Journal of Hydraulic Engineering

This paper presents a mechanistic model to simulate multiple jets of a unidirectional diffuser discharging in shallow water with a strong crossflow. Due to the shallow water depth and close spacing of the jets, a sheltering effect is considered such that the presence of upstream jets reduces the crossflow velocity experienced by a jet. In addition, an induced flow field due to the entrainment of individual jets is calculated by considering point sinks located at jet nozzles and is superimposed on the ambient current. An integral model is used to simulate the trajectory and the mixing of the diffuser’s individual jets. Individual jets are considered to merge to form an aggregate jet when their inner boundaries intersect. An integral model is also used to calculate the trajectory and mixing of the aggregate jet. The sheltering factor, crossflow entrainment coefficient, and drag coefficient used in the model are calibrated using experimental observations of jet trajectory and dilution. The predictions of dilution at the edge of a mixing zone are shown to agree well with the observations for strong currents and moderate values of the ratio of jet spacing to water depth. The numerical model presented shows a significant improvement over existing models.

Scale effects generated in the flow over nonlinear weirs have been studied on a limited number of occasions. Furthermore, the existing studies have been almost exclusively focused on the flows upstream of the weir, while criteria to minimize scale effects downstream of the weir remain to be examined. This study investigates the scale effects that arise in several aspects of the flow over a labyrinth weir and spillway with scale series based on three-dimensional (3D) computational fluid dynamics (CFD) simulations. Results showed that, overall, scale effects decreased with increasing Reynolds number. Changes in the position of the channel-dominant cross waves were observed as a function of the simulation scale and tended to diminish with decreasing scale factor. The flows on the spillway channel generally exhibited relatively small scale effects on the main flow properties (i.e., mean flow depths, mean velocities, and Froude numbers) for Reynolds numbers greater than $3\times {10}^4$. However, higher values ($>5\times {10}^4$) would be required to minimize changes in the positions of the cross waves in the channel. Additionally, an upstream head over the weir crest of approximately 0.03 m was found to be sufficient to avoid scale effects in the prediction of the labyrinth weir rating curve. The limiting criteria estimated for the rating curve and the main flow properties on the spillway channel are closely correlated with available literature limits and may constitute valuable guidance for future practice.

A new set of open-channel flow experiments and turbulence resolved data are presented in heavy particle sheet flows (Shields number $0.35\le \theta \le 0.85$) for which the proportions of bedload and suspended load are both important (ratio of settling velocity and friction velocity in the range $0.8\le w_s/u_{*}\le 1.3$). The effects of sediments and particularly the bedload on the turbulent suspension have been addressed by gradually increasing the concentration from clear water to capacity conditions. Distinction between the bedload and the suspension layer is discussed on the basis of the linearity of turbulent mixing length profiles. It is shown that the bedload layer has important impact on the vertical structure of the particle-laden flow. An upward shift of the logarithmic velocity layer is seen to be accompanied by a strong reduction of turbulent momentum mixing. The modification of the mixing length affects the theoretical formulation of both velocity and concentration profiles in the suspension layer. A modified analytical solution is derived for the suspended sediment concentration profile taking into account the presence of the bedload layer for improved predictions compared with the classical Rouse equation. Based on the present experiments, as well as literature data, an alternative parametrization for the $\beta$-factor (ratio of sediment and momentum diffusivities) is proposed over an extended range of suspension number, $0<w_s/u_{*}<1.5$.

The computational fluid dynamics (CFD) solver FANS3D [Finite-Analytic Navier-Stokes code for three-dimensional (3D) flow] is coupled with a sediment transport model to simulate scour hole backfilling under unidirectional flows (current-only). FANS3D solves 3D, unsteady, incompressible Navier-Stokes equations in nonstaggered, general curvilinear coordinate systems. For the present study, the $k\text{-}\epsilon$ model is used for turbulence closure. The overset grid technique is utilized to generate the computational domain consisting of multiple blocks with different structures. The coupled model is validated with both clear-water and live-bed scour experiments. The numerical solution is also verified to be consistent against changes in time step size and grid density. Backfilling is initiated by first obtaining the equilibrium scour under a “flood” and then reducing the approach velocity to a “normal” flow, both of which conditions are in a live-bed scour regime. Using this approach, backfilling is successfully simulated around a cylindrical pier with three different hydrographs (variable velocity). The backfilled scour hole is compared with the equilibrium scour hole formed under normal flow (constant velocity). This study found that a given unidirectional flow velocity results in the same equilibrium scour depth regardless of the initial bed morphology. The location of the maximum depth inside the scour hole is also found to be a characteristic of the flow velocity.