Enhancing Utility of Submerged Vanes with Collar

Submerged vanes are submerged foils of low height and larger length, constructed in a river at an angle of attack α to the flow to modify the near-bed flow pattern and redistribute flow and sediment transport within the channel cross section. At a Froude number (F) of 0.13, the local scour development around the submerged vane without a collar was not enough to dislodge the vane whereas at F = 0.25, there was a significant local scour hole around the vane and the vane was dislodged. With the introduction of a collar at the leading edge of a submerged vane, the scour depth at the leading edge of the vane was reduced to zero. A collar of circular shape was found more suitable for a rectangular vane. Recommendations for sizing collars at two values of F are given. The optimal α for a rectangular vane with a collar was found close to 40°. The study clearly indicates the advantages of using collars in case of submerged vanes and provides insight into selection of appropriate collar shapes.     

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.     

Bank Profile of Threshold Channels: A Simplified Approach

A simplified model is presented for the computation of shape and dimensions of the cross section of a self-formed straight threshold channel with noncohesive uniform sediments. The model is based on the equilibrium of the individual sediment particles lying on the channel bed under the threshold condition, due to the hydrodynamic force acting on it. The transverse momentum diffusion, caused by the Reynolds stresses, is assumed as a function of the transverse distance from the center. Channel dimensions predicted by this model are in agreement with those obtained from previous models. However, the model slightly underestimates the experimental data.     

Sediment Exchange between a River and Its Groyne Fields: Mobile-Bed Experiment

Experiments have been carried out in a mobile-bed laboratory flume in order to study the sediment exchange process between the main channel and the groyne fields. The flume represented half the width of a schematized river reach with a series of groynes. The experiment was designed to represent typical dimensions of the Dutch River Waal at a geometrical scale of 1:100. The conditions were set to guarantee bed load as well as suspended load sediment transport. Conditions with submerged and emerged groynes were investigated. In addition to traditional measurements, viz., bed-level changes, suspended sediment concentrations, and flow velocities, bed-form propagation was measured in two dimensions using a the particle image velocimetry technique. The results were analyzed with focus on sediment exchange mechanisms and sediment transport patterns. The results demonstrate that under all flow conditions there is a net import of sediment into the groyne fields. The prevailing transport mechanisms vary with the flow stage: if the groynes are emerged it is mainly advection by the primary circulation cell, whereas if the groynes are submerged it is rather residual advection by large-scale coherent flow structures (in a straight reach). Additional entrainment of sediment by enhanced turbulence complicates the erosion/deposition patterns.     

Optimal Design of Composite Channels Using Genetic Algorithm

In the past, studies involving optimal design of composite channels have employed Horton’s equivalent roughness coefficient, which uses a lumped approach in assuming constant velocity across a composite channel cross section. In this paper, a new nonlinear optimization program (NLOP) is proposed based on a distributed approach that is equivalent to Lotter’s observations, which allows spatial variations in velocity across a composite channel cross section. The proposed NLOP, which consists of an objective function of minimizing total construction cost per unit length of a channel, is solved using genetic algorithm (GA). Several scenarios are evaluated, including no restrictions, restricted top width, and restricted channel side slopes, to account for certain site conditions. In addition, the proposed NLOP is modified to include constraints on maximum permissible velocities corresponding to different lining materials of the composite channel cross section, probably for the first time. The proposed methodology is applied to trapezoidal and triangular channel cross sections but can be easily extended to other shapes or compound channels. Optimal design graphs are presented to determine the channel dimensions of a composite trapezoidal channel cross section. The results obtained in this study indicate that cost savings up to 35% can be achieved for the unconstrained velocity case and up to 55% for the limiting velocity case when the proposed NLOP is solved using GA as compared with the existing NLOP solved using either the classical optimization solution technique or GA.     

Effects of Vanes and W-Weir on Sediment Transport in Meandering Channels

Sediment transport patterns in a meandering channel with instream restoration structures (vane and W-weir) have been studied. Laboratory experiments were conducted in a large-scale mobile-bed channel with graded materials under bank-full and overbank flow conditions. Bed-load samples were collected with a calibrated minisampler. Vanes, constructed against the outer bank in a meander bend, relocated the scour hole toward midchannel, thereby protecting the bank from erosion. The sediment sizes (d50,d90) in the bend became slightly more coarse and more uniform in the center of the channel. The W-weir installed immediately below a riffle section created two scour holes without affecting the upstream bed or the natural sediment transport of the channel. Predictions of bed-load transport by selected deterministic and stochastic methods showed large deviation from measurements using Helley–Smith sampler in sections downstream of the bend apex. In addition to creating local scour holes, the structures also relocated the locus of sediment transport at downstream sections. This issue should be considered when installing vanes and weirs in meandering rivers with significant bed-load transport.     

Three-Dimensional Modeling of Nonuniform Sediment Transport in an S-Shaped Channel

A three-dimensional numerical model was applied to compute uniform and nonuniform sediment transport and bed deformation in an S-shaped laboratory channel located at the University of Innsbruck, where detailed measurements of the velocity field and bed elevation changes were made. The channel had two bends, a trapezoidal cross section, and a slope of S = 0.005. Gravel with a mean diameter of 4.2?mm was used as movable bed material and for sediment feeding. Wu’s formula for multiple grain sizes was compared with van Rijn’s formula using one grain size. Fairly good agreement was found between the computed and measured bed elevations for both approaches, whereas Wu’s formula could further improve the numerical results. Looking at the physics of the erosion pattern, the computed scour areas were located slightly more downstream than what was observed in the physical model. The current study also includes several parameter tests: grid distribution in vertical, lateral, and longitudinal direction; time step; number of inner iterations/time step; active sediment layer thickness; and the Shields coefficient. The variation of those parameters gave some differences in the results, but the overall pattern of bed elevation changes remained the same.     

Parallel Walls as an Abutment Scour Countermeasure

Scour at bridge abutments can cause damage or failure of bridges and result in excessive repairs, loss of accessibility, or even death. To mitigate abutment scour, both clear-water and live-bed laboratory experiments in a compound channel were performed using parallel walls. Two types of parallel walls were tested: the first was made of a solid thin wood plate and the second was made of piled rocks. For solid parallel walls, a series of vertically oriented, rectangular, straight plates of different lengths attached to the upstream end of a wing wall abutment parallel to the flow direction were employed. Three velocities of 0.9, 1.5, and 2.3 times the incipient motion value for bed sediment movement were used. The bed material was sand with a mean diameter of 0.8?mm and a standard deviation of 1.37. All the plates were seated at the bottom of the compound channel bank slope and were even with the abutment face. It was found that straight plates thus situated are able to move the scour hole away from the upstream corner of the abutment. As the length of the plate increased, the scour at the abutment declined. It was found that a length of 1.6L, with L being the length of the abutment perpendicular to the flow, caused the scour to be eliminated at the abutment for a velocity ratio (U/Uc) of 0.9 (clear-water scour). Similarly, a 1.6L long wall can reduce the time-averaged scour depth at the abutment by 100% for a velocity ratio of 1.5, and 70% for a velocity ratio of 2.3. If the upstream end of the wall is anchored below the scour depth, this countermeasure would likely be feasible for situations where rock is expensive. For parallel rock walls, various values of wall length and protrusion length into the main channel were tested. It was found that a wall that does not protrude into the main channel and having a length of 0.5L minimizes scour at the abutment for all three different velocity ratios (0.9, 1.5, and 2.3).     

Hydraulic Evaluation of W-Weir for River Restoration

Various structural measures have been advocated for river restoration and habitat improvement schemes. The W-weir is one such structure that can be used in mobile bed alluvial rivers to diversify habitat and provide grade control. Laboratory studies have been carried out in a large-scale meandering channel with a mobile bed to investigate their effects on flow and sediment transport processes. A W-weir placed immediately downstream of a riffle section created a strongly three-dimensional flow pattern and high-turbulence zones. Two adjacent scour holes of different depths and substrate are formed under clearwater and live bed conditions. The continuity of sediment transport along the channel was not interrupted by the structure and the upstream afflux is minimal. Overbank flow significantly influenced the action of the weir and the scour hole was shifted closer to the structure. In a relatively tight bend followed by a short crossover reach, the weir may affect bed load transport pathways in the downstream bend. Finally, the study provides insights to guide their design for restoration projects.     

Improved Channel Cross Section with Two-Segment Parabolic Sides and Horizontal Bottom

A channel cross section with parabolic sides and horizontal bottom has been recently published and proved to be more economical (provide lesser construction cost per unit length) than the trapezoidal cross section. This paper presents a new and improved cross section with two-segment parabolic sides and horizontal bottom. Each side of the cross section consists of two parabolic segments smoothly connected. Closed-form relationships for the cross-sectional area and perimeter are developed. For specific parameter conditions, the new cross section produces most of the common cross sections, including the parabolic sides—horizontal bottom and trapezoidal cross sections, as well as new cross-sectional shapes. It provides an additional degree of freedom in determining the optimal cross-sectional design. A spreadsheet-based optimization model for the new cross section that minimizes the total construction cost (excavation and composite linings) is developed. The constraints of the model include channel discharge and physical requirements, such as flow depth, top width, and side slope with fixed or depth-dependent freeboard. The model was validated and the cross-sectional performance was evaluated using different design scenarios. The optimization results show that the new cross section is more economical and more flexible than a cross section with (one-segment) parabolic sides. As such, it should be of interest to the irrigation and drainage engineers.     

Accuracy of Cross-Channel Sampled Sediment Transport in Large Sand-Gravel-Bed Rivers

The accuracy of cross-channel integrated sediment transport of bed material is determined with an elaborate set of field measurements in the Waal River, The Netherlands. The measurements were done during a discharge wave in the upstream part of the river, which has a bimodal sand-gravel bed. The sampling strategy should take both spatial and temporal aspects into account to obtain maximum accuracy. Presence of moving bedforms, differences in bed-sediment grain size in the cross section, and presence of preferential transport lanes dictate that at least five subsections for sampling in the cross section are necessary. The accuracy of cross-channel integrated bedload transport depends mainly on the measurement strategy. An uncertainty of <20% (bedload) and 7% (suspended load) of cross-channel integrated sediment transport is shown to be feasible if 30 samples of bedload and two vertical profiles of suspended bed-material load are taken in one subsection, provided that the cross section of the river is divided into at least five subsections. The samples in one subsection should be distributed over the length of the bed form. Changes of discharge during the measurements cause systematic differences between the subsections. To minimize this uncertainty a compromise between the spatial and temporal accuracy is necessary. Therefore, when only one vessel with instruments is available for doing the measurements, the number of sampling positions and subsections must be reduced if the rate of change of discharge is large. Based on the results a prediction method is given to estimate the feasible accuracy in the planning phase of future campaigns, and the necessary time and financial investment for that accuracy.     

Quick Method for Open-Channel Discharge Measurements Using Air Bubbles

An economical methodology is proposed by which distinct air bubbles released at the bottom of a channel may be utilized for determining the local flow discharge q per unit width. Simple theoretical analysis shows that q is linearly dependent on the rise length L of bubbles released at the bottom. This length is the horizontal displacement of the bubbles between the release cross section and the cross section where they emerge. The theoretical findings were compared with measurements in three laboratory flumes and in an irrigation canal. Based on the above, a relationship between L and q has been established. The empirically proposed relationship is very useful for fast discharge measurements in channels and natural streams.     

Effect of Shape on Incipient Motion of Large Solitary Particles

The aim of this study is to investigate the effect of shape and size of solid particles on their initiation of motion in open channel flows. Initial motions of 22 solitary particles having different shapes and sizes were observed in a tilting flume of rectangular cross section. A smooth fixed bed and an obstructing element of smaller height with respect to the particle size was used throughout the experiments. The ratio of the height of the obstructing element to the height of the particle was kept constant at 1/5. By either changing the slope of the tilting flume or the discharge, or both, a range of shear stress values was obtained. Various equations and graphical representations in terms of dimensionless bed shear stress, grain Reynolds number, and the ratio of flow depth to grain diameter were presented to determine the flow conditions corresponding to the initiation of motion of solitary particles of given shapes. The experiments have revealed that critical flow conditions are dependent not only on the particle size and shape but also on the ratio of flow depth to grain diameter.     

3D Numerical Modeling of Flow and Sediment Transport in Laboratory Channel Bends

The development of a fully three-dimensional finite volume morphodynamic model, for simulating fluid and sediment transport in curved open channels with rigid walls, is described. For flow field simulation, the Reynolds-averaged Navier–Stokes equations are solved numerically, without reliance on the assumption of hydrostatic pressure distribution, in a curvilinear nonorthogonal coordinate system. Turbulence closure is provided by either a low-Reynolds number k?ω turbulence model or the standard k?ε turbulence model, both of which apply a Boussinesq eddy viscosity. The sediment concentration distribution is obtained using the convection-diffusion equation and the sediment continuity equation is applied to calculate channel bed evolution, based on consideration of both bed load and suspended sediment load. The governing equations are solved in a collocated grid system. Experimental data obtained from a laboratory study of flow in an S-shaped channel are utilized to check the accuracy of the model’s hydrodynamic computations. Also, data from a different laboratory study, of equilibrium bed morphology associated with flow through 90° and 135° channel bends, are used to validate the model’s simulated bed evolution. The numerically-modeled fluid and sediment transportation show generally good agreement with the measured data. The calculated results with both turbulence models show that the low-Reynolds k?ω model better predicts flow and sediment transport through channel bends than the standard k?ε model.     

Three-Dimensional Modeling of Sediment Transport in a Narrow 90° Channel Bend

A three-dimensional numerical model was used for calculating the velocity and bed level changes over time in a 90° bended channel. The numerical model solved the Reynolds-averaged Navier-Stokes equations in three dimensions to compute the water flow and used the finite-volume method as the discretization scheme. The k-ε model predicted the turbulence, and the SIMPLE method computed the pressure. The suspended sediment transport was calculated by solving the convection diffusion equation and the bed load transport quantity was determined with an empirical formula. The model was enhanced with relations for the movement of sediment particles on steep side slopes in river bends. Located on a transversally sloping bed, a sediment particle has a lower critical shear stress than on a flat bed. Also, the direction of its movement deviates from the direction of the shear stress near the bed. These phenomenona are considered to play an important role in the morphodynamic process in sharp channel bends. The calculated velocities as well as the bed changes over time were compared with data from a physical model study and good agreement was found.     

Broad-Crested Weirs with Rectangular Compound Cross Sections

A series of laboratory experiments was performed in order to investigate the effects of width of the lower weir crest and step height of broad-crested weirs of rectangular compound cross section on the values of the discharge coefficient, the approach velocity coefficient, and the modular limit. For this purpose, nine different broad-crested weir models with rectangular compound cross sections and a model with a rectangular cross section were tested in a horizontal laboratory flume of 11.0 m length, 0.29 m width, and 0.70 m depth for a wide range of discharges. The compound cross sections were formed by a combination of three sets of step heights and three sets of lower weir crest widths. The sill-referenced heads at the approach channel and at the tailwater channel were measured in each experiment. The dependence of the discharge coefficient, approach velocity coefficient, and modular limit values on model parameters was investigated, and these quantities were compared with those of the broad-crested weir models with a rectangular cross section.     

Trapping and Generation of Waves by Vertical Porous Structures

The trapping and generation of surface waves by submerged vertical permeable barriers or plates kept at one end of a semi-infinitely long channel of finite depth are investigated for various barrier and plate configurations. The various fixed barrier configurations are (1) a surface-piercing barrier; (2) a bottom-touching barrier; (3) a barrier with a gap; and (4) a fully submerged barrier. The different moving plate (or wavemaker) configurations are of types 1, 2, and 4, respectively. The boundary value problems are converted to dual∕triple series relations by a suitable application of the eigenfunction expansion method and then the full solutions are obtained by the least-squares method. The variations of reflection coefficients are obtained and discussed for different values of the porous-effect parameter, the normalized distance between the barrier and the channel end-wall, and the length of submergence of barriers for all types of barrier configurations. The dynamic pressure distributions for various porous-effect parameters are analyzed for the three types of wavemakers. The wave amplitudes at large distances are obtained and analyzed for different values of the porous-effect parameter and the distance between the wavemaker and the channel end-wall.     

Best Hydraulic Section of a Composite Channel

The half-circle is the ideal shape of the best hydraulic section of open channels, but semicircular channels are not practical to construct. The semicircular section is approximated by a composite section that is composed of a trapezoidal section at the bottom and a rectangular section at the top. Such a composite channel can be easily constructed in rocks. This technical note presents an analysis for determining the channel proportions that yield a minimum wetted perimeter for a given flow area of the composite channel. The results of the analysis show that the best hydraulic section has the shape of a half-octagon for composite channel and a composite section is more efficient than a trapezoidal section.     

Overtopping Breaching of Noncohesive Homogeneous Embankments

Homogeneous small-amplitude embankments were constructed in flumes from a range of uniform noncohesive materials and breached by overtopping flows under constant reservoir level conditions. Embankment erosion evolves from primarily vertical to predominantly lateral in nature. The breach channel initially erodes the downstream face of the embankment with an invert slope parallel to the face, the breach invert slope then progressively flattening to a terminal value by rotating about a fixed pivot point along the base of the embankment, the location of this pivot point being a function of the size of the embankment material. The breach channel is of a curved (hourglass) shape in plan. Below the water line, breach cross-section width B variation with elevation y above the breach invert is nondimensionally described by B? = 2k?y?0.5, where for the breach cross section at the embankment crest k? = ?2.82[ln(Hb?)]+0.351, and Hb is the centerline breach crest elevation. Breach discharge Qb can be nondimensionally expressed as a function of the head hb on the breach-crest centerline and the breach crest length in plan Lb using Qb? = 0.242?Lb?(hb?)1.5. All expressions presented are applicable to full-width breach sections (double the half-breach section tested). The present findings enable prediction of the development with time of breach cross section, breach longitudinal profile, eroded volumes, and breach flows. The findings can be utilized for predictions of erosion and flooding occurring as the result of embankment failure, although in an engineering sense the quantitative findings of the present work await confirmation for larger embankments.