Three-Dimensional Numerical Study of Flows in Open-Channel Junctions

An open-channel junction flow is encountered in many hydraulic structures ranging from wastewater treatment facilities to fish passage conveyance structures. An extensive number of experimental studies have been conducted but a comprehensive three-dimensional numerical study of junction flow characteristics has not been performed and reported. In this paper, a three-dimensional numerical model is developed to investigate the open-channel junction flow. The main objective is to present the validation of a three-dimensional numerical model with high-quality experimental data and compare additional simulations with classical one-dimensional water surface calculations. The three-dimensional model is first validated using the experimental data of a 90° junction flow under two flow conditions. Good agreement is obtained between the model simulation and the experimental measurements. The model is then applied to investigate the effect of the junction angle on the flow characteristics and a discussion of the results is presented.     

Nonlinear Mixing Length Model for Prediction of Secondary Currents in Uniform Channel Flows

A nonlinear turbulence model for numerical solution of uniform channel flow is presented. Turbulent stresses are evaluated from a nonlinear mixing length model that relates turbulent stresses to quadratic products of the mean rate of strain and the mean vorticity. The definition of the mixing length, based on a three-dimensional integral measure of boundary proximity, eliminates the need for solution of additional transport equations for the turbulence quantities. Experimental data from the literature for closed and open-channel flows are utilized to validate the model. The model produced the secondary flow vortices successfully. Velocity field and wall shear stresses affected by secondary flow vortices are accurately computed. Bulging of velocity contour lines toward the corners and dipping phenomena of maximum velocity are successfully simulated.     

Analysis of Dynamic Wave Model for Unsteady Flow in an Open Channel

The models for flood propagation in an open channel are governed by Saint-Venant’s equations or by their simplified forms. Assuming the full form of hyperbolic type nonlinear expressions, the complete or dynamic wave model is obtained. Hence, after first-order linearization procedure, the dispersion relation is obtained by using the classical Fourier analysis. From this expression, the phase and group speed and the variations of the amplitude of the waves are defined and investigated. Adopting Manning’s resistance formula, the effects of the variations of the Froude number, Courant number, and friction parameter are examined in the wave number domain for progressive and regressive waves. For small and high wave numbers, the simplified kinematic and gravity wave models are recovered, respectively. Moreover, the analysis confirms, according to the Vedernikov criterion, the Froude number value corresponding to the stability condition to contrast the development of roll waves. In addition, for stable flow on the group speed versus wave number curves, the results show critical points, maximum and minimum for progressive and regressive waves, respectively.     

Theoretical Development of Stage-Discharge Ratings for Subcritical Open-Channel Flows

Ratings relating stage and flow discharge have been traditionally established through measurements of discharge and concurrent stage. Inherent in this approach are several difficulties and shortcomings that have resulted in widely recognized problems in developing and applying ratings, such as looped ratings. Purely empirical methods that attempt to improve the agreement between ratings and measurements have met with limited success. This paper suggests a theoretical basis for discharge ratings that reflects the hydraulics of unsteady, nonuniform, subcritical flow. Simplification of the Saint-Venant equations for rating applications results in an approximation of the dynamics of flow that is summarized in the hydraulic performance graph, from which discharge ratings can be developed and updated theoretically. The resulting ratings apply a quasi-steady approximation of the flow, along with semiempirical correction factors developed for the site to estimate the discharge using the same information that is needed for “stage-fall-discharge ratings,” while addressing some of the shortcomings of this type of rating. Comparison of ratings developed using the resulting procedure against laboratory and field observations yields encouraging results.     

Local Time Stepping for Modeling Open Channel Flows

This paper presents two time accurate local time stepping (LTS) algorithms developed within aeronautics and develops the techniques for application to the Saint-Venant equations of open channel flow. The LTS strategies are implemented within an explicit finite volume framework based on using the Roe Riemann solver together with an upwind treatment for the source terms. The benefits of using an LTS approach over more traditional global time stepping methods are illustrated through a series of test cases, and a comparison is made between the two LTS algorithms. The results demonstrate how local time stepping can reduce computer run times, increase the reliability of the error control, and also increase the accuracy of the solution in certain regions.     

One-Dimensional Numerical Model for Nonuniform Sediment Transport under Unsteady Flows in Channel Networks

In this study, the proposed one-dimensional model simulates the nonequilibrium transport of nonuniform total load under unsteady flow conditions in dendritic channel networks with hydraulic structures. The equations of sediment transport, bed changes, and bed-material sorting are solved in a coupling procedure with a direct solution technique, while still decoupled from the flow model. This coupled model for sediment calculation is more stable and less likely to produce negative values for bed-material gradation than the traditional fully decoupled model. The sediment transport capacity is calculated by one of four formulas, which have taken into consideration the hiding and exposure mechanism of nonuniform sediment transport. The fluvial erosion at bank toes and the mass failure of banks are simulated to complement the modeling of bed morphological changes in channels. The tests in several cases show that the present model is capable of predicting sediment transport, bed changes, and bed-material sorting in various situations, with reasonable accuracy and reliability.     

Turbulence Measurements of Dye Concentration and Effects of Secondary Flow on Distribution in Open Channel Flows

This paper presents simultaneous turbulence measurements of velocity and tracer concentration using a combination of laser Doppler anemometer (LDA) and laser induced fluorescence (LIF) in rectangular and compound channels. Secondary flow, Reynolds stresses, Reynolds fluxes, and dye concentration distributions were measured near the water surface in both channels. An investigation of the effect of secondary flow on passive contaminant diffusion processes was carried out with relatively weak secondary flow in the rectangular channel and relatively strong secondary flow in the compound channel. The results show that the secondary flow clearly influences the spreading of the tracer concentration and the location of concentration peak, being different from the injection location. The transport rate of solute due to the secondary flow is not significant in the rectangular channel case but significant in the compound channel case. The transverse eddy viscosity is demonstrated to be equal to the transverse eddy diffusivity. The transverse eddy diffusivity near the water surface is larger than the vertical one. The Fickian law is valid in most regions investigated, but there are some regions where the Reynolds flux and concentration gradients are locally of the same sign due to the influence of secondary flow on the concentration distribution.     

Shear Stress in Smooth Rectangular Open-Channel Flows

The average bed and sidewall shear stresses in smooth rectangular open-channel flows are determined after solving the continuity and momentum equations. The analysis shows that the shear stresses are function of three components: (1) gravitational; (2) secondary flows; and (3) interfacial shear stress. An analytical solution in terms of series expansion is obtained for the case of constant eddy viscosity without secondary currents. In comparison with laboratory measurements, it slightly overestimates the average bed shear stress measurements but underestimates the average sidewall shear stress by 17% when the width–depth ratio becomes large. A second approximation is formulated after introducing two empirical correction factors. The second approximation agrees very well (R2>0.99 and average relative error less than 6%) with experimental measurements over a wide range of width–depth ratios.     

Omission of Critical Reynolds Number for Open Channel Flows in Many Textbooks

During the analysis of an open channel flow experiment, students were asked to determine whether the flow was laminar or turbulent. The array of answers highlighted the different information carried in fluid mechanics textbooks. It was noted that approximately 50% of the books did not mention the fact that the critical Reynolds number would be different in open channels as compared to circular pipes flowing full.     

Open Channel Flow Resistance

In 1965, Rouse critically reviewed hydraulic resistance in open channels on the basis of fluid mechanics. He pointed out the effects of cross-sectional shape, boundary nonuniformity, and flow unsteadiness, in addition to viscosity and wall roughness that are commonly considered. This paper extends that study by discussing the differences between momentum and energy resistances, between point, cross-sectional and reach resistance coefficients, as well as compound/composite channel resistance. Certain resistance phenomena can be explained with the inner and outer laws of boundary layer theory. The issue of linear-separation approach versus nonlinear approach to alluvial channel resistances also is discussed. This review indicates the need for extensive further research on the subject.     

Numerical Simulation of Flows in Cut-Throat Flumes

A numerical simulation is presented to obtain the flow characteristics of cut-throat flumes in rectangular open channels. Cut-throat flumes with a horizontal floor are used as simple devices for flow measurement in open channels. Since the flow in the throat section is highly three dimensional and curvilinear, the three-dimensional turbulence Reynolds stress model was applied in the present study to obtain the flow parameters such as the water surface profiles, the pressure distributions, and the mean velocity distributions. The volume of fluid scheme was used to determine the shape of the free surface by computing the fraction of each near-interface cell of a fixed grid that is partially filled with water. The previously published experimental data as well as data based on a new test related to cut-throat flumes were used to validate the simulation results.     

Turbulence Characteristics and Interaction between Particles and Fluid in Particle-Laden Open Channel Flows

Mechanism of sediment transport is composed of complicated interactions between turbulent flow, particle motion, and bed configurations. Of particular significance is the interaction between turbulence and particle motion, although turbulence measurements of particle-laden two phase flow have been a problem for a long time, especially in the near-wall region. In this study, simultaneous measurements of both the particles and fluid (water) were conducted in particle-laden two phase open channel flows by means of a discriminator particle-tracking velocimetry. The mean velocity and turbulence characteristics for fluid and particles each were examined in comparison with those in clear-water (particle-free) flow, together with previous existing data measured by laser Doppler anemometer and phase Doppler anemometer. The relative velocity and the turbulence modulation, which are the most important topics in two phase-flow approach, were revealed by varying the particle diameter and specific density. The fluid-sweeps are more contributory to the motion of particles than the fluid ejections in the near-wall region. In turn, the particle-sweeps transport the high momentum to the carrier fluid and enhance the turbulence intensities of fluid.     

Comparisons of Sidewall Correction of Bed Shear Stress in Open-Channel Flows

When investigating sediment transport in laboratory open-channel flows, it is often necessary to remove sidewall effects for computing effective bed shear stress. Previous sidewall correction methods are subject to some assumptions that have not been completely verified, and different values of the bed shear stress may be obtained depending on the approach used in making sidewall corrections. This study provides a quantitative assessment of the existing correction procedures by comparing them to a new sidewall correction model proposed in this study. The latter was derived based on the shear stress function and equivalent roughness size for both rigid and mobile bed conditions, which were obtained directly from experimental measurements. The comparisons show that the Einstein correction formula and the Vanoni and Brooks method generally predict relatively lower and higher bed shear stresses, respectively, while the Williams’ empirical function leads to more scatter. This study also demonstrates that the widely used Vanoni and Brooks approach can be well approximated by a simple formula derived based on the Blasius resistance function. The sidewall effects, when removed in the different ways, would consequently affect the presentation of the bedload function. Experimental results of bedload transport, when plotted as the dimensionless transport rate against the dimensionless shear stress with the latter being corrected using the present model, exhibit less scatter than those associated with the previous procedures.     

Double-Averaging Concept for Rough-Bed Open-Channel and Overland Flows: Theoretical Background

The goal of this paper is to discuss the spatial averaging concept in environmental hydraulics and develop it further by considering transport equations for fluid momentum, passive substances, and suspended sediments. The averaging theorems, the double-averaged (in time and in space) fluid momentum equation, and advection-diffusion equations for a passive substance and suspended sediments are introduced and their limitations and applications for modeling rough-bed flows, experimental design, and data interpretation are discussed. The suggested equations differ from those considered in terrestrial canopy aerodynamics and porous media hydrodynamics by accounting for roughness mobility, change in roughness density in space and time, and particle settling effects for the case of suspended sediments. We show that the form of the double-averaged equations may depend on the type of decomposition of flow variables and that this difference may have important implications for modeling. We also show that the suggested methodology offers better definitions for hydraulic characteristics, variables, and parameters such as flow uniformity, flow two dimensionality, and bed shear stress.     

Simple Flume for Flow Measurement in Sloping Open Channel

First, this paper presents a new flume for measuring flow discharge in sloping channels, originally proposed by Samani and Magallanez for use in a horizontal channel. The flume is obtained by inserting two semicylinders in a rectangular cross section. Then, using dimensional analysis and the self-similarity theory, the stage-discharge relationship of the flume is theoretically deduced. For determining the two coefficients of the power stage-discharge equation, some experimental runs are carried out using flumes characterized by different values of the contraction ratio (ranging from 0.17 to 0.81) and of the flume slope (ranging from 0.5 to 3.5%). Finally, for a given range of the contraction ratio, the relationships for estimating the two coefficients of the stage-discharge equation are obtained.     

Numerical Simulation of Equal and Opposing Subcritical Flow Junctions

This study presents measured and computational results of a flow pattern at a junction with equal and opposing flows in the upstream channel that collide and turn 90° into the branch channel. The computational results are obtained using a two-dimensional, depth-averaged model with the k-ε turbulent closure scheme. The aim is to predict the recirculation zones that form as the flow turns into the branch channel. The simulated depth and velocity profiles in the upstream main and the downstream branch channels are found to compare well with the measurements made in the physical model for various inlet Froude numbers and width ratios of the main channel to the branch channel. The absolute relative error between the measured and computed contraction coefficient, a measure of the recirculation zone size, is less than 4.7%. The computational model is then used to develop curves for the contraction coefficient for various inlet Froude numbers and ratios of main channel width to the branch channel width for design purposes.     

Numerical and Experimental Study of Dividing Open-Channel Flows

Dividing flows in open channels are commonly encountered in hydraulic engineering systems. They are inherently three-dimensional (3D) in character. Past experimental studies were mostly limited to the collection of test data on the assumption that the flow was 1D or 2D. In the present experimental study, the flow is treated as 3D and test results are obtained for the flow characteristics of dividing flows in a 90°, sharp-edged, rectangular open-channel junction formed by channels of equal width. Depth measurements are made using point gauges, while velocity measurements are obtained using a Dantec laser Doppler anemometer over grids defined throughout the junction region. A 3D turbulence model is also developed to investigate the dividing open-channel flow characteristics. The predicted flow characteristics are validated using experimental data. Following proper model validation, the numerical model developed can yield design data pertaining to flow characteristics for different discharge and area ratios for other dividing flow configurations encountered in engineering practice. Energy and momentum coefficients based on the present 3D model yield more realistic energy losses and momentum transfers for dividing flow configurations. Data related to secondary flows provide information vital to bank stability, if the branch channel sides are erodible.     

Dynamic Wave Study of Flow in Tidal Channel System of San Juan River

In this work the complete equations of one-dimensional unsteady flow in open channels in integral form, and compatibility equations at the junctions of a channel network, are solved numerically. Analytical integration in space is used between each pair of consecutive irregular sections of a channel, and the nonprismatic term is expressed in terms of uncoupled functions of the geometry at the sections. The linearized system of equations for each time interval is solved by an elimination method based on a double-sweep algorithm. The model is applied to the estuary of the San Juan River in Venezuela, where oscillating currents by effect of semidiurnal tides take place and the amplitude of the wave at the mouth is amplified toward the inland direction. Alternating drying and filling is simulated by means of slight modifications in the bed geometry of upper river sections. Measured water elevation and flow rates available at two stations are used to calibrate the model, and a very accurate adjustment of the tidal levels observed in the river is obtained.