A numerical investigation of the asymmetric wake mode of a squareback Ahmed body – effect of a base cavity

Abstract

Numerical simulations of the turbulent flow over the flat backed Ahmed model at Reynolds number $Re\simeq 4\times 10^{5}$ are conducted using a lattice Boltzmann solver to clarify the mean topology of the static symmetry-breaking mode of the wake. It is shown that the recirculation region is occupied by a skewed low pressure torus, whose part closest to the body is responsible for an extra low pressure imprint on the base. Shedding of one-sided vortex loops is also reported, indicating global quasi-periodic dynamics in conformity with the seminal work of Grandemange et al. (J. Fluid Mech., vol. 722, 2013, pp. 51–84). Despite the limited low frequency resolution of the simulation, power spectra of the lateral velocity fluctuations at different locations corroborate the presence of this quasi-periodic mode at a Strouhal number of $St=0.16\pm 0.03$. A shallow base cavity of $5\,\%$ of the body height reduces the drag coefficient by $3\,\%$ but keeps the recirculating torus and its interaction with the base mostly unchanged. The drag reduction lies in a global constant positive shift of the base pressure distribution. For a deep base cavity of $33\,\%$ of the body height, a drag reduction of $9.5\,\%$ is obtained. It is accompanied by a large elongation of the recirculation inside the cavity that considerably attenuates the low pressure sources therein together with a symmetrization of the low pressure torus. The global quasi-periodic mode is found to be inhibited by the cavity.

Simulations of the bi-modal wake past three-dimensional blunt bluff bodies

“…Simulations which accurately capture the wake unsteadiness at high Reynolds number, and which furthermore extend over the large time scales of bi-modal switching, are very costly. Unsteady simulations of simplified bluff body flows have been performed using partially averaged Navier-Stokes (PANS), simulations (Mirzaei, Krajnović & Basara 2015;Rao et al 2018a), unsteady Reynolds-averaged Navier-Stokes simulations (Khalighi, Chen & Iaccarino 2012), detached eddy simulations and large eddy simulations (Krajnović & Davidson 2003;Serre et al 2013;Aljure et al 2014;Östh et al 2014;Rao et al 2018b), some also employing a lattice Boltzmann formulation (Roumeas et al 2009;Lucas et al 2017 The present study achieves what we believe are the first simulations of wake bi-modality, capturing both asymmetric states, for a blunt bluff body. No artificial forcing nor inlet perturbations are applied to trigger bi-modality; the flow develops naturally from a steady inlet velocity condition, with bi-modal switches occurring randomly.…”

“…For blunt bluff body flows, it is well known that a low-pressure toroidal vortex structure typically appears in the near wake, and can be visualised by considering iso-contours of negative pressure coefficient (Krajnović & Davidson 2003;Roumeas et al 2009;Lucas et al 2017). Figure 9 shows high-frequency snapshots of these pressure iso-contours for the very fine grid simulations of the lorry and the baseline grid simulations of the Ahmed body, respectively exhibiting vertical and horizontal bi-modality.…”

“…Eventually, a baseline mesh composed of 56.6 million cells was chosen for both bluff bodies (figure 2). These baseline meshes were already refined compared with similar numerical studies performed at higher Reynolds number (Krajnović 2014;Östh et al 2014;Lucas et al 2017), and are sufficiently refined near the body walls such that y + 1 for both cases, the widely held benchmark for which the turbulent boundary layer can be taken to be properly resolved. Additional finer meshes were also used for comparison, these having the same first cell height (and hence y + ) as the baseline grid, but more closely spaced cells in the boundary layer region beyond this, around the bluff body and in the wake.…”

Three dimensional structure of the unsteady wake of an axisymmetric body

“…31 The fact that only one of these two states remains when the data are filtered with either a low-pass filter or a high-pass filter (both with a cut-off frequency of 5 Hz) provides useful information for the implementation of flow control strategies aiming to reduce the drag. It is shown that the selection of an axisymmetric pressure distribution is not a necessary condition to achieve a base drag reduction, although it is the only admissible low-drag scenario when the short-time wake dynamics are filtered-out, for example, by adding a cavity to the model base, as shown by Lucas et al 25 The existence of a link between the "pumping mode" described in the work of Berger et al 5 and the flapping mode isolated at St D ≈ 0.10 by Rigas et al 36 is also proposed. Both modes appear to be associated with the alternate expansion and contraction of the coherent structures forming the "hairpin vortex," with characteristic frequencies ranging from St D = 0.08, close to the centre of the base, up to St D = 0.095 in proximity to the model trailing edge.…”

“…Their shedding has been found to be at the origin of the flapping motions of the wake closure that characterises the short-time wake dynamics. 18,25 Additional information on such dynamics can be gathered from the spectral analysis of the signals recorded by pressure taps located at different radial locations. As shown in Fig.…”