Investigation of Consolidation-Induced Solute Transport. II: Experimental and Numerical Results

This paper presents an experimental and numerical investigation of consolidation-induced solute transport. Diffusion and large strain consolidation tests were performed on composite specimens of kaolinite clay consisting of an upper uncontaminated layer and a lower layer contaminated with potassium bromide. Experimental measurements of effluent concentration, solute mass outflow, and final concentration profiles were obtained for a variety of initial, boundary, and loading conditions, including unload/reload. Numerical simulations were conducted using a computational model in which solute transport occurs by advection, dispersion, and sorption and is consistent with temporal and spatial variations of porosity and seepage velocity in the consolidating layer. Large strains were taken into account as well as variation of effective diffusion coefficient with porosity and nonlinear nonequilibrium sorption effects. The numerical simulations are in good to excellent agreement with the experimental measurements. Results indicate that, depending on conditions, diffusion and consolidation-induced advection can make important contributions to solute transport and mass outflow. Thus, both mechanisms should be considered for transport analyses involving soft contaminated clays undergoing large volume change. Results also indicate that nonequilibrium sorption effects were not significant for the materials and test conditions used in this study.     

Eutrophication Model for a Coastal Bay in Hong Kong

Flow and transport in a natural water body commonly interact with density stratification and in some cases the stratification may be characterized as a two-layered system. A rigorous, two-layered, two-dimensional (2D) finite difference numerical model for eutrophication dynamics in coastal waters, based on the numerically generated, boundary-fitted, orthogonal curvilinear grid system as well as a grid “block” technique, is proposed here. The model simulates the transport and transformation of up to nine water quality constituents associated with eutrophication. The structure of the model is based on a generally accepted framework with the exception of the interaction between the two layers via vertical advection and turbulent diffusion. Some kinetic coefficients are calibrated with field data specifically for the scenario in Tolo Harbour, Hong Kong. The pollution sources are unsteady and hourly solar radiation is imposed. Sediment oxygen demand (SOD) and nutrient releases from sediment are incorporated in the model based on the relevant in-situ sampling analysis. The hydrodynamic variables are predicted simultaneously with a hydrodynamic model previously developed. The computed results show that the present model successfully reproduces the stratification tendency in all the water quality constituents, showing an obvious bottom water anoxic condition during the summer, which is consistent with the density stratification and the unsteady layer-averaged 2D eutrophication processes in Tolo Harbour.     

BIEM Modeling of 3D Circulation and Transport in Stratified Estuaries

Here the boundary integral equation method (BIEM) is used for 3D modeling of hydrodynamics and pollutant transport in stratified estuaries. The flow computations are made using a newly developed BIEM solution. The transport modeling has been done using an Eulerian-Lagrangian BIEM (ELBIEM) model. In ELBIEM, the advection part in the transport equation is treated by the concept of the Eulerian-Lagrangian scheme, which overcomes the limitation of traditional BIEM to deal with an arbitrary velocity field. The coupling of the 3D shallow water BIEM model and advection-diffusion ELBIEM model enables one to effectively deal with fluctuation of free surface and density stratification in an estuary. The main advantages of the BIEM model include reduction in computational dimensions, ease in discretization and data preparation, accurate free surface simulation, less numerical diffusion and dispersion problems, and direct flux solution at boundaries. The numerical simulation results are compared with other model results and found to be satisfactory. The illustrated case study shows the effectiveness of the model in the simulation of mass, momentum, and heat transfer due to air-water interaction in stratified estuary problems.     

Simulation of Flow and Mass Dispersion in Meandering Channels

This paper reports the development of an enhanced two-dimensional (2D) numerical model for the simulation of flow hydrodynamics and mass transport in meandering channels. The hydrodynamic model is based on the solution of the depth-averaged flow continuity and momentum equations where the density of flow varies with the concentration of transported mass. The governing equation for mass transport model is the depth-averaged convection and diffusion equation. The dispersion terms arisen from the integration of the product of the discrepancy between the mean and the actual vertical velocity distribution were included in the momentum equations to take into account the effect of secondary current. Two laboratory experimental cases, flow in mildly and sharply curved channels, were selected to test the hydrodynamic model. The comparison of the simulated velocity and water surface elevation with the measurements indicated that the inclusion of the dispersion terms has improved the simulation results. A laboratory experiment study of dye spreading in a sine-generated channel, in which dye was released at the inner bank, centerline, and outer bank, respectively, was chosen to verify the mass transport model. The simulated concentration field indicated that the Schmidt number can be used as a calibration parameter when dispersion is computed using a 2D approach with a simplified turbulence model.     

Novel Approach to Integration of Numerical Modeling and Field Observations for Deep Excavations

Precedent and observation of performance are an essential part of the design and construction process in geotechnical engineering. For deep urban excavations designers rely on empirical data to estimate potential deformations and impact on surrounding structures. Numerical simulations are also employed to estimate induced ground deformations. Significant resources are dedicated to monitor construction activities and control induced ground deformations. While engineers are able to learn from observations, numerical simulations have been unable to fully benefit from information gained at a given site or prior excavation case histories in the same area. A novel analysis method, self-learning in engineering simulations (SelfSim), is introduced to integrate precedent into numerical simulations. SelfSim is an inverse analysis technique that combines finite element method, biologically inspired material models, and field measurements. SelfSim extracts relevant constitutive soil information from field measurements of excavation response such as lateral wall deformations and surface settlement. The resulting soil model, used in a numerical analysis, provides correct ground deformations and can be used in estimating deformations of similar excavations. The soil model can continuously evolve using additional field information. SelfSim is demonstrated using two excavation case histories in Boston and Chicago.     

Numerical Study of Flow Affected by Bendway Weirs in Victoria Bendway, the Mississippi River

It has been observed that submerged weirs in bendways realign the flow and in general improve navigation conditions. This qualitative observation has been the basis for field design. This paper presents a study of hydrodynamics in the Victoria Bendway in the Mississippi River using three-dimensional numerical simulations. A numerical model, CCHE3D, was applied and computational results were compared to three-dimensional velocity data provided by the U.S. Army Corps of Engineers with reasonable agreement. The numerical simulation results were then used to analyze helical currents due to the channel curvature and the presence of submerged weirs. The simulated flow realignment near the free surface indicates that the flow conditions in the bendway were improved by the submerged weirs, however, the effectiveness of each weir depends on its alignment, local channel morphology, and flow conditions.     

The place of life in our theories

The paper deals with the iterative three-dimensional (3D) smoothing of tomograms acquired by fast Magnetic Resonance (MR) imaging methods. The smoothing method explored, which is aimed basically at the improvement of 3D visualization quality, uses the physical concept of geometry-driven diffusion with a variable conductance function, based on a specific measure of the 3D neighborhood homogeneity. A novel stopping criterion is proposed for iterative 3D diffusion processing. A study of the transition from 2D to 3D algorithms is carried out. The main structure of the program implementation of the smoothing algorithms developed is described. Three smoothing/filtering methods, aimed at the improvement of 3D visualization of MR tomograms of the brain, are quantitatively and visually compared using real 3D MR images. The results of computer simulations with 3D smoothing, segmentation and visualization are presented and discussed.     

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.     

Investigations on Flow Pattern and Pressure inside SEN below Stopper Rod

In continuous casting of steel, the casting rate is often controlled by a stopper rod placed in the tundish outlet where the submerged entry nozzle (SEN) tube begins. The flow pattern inside the SEN plays an important role for the bubble formation at the argon injection nozzle at the stopper rod tip. High flow velocities are reached in the small gap between stopper rod and the surrounding SEN walls, and a flow separation has to be expected after the gap due to the fast expansion of the cross section. According to theoretical considerations and to the simulations, the absolute pressure in the gap becomes very low for liquid steel, which can cause cavitation‐like effects. PIV‐flow measurements in a 1:1 scaled water model of the caster show a highly oscillating and asymmetric flow pattern with rapidly changing separation regions. The low pressure effects expected in liquid steel cannot be investigated on the water‐model due to the lower density of water. In numerical simulations of the water‐model, the choice of the turbulence model and the usage or the non‐usage of geometrical symmetries for the bound of the computational domain have a great impact on the resulting flow pattern and the accuracy of the predicted pressure drop. The results of various turbulence models are compared with results from measurements on a water‐model. It turns out that only a 3D model using advanced turbulence models (SST k‐ω or Large Eddy) produce acceptable results, while 2D simulations completely fail and the standard turbulence models (e.g. k‐ε) significantly underestimate the pressure drop even in a 3D simulation.     

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.     

Field Experiment Study of Transient Stratified Flow in an Estuary

An experimental study of stratified flow was conducted in this study. An electromagnetic measurement instrument, the S4 current meter, was used in field data collections of salinity and currents in the lower Apalachicola River estuary, Florida. The S4 current meter has an advantage in field deployments for long periods of time due to its preprogrammable capability for automatic data sampling and recording of fluid flow. Time series of surface and bottom salinity and currents obtained from field experiments were used to characterize the stratified flow at the measurement location in the Apalachicola River. Analysis of field data indicated that the river was strongly stratified. The stratification was affected by the upstream river flow and the downstream tidal variations. Stratification was stronger at high tide than at low tide. By removing the tidal signal using low-passing filtering, subtidal salinity, and currents were obtained to investigate the salinity stratification and currents responses to the changes of fresh water input. Subtidal vertical salinity and velocity profiles were presented at different flow conditions. At high flow conditions, both surface and bottom subtidal currents were in the seaward direction. At low flow conditions, the bottom subtidal currents were in the upstream direction due to the strong effects of density gradients. Empirical regression equations were obtained to quantify the effects of river flow on the subtidal salinity and the bottom currents. Regression analysis indicated good linear relationship between subtidal salinity stratification and the bottom currents.     

Numerical Oscillations in Pipe-Filling Bore Predictions by Shock-Capturing Models

The introduction of nonlinear, shock-capturing schemes has improved numerical predictions of hydraulic bores, but significant numerical oscillations have been reported in the predictions of pipe-filling bore fronts associated with the transition between open-channel and pressurized flow regimes. These oscillations can compromise the stability of numerical models. A study of these oscillations indicates that the strength of the numerical oscillations is associated with the sharp discontinuities in the flow parameters across the jump, particularly the wave celerity. Approaches to attenuate oscillations by artificially reducing acoustic wave speeds may result in the loss of simulation accuracy. Two new techniques to attenuate the oscillation amplitudes are presented, the first based on numerical filtering of the oscillations and the second based on a new flux function that judiciously introduces numerical diffusion only in the vicinity of the bore front. Both approaches are effective in decreasing the strength of the numerical oscillations.     

Dynamic Mathematical Modeling of an Isothermal Three-Phase Reactor: Model Development and Validation

A catalytic reactor model (CatReac) that describes the transport and series reactions of compounds in a three-phase fixed-bed catalytic reactor is developed for the purpose of describing the volatile assembly reactor system within the potable water processor on-board the International Space Station. CatReac includes these mechanisms: advective flow, axial dispersion, gas-to-liquid and liquid-to-solid mass transport, intraparticle mass transport with pore and surface diffusion, and series reactions of multiple compounds. A dimensional analysis of CatReac revealed the following seven dimensionless groups may be used to determine the controlling transport and/or reaction mechanisms: (1) the Peclet number is the ratio of the advective to the dispersive transport; (2) the Stanton number is the ratio of the external mass transfer rate to the advective rate; (3) the Damk?hler number compares the reaction rate to the advective transport rate; (4) the surface diffusion ratio equals the rate of transport by surface diffusion divided by the rate of transport by advection; (5) the pore diffusion modulus is the ratio of the rate of transport by pore diffusion to the rate of transport by advection; (6) the ratio of the gas to liquid advective rates; and, (7) the Biot numbers for surface and pore diffusion compare the external mass transfer rate to the intraparticle mass transfer rate. These dimensionless numbers are used to evaluate the impacts of the different mechanisms on the overall performance of the reactor. The numerical solution using orthogonal collocation was validated for a wide range of controlling mechanisms by comparing model simulations with several analytical solutions: (1) Gas-to-Liquid mass transfer controlling the overall mass transfer-reaction mechanisms, for a wide range of Pe number values; (2) Liquid-phase dispersion controlling the overall process; (3) Liquid-to-solid mass transfer resistance controlling the overall mass transfer-reaction process; (4) Reactions in series with two possibilities (4a): No intraparticle mass transfer resistance, and (4b): Significant intraparticle mass transfer resistance; (5) Langmuir isotherm (5a): single compound, no mass transfer resistance, and (5b): multicomponent competitive adsorption without mass transfer resistance; (6) Unsteady state operation: Plug flow with mass transfer and no reaction. These validations systematically examine all the mechanisms that are included in the general model and examine the model limitations based on the controlling mechanisms.     

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.     

Method for Calculating the Edge Moisture Variation Distance

A three-dimensional moisture diffusion and volume change model was developed for determining the distribution of soil suction and the associated volume changes in an expansive soil mass under a covered area (e.g., slab foundations or pavements) with respect to time. The model was used to determine a relationship among the edge moisture variation distance, em, the amplitude of surface suction change, U0, and the diffusion coefficient of the soil, α. The edge moisture variation distance calculation is based on the change in soil suction beneath the covered area as a result of climate changes. The edge moisture variation distance is considered to be the distance between the edge of the covered area and the point beneath the covered area where suction change is no more than 0.12 kPa (0.1 pF). Comparison between the predicted values of edge moisture variation distance by using the proposed relationship to that measured in the field or predicted by other methods is also presented.     

Purging of a Neutrally Buoyant or a Dense Miscible Contaminant from a Rectangular Cavity. I: Case of an Incoming Laminar Boundary Layer

The flow past two-dimensional (2D) channel cavities along with the removal of neutrally buoyant or dense miscible contaminants introduced instantaneously inside the cavity are studied using eddy resolving techniques. In the simulations, the incoming boundary layer is laminar and the flow is observed not to transition to turbulence as it is convected over the cavity. As for these flow conditions the main coherent structures in the separated shear layer over the cavity are quasi-dimensional, 2D simulations are performed. 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 case the contaminant is purged from the cavity mostly due to the interactions between the vortices shed in the separated shear layer with the main recirculation eddies inside the cavity and with the trailing edge corner. In the simulations in which a dense contaminant is introduced inside the cavity, after the initial stages of the mass exchange process, the main phenomenon is the presence of a large amplitude internal wave motion which interacts with a strong cavity vortex situated near the trailing edge corner in between the shear layer and the density interface. The density variation across this oscillatory interface is strong. Through this interaction wisps of denser contaminant are extracted from the region beneath the density interface, before being ejected from the cavity by the separated shear layer vortices. The values of the global mass exchange coefficients for the different phases of the purging process are estimated from simple dead-zone models. As expected, the purging process is delayed in the case in which the density of the contaminant is larger than the one of the carrying fluid.     

Coupled Large Strain Consolidation and Solute Transport. II: Model Verification and Simulation Results

The results of numerical simulations for coupled large strain consolidation and solute transport, obtained using the CST1 model, are presented. CST1 accounts for advection, longitudinal and transverse dispersion, first-order decay reactions, and linear equilibrium sorption. Verification checks of CST1 show excellent agreement with analytical solutions for one-dimensional (1D) transport in rigid porous media, including various Peclet numbers and concentration boundary conditions. Similarly excellent agreement is observed for two-dimensional advection-dispersion transport in rigid media and 1D advection-dispersion transport in compressible media undergoing large strain consolidation. CST1 is then used to investigate consolidation-induced solute transport for a single composite liner system and a confined disposal facility for dredged contaminated sediments. In both cases, solute transport was found to be strongly affected by consolidation-induced advection both during and after the consolidation period. Consolidation has 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.     

Modeling Nitrogen Transport in Duckweed Pond for Secondary Treatment of Swine Wastewater

A mathematical model was developed to describe nitrogen transport in duckweed-covered static ponds for nutrient recovery from swine lagoon water. A finite difference technique was used to solve the partial differential equations describing the ammonia transport and concentration in the pond. The key parameters in the model include the diffusion coefficient of ammonium in the medium (D) and kinetic constant of nitrogen uptake by duckweed (k). Using one order of magnitude parameter variations, the simulations showed that the model was clearly much more sensitive to D than to k, indicating the process of nitrogen removal in a static pond by duckweed is diffusion limited. Laboratory testing was conducted with Spirodela punctata 7776, a duckweed strain, to calibrate the model. The calibration of the model with experimental data yielded a new ammonium transport coefficient (T) that is 85 times of D value. Model results showed good agreement with depth-wise experimental ammonium concentration and the model also demonstrates that intermittent mixing every 3 h can enhance ammonium uptake. Additionally, an apparent drop in pH near the duckweed mat at the surface was observed that may explain low rates of ammonia emission from duckweed ponds.     

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.     

Practical Equivalent Continuum Model for Simulation of Jointed Rock Mass Using FLAC3D

A simple practical equivalent continuum numerical model for simulating the behavior of jointed rock mass has been extended to three-dimensional using FLAC3D. This model estimates the properties of jointed rock mass from the properties of intact rock and a joint factor (Jf), which is the integration of the properties of joints to take care of the effects of frequency, orientation, and strength of joint. A new FISH function has been written in FLAC3D specifically for modeling jointed rocks using the Duncan and Chang hyperbolic model. This model has been validated first with simple element tests at different confining pressures for different rocks with different joint configurations. Explicit modeling of the joints has also been done in element tests and results obtained compare well with the results of equivalent continuum model and also with experimental results. Further, this has been applied for a case study of a large underground power house cavern in the Himalayas. The analysis has been done under various stages of excavation, assigning a null model available in FLAC3D for simulating the excavation.