Drag Reduction in Channel Flows with Longitudinal Ridges of Varying Height

Abstract

Large eddy simulations LESs of smooth-bed open channel flows over streamwise orientated ridges are performed to evaluate the impact of ridge height on the hydraulic resistance. Four heights are chosen in the range of 3 mm ≤ ∆ ≤ 6 mm and 20 ridges with fixed spacing and total water depth ratio of S/H = 0.4 in all cases, where ∆ is the ridge height, S is the ridge spacing and H is the total water depth. Such heterogeneous bed was found to induce secondary currents (SCs) that alter the mean flow characteristics. A channel division method is used to estimate local and total skin friction coefficient that neglect any effect of SCs on the bed resistance and then it is compared to the computed friction factor from the LESs. It is found that the drag is reduced at the valley regions when increasing the ridge height, and at the same time it is increased over the ridge regions. The total estimated friction factor shows a drag increase at all heights, however, the maximum value occurred at ∆ = 5mm, and not at 6mm. Careful inspection of the Reynolds stresses reveals that peaks of the turbulent stresses occur at the valley in low ridge height and it is limited at higher cases due to tertiary flows generated at the bottom-ridge interface with the valley. These tertiary currents are limited in growth due to the SCs at fine ridge heights, ∆ ≤ 4mm, and due to the spacing at higher ridges, ∆ ≤ 4mm, and it is attributed to be the reason of the drag shift at certain ridge height that scale with the ridge spacing.