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.     

Optimal Design of a Special Class of Curvilinear Bottomed Channel Section

Section elements of a new class of curvilinear bottomed channel whose boundary maps along a circle onto the hodograph plane have been investigated in the study. The perimeter of this type of channel always lies between an ellipse and a parabola of the same top width and flow depth. Presented herein are optimal section properties from least area and minimum seepage loss point of view for the curved channel section. The study also addresses the constraints on the channel dimensions and the velocity of flow. A nondimensional parameter approach has been used to simplify the analysis. Design procedures for different cases have been presented to demonstrate the simplicity of the method.     

Critical Flow over Circular Crested Weirs

The critical flow principle is a useful approach for the hydraulic analysis of round-crested weirs due to their single head-discharge relationships. The hydraulics of circular-crested weirs is examined using simplified models incorporating streamline curvature effects, comparing their predictions with experimental data. A generalized one-dimensional model based on the critical flow in curvilinear motion has been developed. The discharge coefficient increases with the specific energy normalized with the radius of curvature, E/R, when streamline curvature effects are included. The relative flow depth at the crest decreases as E/R increases. The flow at the weir crest is only critical for a normalized specific energy value of E/R ≈ 0.5–0.6. For larger heads, the flow at the weir crest has been found to be supercritical.     

Optimal Design of Channel Having Horizontal Bottom and Parabolic Sides

The cost of open channels can be minimized by using (1) the optimal design concept; (2) a new geometric shape to substitute for the trapezoidal channels, and/or (3) a composite channel. The channels in which the roughness along the wetted perimeter become distinctly different from part to part of the perimeter are called composite channels. The feasibility of a new cross-sectional shape that has a horizontal bed and two parabolic sides and lined as a composite channel is investigated to substitute for the trapezoidal cross section. The optimal design concept is used to establish the efficacy of the proposed new cross-sectional shape, because it gives the best and unique design of open channels. In optimal design concept, the geometric dimensions of a channel cross section are determined in a manner to minimize the total construction costs. The constraints are the given channel capacity and other imposed restrictions on geometric dimensions. The Lagrange multiplier technique is used to solve the resulting channel optimization models. The developed optimization models are applied to design the proposed and trapezoidal channels to convey a given design flow considering various design scenarios which include unrestricted, flow depth constrained, side slopes constrained, and top width constrained design. Each of these design scenarios again takes into account fixed freeboard, and depth-dependent freeboard cases of design. An analysis of the optimization results establishes the cost-saving capability of the proposed cross-sectional shape in comparison to a trapezoidal cross section.     

Minimum Specific Energy and Critical Flow Conditions in Open Channels

In open channels, the relationship between the specific energy and the flow depth exhibits a minimum, and the corresponding flow conditions are called critical flow conditions. Herein they are reanalyzed on the basis of the depth-averaged Bernoulli equation. At critical flow, there is only one possible flow depth, and a new analytical expression of that characteristic depth is developed for ideal-fluid flow situations with nonhydrostatic pressure distribution and nonuniform velocity distribution. The results are applied to relevant critical flow conditions: e.g., at the crest of a spillway. The finding may be applied to predict more accurately the discharge on weir and spillway crests.     

Hydraulic Models of the Flow Distribution in a Four Branch Open Channel Junction with Supercritical Flow

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.     

Transcritical Flow due to Channel Contraction

The singular point is a physical phenomenon consistent with critical flow conditions, and, consequently, the real control section of a water surface profile. A general method to study the location, type, and water surface slope of a singular point is described. This method, in addition to improving the classic gradually-varied flow theory, can be used for the design of channel contractions involving transcritical flows, as in the case of chute spillways and inlets to river diversion tunnels. The method is explained in the case of a chute spillway and verified against experimental data recorded in a Venturi channel.     

Flooding Probability-Based Optimal Design of Trapezoidal Open Channel Using Freeboard as a Design Variable

A flooding probability based cost effective design of open channel section has been proposed using freeboard as an additional design variable. The freeboard of the channel is calculated based on the flooding probability value. The proposed model is solved using classical optimization techniques as well as a nondominated sorting genetic algorithm. The results of the model are compared with an earlier reported model to demonstrate its superiority and field applicability.     

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.     

Optimal Design of a Stable Trapezoidal Channel Section Using Hybrid Optimization Techniques

A cost effective channel section for a specified flow rate, roughness coefficients, longitudinal slope, and various cost parameters can be determined using an optimization technique. However, the derived optimal channel section may not be feasible for construction because of in situ conditions. The local soil conditions may not support the optimal side slope of the channel and if constructed, the slope may fail. It is therefore necessary to also incorporate the criteria for side slope stability in designing an optimal open channel section. In this paper, a new methodology has been developed to design a stable and optimal channel section using hybrid optimization techniques. A genetic algorithm based optimization model is developed initially to determine the factor of safety of a channel slope for given soil parameters. This optimization model is then externally linked with a separate sequential quadratic programming based optimization model to evaluate the parameters of the stable and optimal channel section. Solution for various example problems incorporating different soil parameters are illustrated to demonstrate the applicability of the developed methodology.     

Free-Surface–Vorticity Interactions in an Open Channel Flow

The interactions between vortical structures, free surface, and background shear in an open channel flow is experimentally investigated. Deterministic structures are generated by a vertical injection from the channel bottom and a number of disturbances characterized by different jet amplitudes and Reynolds number are considered. Three cases are selected as representatives of the whole phenomenology and their evolution is discussed in detail. The streamwise perturbation is visualized by fluorescein while the streamwise component of velocity is measured by a laser Doppler anemometer. The perturbation in the cross stream plane is analyzed quantitatively and the velocity field is reconstructed on the symmetry plane, to extract the traces of the individual vortical structures. Depending on the intensity of the external perturbation, the structures either evolve as in the absence of the interface (small intensity) or they approach the free surface to undergo a topological change due to their reconnection with the free surface. The process originating in the so-called blockage and viscous layers is analyzed in detail. As a major conclusion, the interaction with the free surface is found to deplete the velocity gradients generated by the liftup of the quasi-streamwise vortices. This effect is suggested to be a major cause of stabilization of the open channel flow, with respect to a closed channel at the same Reynolds number.     

Critical Depth Relationships in Developing Open-Channel Flow

Doubts have been expressed about the validity of the critical depth defined in terms of the minimum specific energy head of the free-surface streamline when dealing with developing open-channel flows. This note examines the two approaches for defining critical flow, that based on the minimum specific energy of the free-surface streamline and that based on the mean energy head of the whole flow section. Large differences for the dimensionless critical depths are obtained with the two methods due to each critical depth proving to be a different control point on the free-surface profile. It is argued that both methods are different alternatives, although the critical depth concept was different in each case. Theoretical support to critical flow computations based on the free streamline is provided. An alternative approach for computing the discharge characteristics of broad-crested weirs based on the energy loss inside the boundary layer is also proposed.     

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.     

Flow in Compound Channel with Abrupt Floodplain Contraction

Flooding rivers usually present transition reaches where the floodplain width can significantly vary. The present study focuses on an abrupt floodplain contraction (mean angle 22°) in order to determine whether one-dimensional (1D) models, developed for straight and slightly converging geometry, are equally valid for such a geometry. Experiments on a contraction model were carried out in an asymmetric compound channel flume. Severe mass and momentum transfers from the floodplain towards the main channel were observed, giving rise to a noteworthy transverse slope of the water surface and different head loss gradients in the two subsections. Three 1D models and one 2D simulation were compared to experimental measurements. Each 1D model incorporates a specific approach for the modeling of the momentum exchange at the interface boundary between the main channel and the floodplain. The increase of the lateral mass transfer generates moderate errors on the water level values but significant errors on the discharge distribution. Erroneous results arise because of incorrect estimations of both momentum exchange due to lateral mass transfers and boundary conditions which are imposed by the tested 1D models.     

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.     

Depth-Averaged Two-Dimensional Numerical Modeling of Unsteady Flow and Nonuniform Sediment Transport in Open Channels

A depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow water equations are solved by the SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment transport. The bed load and suspended load are calculated separately or jointly according to sediment transport mode. The sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes. An empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed-load movement direction in channels with steep slopes. Flow and sediment transport are simulated in a decoupled manner, but the sediment module adopts a coupling procedure for the computations of sediment transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement between the simulated results and measured 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.     

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.     

Gradually Varied Flow Computation in Cyclic Looped Channel Networks

A novel and computationally efficient algorithm is presented to compute the water surface profiles in steady, gradually varied flows of open channel networks. This algorithm allows calculation of flow depths and discharges at all sections of a cyclic looped open channel network. The algorithm is based on the principles of (1) classifying the computations in an individual channel as an initial value problem or a boundary value problem; (2) determining the path for linking the solutions from individual channels; and (3) an iterative Newton–Raphson technique for obtaining the network solution, starting from initial assumptions for discharges in as few channels as possible. The proposed algorithm is computationally more efficient than the presently available direct method by orders of magnitude because it does not involve costly inversions of large matrices in its formulation. The application of this algorithm is illustrated through an example network.     

Analysis of Velocity Lag in Sediment-Laden Open Channel Flows

Laboratory experiments have recently confirmed that the streamwise particle velocity is largely less than that of the fluid in sediment-laden flows. This velocity lag is investigated analytically in the present study based on the drag force exerting on a particle in the presence of other neighbors. The normalized drag force or the hindrance coefficient is found generally dependent on the particle concentration, particle Reynolds number, and specific gravity. The velocity lag is then derived by relating the hindrance coefficient to the shear stress distribution for uniform sediment-laden open channel flows. The analysis shows that the profile of the velocity lag, when normalized by the shear velocity, is associated with the shear Reynolds number, dimensionless particle diameter, and specific gravity. For the dilute condition, the velocity lag distribution varies only with the shear Reynolds number, and the lag can be ignored if the shear Reynolds number is less than unity. The theoretical predictions are comparable to limited experimental results.