Journal of Hydraulic Engineering

Fluvial bed load transport is often considered to assume a capacity regime exclusively determined by local flow conditions, but its applicability in naturally occurring unsteady flows remains to be theoretically justified. In addition, mathematical river models are often decoupled, being based on simplified conservation equations and ignoring the feedback impacts of bed deformation to a certain extent. So far whether the decoupling could have considerable impacts on the fluvial processes with bed load transport remains poorly understood. This paper presents a theoretical investigation of both issues. The multiple time scales of fluvial processes with bed load sediment are evaluated to examine the applicability of bed load transport capacity and decoupled models. Numerical case studies involving active bed load transport by highly unsteady flows complement the analysis of the time scales. It is found that bed load transport can sufficiently rapidly adapt to capacity in line with local flow because sediment exchange with the bed overwhelms the advection of bed load sediment by the mean flow. The present work provides theoretical justification of the concept of bed load transport capacity in most circumstances, which is underpinned by existing observations of bed load transport by flash floods. For fluvial processes with bed load transport, the feedback impacts of bed deformation are limited; therefore, decoupled modeling is, in this sense, appropriate.

This paper presents a stochastic approach to model input uncertainty with a general statistical distribution and its propagation through the nonlinear long-wave equations. A Godunov-type scheme mimics breaking waves as bores for accurate description of the energy dissipation in the runup process. The polynomial chaos method expands the flow parameters into series of orthogonal modes, which contain the statistical properties in stochastic space. A spectral projection technique determines the orthogonal modes from ensemble averages of systematically sampled events through the long-wave model. This spectral sampling method generates an output statistical distribution using a much smaller sample of events comparing to the Monte Carlo method. Numerical examples of long-wave transformation over a plane beach and a conical island demonstrate the efficacy of the present approach in describing uncertainty propagation through nonlinear and discontinuous processes for flood-hazard mapping.

Intense rainfall on urban areas can generate severe flooding in the city, and if the conditions are right, the flow in the streets can be supercritical. The redistribution of the flow in street intersections determines the flow rates and water levels in the street network. We have investigated the flow that occurs when two supercritical flows collide in a 90° junction formed by streets of identical cross section. Several flow configurations within the intersection are possible, depending on the position of the hydraulic jumps that form in and upstream of the intersection. Previous work has identified three flow types, with Type II flows being further classified into three subregimes. Hydraulic models have been developed, based on the principles of the conservation of flow and momentum flux in the intersection, which predict the angles at which the jumps will form. These models can be used to determine the flow type that will occur. Moreover, additional models have been developed for computing the outflow discharge distribution. For Type I flows, it has not been possible to develop such a hydraulic model for the discharge distribution, but some data are provided for one configuration to indicate the influence of different parameters. For Type II and Type III flows, such models are developed, and their predictions agree with data obtained from the channel intersection facility at the Laboratory of Fluid Mechanics and Acoustics in Lyon.

This paper documents measurements of the mean velocity field and turbulence statistics of an isothermal, round jet entering a shallow layer of water. The lower boundary of the jet was a solid wall and the upper boundary a free surface. The jet axis was midway between the solid wall and the free surface in all cases. Experiments were performed at a Reynolds number of 22,500 for water layer depths 15, 10, and 5 times the jet exit diameter (9 mm). Particle image velocimetry measurements were made on vertical and horizontal planes—both containing the axis of the jet. The measurements were taken from 10 to 80 jet diameters downstream. Results showed that, for the highly confined cases at downstream locations, the axial velocity was quite uniform over the depth, with a mild peak below the jet axis. In the horizontal plane, the velocity profiles were slightly narrower than the free jet profile, but in the vertical plane, they were wider. The mean vertical velocity profiles showed that entrainment was suppressed in the vertical direction. At the same time, the lateral velocity profiles indicate that fluid flows from the sides toward the jet centerline. For the shallow cases, the mean vertical velocity becomes negative over most of the depth at downstream locations, indicating that this inflow from the sides is directed downward toward the solid wall. The relative turbulence intensity results were suppressed in the axial and vertical directions and mildly enhanced in the lateral direction. As well, the Reynolds shear stress in the vertical plane was significantly reduced by the vertical confinement, while in the horizontal plane it was only slightly affected by the confinement.

Turbulent flow in porous media, terrestrial and aquatic canopies, and urbanlike roughness is usually investigated using the macroscopic approach, which is based on the volume average theory (VAT). Two different methodologies have been developed in the past leading to different equations for both the mean and the turbulence quantities: time-averaging the volume-averaged equations and volume-averaging the time-averaged equations. In this study four models of the volume-averaging methodology are applied for modeling the flow in open channels with submerged vegetation. The vegetation is considered rigid, simulated as cylindrical roughness in a staggered or nonstaggered arrangement. Three of the models are of the $k\mathrm{\text{-}}\epsilon$ type and one is of the Reynolds stress type. The latter has been applied using a modified ε equation to account for the extra dissipation attributable to vegetation. Numerical results for both mean and turbulence flow characteristics are compared against available experimental measurements for dense canopies under shallow and deep flow conditions. In addition, relevant characteristics (displacement thickness, canopy shear layer parameter, mixing length, penetration length scale, and etc.) are calculated for both computed and experimental data for assessing the performance of the models.

Particle image velocimetry scalar measurements were carried out on the body of a stably stratified density current with an inlet Reynolds number of 2,300 and bulk Richardson number of 0.1. These measurements allowed the mass and momentum transport between the current and the less dense ambient fluid to be investigated. Reynolds stress, Reynolds flux, and shear production of turbulent kinetic-energy profiles revealed local maxima at the bed, as well as at the interface with the ambient fluid. Profiles of excess density variance and buoyancy production of turbulent kinetic energy revealed only local maxima at the interface with the ambient. These maxima decreased downstream as the stable density gradient reduced the turbulent intensities, until turbulence collapsed. A two-dimensional, unsteady, Reynolds-averaged Navier-Stokes (2DV-URANS) simulation was also performed on this density current. Good agreement was found between the modeled and measured normalized mean flow profiles. A comparison was also made between the measured and modeled outer flow scales of the density current.

Settling tanks are used to remove solids at wastewater treatment plants. Many numerical models have been proposed to simulate the settling process and to improve tank efficiency. In this research, a three-dimensional (3D) numerical model is developed to simulate large primary settling tanks. In the proposed model, the non-Newtonian properties of the sludge flow in the settling tank are described by a Bingham plastic rheological model. To eliminate the singularity inherited in the rheological model, a modified constitutive relation is used in both the yielded and unyielded regions. Hindered settling of particles in the settling tank is also modeled. Tracer study, where a massless scalar is injected and transported, is done to investigate the tank’s residence time. This numerical model is used to improve the design of the primary settling tanks, which will be built in Chicago. The Metropolitan Water Reclamation District of Greater Chicago (MWRDGC) is in the process of building new preliminary treatment facilities at their Calumet Water Reclamation Plant (CWRP), including twelve 155-ft-diameter primary settling tanks (PSTs) designed to treat flows up to ($480\mathrm{million}\mathrm{gal}./\mathrm{day}$ (MGD). The computational fluid dynamics (CFD) model simulated solids removal efficiencies based on a particle size distribution similar to the one observed in the CWRP influent. The results were used to establish the design basis for tank side-water depth, inlet feedwell dimensions, etc., resulting in improved performance and substantial reduction in construction costs.

Measurements of stratification and dissolved oxygen (DO) illustrate a hypersaline gravity current with salt loads similar to a desalination plant brine discharge. Over a 48-h sampling period in August 2005, alternating cycles of high- and low-temperature hypersaline water were observed along the bottom of Corpus Christi Bay in Texas, coincident with low benthic DO and tidal flushing from an adjacent smaller bay. The gravity current underflow was typically less than 10% of the overall water depth. Strong salinity gradients prevented wind-mixing of the entire water column. Hypoxic and near-hypoxic conditions were associated with limited DO replenishment from the ambient water. High DO levels in the underflow source water did not deter the development of offshore benthic hypoxia. A quasi-Lagrangian analysis is used to evaluate the relationship between ambient mixing and lateral mixing within the underflow. The analysis is further applied to estimating DO demand rates in the hypersaline plume. Mixing between the ambient water and the underflow predominately occurs over the sloping bay boundary. Once the gravity current reaches the flatter section of the bay, mixing is substantially reduced and DO is progressively depleted at the bottom. The transit time of the underflow (i.e., residence time or isolation time for water near the bottom) and wind-mixing energy appear to be key factors governing stratification persistence and potential hypoxia development. The observations and analyses provide insight into possible fate, impacts, and open questions associated with similarly scaled salt loadings from a desalination plant into a shallow bay.

At the South Branch of the Changjiang Estuary near Baimao Shoal, two in situ approaches were used to estimate the settling velocity, $w_s$ , of suspended, fine-grained sediments. The first approach was used when the current was less than $1.5\mathrm{m}/\mathrm{s}$ and was based on measurements from an optical backscatter sensor (OBS-3A) and a laser in situ scattering and transmissometer (LISST-100, Type C). A modification, using the measured ratio of volume concentration for each floc size class to the total volume concentration as a weighting factor. To improve a previously published approach, a better algorthim was implemented to estimate $w_s$ . Results of the modified approach (0.4 to $4.6\mathrm{mm}/\mathrm{s}$ ) are about twice those of the original approach, which assumes that all sizes of flocs have the same floc density. The second approach used the Rouse equation to estimate the depth-averaged $w_s$ when the current was strong and nearly steady around maximum ebb. Results from the second approach show a much greater depth-averaged $w_s$ (4– $8.5\mathrm{mm}/\mathrm{s}$ ). This is attributed to the large bed shear stresses (between 3 and 3.6 Pa) bringing large sediments into the water column.

A series of two-dimensional computational fluid dynamics (CFD) simulations of merging turbulent plane jets were conducted to establish the point at which the jets can be regarded as having merged to form a single jet. Simulations were conducted to quantify the influence of the nozzle width, jet axis separation, Reynolds number, and the relative jet strength on the distance from the source to the merger point. The simulation results were then compared with experimental results published in literature. As the jet fluid exited the two nozzles, the shear layer between the jet and the ambient fluid drove the ambient fluid entrainment into the jets. However, a finite volume of fluid trapped was between the two jets, and a recirculation zone with two counterrotating vortices was established. This vortex pair reduced the pressure between the jets, drawing them together more rapidly than theoretical models predicted. The simulation results indicated that equal-strength jets merged at a distance downstream of 1.4 times the initial nozzle centerline separation provided that the nozzle-separation-to-nozzle-width ratio was greater than 18. As the source momentum flux of one jet decreased relative to the other, the relative distance to merger also decreased. However, for source momentum flux ratios between 0.2 and 0.9, the merger distance was only a very weak function of the momentum flux ratio. The CFD-measured merging distance was significantly closer to the jet nozzles than current models predict. Therefore, the mixing of pollutants by using parallel plane jets is less efficient than currently thought.

This paper presents a rapid method for propeller current meter calibration, enabling calibration of current meters in their actual working conditions using simpler equipment than what is currently used in traditional calibrations, and exploiting the uniform velocity profile present through submerged outflows (e.g., flow nozzles and orifices). Experiments were performed to confirm the fundamental hypothesis of uniform horizontal and vertical velocity distribution downstream of a submerged jet. Two experimental velocities were adopted to determine the calibration curve: one based on the discharge and the outflow area; the other derived from Torricelli’s formula, which relies on the head difference between two reservoir levels. Because a current meter measures local velocity, the influence on the measurements’ reliability as a function of current meter position in the submerged outflow jet was investigated. An uncertainty analysis was also performed, and a comparison of the results with the preexisting calibration lines obtained by towing tank is presented.

This paper presents and discusses an extension of the pseudotransient continuation-based steady state solver for hydraulic networks proposed previously to the case of zero flow rates. The original solver, which reduces the solution of the governing nonlinear algebraic equations to the numerical integration of an initial-value problem, has problems in situations in which the head derivative of the flow rate tends to infinity, as is the case with zero flow rates. The extension is on the basis of the use of a model headloss-flow relationship that coincides with the true one at zero and has a finite head derivative at that point. This modified steady state solver is free from some convergence problems that occur in Newton-Raphson method-based solvers when analyzing a pipe network with control devices. The paper includes the results of the numerical analysis of test networks, which demonstrate the convergence of the modified steady state solver for cases in which existing steady state solvers have troubles.