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.     

Open Channel Flow through Different Forms of Submerged Flexible Vegetation

Laboratory experiments are used to explore the effect of two forms of flexible vegetation on the turbulence structure within a submerged canopy and in the surface flow region above. The two simulated plant forms involve flexible rods (stipes) of constant height, and the same rods with a frond foliage attached. These plant forms were arranged in a regular staggered configuration, set at the same stipe density. The plant geometry and its mechanical properties have been scaled from a real aquatic plant using Froudian similarity, and the methods used for quantifying the bending stiffness, flexural rigidity, and drag force–velocity relationship of the vegetation are outlined. Experimental results reveal that within the plant layer, the velocity profile no longer follows the logarithmic law profile, and the mean velocity for the rod/frond canopy is less than half of that observed for the simple rod array. In addition to the mean flow field, the turbulence intensities indicate that the additional superficial area of the fronds alters the momentum transfer between the within-canopy and surface flow regions. While the frond foliage induces larger drag forces, shear-generated turbulence is reduced due to the inhibition of momentum exchange by the frond surface area. It is known that the additional drag exerted by plants reduces the mean flow velocity within vegetated regions relative to unvegetated ones, but this research indicates that plant form can have a significant effect on the mean flow field and, therefore, potentially influence riverine and wetland system management strategies.     

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.     

Outer Scaling for Open Channel Flow over a Gravel Bed

Similarity analysis is performed for hydraulically rough open channel flow over a gravel bed to provide mixed outer scaling of the mean-velocity profile. The analysis is based on equilibrium turbulent boundary-layer theory derived using the asymptotic invariance principle. Outer scaling based on the similarity theory is validated with velocity measurements from the laboratory and field, having a Reynolds number range that includes 1×104, 1×105, and 1×106 and a Froude number range from 0.26 to 0.83. The results show that the free-stream velocity is an appropriate outer scale for gravel-bed river flows at moderate and bankfull stage. The results agree well with the velocity measurements and collapse laboratory and field data, which allow an important connection between open channel research in the laboratory and the applications for which the research is performed in the field. The results show that the R/aD84 roughness parameter is consistent with the mixed scale used in boundary-layer velocity scaling. This is in agreement with the consistent turbulent structure of the flow for both flat plate boundary-layer and open channel flow scenarios. While R/D84 has been used empirically with depth-averaged velocity and roughness laws for many years, this roughness parameter is shown in a theoretical context due to its influence on the turbulent structure of the flow. The results are applicable to modeling the velocity distribution under fundamental gravel-bed flow cases that span to the bankfull flow regime, which provides a contribution to stream engineering.     

Stone Stability in Nonuniform Flow

This paper presents the results of an experimental study on stone stability under nonuniform turbulent flow, in particular expanding flow. Detailed measurements of both flow and turbulence and the bed stability are described. Than various manners of quantifying the hydraulic loads exerted on the stones on a bed are extensively reviewed and extended. On the basis of the data, a new relationship between flow parameters and bed damage—expressed as a stone entrainment formula—has been established for nonuniform flow. As the present data is in line with existing data on other flows, the present relation seems applicable for other types of nonuniform flow as well. Such a relationship could provide more consistent design criteria and allow an estimate of the cumulative damage over time, which is important for making decisions regarding maintenance frequency and lifetime analysis of hydraulic structures.     

Conservative Formulation for Natural Open Channels and Finite-Element Implementation

This investigation considers an approximate formulation of the St. Venant equations for natural channels, in which the fully conservative form is developed by revising the boundary pressure term accounting for the topographic variation in the momentum equation. As such a formulation has the potential to enhance the performance of existing models used in practice, the accuracy implications for this approximate formulation are examined using an error analysis for a simplified case. Further, an energy calculation is performed which illustrates that an earlier formulation actually results in energy gain for some cases. A more general formula for the constant water surface elevation that corrects this is introduced and tested. It is found that the refined formulation presented here is accurate for hydraulic jumps, steep surge waves, and flood wave propagation in natural channels. The shock capturing capability of the approximate formulation is illustrated for both steady- and unsteady-flow situations using the finite-element method, for which this approximate equation formulation adapts naturally. Using the characteristic-dissipative-Galerkin finite-element scheme, good results are obtained for the case of a hydraulic jump in a diverging rectangular channel, with the maximum percent error associated with the approximate formulation determined to be only 0.34%. For the case of dam break wave propagation in a converging and diverging rectangular channel, the model performs similarly well, with the maximum error only 0.0064%. Further, the approximate formulation is used to simulate the flood routing in a natural channel, the Oldman River in southern Alberta. The computational results are in good agreement with the observed data. The arrival time of peak flow is 5?h earlier and the magnitude of peak discharge is only 3.8% lower than the observed value.     

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.     

Finite Difference Method for Computation of 1D Pollutant Migration through Saturated Homogeneous Soil Media

The physical processes such as advection, dispersion, and diffusion and interaction between the solution and the soil solids such as sorption, biodegradation, and retention processes have been considered in the governing equation used in the present study. Finite difference method has been adopted herein to solve the one-dimensional contaminant transport model to predict the pollutant migration through soil in waste landfill. In the finite difference technique, the velocity field is first determined within a hydrologic system, and these velocities are then used to calculate the rate of contaminant migration by solving the governing equation. A total of seven contaminants have been chosen for analysis to represent a wide variety of wastes both organic and inorganic. A computer software CONTAMINATE has been developed for solution of the contaminant transport model. Results of this study have been compared with existing analytical solution for validation of the proposed solution technique. Design charts for liners have also been developed to facilitate the designers. The liner thickness has been optimized by considering the effect of velocity of advection, dispersion coefficient, and geochemical reactions for all the contaminants of this study.     

Reynolds Stress in Open Channel Flow with Upward Seepage

Nonuniform-unsteady flow in open channels with streamwise sloping beds having uniform upward seepage is theoretically analyzed. Expressions for the Reynolds stress and bed shear stress are developed, assuming a modified logarithmic law of velocity profile due to upward seepage, and using the Reynolds and continuity equations of two-dimensional open channel flow. The computed Reynolds stress profiles are in agreement with the experimental data.     

Simple, Robust, and Efficient Algorithm for Gradually Varied Subcritical Flow Simulation in General Channel Networks

This paper details the development of a method for subcritical flow modeling in channel networks by using the implicit finite-difference method. The method treats backwater effects at the junction points on the basis of junction-point water stage prediction and correction (JPWSPC). It is applicable to flows in both looped and nonlooped channel networks and has no requirement on the flow directions. The method is implemented in a numerical model, in which the Saint-Venant equations are discretized by using the four-point implicit Preissmann scheme, and the resulting nonlinear system of equations is solved by using the Newton-Raphson method. With the help of JPWSPC, each branch is computed independently. This guarantees the simplicity, efficiency, and robustness of the numerical model. The model is applied to two hypothetic channel networks and a real-life river network in South China. All the networks contain both branched and looped structures. The simulated results compare well with the results from literature or the measurements.     

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.     

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.     

3D Numerical Simulation of Turbulent Buoyant Flow and Heat Transport in a Curved Open Channel

A three-dimensional buoyancy-extended version of k–ε turbulence model was developed for simulating the turbulent flow and heat transport in a curved open channel. The density-induced buoyant force was included in the model, and the influence of temperature stratification on flow field was considered. The flow and temperature fields were simulated simultaneously. The model was validated by comparison with laboratory measurements, and the simulated fields were generally in good agreement with experimental data. A comparison of velocity fields in thermal and isothermal flow in curved open channel is presented and the effects of channel curvature and buoyant force on the velocity fields are also discussed.     

Linearized Stability and Accuracy for Step-by-Step Solutions of Certain Nonlinear Systems

In this work, stability and accuracy of the Newmark method for nonlinear systems are obtained from a linearized analysis. This analysis reveals that an unconditionally stable integration method for linear elastic systems is unconditionally stable for nonlinear systems and a conditionally stable integration method for linear elastic systems remains conditionally stable for nonlinear systems except that its upper stability limit might vary with the step degree of nonlinearity and step degree of convergence. A sufficient condition to have a stable computation for nonlinear systems in a whole step-by-step integration procedure is also developed in this study. Furthermore, it is also found that numerical accuracy in the solution of nonlinear systems is closely related to the step degree of nonlinearity and step degree of convergence although its characteristics are similar to those of the preceding works for linear elastic systems. Since these results are obtained from a linearized analysis, they can be applicable to the nonlinear systems that satisfied the simplifications for the analysis but may not be applicable to general nonlinear systems.     

Optimal Design of Open Channel Section Incorporating Critical Flow Condition

The flow at critical condition of an open channel is unstable. At critical condition, a small change in specific energy will cause abrupt fluctuation in water depth of the channel. This is because the specific energy curve is almost vertical at critical state. Therefore, if the design depth of the channel is near or equal to critical depth of the channel, the shape of the channel must be altered to avoid a large fluctuation in water depth. In the present study, a nonlinear optimization model is presented for designing an optimal channel section incorporating the critical flow condition of the channel. The optimization model derives the optimal channel section at a desirable difference from the critical condition of the channel so that a small change in the specific energy of the channel will not cause an abrupt change in flow depth. The objective of the optimization model is to minimize the total construction costs of the channel. Manning’s equation is used to specify the uniform flow condition in the channel. The developed optimization model is solved by sequential quadratic programming using MATLAB. Applicability of the model is demonstrated for a trapezoidal channel section with composite roughness. However, it also can be extended to other shapes of channel.     

Scale Independent Linear Behavior of Alluvial Channel Flow

For flow in a rigid open channel with no bed sediment, the achievement of the special state of stationary equilibrium yields a linear characteristic. To examine the existence of a linear characteristic in alluvial channel flow, this study presents a direct formulation of the special equilibrium state following a variational approach. It finds that a linear relationship between shear stress and width/depth ratio of alluvial channels emerges under the commonly identified flow resistance and sediment transport conditions. Most importantly, this linear relationship yields not only the theoretical equilibrium channel geometry that is very close to a widely identified empirical counterpart but also a nondimensional number H, defined as the ratio of the relative increment of shear stress to the increment of width/depth ratio. This study suggests that H needs to be adopted as a criterion of hydraulic similitude for modeling sediment (bed-load) transport in alluvial channels.     

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.     

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.     

Flow Resistance and Momentum Flux in Compound Open Channels

New formulations are presented for flow resistance and momentum flux in compound open channels. As implemented in the St. Venant equations, these formulations facilitate a physically enhanced approach to evaluating conveyance, roughness, stage-discharge relationship, and unsteady flood routing in compound open channels. An analysis using steady flow data from the well-controlled experiments at the large-scale Flood Channel Facility, HR Wallingford, demonstrates the ability of the present approach to properly resolve the discontinuity of overall roughness across the main-channel bankfull level. Also, the proposed formulations are shown to be conducive to obviating the long-standing computational difficulty in unsteady flood routing due to small flow depths over flat and wide floodplains. The present work should find general applications in one-dimensional computation of river flows.     

基于有限差分法的工作辊弯辊挠曲计算

以弯曲变形的微分方程为理论基础,运用有限差分法相关原理对这些微分方程进行了相关推导,得出了一定弯辊力作用下工作辊挠曲变形计算的线性方程组表达式。通过给定的计算实例,编制了相关计算程序,完成了一定弯辊力作用下某工作辊的挠曲变形计算。结果表明:在较大弯辊力作用下,工作辊沿x轴正向各截面的挠曲呈非线性变大趋势,且在弯辊轴承中心作用点处达到最大。此外,有限差分法不失为一种快速有效地求解工作辊多点挠度的计算方法。