Flow and coherent structures generated by a circular array of rigid, emerged cylinders in a shallow channel

Abstract

The study investigates the flow structure, dynamics of the large-scale coherent structures, drag forces and sediment entrainment mechanisms generated by a circular array of diameter D containing rigid emerged circular cylinders of diameter d placed in a smooth-bed channel of depth h under strong shallow flow conditions (D/h = 20, d/D = 0.0125 and 0.025). Eddy resolving simulations are conducted with different values of the solid volume fraction 0.025 ≤ SVF ≤ 0.1 and non-dimensional frontal area per unit volume (2.56 ≤ aD ≤ 10.2, where for the present configuration, a = SVF(1/d)4/ ${\rm \pi}$ ) and a fixed channel Reynolds number (Reh = 10 000). The flow conditions are such that a vortex street (VS)-type of shallow wake is expected to form for a solid cylinder of diameter D. Findings are compared with previous results obtained for cases with moderately shallow conditions 2.5 ≤ D/h ≤ 3.5 and with the limiting case of flow past a solid cylinder with D/h = 20. For moderately shallow conditions, the core of the main horseshoe vortex (HV) forming around the array occupies a small fraction of the water column and its coherence is the largest in front of the array. By contrast, for very shallow conditions, multiple HVs form around the array and their cores occupy a large fraction of the water column. Moreover, the coherence of most of these HVs peaks close to the sides of the array. Only for relatively large aD values, the main HV extends over the whole upstream face of the array, similar to the limiting case of a solid cylinder. For sufficiently high aD, a secondary instability is present inside the near wake that leads to the formation of parallel horizontal vortices in the vicinity of the wake roller vortices. The changes in the wake structure with decreasing SVF and aD are qualitatively similar to those observed for cases with moderately shallow flow conditions, with the antisymmetric wake shedding mode being suppressed for aD ≤ 2.5. However, the Strouhal number associated with the shedding of wake rollers, which is still close to 0.2 for a solid cylinder with D/h = 20, can be as high as 0.4 for aD = 2.5. The paper also discusses how the steady wake and total wake lengths and the strength of the bleeding flow vary with the SVF. Simulation results show that the capacity of the flow to entrain sediment inside and around the array peaks for SVF = 0.05 and aD = 5.2, with sediment entrainment monotonically increasing with the SVF outside the array and monotonically decreasing inside the array. Despite the differences in the flow structure next to and inside the array, the variation of the mean, time-averaged streamwise drag coefficient of the solid cylinders ${\bar{C}_d}$ with aD is close to that observed for arrays with moderately shallow flow conditions. The combined drag coefficient for the array decreases with increasing flow shallowness, with the decay being stronger for relatively large values of aD.