Effects of Secondary Currents on Turbulence Characteristics of Supercritical Open Channel Flows at Low Aspect Ratios

Abstract

In this paper, we present secondary current effects on the turbulence characteristics of supercritical narrow open channel flows over a smooth fixed bed. The main hydraulic parameters are low channel width to flow depth ratios varying between 1 and 2, and Froude numbers (F) ranging from 2 to 4. Detailed profiling of instantaneous streamwise and vertical flow velocities was conducted in a laboratory flume using a 2D laser Doppler anemometry. The cross-sectional distributions of mean flow velocities, turbulence intensities, Reynolds, and bed shear stresses were obtained from the measurements. The mean streamwise and vertical flow velocity distributions reveal that four pairs of secondary current cells are formed: a pair of well-developed free-surface vortices near the water surface, a pair of bottom vortices near the bed, and two pairs of mid-vortices between the free-surface and bottom vortices. These secondary currents cause bulging of the contour lines of the streamwise velocities with respect to the water surface and the bottom corner bisectors resulting in an undulated pattern of the mean velocity distribution across the cross-section. Furthermore, they cause the velocity dip phenomenon, i.e., the maximum flow velocity occurs well below the surface, and redistribute the Reynolds and bed shear stresses in transverse direction. The results demonstrate that decreasing the aspect ratio increases the strength of the secondary currents causing a significant change in flow patterns with larger free-surface vortices compared to the bottom vortices. Compared to the aspect ratio effect, the Froude number only slightly impacts the flow characteristics as a result of flow non-uniformity. For all investigated aspect ratios and Froude numbers, bed shear stresses are concentrated at the flume center, and on average 5 to 10% higher than their mean values. The modified wake-log-law holds both in the inner and outer regions, matching well with the experimental data for all test conditions. The present findings are discussed with literature data, and their impact on engineering applications is demonstrated.

Combining Fish Passage and Sediment Bypassing: A Conceptual Solution for Increased Sustainability of Dams and Reservoirs

“…In conditions where b/h < ~2, eight secondary cells develop and cause bed shear stress undulation (Figure 2c). Bed shear stresses are lowest near the tunnel walls, reach maxima, and then flatten towards the tunnel center (Figure 2c, [62]). For ratios 2 ≤ b/h < 4 to 5, four secondary cells have been found to develop [61], resulting in high bed shear stresses near the tunnel walls.…”

“…This is the result of the presence of non-homogeneity and anisotropy of turbulence in the tunnel. These secondary currents superimpose the primary flow influencing mean flow velocities, turbulence intensities, and Reynolds and bed shear stresses [59][60][61][62]. In conditions where b/h < ~2, eight secondary cells develop and cause bed shear stress undulation (Figure 2c).…”

“…For ratios 2 ≤ b/h < 4 to 5, four secondary cells have been found to develop [61], resulting in high bed shear stresses near the tunnel walls. Demiral et al [62] and Auel et al [61] indicated that b/h ≈ 2 is critical, determining the number of secondary cells created, and their bed shear stress distributions. Bed shear stress plays a critical role in sediment transport, with higher values leading to higher bedload transport (detailed information can be found in Müller-Hagmann [48]).…”

Field Investigation of Hydraulics and Fish Guidance Efficiency of a Horizontal Bar Rack-Bypass System

“…These velocities were normalized with the cross-sectionally averaged approach flow velocity U0 of 0.59 m/s calculated from CS07, which was downstream of the fish pass exit. For S1 the maximum flow velocity lied at z/h0 = 0.6 (with h0 = 2.95 m) indicating the velocity dip-phenomena caused by secondary currents [36,37]. At S4 to S6, flow velocities were lower than at S1 as a portion of the flow passed the rack and the maximum velocities at S4 to S6 occurred closer to the water surface because of the backwater effect caused by the presence of the rack and bypass gate.…”

“…The highest velocities obtained from the cross-sectional velocity distributions occurred at z/h 0 = 0.88. The occurrence of maximum velocities below the water surface, the so-called velocity-dip phenomenon, is related to the secondary currents of Prandtl's second kind driven by turbulence anisotropy [35][36][37][38]. Such secondary currents exist when the channel width to water depth aspect ratio is less than 4 to 5, creating a 3D flow pattern.…”