Large-eddy simulations of ducts with a free surface

Abstract

This work studies the momentum and energy transport mechanisms in the corner between a free surface and a solid wall. We perform large-eddy simulations of the incompressible fully developed turbulent flow in a square duct bounded above by a free-slip wall, for Reynolds numbers based on the mean friction velocity and the duct width equal to 360, 600 and 1000. The flow in the corner is strongly affected by the advection due to two counter-rotating secondary-flow regions present immediately below the free surface. Because of the convection of the inner eddy, as the free surface is approached, the friction velocity on the sidewall first decreases, then increases again. A similar behaviour is observed for the surface-parallel Reynolds-stress components, which first decrease and then increase again very close to the surface. The budgets of the Reynolds stresses show a strong reduction of all terms of the dissipation tensor in both the inner and outer near-corner regions. They exhibit a reduction in both production and dissipation towards the free surface. Very close to the solid boundary, within 15-20 viscous lengths of the sidewall, the turbulent kinetic energy production and the surface-parallel fluctuations rebound in the thin layer adjacent to the free surface. The Reynolds-stress anisotropy appears to be the main factor in the generation of the mean secondary flow. The multi-layer structure of the boundary layer near the free surface is also discussed.

Direct numerical simulation of low Reynolds number flows in an open‐channel with sidewalls

“…In the present DNS, the division of inner and outer secondary flows at the free surface is about 40 in wall units. In the LES data reported by Broglia et al [17], the locations of the division from their three simulation results are about y + ≈ 40, which is the same as the present result. In Figure 4, the mean streamwise velocity along the middle plane by the present DNS is compared with LES data by Broglia et al [17] and measured data by Nezu and Rodi [26].…”

“…The present domain size for the streamwise direction is sufficient to maintain the longest turbulent structure, as has been pointed out by Broglia et al [17]. The mesh properties and flow conditions are given in Table I.…”

Secondary Currents and Turbulence over a Non-Uniformly Roughened Open-Channel Bed

“…Terms B and C are generation terms of streamwise vorticity and both involve turbulent Reynolds stresses. The origin of secondary currents has been argued about amongst researchers [4,50,51], however, Broglia et al [26] suggest that in open channels the turbulence anisotropy of the normal stresses (i.e., '…”

“…Among large-eddy simulations of the flow in square ducts some were performed at similar Reynolds numbers to the DNSs described above (e.g., [24]) and others at much higher Reynolds numbers [25]. A detailed study of flows in narrow ducts with a free surface is provided by Broglia et al [26]. They investigated the mean flow field and a variety of turbulence statistics and highlighted the complex structure of the flow near the corners formed by the free surface and the side wall.…”

“…They investigated the mean flow field and a variety of turbulence statistics and highlighted the complex structure of the flow near the corners formed by the free surface and the side wall. Broglia et al [26] were able to explain the existence and origination of secondary motions in the context of stress balance equations. Shi et al [27] performed an LES in a smooth rectangular channel at a Reynolds number of approximately 90,000 and showed that LES allows very accurate predictions of turbulence statistics and boundary shear stress distributions are feasible.…”