Gauging Rivers during All Seasons Using the Q2D Velocity Index Method

This paper presents a new model (Q2D) for the velocity distribution in a channel cross section for use in estimating discharge. It describes the model and its theoretical basis and presents the results of a case study. The distribution is determined by combining the principle of maximum entropy with a probability distribution obtained by the solution of the Poisson equation over the cross section. The model uses observed depth and velocity in the water column, where an acoustic Doppler current profiler is installed to determine three key flow parameters to obtain velocity and discharge. In addition, if supporting field discharge measurements are available, the model can be further calibrated to account for any asymmetry in the flow. If velocity distribution data exist for the entire cross section, the model can be adjusted to stretch the predicted velocity pattern to better conform to experimental observations. When applied to the Chateauguay River, Quebec, for both ice covered and open water, Q2D predicted 12 gauged discharges with a ?4% bias and an average absolute error of 7% prior to calibration. After removing the bias through calibration, the average absolute error was reduced to 5%.     

Experimental Study and 3D Numerical Simulations for a Free-Overflow Spillway

The main objectives of the present work were to investigate the flow field over a spillway and to simulate the flow by means of a three-dimensional (3D) numerical model. Depending on the wall curvature, the boundary layer parameters decreased or increased with increasing distance along the spillway. The growth of the boundary layer along the spillway is better described as a function of Reynolds number than the normalized streamwise length. A simplified form of the 3D momentum equation can be used to obtain a rough estimate of the skin friction. The velocity profile in the boundary layer along the spillway is described by a velocity–defect relationship. Numerical models provide a cost-effective means of simulating spillway flows. In this study, the water surface profiles and the discharge coefficients for a laboratory spillway were predicted within an accuracy range of 1.5–2.9%. The simulations were sensitive to the choice of the wall function, grid spacing, and Reynolds number. A nonequilibrium wall function with a grid spacing equal to a distance of 30 wall units gave good results.     

Flow Variation of Duckbill Valve Jet in Relation to Large Elastic Deformation

Duckbill-shaped elastomer valves are often installed on wastewater effluent diffusers, stormwater outfalls, and industrial flow systems to prevent backflow and sediment/salt water intrusion. Unlike fixed diameter nozzles, the flow from a duckbill valve (DBV) depends both on the driving pressure and the size of the valve opening. A nonlinear large deformation finite element analysis of a prototype DBV is reported herein. The elastomer is modeled as a hyperelastic incompressible solid, and the flow inside the DBV, shaped like a converging nozzle, is treated as energy conserving. The deformed valve is computed iteratively from sequential standard large deformation analysis of the internal flow and pressure loading. The calculations show that the valve opening is lip shaped, and the maximum stress occurs around the two sides of the saddle of the DBV; maximum strains are on the order of 5%. In contrast to the traditional square-root head–discharge dependence, a linear pressure–discharge relation is predicted for a range of elastomer thickness; the jet velocity/valve opening area varies nonlinearly with discharge. The normalized predictions of valve discharge flow and opening area as a function of the driving pressure are in excellent agreement with experimental data.     

Method of Solution of Nonuniform Flow with the Presence of Rectangular Side Weir

An iterative step method for solving the nonlinear ordinary differential equation, governing spatially varied flows with decreasing discharge, like the flow over side weirs, is developed. In the procedure, starting at a known flow depth and discharge in the control section, the analytical integration of the dynamic equation with bed and friction slope is carried out. The specific energy, the weir coefficient and the velocity distribution coefficient are considered as local variables, then for the explicit integration, the respective average values along the short side weir elements are assumed. The water surface profiles and the discharges for flow over side weirs, obtained with the proposed relation and valid for rectangular channels, are compared with experimental data for subcritical and supercritical flow conditions. The validation of the method is accomplished by the comparison with the solution obtained by De Marchi’s classical hypothesis, about the specific energy, which is constant along a side weir. In addition, the influence of the coefficient velocity distribution is considered.     

Modeling solidification of turbine blades using theoretical phase relationships

The solidification of hot-stage turbine blades made from René N4 nickel-base superalloy has been modeled to show the morphology of porosity and the local changes in solute concentration. The key task of the present study was the calculation of the solid-liquid phase equilibria of this 9-component nickel-base superalloy from the thermodynamic values of these phases. The Gibbs energies of the solid and liquid phases were obtained from those of the 36 binaries using the Muggianu and Kohler methods of extrapolation. The phase equilibrium data were then used to compute the change in fraction solid with temperature, initially using the complete mixing approximation (Scheil equation). The predicted freezing range was somewhat longer than measured. A modified Scheil equation was derived assuming incomplete mixing. Assuming 60 pct mixing of the solute, the calculated freezing range agreed with experiments. Fraction solid temperature allowed the detailed morphology of the“mushy”zone to be predicted. Using measured dendrite spacings and assuming the crystals to grow in a cubic array, the shape of the crystals and, consequently, the size of the liquid channels were predicted as a function of position. Hence, computation of the rate of fluid flow in the channels (from the known changes of temperature with time) allowed the pore morphology to be inferred.     

Side Outflow from Supercritical Channel Flow

Side flow on a flood plain from a side outlet of the main channel is investigated both theoretically and experimentally for supercritical main flow. The side outlet as a model simulates a failure of a river bank in a prototype. The discharge ratios of the side outflow to that of the main channel flow, the water depth, and the velocity at the side outlet are obtained. The theoretical discharge ratio is a function of the Froude number of the main channel flow. The theoretical spreading angle of the side flow and the theoretical relationship between the velocities and the distance from an upstream point of the side outlet are also compared and predicted. All the theoretical results are found to be in good agreement with the experimental data.     

Street Storm Water Conveyance Capacity

The street hydraulic capacity to convey storm water is dictated by the street gutter geometry and hydraulic characteristics. With the consideration of traffic safety, the street hydraulic conveyance capacity (SHCC) is also subject to a reduction defined by the water velocity and flow depth in the street gutter. In this study, the street hydraulic equation is rearranged to demonstrate that the water velocity and depth product in a gutter flow can serve as a safety criterion for determining the allowable SHCC. The velocity and water depth product and discharge reduction methods were examined and revised to establish the consistency in predictions. The revised design procedures developed in this study replace the current iterative process with a direct estimation of the allowable SHCC when a safety criterion is specified.     

Chute Aerators. II: Hydraulic Design

Chute aerators are applied if cavitation damage on spillways is expected or observed. The aerator efficiency is usually described with the ratio of the air discharge entrained through the air supply ducts and the water discharge, which does however not account for the resulting air concentration distribution within the flow or for air detrainment. The present study investigates the streamwise development of the air transport along the flow downstream of chute aerators. Based on an extensive test program in which six governing parameters were systematically varied, the development of the average and the bottom air concentrations is provided up to the self-aeration point. Based on this information, an optimization of aerators in terms of increased air entrainment and reduced detrainment rates is possible, by assuming minimum required air concentrations. The main parameters influencing the air transport downstream of aerators are the approach flow Froude number, the deflector angle and the chute bottom angle.     

Fluid Mechanics of Triangular Sediment Oxygen Demand Chamber

Benthal respiration rates are often measured in situ by a sediment oxygen demand (SOD) chamber in which a continuous flow is generated above the sediment. The steady three-dimensional turbulent flow field inside a triangular SOD chamber (previously used in field investigations) is computed using the renormalization group (RNG) k–ε model on an unstructured tetrahedral mesh. The numerical predictions reveal a highly complicated flow characterized by (1) a jet flow near the level of the inlet, with strong downflow near the outlet end; (2) significant reverse bottom currents; and (3) strong secondary circulations in the triangular cross section. Good mixing is achieved, with mean near-bottom velocities about 10 times greater than that determined from the inflow discharge and cross-sectional area. The computed velocity field is well supported by laboratory velocity measurements using laser-Doppler anemometry (LDA). The implications on SOD chamber design are also discussed with reference to computed flow fields in representative dome-shaped and rectangular chambers used in field application. The present study explains the previous large discrepancies in SOD field measurement using chambers of different designs, and points to the importance of hydrodynamics of SOD chambers.     

Boundary Shear Stress in Spatially Varied Flow with Increasing Discharge

The distribution of the wall shear stress on the bed and sidewalls of an open channel receiving lateral inflow was obtained from experimental measurements of the distribution of the velocity in the viscous sublayer using a laser doppler velocimeter. The experiments were conducted in a 0.4 m wide by 7.5 m long flume. Lateral inflow was provided into the channel from above via sets of nozzles positioned toward the downstream end of the flume. Lateral inflow was provided over a length of 1.9 m. The results indicate that the local boundary shear stresses are significantly influenced by lateral inflow. The significant variation occurs near and around the region where the lateral inflow enters the channel. At various measurement positions along the lateral inflow zone, mean boundary, mean wall, and mean bed shear stresses were obtained and compared. The results indicate that the mean boundary shear stresses increase from the upstream to the downstream ends of the lateral inflow zone. The results also indicate that the mean bed shear stress is always greater than the mean wall shear stress, which are approximately 30–60% of the mean bed shear stress. The friction factor in the Darcy–Weisbach equation was obtained from both the mean boundary shear stress and from the equation describing the water surface elevation in an open channel receiving lateral inflow (equation for spatially varied flow with increasing discharge). The results indicate that the estimated friction factors from the latter approach are significantly larger. Also, the estimated friction factors from both approaches are higher than the values predicted from the Blasius equation which describes the friction factor for wide uniform open channel flows. They were also higher than values predicted from the Keulegan equation, which is an empirically derived equation for flow in roof drainage gutters. The study highlights the deficiencies in the existing equations used to predict friction factors for spatially varied flow and that further research is required to explore the distribution of boundary shear stress in an open channel receiving lateral inflow.     

Discharge Rating Equation and Hydraulic Characteristics of Standard Denil Fishways

This paper introduces a new equation to predict discharge capacity in the commonly used Denil fishway using water surface elevation in the upstream reservoir and fishway width and slope as the independent variables. A dimensionless discharge coefficient based only on the physical slope of the fishway is introduced. The discharge equation is based on flow physics, dimensional analysis, and experiments with three full-scale fishways of different sizes. Hydraulic characteristics of flow inside these fishways are discussed. Water velocities decreased by more than 50% and remained relatively unchanged in the fully developed flow downstream of the vena contracta region, near the upstream baffle where fish exit the fishway. Engineers and biologists need to be aware of this fact and ensure that fish can negotiate the vena contracta velocities rather than velocities within the developed flow region only. Discharge capacity was directly proportional to the fishway width and slope. The new equation is a design tool for engineers and field biologists, especially when designing a fishway based on flow availability in conjunction with the swimming capabilities of target fish species.     

A mathematical model of aluminum depth filtration with ceramic foam filters: Part II. Application to long-term filtration

The mathematical model to compute the efficiency of depth filtration of molten aluminum, previously presented in Part I, was further developed and applied to study long-term filtration. In this case, the incoming suspension entering the unit cell was not assumed homogeneous, and the times and positions of particle at the inlet were obtained stochastically from a random number generator. The particles that were transported by the fluid flow to the wall and collided against this surface remained attached to the wall and accumulated within the domain. The accumulation of particles decreased the effective area for fluid to flow through the pore, causing distortion of the overall velocity field in the domain. The flow field was obtained from the numerical solution of the continuity and Navier-Stokes equations for transient flow, the particle trajectories were calculated using the Langrangian motion equation including the buoyancy, and the viscous drag force corrected for the wall effect. The model predicted a preferred particle accumulation around the windows to form a cake of particles and the effect that inclusion accumulation has on the flow field, pressure drop, and filtration coefficient. This work studied the influence of particle concentration and fluid velocity on the evolution of the filtration coefficient and pressure drop. It was found that these quantities were practically constant for TiB₂ particles suspended in aluminum at a concentration of 1 ppm and filtered during 60 minutes through the unit cell of a 30 ppi foam filter. However, at a particle concentration of 10 ppm, the model predicted that the filtration coefficient and pressure drop changed appreciably for the same period of filtration. The results, obtained from first principles, provide a rationale to explain fluctuations of the filtration coefficient and pressure drop, reported in the literature, without introducing any empirical or probability factor in the respective equations.     

Development of a Hydro-Salinity Simulation Model for Colorado’s Arkansas Valley

A model to calculate the quantity and quality of river flows by simulating hydro-chemical processes in soil and the spatial/temporal distribution of irrigation return flows is introduced. By simulating the hydro-chemical processes, the quantity and quality of the deep percolating water can be predicted. The spatial and temporal distribution of the deep percolating water is simulated by constructing a groundwater flow path and calculating the groundwater travel time using response functions. A probabilistic approach was developed to calculate the groundwater travel time taking into account the fact that some irrigated fields have subsurface drainage which shortens travel times. All related hydrological components are integrated into the computation of river flow quantity and quality including groundwater return flow, irrigation tail water, tributary inflow, river diversion, phreatophyte consumption, river channel losses, and river depletion due to pumping. An illustrative example is included to demonstrate the capabilities of the model. The results of this example show that river salinity is lower during the irrigation season and higher during the off season. Due to salts carried by return flows, downstream reaches have higher salinity levels than upstream reaches.     

Three-Dimensional Modeling for Estimation of Hydraulic Retention Time in a Reservoir

A three-dimensional computational fluid dynamics model is used to estimate the hydraulic residence time for a portion of the Wachusett Reservoir in central Massachusetts. The basin under consideration has several major inflows and exhibits complex flow patterns. The basin is modeled using the FLUENT software package with particles used to track travel time in a steady-state flow field. A tetrahedral mesh with over 1.6 million cells is used with accurate depiction of basin bathymetry and inlet and outlet geometries. Modeling is performed to simulate behavior during a period when conditions are isothermal. It is determined that mean hydraulic residence time is 3–4?days; approximately half of what would be expected assuming strictly plug flow. The presence of a primary flow path, large scale eddies and stagnation zones contribute to the faster travel times. Reductions in inflow rates produce increased residence times and significant changes in flow patterns.     

Spoiler Baffles in Circular Culverts

In many situations the design of culverts prevents the upstream migration of fish because water velocity in the barrel is greater than that of the natural channel. One way to reduce the water velocity within the culvert is to install spoiler baffles on the base. The current investigation uses a three-dimensional numerical tool to examine the influence of the baffle geometry on flow within culverts of varying diameters. The results indicate that spoiler baffles can reduce velocities in the culvert dramatically. The final choice of design hinges on the need of the fish and the discharge capacity of the culvert.     

Diameter and Surcharge Effects on Solute Transport across Surcharged Manholes

New data are presented describing the retention time and longitudinal dispersion of a solute tracer across circular surcharged manhole structures of different diameters. The variations with both discharge and surcharge level are described and the relationships quantified. The variation of the longitudinal dispersion coefficient exhibits poorly defined trends, however using an aggregated dead zone technique both the reach time delay and travel time show clear variations. A surcharge threshold level for these parameters is evident at the larger manhole diameters and this is explained in relation to jet theory. The variation of the surcharge mean time delay and postthreshold mean travel time are quantified, while the prethreshold travel times are shown to be dependent on both discharge and surcharge. The relationships allow for inclusion in sewer water quality modeling and provide a method for improving predictive techniques.     

Numerical computation of flow phenomena in gas-stirred ladle systems

Quasi-single-phase mathematical models as applied to the ladle hydrodynamics have been analysed rigorously. It is shown that choice of convergence criteria, nodal configuration and differencing schemes all influence the computed results significantly and consequently, results independent of these numerical parameters must first be established to draw any useful conclusion. Several quasi-single-phase computational procedures reported in the literature to study the gas-injection-induced flow phenomena have been critically examined. To this end, experimentally measured bulk flow-fields, plume-rise velocity and gas voidages have been compared with those predicted numerically. Such comparisons indicate that the bottom injection phenomena (viz., bulk flow, plume-rise velocity, and gas volume fraction within the plume etc.) can be adequately represented by assuming bubble slippage and considering a constant rise velocity in the two-phase region in the numerical solution scheme.     

Local Scouring at Bed Sills in a Mountain River: Plima River, Italian Alps

The main characteristics of local scouring below 26 bed sills constituting a sequence of grade-control structures in a mountain river (Plima River, Italian Alps) have been surveyed. Bed sills were built with concrete strengthened boulders and other loose boulders were placed in the river bed to enhance habitat diversity for fish. The most likely formative water discharge is used to evaluate specific flow energy at each bed sill. Measured maximum scour depths are well predicted by an empirical equation developed through laboratory results, showing an average relative error of 0.15.     

Analytical Solution of the Burgers Equation for Simulating Translatory Waves in Conveyance Channels

A Burgers equation model (BEM) for simulating translatory waves in conveyance channels is extracted from the Saint-Venant equations for small perturbations in initial uniform flow. The present study improves upon the previous model and presents analytical solutions for the simulation of translatory waves occurring in conveyance channels. The BEM is reduced to the linear diffusion equation using the Cole–Hopf transformation and then solved by means of the Green’s function assuming an infinite domain. The simulation studies performed show that the BEM results are comparable to those of the Saint-Venant equations for small perturbations in the initial uniform flow conditions and for Froude numbers within the subcritical region. The BEM could be useful for flood routing and for simulating release of water from a reservoir into a conveyance channel when the flow perturbation is small.     

Mechanism of fluid flow in a continuous casting tundish with different turbo‐stoppers

The fluid flow in a continuous casting tundish affects the separation of non‐metallic particles and the cleanliness of the steel. Today, laser‐optical investigations of water models are state of the art and enable detailed information about the effect of baffles, i. e. dams, weirs and turbo‐stoppers, on the flow. In this work 3D‐LDA and 2D‐DPIV‐investigations for different turbo‐stoppers in a water model on a scale of 1:1.7 of a 16 t single strand tundish are presented. Three circular turbo‐stoppers are investigated. Detailed measurements of the mean velocity and turbulence intensity in the tundish with and without turbo‐stopper are shown. With a suitable turbo‐stopper geometry the recirculation area in the tundish centre and short‐circuit flows along the side walls can be avoided and thus more favourable residence time distributions can be obtained. It is shown that the turbo‐stopper produces higher turbulence in the inlet region of the tundish, which is spatially more limited, however, in relation to the flow without turbo‐stopper. Thereby a more homogeneous flow is created at the discharge of the tundish with better conditions for the particle separation. The experimental data yield a good understanding of the flow phenomena in a tundish with turbo‐stopper and are used as validating criterion for numerical simulations (Fluent 5.5) on the basis of the Reynolds equations. The turbulence modelling is based on a two‐equation model (realizable k‐ε model).