Disappearing Wakes and Dispersion in Numerically Simulated Flows Through Tube Bundles

Abstract

Flow through a staggered array or ‘bundle’ of parallel rigid cylinders of diameter D is computed with the help of a three-dimensional direct numerical simulation (DNS) at various values of Reynolds number between 50 and 6000. Two different spacings L of the tubes, i.e. L/D= 2 and L/D= 3, have been considered. When Re≲ 500 the flow is laminar. In that case the converging flow between a pair of adjacent cylinders brings the oppositely signed vorticity at the two edges of the wake closer together behind the upstream cylinder so that the vorticity decreases quickly due to cancellation by diffusion. At Re≈ 6000, when the flow is highly turbulent, the wake vorticity disappears rather by turbulent diffusion. This ‘disappearance’ of the wakes in the closely packed flows (i.e. L/D≲ 2) causes the mean flow in a ‘cell’, which consists of the region around a single cylinder, to be effectively independent of that in other cells. Another consequence is that the mean velocity field can be very well approximated by potential flow except in a thin boundary layer along the cylinder and a short wake behind it. The results have been applied to the transport of scalars in closely packed arrays. As in other complex flows, the dispersion of the scalars is dominated by the divergence and convergence of the streamlines around the cylinder rather than by the wake turbulence. Approximate expressions are derived for this ‘topologically’ influenced dispersion in terms of the geometry of the array. The fact when most of the flow in the array can be approximated by a potential flow, allows us to introduce a fast approximate calculation method to compute the dispersion.