Volume of Fluid Model for Turbulence Numerical Simulation of Stepped Spillway Overflow

The stepped spillway has increasingly become an effective energy dissipator. When the hydraulic performance of the overflow is clearly known, the energy dissipation could be increased. However, the study of stepped spillway overflow has been based only on model tests until now. In this paper, the k–? turbulence model is used to simulate the complex turbulence overflow. The unstructured grid is used to fit the irregular boundaries and the volume of fluid method is introduced to solve the complex free-surface problem. The free surface, velocities, and pressures on the stepped spillway are obtained by the turbulence numerical simulation. Furthermore, the simulation results compare well with measured data. The study indicates that the turbulence numerical simulation is an efficient and useful method for the complex stepped spillway overflow.     

Case Study of an S-Shaped Spillway Using Physical and Numerical Models

The spillway studied in this paper was designed as an “S” shape in plan view, characterized in two curved conduits, steep slopes, and small curvature radiuses. An approach of the combination of physical and numerical models was adopted to study the hydraulic characteristics and examine the feasibility of the design. By setting proper sills whose specific layouts were determined by numbers of experiments at the bottom of the curved conduits, the flow pattern was significantly improved. The k–ε turbulence model was used to simulate the three-dimensional turbulent flow. The free water surface was determined by the volume of fluid method, and the governing equations were solved by the finite volume method. Simulated results of the free water surface and the velocity are in good agreement with measured data. It is shown that S shaped spillways are feasible in practical projects. Moreover, numerical simulations are useful for the design and analysis of S shaped spillways.     

Numerical and Experimental Study of Dividing Open-Channel Flows

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

Stepped Spillway with Hydraulic Jumps: Application of a Numerical Model to a Scale Model of a Conceptual Prototype

Hydraulic jumps on the steps of a stepped spillway were investigated analytically, physically, and numerically. Using classic hydraulic formulae, a conceptual prototype was designed. A large scale model was adapted and an experimental study was conducted to examine similarity of hydraulic jumps on each step, minimizing hydraulic jump length and maximizing discharge per unit width. A numerical model based on the 2D Reynolds averaged equations, where the free-surface is represented using a refined volume-of-fluid algorithm, the internal obstacles are described by means of the fractional area-volume obstacle representation method, and the turbulence is represented by a specially developed RNG (Renormalization Group) k-ε closure model was used for evaluating velocities and pressures, and for characterizing hydrodynamic forces on the baffles and sills. Preliminary design criteria are proposed for stepped spillways with hydraulic jump formation of simple shapes and adequate relations of critical depth/step height and the application of computational fluid dynamics to such problems is studied.     

Ice Boom Simulations and Experiments

A three-dimensional discrete element model (DEM) was developed to simulate ice boom operation in a rectangular channel. The model simulates the motion of each individual ice floe, the interaction between adjacent floes, the interaction of the floes with the walls and boom, and the water drag applied to the floes on the underside of the ice accumulation. The DEM simulations were compared with a parallel set of physical model tests using natural ice. The DEM successfully reproduced the observed magnitude and distribution of the forces on the boom and the channel sides as the boom retained a surge of drifting ice. Variations in channel side roughness produced similar changes in the division of forces between the boom and sidewalls in the simulations and model tests. Finally, the load distribution between the boom and the channel sides and the effect of channel side roughness in the context of granular ice-jam theory were analyzed.     

Physical and Numerical Comparison of Flow over Ogee Spillway in the Presence of Tailwater

Data obtained from two physical models were compared to the results obtained from numerical model investigations of two ogee-crested spillways. In 2001, Savage and Johnson investigated ogee-crested spillways without the effect of tailwater; the present study includes the influence of tailwater on the spillway. The comparison showed that numerical modeling can accurately predict the rate of flow over the spillway and the pressure distribution on the spillway. The results of this study provide users of numerical models performance information that can be used to aid them in determining which tool to use to effectively analyze dams and their associated spillways.     

Simulation of a 3D Numerical Viscous Wave Tank

A numerical scheme was developed to solve the unsteady three-dimensional (3D) Navier–Stokes equations and the fully nonlinear free surface boundary conditions for simulating a 3D numerical viscous wave tank. The finite-analytic method was used to discretize the partial differential equations, and the marker-and-cell method was extended to treat the 3D free surfaces. A piston-type wave generator was incorporated in the computational domain to generate the desired incident waves. This wave tank model was applied to simulate the generation and propagation of a solitary wave in the wave tank and the diffraction of periodic waves by a semiinfinite breakwater. The computation was carried out by a PC cluster established by connecting several personal computers. The message passing interface (MPI) parallel language and MPICH software were used to write the computer code for parallel computing. High consistency between the numerical results and the theoretical solutions for the wave and velocity profiles confirms the accuracy of the proposed wave tank model.     

Impact of Converging Chute Walls for Roller Compacted Concrete Stepped Spillways

A study utilizing a three-dimensional, 1:22 scale, physical model was conducted to evaluate the flow characteristics in the spillway with varying training wall convergence angles. The wall height required to contain the flow for conditions tested varied from critical depth at a 15° convergence angle to three times the critical depth at a 52° convergence angle. The results of the study may be used to estimate minimum training wall height for conditions where bulking due to air entrainment may reasonably be neglected.     

Comparison of HYDRUS-2D Simulations of Drip Irrigation with Experimental Observations

Realizing the full potential of drip irrigation technology requires optimizing the operational parameters that are available to irrigators, such as the frequency, rate, and duration of water application and the placement of drip tubing. Numerical simulation is a fast and inexpensive approach to studying optimal management practices. Unfortunately, little work has been done to investigate the accuracy of numerical simulations, leading some to question the usefulness of simulation as a research and design tool. In this study, we compare HYDRUS-2D simulations of drip irrigation with experimental data. A Hanford sandy loam soil was irrigated using thin-walled drip tubing installed at a depth of 6 cm. Three trials (20, 40, and 60 L?m?1 applied water) were carried out. At the end of each irrigation and approximately 24 h later, the water content distribution in the soil was determined by gravimetric sampling. The HYDRUS-2D predictions of the water content distribution are found to be in very good agreement with the data. The results support the use of HYDRUS-2D as a tool for investigating and designing drip irrigation management practices.     

Numerical Efficiency in Monte Carlo Simulations—Case Study of a River Thermodynamic Model

Trade-offs between precision of numerical solutions to deterministic models of the environment, and the number of model realizations achievable within a framework of Monte Carlo simulation, are investigated and discussed. A case study of a model of river thermodynamics is employed. It is shown that the tractability of Monte Carlo simulation relies on adaptation of the numerical solution time-step, giving results with a guaranteed error in the time domain as well as near-optimum speed of calibration under any chosen accuracy criteria. Time-step control is implemented using two adaptive Runge–Kutta methods: a second order scheme with first order error estimator, and an embedded fourth-fifth order scheme. In the case study, where the effects of sparse and imprecise data dominate the overall modeling error, both the schemes appear adequate. However, the higher order scheme is concluded to be generally more reliable and efficient, and has wide potential to improve the value of applying the Monte Carlo method to environmental simulation. The problem of reconciling spatial error with the specified temporal error is discussed.     

3D Simulation of Combining Flows in 90° Rectangular Closed Conduits

Combining flows are encountered often in environmental engineering and hydraulic engineering. Experimental data are available to assist the engineers who need the various loss coefficients associated with combining flows in closed conduits. For the combining flows in 90° rectangular conduit junctions, the Reynolds averaged Navier–Stokes equations are applied, while using the three-dimensional k-ω model. The energy loss coefficients and the mean flow pattern are obtained and validated by experimental data. The numerical modeling is less time-consuming and less expensive to obtain the various flow parameters needed for engineering design.     

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.     

Stop Logs for Emergency Spillway Gate Dewatering

Emergencies resulting in uncontrolled flow through spillway gates often lead to millions of dollars lost to repairs, lack of dam productivity, property damages, and risks to public health and safety. A considerable need exists for reliable emergency dewatering systems to prevent these consequences. Stop logs are the most commonly used dewatering system for spillway gates but are typically designed for maintenance purposes only. They have been found in most cases to be unreliable for emergency closure under flowing conditions. Considering the economic advantages a dewatering system would provide were it functional for the dual purposes of maintenance as well as emergency closure, a new stop log design was developed. This study assesses the design that enables deployment under no-flow conditions as well as flowing, or emergency conditions. The information found in this study provides dam owners, operators, and engineers with options to reduce damages resulting from uncontrolled releases owing to partial or complete failure of spillway gates, including the failure of gates to close after having been raised.     

2D and 3D Numerical Modeling of Combined Surcharge and Vacuum Preloading with Vertical Drains

This paper presents a three-dimensional (3D) and two-dimensional (2D) numerical analysis of a case study of a combined vacuum and surcharge preloading project for a storage yard at Tianjin Port, China. At this site, a vacuum pressure of 80?kPa and a fill surcharge of 50?kPa were applied on top of the 20-m-thick soft soil layer through prefabricated vertical drains (PVD) to achieve the desired settlements and to avoid embankment instability. In 3D analysis, the actual shape of PVDs and their installation pattern with the in situ soil parameters were simulated. In contrast, the validity of 2D plane strain analysis using equivalent permeability and transformed unit cell geometry was examined. In both cases, the vacuum pressure along the drain length was assumed to be constant as substantiated by the field observations. The finite-element code, ABAQUS, using the modified Cam-clay model was used in the numerical analysis. The predictions of settlement, pore-water pressure, and lateral displacement were compared with the available field data, and an acceptable agreement was achieved for both 2D and 3D numerical analyses. It is found that both 3D and equivalent 2D analyses give similar consolidation responses at the vertical cross section where the lateral strain along the longitudinal axis is zero. The influence of vacuum may extend more than 10?m from the embankment toe, where the lateral movement should be monitored carefully during the consolidation period to avoid any damage to adjacent structures.     

Techniques for Numerical Simulations of Concrete Slabs for Demolishing by Blasting

The subject of this article is the numerical simulation of concrete under explosive loading using a meshbased and a meshfree discretization technique. The presented techniques are verified by experimental data. Experimental evidence suggests that the complete stress–strain history relation must be considered as a basis for constitutive modeling if concrete is subjected to high loading rates. These dynamic phenomena cause a retardation of damage activation which must be taken into account when constitutive modeling is pursued on mesolevel instead of microlevel. By including a dynamic relaxation formulation within the framework of a general three-dimensional coupled continuum damage-plasticity law, it is shown that the solution of the wave propagation problem in materials with strain-softening becomes independent of mesh size. As the simulation of concrete under contact detonation causes severe numerical problems because of the large deformations, special numerical spatial discretization techniques have to be used. In this article we compare the results of a concrete slab under contact detonation using the finite element method code LS-DYNA with an arbitrary Lagrangian Eulerian coupling and the results obtained by a MLSPH code developed at our institute with experimental data. The same constitutive model for concrete and the same equation of state for the explosive is implemented in the two codes. The results of the different numerical simulations and the experimental data agree with each other well.     

3D Surface Modeling and Measuring System for Pneumatic Caisson

In order to build a 3D model environment of a pneumatic caisson for excavator operators and managers, a modeling and measuring 3D surface system of unmanned pneumatic caisson was presented in this paper. The whole system is based on two 3D laser scanners for the pneumatic caisson by acquiring the surface data of pneumatic caisson and successive data processing for surface reconstruction and measurement. Registration and reconstruction are also discussed in this paper. In order to convert two point sets into one common coordinate, Hough transforms were used to extract planes and then by using their parameters to register the two point sets. As for surface reconstruction using triangular meshing, a new method based on curves was presented. When combined with the real-time pose and location of the excavators, the 3D environment can be used as a “virtual reality” operating environment for excavation operators. The whole system has been applied in a pneumatic caisson of an underground project in a Shanghai subway, which proved to be working well, with less than 16-s work cycle (period of a single 180° 3D laser scan), at an estimated resolution of less than 20 mm.     

Case Study: Numerical Simulations of Debris Flow below Sto?e, Slovenia

In November 2000 a landslide–debris flow with a volume of 1.2×106?m3 slid down from Sto?e Mountain in NW Slovenia. It partly or totally destroyed 23 buildings in the village of Log pod Mangartom and killed 7 people. As landslides of the same or even greater initial mass could endanger the village in the future, numerical simulations of these possible events were carried out. A hazard map of the area, and the most effective protection measures were determined in detail. A one-dimensional model DEBRIF1D, developed from a dam-break flow model, was used for simulations along the canyon in the upper part of the reach. Downstream, in the region of the village, two two-dimensional models were used: a newly developed PCFLOW2D, and a commercial model FLO-2D. The three models were calibrated by field measurements. A special feature of the DEBRIF1D model enables direct computation of the initial hydrograph. Validity of the quadratic equation expressing the resistance was roughly confirmed by field measurements, and a comparison of the accuracy and applicability of the three models is given.     

Purging of a Neutrally Buoyant or a Dense Miscible Contaminant from a Rectangular Cavity. II: Case of an Incoming Fully Turbulent Overflow

Fully three-dimensional (3D) large-eddy simulation calculations of the flow past two-dimensional cavities for the case in which the incoming flow is fully turbulent are conducted to study the purging of neutrally buoyant or dense miscible contaminants introduced instantaneously inside the cavity. 3D simulations are needed because in the turbulent case (TC), as opposed to the laminar inflow case (LC) considered in the companion paper, the interactions between the coherent structures advected from the incoming channel and the eddies inside the cavity are highly 3D and have a nonnegligible effect on the mass exchange processes between the cavity and channel. Similar to the LC, it is found that the mechanism of removal of the contaminant is very different between the neutrally buoyant and buoyant cases. In the neutrally buoyant TC simulation the contaminant is ejected from the cavity due to the interactions among the large scale eddies in the separated shear layer, the coherent structures convected from the upstream channel over the cavity, and the main recirculation eddies inside the cavity. In the TC simulation with a negatively buoyant contaminant, internal wave breaking is observed to occur over the initial phases of the mixing which, along with other turbulent mixing phenomena, reduces the mean density gradient across the density interface. In the later stages, the contaminant removal and mixing processes are controlled by the interactions of the trailing edge vortex with the bottom layer containing denser contaminant beneath it and upstream of it (for the final stages when the vortex touches the cavity bottom). The oscillations in the size, position, and intensity of the trailing edge vortex are larger than the ones observed in the LC. As expected, turbulent mixing accelerates the purging process in the TC simulations.     

3D Modeling of Ripping Process

Due to environmental constraints and limitations on blasting, ripping as a ground loosening and breaking method has become more popular than drilling and blasting method in both mining and civil engineering applications. The best way of estimating the rippability of rocks is to conduct direct ripping runs in the field. However, it is not possible to conduct direct ripping runs in all sites using different dozer types. Therefore, the utilization of numerical modeling of ripping systems becomes unavoidable. A complex ripping system can better be understood with three-dimensional (3D) models rather than two-dimensional models. In this study, 3D distinct element program called 3DEC was used to investigate the ripping process. First, the ripping mechanisms were investigated and then the individual factors that affect the rippability performance of dozers were reviewed. The rippabilities of rocks depend not only on the rock properties, but also machine or dozer properties. Thus, ripper production and rock rippability with D8 type of dozers were also determined by direct ripping runs on different open pit lignite mines within the scope of this research. Production values obtained from numerical modeling were compared with field production values obtained from the case studies. This comparison shows that the model gives consistent and adequate results. Hence, a link has been established between the field results and the 3D models.     

Case Study on Hydraulic Performance of Brent Reservoir Siphon Spillway

The Brent Reservoir was constructed in the mid-1830s and its siphon spillways were completed in 1936 to protect the dam from overtopping in the event of an extreme flood. Since completion, there have been problems with the hydraulic performance of the siphons, some of which primed simultaneously, causing flooding downstream. A physical hydraulic model study has been conducted to investigate the hydraulic performance of the siphons in order to establish reliable stage discharge relationships. The existing bellmouth siphon system was found to be unsuitable, causing the siphons to prime suddenly at discharges of around 3 m3/s. This was due to the sudden removal of an air pocket from the siphon’s crown. The model tests were carried out in two stages. In the first stage, the existing geometry was examined. Based on the results from stage 1 of the experiments, it was concluded that the air inlet requires redesign and various options to improve the air regulation should be considered. In the second stage, various options to regulate the inlet of air and establish stable siphon performance over the entire range of discharges were considered. It was found that the most stable conditions are provided by an air slot being cut into the spillway hood at an appropriate level. This geometry provides excellent air-regulated stability, unimpaired spillway capacity, and is insensitive to tail water level and wave conditions in the reservoir.