Re = 5.2 × 104 in Dalla Longa et al. (2019). Although there is no symmetry in the vertical direction (due to the ground a
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