Reynolds Number Effects on the Coherent Dynamics of the Turbulent Horseshoe Vortex System

Abstract

The adverse pressure gradient induced by a surface-mounted obstacle in a turbulent boundary layer causes the approaching flow to separate and form a dynamically rich horseshoe vortex system (HSV) in the junction of the obstacle with the wall. The Reynolds number of the flow (Re) is one of the important parameters that control the rich coherent dynamics of the vortex, which are known to give rise to low-frequency, bimodal fluctuations of the velocity field (Devenport and Simpson, J Fluid Mech 210: 23-55, 1990; Paik et al., Phys Fluids 19:045107, 2007). We carry out detached eddy simulations (DES) of the flow past a circular cylinder mounted on a rectangular channel for Re = 2.0 × 10 4 and 3.9 × 10 4 (Dargahi, Exp Fluids 8: [1][2][3][4][5][6][7][8][9][10][11][12] 1989) in order to systematically investigate the effect of the Reynolds number on the HSV dynamics. The computed results are compared with each other and with previous experimental and computational results for a related junction flow at a much higher Reynolds number (Re = 1.15 × 10 5 ) (Devenport and Simpson, J Fluid Mech 210: 23-55, 1990; Paik et al., Phys Fluids 19:045107, 2007). The computed results reveal significant variations with Re in terms of the mean-flow quantities, turbulence statistics, and the coherent dynamics of the turbulent HSV. For Re = 2.0 × 10 4 the HSV system consists of a large number of necklace-type vortices that are shed periodically at higher frequencies than those observed in the Re = 3.9 × 10 4 case. For this latter case the number of large-scale vortical structures that comprise the instantaneous HSV system is reduced significantly and the flow dynamics becomes quasi-periodic. For both cases, we show that the instantaneous flowfields are dominated by eruptions of wall-generated vorticity associated with the growth of hairpin vortices that wrap around and disorganize the primary HSV 232 Flow Turbulence Combust (2011) 86:231-262 system. The intensity and frequency of these eruptions, however, appears to diminish rapidly with decreasing Re. In the high Re case the HSV system consists of a single, highly energetic, large-scale necklace vortex that is aperiodically disorganized by the growth of the hairpin mode. Regardless of the Re, we find pockets in the junction region within which the histograms of velocity fluctuations are bimodal as has also been observed in several previous experimental studies.

Quantitative Spatio-Temporal Characterization of Scour at the Base of a Cylinder

“…Also, the slopes of the radial profiles (Figure 9) within the wake region are becoming flatter towards the wake region. According to the literature, the flow components that drive the temporal evolution and the shape of the wake region are the vortices that are shed periodically downstream of the pier [4,40] and the oscillating legs of the horseshoe vortex [28,29,40]. Similar to the observations at the front and the side regions, there is not an evident imprint of the aforementioned flow components in the scour rate maps.…”

“…The reduced scour rates, at the front and side regions, are commonly explained by the increase in the size of the horseshoe vortex that scales with the span of the scour hole [13,28,29]. As the size of the horseshoe vortex increases, its strength decreases and exerts lower shear stresses on the bed.…”

“…Thorough descriptions of the evolving morphological characteristics of the bed and correlations with the flow are provided in recent numerical simulations in [27][28][29]. These groups carried out coupled modelling of the flow characteristics and the bed evolution in an effort to identify the cause and effect relationships that drive scour.…”

Time-resolved flow dynamics and Reynolds number effects at a wall–cylinder junction

“…More recent studies employing the state-of-the-art in physical and numerical modelling (Praisner & Smith 2006b;Paik, Escauriaza & Sotiropoulos 2007;Kirkil & Constantinescu 2009;Sabatino & Smith 2009;Escauriaza & Sotiropoulos 2011c) showed that the time-averaged horseshoe vortex system consists of: (i) a primary vortex (HV1), which rotates in a clockwise sense (assuming that flow enters the junction region from the left), (ii) a secondary vortex (HV2) again with a clockwise sense of rotation and located upstream of HV1 and (iii) a corner vortex (CV) of counterclockwise rotation positioned downstream of HV1. A tertiary vortex (HV3) is frequently resolved in instantaneous topologies and is located at the saddle between HV1 and HV2 (Praisner & Smith 2006a;Gand et al 2010;Escauriaza & Sotiropoulos 2011c). Occasionally, the cinematography of the flow field reveals various smaller and short-lived vortical structures upstream of HV2.…”

“…Occasionally, the cinematography of the flow field reveals various smaller and short-lived vortical structures upstream of HV2. However, the dependence of the dynamics of the instantaneous junction vortices, including their number, on Re D remains unclear (Dargahi 1989;Escauriaza & Sotiropoulos 2011c).…”