Properties of the mean recirculation region in the wakes of two-dimensional bluff bodies

Abstract

The properties of the time-and span-averaged mean wake recirculation region are investigated in separated flows over several different two-dimensional bluff bodies. Ten different cases are considered and they divide into two groups : cylindrical geometries of circular, elliptic and square cross-sections and the normal plate. A wide Reynolds number range from 250 to 140 000 is considered, but in all the cases the attached portion of the boundary layer remains laminar until separation. The lower Reynolds number data are from direct numerical simulations, while the data at the higher Reynolds number are obtained from large-eddy simulation and the experimental work of Cantwell & Coles (1983), Krothapalli (1996, personal communication), Leder (1991 and Lyn et al. (1995). Unlike supersonic and subsonic separations with a splitter plate in the wake, in all the cases considered here there is strong interaction between the shear layers resulting in Ka! rma! n vortex shedding. The impact of this fundamental difference on the distribution of Reynolds stress components and pressure in relation to the mean wake recirculation region (wake bubble) is considered. It is observed that in all cases the contribution from Reynolds normal stress to the force balance of the wake bubble is significant. In fact, in the cylinder geometries this contribution can outweigh the net force from the shear stress, so that the net pressure force tends to push the bubble away from the body. In contrast, in the case of normal plate, owing to the longer wake, the net contribution from shear stress outweighs that from the normal stress. At higher Reynolds numbers, separation of the Reynolds stress components into incoherent contributions provides more insight. The behaviour of the coherent contribution, arising from the dominant vortex shedding, is similar to that at lower Reynolds numbers. The incoherent contribution to Reynolds stress, arising from small-scale activity, is compared with that of a canonical free shear layer. Based on these observations a simple extension of the wake model (Sychev 1982 ; Roshko 1993 a, b) is proposed.

Aerodynamic drag of a transiting sphere by large-scale tomographic-PIV

“…Along the wake the contribution of the Reynolds normal stress is significant and cannot be neglected when computing the aerodynamic drag. This agrees with the study of Balachandar et al (1997) who evaluated the contribution of the Reynolds normal stress to the wake of two-dimensional bluff bodies and suggested the presence of shear layer interactions in the vortex shedding dynamics.…”

Harbor seal vibrissa morphology suppresses vortex-induced vibrations

“…The validity of the simulation method as well as the grid independency were confirmed by calculating the wake of a circular cylinder at a Reynolds number (Re) of 500 and performing a detailed comparison with numerical and experimental data from various sources (Balachandar et al, 1997;Brede et al, 1996;Leder, 1991;Zdravkovich, 1995;Zdravkovich, 2003). The results were in very good agreement with the literature concerning the Strouhal number, separation angle and Reynolds stresses of the flow.…”

The wake of two side-by-side square cylinders

“…An alternative definition is the transverse separation between the two maxima in the u * rms -contours (Griffin & Ramberg 1974;Ramberg 1983), which has been widely used (e.g. Roshko 1993;Balachandar, Mittal & Najjar 1997;Paranthoen et al 1999;Alam & Zhou 2007b). This width is linked with the fluid forces on the wake generator.…”