Bi-stability in the turbulent wake past parallelepiped bodies with various aspect ratios and wall effects

Abstract

The turbulent wake past parallelepiped bodies with a rectangular blunt trailing edge of height H and width W is investigated in wall proximity: various aspect ratios H* = H/W ∈ [0.51, 1.63] and ground clearances C* = C/W ∈ [0, 1.00] are explored at a Reynolds number of 4.5 × 104 based on the body width W. Base pressure measurements and particle image velocimetry show that the close wake often undergoes antisymmetric instabilities that can be either in the lateral direction (parallel to the wall) or in the vertical direction (normal to the wall). The instantaneous wake presents preferred states with high degrees of asymmetry; in some configurations, topology shifts are observed after long time scales Tl ∼ 103W/U0 leading to bistable behaviors. The effect of ground proximity is thoroughly studied for H* = 0.74 corresponding to the reference Ahmed geometry and for a case with a height dimension larger than its width H* = 1/0.74 = 1.34. When C* > 0.08, it is found that the Ahmed body is bistable in the lateral direction while the wake past the second geometry develops an instability in the vertical direction. In both cases, the instabilities vanish for sufficiently small values of ground clearance (C* < 0.08) which are associated with the apparition of a detachment of the underbody flow on the ground. However, the wall proximity does not necessarily stabilize the wake in the plane of symmetry since the flow retrieves the bi-stability in the lateral direction for C* < 0.03 and H* < 0.65. A general criterion for the existence of the instabilities is deduced from the parametric study in the domain (H*, C*) together with symmetry considerations.

Simulation and feedback control of the Ahmed body flow exhibiting symmetry breaking behaviour

“…This suggests that the initial symmetry breaking occurs once the Reynolds number is sufficiently high to create enough underbody flow for the top and bottom shear layers to interact and recirculate back towards the base. This further corroborates observations by Barros et al (2016) and Grandemange et al (2013a) that ground presence affects the boundary layer development along the body and thus influences the transverse asymmetry in the wake. It is further postulated that when the wake is symmetric, the two recirculating regions located horizontally side by side originate from the side shear layers interacting -a relationship that is broken at higher Reynolds numbers due to the strong bottom shear layer and the aspect ratio of the base (the top and bottom shear layers are closer to one another than the side shear layers).…”

“…The changes in the mean position of the wake Z w in the z-direction, observed in the numerical simulations as Reynolds number was increased, are shown in the bifurcation diagram in figure 2, alongside the experimental findings of Grandemange et al (2012 figure 3. At Re H = 310, the wake is 'steady symmetric' and consists of two recirculating regions aligned horizontally next to one another, as shown in the 3D streamlines on the right.…”

Fluid force and symmetry breaking modes of a 3D bluff body with a base cavity

“…As already pointed out by the previous studies of Grandemange et al (2013aGrandemange et al ( ,b, 2014bGrandemange et al ( , 2015, this flow is highly sensitive to any symmetry defects comprising both main flow inhomogeneities and geometrical imperfections. This sensitivity can be characterized by changing accurately the yaw angle β of the model.…”

Evolution of the bi-stable wake of a square-back automotive shape

“…12a) produces a distribution similar to that obtained by Gentile et al (2016) for the first two modes extracted from stereoscopic PIV cross-planes at a similar distance from the base of an axisymmetric body. In the axisymmetric body case, the symmetry breaking mode takes all azimuthal positions, so that the values of the temporal coefficients related to the two symmetry breaking modes are arranged around a uniform circular pattern, whereas here, the data tend to cluster around two distinct attractors, as the base aspect ratio allows the selection of only two stable asymmetric states (Grandemange and Gohlke 2013a). However, since there is still a dispersion of points around the centre of the plot and the related spatial modes are in quadrature, it was decided to fit a 1 (t) and a 3 (t) with a pair of trigonometric functions, such that the temporal coefficients could be reordered in phase (see Fig.…”

“…Focusing on the effects of base aspect ratio on the bistable mode Grandemange et al (2013a) showed a bi-stable motion of the wake in the lateral direction for W > H and in the vertical direction when H > W , suggesting the existence of a link between this phenomenon and the multi-stable behaviour already seen for axisymmetric bodies such as spheres (Chrust et al 2013, Grandemange et al 2014a) and cylinders with a sharp trailing edge (Rigas et al 2014, Gentile et al 2016). In the axisymmetric cases, the instantaneous wake has been shown to explore all azimuthal locations W uniformly, because of the infinite number of azimuthal symmetry planes.…”