Drag forces and flow structure around and inside a square array of emerged cylinders in an open channel

Eddy resolving simulations are used to describe the mean flow and turbulence structure inside and around a square array of width D containing emerged (i.e., cylinder extending up, or above, the free surface), rigid cylinders of width d . The array is placed at the centre of a long open channel of width W . The study describes how the structure of the wake and shear layers forming along the lateral sides of the array, the wake spectral content and shedding modes, the bleeding velocity, the lengths of the steady and total wake regions, the coherence of the horseshoe vortices forming around the frontal face of the array, the bed shear stresses and the sediment entrainment capacity of the flow inside and outside the array change with the main geometrical parameters defining the array (i.e. the solid volume fraction, SVF, the non-dimensional frontal area per unit volume of the array, italic aD aD $\textit{aD}$ , the shape of the cylinders and d divided by upper D d / D $d/D$ ) and the blockage ratio, upper W divided by upper D W / D $W/D$ . The effects of varying the same geometrical parameters on the total non-dimensional streamwise drag force acting on the array and on the streamwise distribution of the drag force inside the array are quantified. The mean flow and turbulence inside the array are analysed based on the streamwise distributions of the double-averaged (i.e. over time, D and the flow depth, H ) streamwise velocity, upper U overbar overbar U ¯ ¯ $\overline{\overline{U}}$ , and turbulent kinetic energy. Contrary to wakes generated behind circular arrays of emerged cylinders, several streamwise-oriented vortices are generated inside the wake of square arrays for a limited range of italic aD aD $\textit{aD}$ . These vortices increase flow three-dimensionality and vertical transport behind square arrays. Despite the relatively large values of the array and channel Reynolds numbers (i.e. Re _D = 40 000, Re _H = 14 000), the mean (time and spanwise-averaged) cylinder drag coefficient, upper C prime Subscript d C d ′ ${C}_{d}^{\prime}$ ( x ), defined with d , H and upper U overbar overbar U ¯ ¯ $\overline{\overline{U}}$ is not close to constant over the whole length of the array in some of the dense array simulations. In these cases, upper C prime Subscript d C d ′ ${C}_{d}^{\prime}$ starts increasing monotonically over the downstream part of the array, as the flow transitions from the quadratic drag regime to the linear drag regime. When plotted versus the cylinder Reynolds number ModifyingAbove italic Re Subscript d Baseline With bar equals upper U overbar overbar d slash Re d ¯ = U ¯ ¯ d / $\overline{\textit{Re}_{d}} = \overline{\overline{U}}d/$ ν ( ν is the viscosity), upper C prime Subscript d C d ′ ${C}_{d}^{\prime}$ = 2 α ₀ / ModifyingAbove italic Re Subscript d Baseline With bar Re d ¯ $\overline{\textit{Re}_{d}}$ over the linear drag regime. The parameter α ₀ and the critical value of ModifyingAbove italic Re Subscript d Baseline With bar Re d ¯ $\overline{\textit{Re}_{d}}$ corresponding to the start of the linear drag regime are strongly influenced by the main geometrical parameters of the array and the blockage ratio. Simulation results show that the close-to-constant value of the cylinder drag coefficient characterising the quadratic drag regime, upper C prime Subscript d Baseline overbar comma C d ′ ¯ , $\overline{{C}_{d}^{\prime}},$ increases with italic SVF SVF $\textit{SVF}$ and italic aD aD $\textit{aD}$ for constant d divided by upper D d / D $d/D$ , cylinder shape and upper W divided by upper D W / D $W/D$ . Moreover, upper C prime Subscript d Baseline overbar C d ′ ¯ $\overline{{C}_{d}^{\prime}}$ increases with d divided by upper D d / D $d/D$ for constant italic aD aD $\textit{aD}$ , cylinder shape and upper W divided by upper D W / D $W/D$ , and decreases with upper W divided by upper D W / D $W/D$ for constant italic aD aD $\textit{aD}$ , cylinder shape and d divided by upper D d / ...