Effect of array submergence on flow and coherent structures through and around a circular array of rigid vertical cylinders

Flow past a submerged array of rigid cylinders is more complex compared to the limiting case of an emerged array because part of the flow approaching the array is advected over it and the mean-flow three-dimensionality is increased inside and around the array. For sufficiently high submergence, the flow moving over the top of the array generates a vertical separated shear layer (SSL) and modifies the structure of the wake flow. The case of a circular array of diameter D containing solid cylinders of diameter d (=0.03D) and height h(p) placed in a flat-bed open channel of depth h = 0.56D is investigated. Detached eddy simulations that resolve the flow past the individual cylinders are conducted at a Reynolds number Re-D = 37 500 for two solid volume fractions (SVF) of the array region (SVF = Nd-2/D-2 = 0.09 and SVF = 0.23 corresponding to aD = 3.9 and 9.6, where N is the number of cylinders in the array and aD is the nondimensional frontal area per unit volume for the array) and several values of the relative height of the cylinders (h(p)/h = 0.25, 0.5, 0.75, and 1). Results are also compared with the limiting case of a solid cylinder (SVF = 1). The strong weakening of the antisymmetric vortex-shedding mode observed for submerged cases with h(p)/h <= 0.75 is related to the flow component advected over the array and the formation of a U-shaped vortex behind the array, which impedes the interactions of the two lateral (horizontal) SSLs forming on the sides of the array. For sufficiently high SVFs and high array submergence, the U-shaped vortex penetrates inside the array, which means that fluid and particles from the near wake can enter the array region. The decrease in h(p)/h reduces the coherence of the horseshoe vortex forming in front of the array, the length of the steady wake region, and the Strouhal number associated with the antisymmetric shedding mode. Simulation results show that billow vortices have a much reduced capacity to entrain and carry sediments in the wake of the array even for relatively low array submergences (e.g., for h(p)/h = 0.75) compared to h(p)/h = 1. The decrease in the mean streamwise drag coefficient for the cylinders in the array, Cd, with the decrease in h(p)/h, is nearly linear for h(p)/h > 0.25. The rate of decay of Cd with the decrease in h(p)/h increases with the SVF. Using the simulation results, the paper also discusses how changes in the flow structure triggered by increased array submergence affect nutrient and sediment transport inside and around vegetated patches in natural erodible channels.