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Influence of submergence ratio on flow and drag forces generated by a long rectangular array of rigid cylinders at the sidewall of an open channel
- Mete Koken, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 966 / 10 July 2023
- Published online by Cambridge University Press:
- 27 June 2023, A5
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This paper discusses how the submergence ratio, defined as the ratio between the flow depth, D, and the height, h, of the solid rigid cylinders forming the array affects flow and turbulence structure inside and around a rectangular array of cylinders placed adjacent to one of the channel sidewalls. As the array becomes submerged, a vertical shear layer develops in between the top face of the array and the free surface, which strongly increases flow three-dimensionality and modifies how the momentum exchange between the array and the surrounding open water regions occurs with respect to the case of an emerged array where only a horizontal shear layer forms as part of the incoming flow approaching the array is deflected laterally. Eddy-resolving simulations are conducted for several values of the solid volume fraction, ϕ, and of the submergence ratio, 1.0 ≤ D/h ≤ 4.0. Similar to the limiting case of an emerged array (D/h = 1.0), the width- and depth-averaged streamwise velocity inside the array reaches a constant value after an initial adjustment region in the submerged-array cases. For D/h ≥ 1.33, the mean normal velocities through the top and side faces of the array do not become equal to zero downstream of the initial adjustment region. The flow inside the array reaches an equilibrium regime where the local flux of fluid leaving the array through its side face is balanced by the local flux of fluid entering the array through its top face. This regime is observed until close to the end of the array. For D/h ≥ 2.0, the horizontal shear layer vortices do not generate successive regions of high and low streamwise velocity and bed friction velocity inside the array, as is observed in the emerged cases. With respect to the emerged case, the size of the shear layer vortices and the shear layer width increase for low submergence ratios before decreasing rapidly for D/h ≥ 1.33. Significant three-dimensional effects are present inside the array and the horizontal shear layer for cases with both emerged and submerged arrays. In the ϕ = 0.08 cases, strong upwelling and downwelling motions are observed inside the array for D/h ≥ 1.33, while the circulation of the streamwise-oriented cell of secondary flow forming close to the lateral face of the array peaks when the submergence ratio is close to 1.33. For constant ϕ, the total streamwise drag force normalized with the height and width of the array increases with increasing submergence ratio. As the array submergence increases, the cylinders near the front of the array contribute less to the total force acting on the cylinders forming the array. For constant D/h, the total streamwise drag force acting on the array increases with ϕ for the submerged and emerged cases.
Flow structure inside and around a rectangular array of rigid emerged cylinders located at the sidewall of an open channel
- Mete Koken, George Constantinescu
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- Journal:
- Journal of Fluid Mechanics / Volume 910 / 10 March 2021
- Published online by Cambridge University Press:
- 08 January 2021, A2
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Flow structure inside and around a rectangular array of emerged cylinders located adjacent to the sidewall of an open channel is investigated using eddy-resolving numerical simulations. This configuration is particularly relevant for understanding how patches of aquatic vegetation developing near a river's banks affect flow and transport. The array of width W = 1.6D and length L = 33D–35D (D is the flow depth) contains rigid cylinders. Simulations with incoming, fully developed turbulent flow (channel Reynolds number, ReD = 12 500) are conducted with different values of the solid volume fraction (0.02 < ϕ < 0.1), frontal area per unit volume of the array, a (0.41 < aW < 1.63), diameter of the solid cylinders (d = 0.1D and 0.2D) and cylinder shape (circular and square). The paper focuses on investigating flow and turbulence structure inside and downstream of the array and the role played by coherent structures (e.g. vortices forming in the horizontal shear layer at the lateral face of the array, vortices shed in the wake of the solid cylinders) in sediment entrainment and transport. Simulation results show that significant upwelling and downwelling motions are generated near the front and lateral faces of the array and inside the shear layer. Moreover, some distance from the front face of the array, the shear layer vortices generate successive regions of high and low streamwise velocity inside the patch. The frequency associated with these wave-like oscillations is approximately half of the frequency associated with the advection of vortices in the downstream part of the shear layer. These streamwise velocity oscillations induce spanwise patches of high and low bed friction velocity that extend over the regions occupied by the array and the horizontal shear layer. For sufficiently high array resistance, horseshoe vortices form around the upstream corner of the array and provide an additional mechanism for sediment entrainment. For aW > 0.5, mean-flow recirculation bubbles form behind the array. For constant aW, the total size of the region containing recirculation bubbles decreases with increasing d/D. Simulations results are used to quantify the effect of varying ϕ, aW, d/D and the cylinders’ shape on the streamwise decay of the mean streamwise velocity inside the array, turbulent kinetic energy distribution, mean streamwise drag forces acting on the cylinders and mean streamwise drag coefficients.
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