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Reynolds number effects on the coherent dynamics of the turbulent horseshoe vortex system. (English) Zbl 1295.76013
Summary: 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 (W. J. Devenport and R. L. Simpson [J. Fluid Mech. 210, 23–55 (1990)]; J. Paik et al. [Phys. Fluids 19, No. 4, 045107, 20 p. (2007; Zbl 1146.76499)] ). We carry out detached eddy simulations (DES) of the flow past a circular cylinder mounted on a rectangular channel for $$Re = 2.0 \times 10^{4}$$ and $$3.9 \times 10^{4}$$ [B. Dargahi, Exp. in Fluids 8, 1–12 (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 $$(Re = 1.15 \times 10^{5})$$ [Devenport and Simpson (loc. cit.); Paik et al.,(loc. cit.)]. 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 $$Re = 2.0 \times 10^{4}$$ the HSV system consists of a large number of necklace-type vortices that are shed periodically at higher frequencies than those observed in the $$Re = 3.9 \times 10^{4}$$ 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 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.

##### MSC:
 76F65 Direct numerical and large eddy simulation of turbulence 76F40 Turbulent boundary layers
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