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Unstable wake dynamics of rectangular flat-backed bluff bodies with inclination and ground proximity

  • Guillaume Bonnavion (a1) and Olivier Cadot (a2)


The paper investigates experimentally the global wake dynamics of a simplified three-dimensional ground vehicle at a Reynolds number of $Re\simeq 4.0\times 10^{5}$ . The after-body has a blunt rectangular trailing edge leading to a massive flow separation. Both the inclination (yaw and pitch angles) and the distance to the ground (ground clearance) are accurately adjustable. Two different aspect ratios of the rectangular base are considered; wider than it is tall (minor axis perpendicular to the ground) and taller than it is wide (major axis perpendicular to the ground). Measurements of the spatial distribution of the pressure at the base and velocity fields in the wake are used as topological indicators of the flow. Sensitivity analyses of the base pressure gradient expressed in polar form (modulus and phase) varying ground clearance, yaw and pitch are performed. Above a critical ground clearance and whatever the inclination is, the modulus is always found to be large due to the permanent static symmetry-breaking instability, and slightly smaller when aligned with the minor axis of the base rather than when aligned with the major axis. The instability can be characterized with a unique wake mode, quantified by this modulus (asymmetry strength) and a phase (wake orientation) which is the key ingredient of the global wake dynamics. An additional deep rear cavity that suppresses the static instability allows a basic flow to be characterized. It is shown that both the inclination and the ground clearance constrain the phase dynamics of the unstable wake in such way that the component of the pressure gradient aligned with the minor axis of the rectangular base equals that of the basic flow. Meanwhile, the other component related to the major axis adjusts to preserve the large modulus imposed by the instability. In most cases, the dynamics explores only two possible opposite values of the component along the major axis. Their respective probability depends on the geometrical environment of the wake: base shape, body inclination, ground proximity and body supports. An expression for the lateral force coefficients taking into account the wake instability is proposed.


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Supplementary materials

Bonnavion et al. supplementary movie
Instantaneous base pressure distribution~$c_{p}(y^{*},z^{*},t^{*})$ for nose-down, baseline and nose-up configurations corresponding to the time series in figure 6. The signals are low-pass filtered by an averaging on a sliding window of time duration~$t_{w}^{*}=33.3$

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