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.     

Block Ramp Design for Efficient Energy Dissipation

Block ramp structure can be a part of a layout of microhydel scheme, depending upon the conditions of topography and geology at the site. Block ramps transmit the flow of stream to a lower level inducing kinetic energy dissipation. Block ramps consists of base material in the form of stones inducing roughness whereas stepped chutes are overflowing structures which consists of step configuration at the bottom of the flowing stream. As there is a common objective of energy dissipation of flow, the geometrical elements of block ramps and stepped chutes are considered to be comparable under similar hydraulic conditions of skimming flow. This paper analyzes the experimental results on both these structures. A mathematical model in dimensionless form is proposed herein, which correlates the representative bed material size of block ramp with the step height of stepped chute. This correlation is expected to facilitate the design of block ramps using the literature available on stepped chutes.     

Turbulence Dissipation in Stirred Jars

A two-compartment analytical model was developed to estimate the turbulent dissipation rates in a standard jar stirred by a radial impeller. A simple numerical simulation was also performed to support the analytical arguments. Results of the numerical model showed that away from the impeller, the turbulent dissipation rate rapidly decays proportionally with z?2, where z is the axial distance. The turbulent velocity away from the impeller region showed a decay proportional to z?0.5. Although the dissipation rates at the wall boundary layer were higher compared to those in the tank interior, the total energy dissipated in the boundary layer is smaller compared to that expended in the impeller zone.     

Hydraulic Design of Stepped Spillways

An experimental study on a large model flume using fiber-optical instrumentation indicated that the onset of skimming flow is a function of critical depth, chute angle, and step height. Uniform mixture depths that determine the height of chute sidewalls and uniform equivalent clear water depths are described in terms of a roughness Froude number containing unit discharge, chute angle and step height. The spillway length needed to attain uniform flow is expressed as a function of critical depth and chute angle. The flow resistance of stepped spillways is significantly larger than for smooth chutes due to the macro roughness of the steps. The friction factor for uniform aerated flow is of the order of 0.1 for typical gravity dam and embankment dam slopes, whereas the effect of relative roughness is rather small. The energy dissipation characteristics of stepped spillways and the design of training walls are also discussed. The paper aims to focus on significant findings of a research program and develops design guidance to lessen the need for individual physical model studies. A design example is further presented.     

Energy Dissipation and Air Entrainment in Stepped Storm Waterway: Experimental Study

For the last three decades, research focused on steep stepped chutes. Few studies considered flat-slope stepped geometries such as stepped storm waterways or culverts. In this study, experiments were conducted in a large, flat stepped chute (θ=3.4°) based upon a Froude similitude. Three basic flow regimes were observed: nappe flow without hydraulic jump, transition flow, and skimming flow. Detailed air–water flow measurements were conducted. The results allow a complete characterization of the air concentration and bubble count rate distributions, as well as an accurate estimate of the rate of energy dissipation. The flow resistance, expressed in terms of a modified friction slope, was found to be about 2.5 times greater than in smooth-chute flow. A comparison between smooth- and stepped-invert flows shows that greater aeration and larger residence times take place in the latter geometry. The result confirms the air–water mass transfer potential of stepped cascades, even for flat slopes (θ<5°).     

CFRP-Based Strengthening Technique to Increase the Flexural and Energy Dissipation Capacities of RC Columns

A strengthening technique, combining carbon fiber-reinforced polymer (CFRP) laminates and strips of wet layup CFRP sheet, is used to increase both the flexural and the energy dissipation capacities of reinforced concrete (RC) columns of square cross section of low to moderate concrete strength class, subjected to constant axial compressive load and increasing lateral cyclic loading. The laminates were applied according to the near surface mounted technique to increase the flexural resistance of the columns, while the strips of CFRP sheet were installed according to the externally bonded reinforcement technique to enhance the concrete confinement, particularly in the plastic hinge zone where they also offer resistance to the buckling and debonding of the laminates and longitudinal steel bars. The performance of this strengthening technique is assessed in undamaged RC columns and in columns that were subjected to intense damage. The influence of the concrete strength and percentage of longitudinal steel bars on the strengthening effectiveness is assessed. In the groups of RC columns of 8 MPa concrete compressive strength, this technique provided an increase of about 67% and 46% in terms of column’s load carrying capacity, when applied to undamaged and damaged columns, respectively. In terms of energy dissipation capacity, the increase ranged from 40%–87% in the undamaged columns, while a significant increase of about 39% was only observed in one of the damaged columns. In the column of moderate concrete compressive strength (29 MPa), the technique was even much more effective, since, when compared to the maximum load and energy dissipation capacity of the corresponding strengthened column of 8 MPa of average compressive strength, it provided an increase of 39% and 109%, respectively, showing its appropriateness for RC columns of buildings requiring upgrading against seismic events.     

Godunov-Type Solutions for Transient Flows in Sewers

This work is part of a long term project which aims at developing a hydraulic model for real-time simulation of unsteady flows in sewers ranging from gravity flows, to partly gravity–partly surcharged flows to fully surcharged flows. The success of this project hinges on the ability of the hydraulic model to handle a wide range of complex boundaries and to provide accurate solutions with the least central processing unit time. This first paper focuses on the development and assessment of two second-order explicit finite-volume Godunov-type schemes (GTS) for unsteady gravity flows in sewers, but with no surcharging. Traditionally, hydraulic transients have been modeled using the method of characteristics (MOC), which is noted for its ability to handle complex boundary conditions (BCs). The two GTS described herein incorporate BCs in a similar manner to the MOC. The accuracy and efficiency of these GTS schemes are investigated using problems whose solution contains features that are relevant to transient flows in sewers such as shock, expansion, and roll waves. The results show that these GTS schemes are significantly faster to execute than the fixed-grid MOC scheme with space-line interpolation, and in some cases, the accuracy produced by the two GTS schemes cannot be matched by the accuracy of the MOC scheme, even when a Courant number close to one and a large number of grids is used. Furthermore, unlike the MOC solutions, which exhibit increasing numerical dissipation with decreasing Courant numbers, the resolution of the shock fronts was maintained by the GTS schemes even for very low Courant numbers (0.001).     

Energy Dissipation in Surface Layer due to Vertically Propagating SH Wave

Vertical array data recorded during the 1995 Kobe earthquake are used to calculate the upward and downward energy flow based on one-dimensional SH-wave multireflection theory, from which the energy dissipation in a surface layer is evaluated as their residual. The dissipated energy thus evaluated in a liquefied site is found to reach about 70% of the upward input energy, which indicates that soil nonlinearity and liquefaction serve as effective energy absorbers. In contrast, more energy returns to deeper ground in sites without strong nonlinear behavior. Furthermore, the dissipated energy in the surface layer tends to increase nonlinearly in a convex shape with increasing equivalent damping ratio of the soil there. A simplified two-layer system indicates that the energy dissipation is influenced not only by the soil damping in the surface layer but also by the impedance ratio between the base and surface layers and the input frequency. The same convex relationship is also obtained in the two-layer system, indicating that the simplified system may reflect some important aspects of the energy dissipation mechanisms in the ground.     

Computer and Experimental Models of Transient Flow in a Pipe Involving Backflow Preventers

Transient flow in a pipe was studied using both experimental and computer models. In the present study, three different numerical models: The method of characteristics model, the axisymmetrical model, and the implicit scheme model are utilized and compared. Experiments for transient flow in a simple pipeline have been conducted to verify the results from the computer models. It was found that head loss coefficient for the 1D models, such as the method of characteristics model and the implicit scheme model, should be much bigger than the Darcy-Weisbach frictional coefficient. Experiments for transient flow with the backflow preventer in a pipe were conducted. Results show that backflow preventer serves as a strong damper to the water hammer generated by the hydraulic transients. Numerical investigation simulating a backflow preventer in transient flow has been performed in this study. It was found that different values of head loss coefficient should be applied for the upstream and downstream of backflow preventer. All of the numerical models were compared with the experiments. The results of different computer models developed in the present study agree well with the experimental data.     

Transient Friction in Pressurized Pipes. III: Investigation of the EIT Model Based on Position-Dependent Coefficient Approach in MIAB Model

Recently, the modified instantaneous acceleration-based (MIAB) model has been improved by the authors by using position-dependent coefficients found from investigation of the convolution-based (CB) model. Although this improvement is not proven general by any means, the fit with experimental results is very good. The three existing classes of one-dimensional models for the water-hammer transient that are applicable from an engineering point of view are the two models mentioned previously and the extended irreversible thermodynamics (EIT) model, which uses a coefficient found from thermodynamical considerations. This paper seeks the equivalent coefficients for the EIT model corresponding to the position-dependent coefficient the MIAB model to investigate the implications to the EIT model by using these coefficients. This is interesting because the EIT model is based on physical considerations using irreversible thermodynamics, and conclusions can possibly be drawn from this approach. The EIT coefficients found based on the position-dependent coefficients are used in simulations, and the results show an improvement compared to classical constant-coefficient EIT simulations. Based on this and discussion of water-hammer transient phenomena, it is suggested that limitations in the original EIT model regarding the coefficients might not be just and may be a possible limitation to the EIT model’s performance.     

Stochastic Model for Landfill Gas Transport and Energy Recovery

Predicting the amount of landfill gas (LFG) that will be recovered at a sanitary landfill is generally associated with a high level of uncertainty, which is primarily due to the uncertainty in the definition of the parameters that control the LFG generation rate and LFG transport. To quantify these uncertainties, a three-dimensional stochastic model for the generation and transport of LFG is proposed. Using Monte Carlo simulations, multiple realizations of key input parameters are generated. For each realization, LFG transport is simulated and then used to evaluate probabilistically the rates and efficiency of energy recovery. For demonstration, the stochastic model is applied to the Kemerburgaz landfill in Istanbul, Turkey. Uncertainty in the definition of three key parameters, namely: the LFG production rate, the waste gas permeability and the soil cover gas permeability were accounted for. Modeling results suggest that the collection system is sufficient to capture most of the generated gas, but that uncertainty in the factors controlling LFG production is the main source of uncertainty in the amount of energy that will be recovered.     

Performance Test of Energy Dissipation Bearing and Its Application in Seismic Control of a Long-Span Bridge

Energy dissipation bearing (EDB) is a conventional steel bridge bearing in connection with well designed mild steel dampers. Seismic performance test was undertaken for both damper units and a prototype bearing, and the results show very stable and high dissipation characteristics. In describing the hysteretic behavior of EDBs, the Wen model is proved to be more reasonable, and the corresponding model parameters are also proposed according to the test results. EDBs have been applied in the seismic control of a long span bridge, the Nanjing Jia River Bridge, for the first time, in both the longitudinal and transverse directions. Sensitivity studies were conducted to investigate the effectiveness and to determine the optimum parameters and distribution of the EDBs through nonlinear time-history analysis. The results show that EDBs achieve a very high effectiveness in seismic control, in both the longitudinal and transverse directions. Compared with other damping devices, they can provide a simple but valid seismic control solution, with low maintenance requirements, especially in the transverse direction.     

Efficient Treatment of the Vardy–Brown Unsteady Shear in Pipe Transients

An accurate, simple, and efficient approximation to the Vardy–Brown unsteady friction equation is derived and shown to be easily implemented within a one-dimensional characteristics solution for unsteady pipe flow. For comparison, the exact Vardy–Brown unsteady friction equation is used to model shear stresses in transient turbulent pipe flows and the resulting waterhammer equations are solved by the method of characteristics. The approximate Vardy–Brown model is more computationally efficient (i.e., requires one-sixth the execution time and much less memory storage) than the exact Vardy–Brown model. Both models are compared with measured data from different research groups and with numerical data produced by a two-dimensional turbulence waterhammer model. The results show that the exact Vardy–Brown model and the approximate Vardy–Brown model are in good agreement with both laboratory and numerical experiments over a wide range of Reynolds number and wave frequencies. The proposed approximate model only requires the storage of flow variables from a single time step while the exact Vardy–Brown model requires the storage of flow variables at all previous time steps and the two-dimensional model requires the storage of flow variables at all radial nodes.     

Self-Aeration and Friction over Rock Chutes in Uniform Flow Conditions

Interaction between the free surface and the bed material in flow over rock chutes under macroroughness conditions leads to a high air entrainment into the flow. The note reports on an experimental study about air diffusion features in the flow over a long rock chute. Air concentration profiles and water depths over a uniform bed material were measured. An empirical equation for the average air concentration in macroroughness condition for steep slopes is proposed. A new Darcy-Weisbach equivalent friction factor for long chutes as a function of the slope and the relative equivalent depth has also been found.     

Simulation of Upward Seepage Flow in a Single Column of Spheres Using Discrete-Element Method with Fluid-Particle Interaction

The interaction between soil particles and pore water makes the behavior of saturated and unsaturated soil complex. In this note, upward seepage flow through a granular material was idealized using a one-column particle model. The motion of the individual particles was numerically simulated using the discrete-element method taking the interaction with the fluid into account. The fluid behavior was simulated by the Navier-Stokes equation using the semi-implicit method for pressure-linked equation. This approach has already been applied in powder engineering applications. However, there are very few studies that have used this approach in geotechnical engineering. This note first describes the qualitative and quantitative validation of this method for hydraulic gradients below the critical one by comparing the results with an analytical solution. Then, the ability of the method to simulate the macroscale behavior due to the interaction between particles and pore water at hydraulic gradients exceeding the critical hydraulic gradient is discussed.     

Analysis of the Friction Term in the One-Dimensional Shallow-Water Model

The numerical simulation of unsteady open channel flows is very commonly performed using the one-dimensional shallow-water model. Friction is one of the relevant forces included in the momentum equation. In this work, a generalization of the Gauckler-Manning friction model is proposed to improve the modeling approach in cases of dominant roughness, unsteady flow, and distorted cross-sectional shapes. The numerical stability conditions are revisited in cases of dominant friction terms and a new condition, complementary to the basic Courant-Friedrichs-Lewy condition, is proposed. Some test cases with measured data are used to validate the quality of the approaches.     

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.     

Bubbly Two-Phase Flow in Hydraulic Jumps at Large Froude Numbers

A hydraulic jump is a sudden, rapid transition from a supercritical flow to a subcritical flow. At large inflow Froude numbers, the jump is characterized by a significant amount of entrained air. For this paper, the bubbly two-phase flow properties of steady and strong hydraulic jumps were investigated experimentally. The results demonstrate that the strong air entrainment rate and the depth-averaged void-fraction data highlight a rapid deaeration of the jump roller. The results suggest that the hydraulic jumps are effective aerators and that the rate of detrainment is comparatively smaller at the largest Froude numbers.     

Fluid–Solid Interaction in Particle-Laden Flows

Using a laser-Doppler split-phase measuring technique, the rates of fluctuation in horizontal and vertical directions of pipe flow containing solid particles were observed. Employing these observations the effect of particles on flow turbulence was analyzed and a formula for determining the initial condition of particles restraining the flow turbulence in the mainstream region was developed. The mechanisms affecting the energy loss of flow were then analyzed.     

Operation and Performance of Horizontal Wells for Leachate Control in a Waste Landfill

This paper presents data on gas and leachate flow rates and leachate levels obtained during a 600?day pumping trial on three retrofitted horizontal wells in a domestic waste landfill at Rainham, United Kingdom. The changes in gas and leachate flow rate with time and atmospheric pressure, and the interaction between the two flows, are discussed. The spatial variability of the response of the leachate levels within the landfill is explored with reference to the anisotropy and heterogeneity of the permeability of the waste. It is shown that horizontal wells can be an effective means of controlling leachate heads near the base of a landfill, and that leachate levels must be measured using piezometers with a discrete response zone rather than fully screened observation wells if meaningful results are to be obtained. It is argued that the large amounts of gas pumped from the nominally saturated zone of the landfill must have come from the ongoing degradation of the waste within the zone of influence of the well.