Design and Calibration of a Compound Sharp-Crested Weir

This paper describes the design and calibration of a compound sharp-crested weir consisting of two triangular parts with different notch angles. This weir provides accurate measurement for a wide range of flows without discontinuities. The lower triangular part of the weir handles the normal range of discharges at the measurement structure while the upper part measures the occasional higher peak flows. This weir will be installed on the crest of small concrete gravity dams for measuring runoff in experimental catchments. The weir was calibrated in the laboratory using a scaled model. Different geometries (combination of notch angles) were tested in order to validate the proposed theoretical discharge equations.     

Case Study: Hydraulic Modeling of Runoff Processes in Ghanaian Inland Valleys

The inland valleys of West Africa are strategic in terms of food security and poverty alleviation, but scientific studies on hydrologic processes happening in these environments have not been well documented. Modeling approaches presented in this paper are an attempt to better comprehend hydraulic phenomena occurring in inland valleys. An inland valley situated in the Northern Region of Ghana is set as the study site. The inland valley comprises well-drained uplands and hydromorphic valley bottoms. There are several earthen dams across the valley bottoms, which are at the same time seasonal wetlands cultivated to rice during the rainy season. A finite volume model for the shallow water equations is developed to numerically simulate surface runoff flows in the valley bottoms during flood events. Innovation is necessitated to handle a series of different hydraulic phenomena. Flux-splitting and data reconstruction techniques are used to achieve stable computation in the complex topography of the valley bottoms. Standard problems of oblique hydraulic jump and dam break flows are used to test the accuracy of the numerical model. The Manning’s roughness coefficient is determined from calibration in another Ghanaian watershed located in the Eastern Region. Using actually observed time series data of rainfall intensity, surface flows during the rainfall events are simulated in the computational domain representing the valley bottoms of the study area. Observed data of water levels in the dams are compared to predictions, and discrepancies between them are examined from the hydrological point of view. In the case of a hypothetical flood event, cascading collapses of the dams and flooding of cultivated fields are reproduced.     

Velocity Distribution and Energy Dissipation along Stepped Chutes Lined with Wedge-Shaped Concrete Blocks

Stepped channels lined with wedge-shaped concrete blocks may constitute a low-cost alternative to provide overtopping protection of embankment dams if the discharge capacity of existing spillways is not adequate or even to be used as the main spillway of newly built embankment dams. This paper addresses the velocity distribution and the energy dissipation, downstream of the inception point, on stepped chutes lined with wedge-shaped concrete blocks. An experimental setup was developed with two flumes designed with a relative scale of 1∶2.5. Air concentration was measured with an optical probe in several cross sections of both flumes. The velocity profiles along chutes lined with wedge-shaped blocks with the upper face sloping downstream were analyzed. The measurements’ accuracy was checked by comparing discharges indicated by a facility flowmeter and obtained by the integration of velocity and air concentration profiles. The effect of the steps-slope in the energy dissipation is studied. Values of the Darcy-Weissbach friction factor are proposed for this type of chute lining, for transition flows, and for skimming flows.     

Upwind Conservative Scheme for the Saint Venant Equations

An upwind conservative scheme with a weighted average water-surface-gradient approach is proposed to compute one-dimensional open channel flows. The numerical scheme is based on the control volume method. The intercell flux is computed by the one-sided upwind method. The water surface gradient is evaluated by the weighted average of both upwind and downwind gradients. The scheme is tested with various examples, including dam-break problems in channels with rectangular and triangular cross-sections, hydraulic jump, partial dam-break problem, overtopping flow, a steady flow over bump with hydraulic jump, and a dam-break flood case in a natural river valley. Comparisons between numerical and exact solutions or experimental data demonstrated that the proposed scheme is capable of accurately reproducing various open channel flows, including subcritical, supercritical, and transcritical flows. The scheme is inherently robust, stable, and monotone. The scheme does not require any special treatment, such as artificial viscosity or front tracking technique, to capture steep gradients or discontinuities in the solution.     

Flood Discharge Prediction using Two-Dimensional Inverse Modeling

A new approach to estimate flood discharges in complex river geometries is presented. Discharges are determined through the combination of nonintrusive measurements of surface velocities and water levels with a Navier–Stokes solver and an inverse optimization algorithm. The numerical model is based on a finite-element solution of the two-dimensional Reynolds-averaged Navier–Stokes equations with a k–ε turbulence model, allowing for computation of the free water surface on adaptive, unstructured grids. The inverse modeling technique uses the Levenberg–Marquardt minimizing algorithm. In order to rule out uncertainties from the numerical model and to strictly quantify the effect of measuring errors, measurements are generated synthetically through forward computations. The methodology is illustrated for the gaging station of the Saltina River at Brig, Switzerland, which involves a complex bed geometry and where laboratory measurements for transcritical flows were available. For perfect measurements the discharge can in principle be estimated to an accuracy of ≈2%, independently of the number of measurements. Measurement errors in the water level have a small influence on the estimated discharge, whereas errors in velocity lead to a major discharge error. This error can be minimized by increasing the number of measurement points and choosing appropriate measurement positions.     

Coupled Creep and Seepage Model for Hybrid Media

The permeability coefficient of a rock mass depends mainly on the aperture of the joint and the porosity of the block, which may alter with time when creep of the rock mass is taken into account. Therefore, a coupled creep and seepage model for hybrid media is proposed in this paper. Large-scale and strongly permeable joints are simulated according to their spatial distributions, while other discontinuities are treated as equivalent continuum. Based on the fundamental mechanism of creep effects on the permeability of the rock mass, together with empirical equations for hydraulic conductivity, coupled creep and seepage equations for filled joints, rough joints, and equivalent continuum are proposed. By application of these equations, governing equations for the coupled creep and seepage model are deduced. A simplified numerical solution is proposed to solve the coupled creep and seepage model. The coupled model is shown to simulate the evolvement of seepage, deformation, and stress field in a gravity dam. By comparing the results derived by coupled and uncoupled models, it is concluded that the coupling between creep and seepage should be taken into account when performing engineering design of large dams.     

Three-Dimensional Numerical Modeling of Initial Mixing of Thermal Discharges at Real-Life Configurations

A three-dimensional Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) model is developed for simulating initial mixing in the near field of thermal discharges at real-life geometrical configurations. The domain decomposition method with multilevel embedded overset grids is employed to handle the complexity of real-life diffusers as well as to efficiently account for the large disparity in length scales arising from the relative size of the ambient river reach and the typical diffuser diameter. An algebraic mixing length model with a Richardson-number correction for buoyancy effects is used for the turbulence closure. The governing equations are solved with a second-order-accurate, finite-volume, artificial compressibility method. The model is validated by applying it to simulate thermally stratified shear flows and negatively buoyant wall jet flows and the computed results are shown to be in good overall agreement with the experimental measurements. To demonstrate the potential of the numerical model as a powerful engineering simulation tool we apply it to simulate turbulent initial mixing of thermal discharges loaded from both single-port and multiport diffusers in a prismatic channel and a natural river. Comparisons of the CFD model results with those obtained by applying two widely used empirical mixing zone models show that the results are very similar in terms of both the rate of dilution and overall shape of the plumes. The CFD model further resolves the complex three-dimensional features of such flows, including the complex interplay of the ambient flow and thermal discharges as well as the interaction between each of discharges loaded from multiple ports, which are obviously not accessible by the simpler empirical models.     

Conservative Scheme for Numerical Modeling of Flow in Natural Geometry

A numerical model is proposed to compute one-dimensional open channel flows in natural streams involving steep, nonrectangular, and nonprismatic channels and including subcritical, supercritical, and transcritical flows. The Saint-Venant equations, written in a conservative form, are solved by employing a predictor-corrector finite volume method. A recently proposed reformulation of the source terms related to the channel topography allows the mass and momentum fluxes to be precisely balanced. Conceptually and algorithmically simple, the present model requires neither the solution of the Riemann problem at each cell interface nor any special additional correction to capture discontinuities in the solution such as artificial viscosity or shock-capturing techniques. The resulting scheme has been extensively tested under steady and unsteady flow conditions by reproducing various open channel geometries, both ideal and real, with nonuniform grids and without any interpolation of topographic survey data. The proposed model provides a versatile, stable, and robust tool for simulating transcritical sections and conserving mass.     

Numerical and Experimental Study on Two-Dimensional Flood Flows with and without Structures

The behavior of two-dimensional (2D) flood flows and the hydrodynamic force acting on structures are investigated numerically and experimentally. Numerical simulations are performed using a model based on the finite-volume method with an unstructured grid system and the flux-difference splitting technique. Experiments on flood propagation in a flood plain, with and without structures were conducted so as to obtain a comprehensive verification of the model. Front positions, depths, and surface velocities of flood flows as well as hydrodynamic forces on structures were observed. Comparisons of numerical results against these experimental data show that the model can predict 2D flood flows and the force on structures with reasonable accuracy.     

3D Numerical Simulation for Water Flows and Sediment Deposition in Dam Areas of the Three Gorges Project

This paper presents a three-dimensional (3D) mathematical model for suspended load transport in turbulent flows. Based on the stochastic theory of turbulent flow proposed by Dou, numerical schemes of Reynolds stresses for anisotropic turbulent flows are obtained. Instead of a logarithmic law, a specific wall function is used to describe the velocity profile close to wall boundaries. The equations for two-dimensional suspended load motion and sorting of bed material have been improved for a 3D case. Numerical results are in good agreement with the measured data of the Gezhouba Project. The present method has been employed to simulate sediment erosion and deposition in the vicinity of the Three Gorges Dam. The size distribution of the deposits and bed material, and flow and sediment concentration at different times and elevations, are predicted. The results agree well with the observations in physical experiments. Thus, a new method is established for 3D simulation of sediment motion in the vicinity of dams.     

Implicit Bidiagonal Scheme for Depth-Averaged Free-Surface Flow Equations

A general fast implicit bidiagonal numerical scheme, based on the MacCormack's predictor-corrector technique requiring the inversion of only block bidiagonal matrices, has been developed and subsequently applied for subcritical and supercritical free-surface flow calculations. The model has been applied to depth-averaged steady flows. There are two main advantages of the proposed method: the technique has fast convergence and utilizes a body fitted nonorthogonal local coordinate system to simulate irregular geometry flows. The model is used to analyze a wide variety of hydraulic engineering problems including flows in a converging-diverging subcritical flume, supercritical expansions at various Froude numbers, and supercritical converging chutes. For each of these test cases, the calculated results are compared with experimental data. The comparisons with measurements as well as with other numerical solutions show that the proposed method is comparatively accurate, fast, and reliable.     

Well-Balanced Scheme between Flux and Source Terms for Computation of Shallow-Water Equations over Irregular Bathymetry

Although many numerical techniques such as approximate Riemann solvers can be used to analyze subcritical and supercritical flows modeled by hyperbolic-type shallow-water equations, there are some difficulties in practical applications due to the numerical unbalance between source and flux terms. In this study, a revised surface gradient method is proposed that balances source and flux terms. The new numerical model employs the MUSCL–Hancock scheme and the HLLC approximate Riemann solver. Several verifications are conducted, including analyses of transcritical steady-state flows, unsteady dam break flows on a wet and dry bed, and flows over an irregular bathymetry. The model consistently returns accurate and reasonable results comparable to those obtained through analytical methods and laboratory experiments. The revised surface gradient method may be a simple but robust numerical scheme appropriate for solving hyperbolic-type shallow-water equations over an irregular bathymetry.     

Performance of Bed-Load Transport Equations Relative to Geomorphic Significance: Predicting Effective Discharge and Its Transport Rate

Previous studies assessing the accuracy of bed-load transport equations have considered equation performance statistically based on paired observations of measured and predicted bed-load transport rates. However, transport measurements were typically taken during low flows, biasing the assessment of equation performance toward low discharges, and because equation performance can vary with discharge, it is unclear whether previous assessments of performance apply to higher, geomorphically significant flows (e.g., the bankfull or effective discharges). Nor is it clear whether these equations can predict the effective discharge, which depends on the accuracy of the bed-load transport equation across a range of flows. Prediction of the effective discharge is particularly important in stream restoration projects, as it is frequently used as an index value for scaling channel dimensions and for designing dynamically stable channels. In this study, we consider the geomorphic performance of five bed-load transport equations at 22 gravel-bed rivers in mountain basins of the western United States. Performance is assessed in terms of the accuracy with which the equations are able to predict the effective discharge and its bed-load transport rate. We find that the median error in predicting effective discharge is near zero for all equations, indicating that effective discharge predictions may not be particularly sensitive to one’s choice of bed-load transport equation. However, the standard deviation of the prediction error differs between equations (ranging from 10% to 60%), as does their ability to predict the transport rate at the effective discharge (median errors of less than 1 to almost 2.5 orders of magnitude). A framework is presented for standardizing the transport equations to explain observed differences in performance and to explore sensitivity of effective discharge predictions.     

Dynamic Model for Subcritical Combining Flows in Channel Junctions

A one-dimensional theoretical model for subcritical flows in combining open channel junctions is developed. Typical examples of these junctions are encountered in urban water treatment plants, irrigation and drainage canals, and natural river systems. The model is based on applying the momentum principle in the streamwise direction to two control volumes in the junction together with overall mass conservation. Given the inflow discharges and the downstream depth, the proposed model solves for each of the upstream depths. The interfacial shear force between the two control volumes, the boundary friction force, and the separation zone shear force downstream of the lateral channel entrance are included. Predictions based on the proposed approach are shown to compare favorably with existing experimental data, previous theories, and conventional junction modeling approaches. The main advantages of the proposed model are that the proposed model does not assume equal upstream depths and that the dynamic treatment of the junction flow is consistent with that of the channel reaches in a network model.     

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).     

Model for Consolidation-Induced Solute Transport with Nonlinear and Nonequilibrium Sorption

A numerical model, called CST2, is presented for coupled large strain consolidation and solute transport in saturated porous media. The consolidation and solute transport algorithms include the capabilities of a previous model, CST1, with the addition of a variable effective diffusion coefficient during consolidation and nonlinear nonequilibrium sorption. The model is based on a dual-Lagrangian framework that tracks separately the motions of fluid and solid phases. Verification checks of CST2 show excellent agreement with analytical and numerical solutions for solute transport in rigid porous media. A parametric study illustrates that, for the test cases considered, variation of effective diffusion coefficient during consolidation has an important effect on solute transport, whereas nonlinearity of the sorption isotherm has a less important effect. Additional simulations show that nonequilibrium sorption can have a strong effect on consolidation-induced solute transport and that this effect becomes more important as the rate of consolidation increases. The simulations also corroborate previous findings that consolidation can have a lasting effect on solute migration because transient advective flows change the distribution of solute mass which then becomes the initial condition for subsequent transport processes.     

Reservoir Routing using Steady and Unsteady Flow through Rockfill Dams

In this paper a two-dimensional (2D) model for flow through rockfill dams is presented and its results have been compared to 1D model. The model is based on the 2D continuity equation. In the model, an exponential relationship between Reynolds number (R) and Darcy-Weisbach coefficient (f) is suggested and combined with the continuity equation. Coefficients of this relationship are estimated by using real data and a nonlinear optimization technique. Introducing inflow hydrograph to the reservoir and rockfill characteristics as input data and utilizing the above model the outflow hydrograph can be determined. The model has been calibrated and verified using real data. The results of the numerical solution have been shown to be more reliable than the 1D model. To demonstrate the model sensitivity to different parameters, a parametric sensitivity analysis has been conducted. Finally, a comparison between the steady- and unsteady-state results is introduced.     

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.     

Finite Volume Model for Two-Dimensional Shallow Water Flows on Unstructured Grids

A numerical model based upon a second-order upwind finite volume method on unstructured triangular grids is developed for solving shallow water equations. The HLL approximate Riemann solver is used for the computation of inviscid flux functions, which makes it possible to handle discontinuous solutions. A multidimensional slope-limiting technique is employed to achieve second-order spatial accuracy and to prevent spurious oscillations. To alleviate the problems associated with numerical instabilities due to small water depths near a wet/dry boundary, the friction source terms are treated in a fully implicit way. A third-order total variation diminishing Runge–Kutta method is used for the time integration of semidiscrete equations. The developed numerical model has been applied to several test cases as well as to real flows. Numerical tests prove the robustness and accuracy of the model.     

Case Study: Efficiency of Slit-Check Dams in the Mountain Region of Versilia Basin

Slit-check dams are widely employed in mountain river control. However an analysis of their performance in the field is still lacking. In the present work a field verification to evaluate the interaction between solid discharge regime and four slit-check dams built in two subcatchments of the Versilia River in Tuscany, Italy is presented. The analysis is based on a relatively detailed field knowledge consisting of hydrological, topographical, and sedimentological data, together with a recent model proposed by Armanini and Larcher. Slit-check dam efficiency is analyzed in terms of deposit formation during major floods and its influence on long-term sediment transport regime. Results suggest that the design efficiency is affected by the high sediment trapping capacity associated with the relatively minor floods. A comparison between the deposit geometry predicted by the theory and the field measurements gathered during a systematic monitoring activity shows good agreement.