Two-dimensional Transport Model Research Articles

A Global Model of Chemical Vapor Deposition of Silicon Dioxide by Direct-Current Corona Discharges in Dry Air Containing Octamethylcyclotetrasiloxane Vapor

A model of the electron distribution in direct current corona plasmas is combined with a global chemistry model and a two-dimensional transport model to predict the rate of chemical vapor deposition of silicon dioxide on the discharge wire in both positive and negative discharges in dry air containing octamethylcyclotetrasiloxane. The gas-phase chemistry includes reactions to form atomic oxygen (O) and additional global reactions to form gaseous silicon dioxide precursors by the impact reactions of electrons and atomic oxygen with silicone molecules. Surface chemistry is approximated by a single step global reaction from gaseous to solid silicon dioxide. The rate coefficient between atomic oxygen and octamethylcyclotetrasiloxane is estimated from prior experiments to be on the order of 10 −12 cm 3 /molecule-s. The effects of discharge polarity, current, wire radius and air velocity (Peclet number for mass transfer) on the deposition rate are considered. Deposition rates can be minimized by using positive coronas instead of negative coronas for Peclet number less than 18.5. At higher Peclet numbers, the deposition rate is slightly higher in positive corona discharges, but devices used indoors should continue to use the positive corona in order to minimize the production of ozone. The deposition rate in the positive corona is relatively insensitive to air velocity for velocities from 0.044 to 10 m/s −1 . However,it may be minimized by operating the corona with the lowest current that provides adequate performance (e.g., particle charging) and the smallest wire that provides adequate mechanical strength.

Simplified modeling of flushing and residence times in 42 embayments in New England, USA, with special attention to Greenwich Bay, Rhode Island

A simplified protocol has been developed to meet the need for modeling hydrodynamics and transport in large numbers of embayments quickly and reliably. The procedure is illustrated with 42 embayments in southern New England, USA, giving special attention to Greenwich Bay, RI. The methodology uses simplifying assumptions. It efficiently uses available information wherever possible, and invokes experience where data are unavailable. It uses two-dimensional hydrodynamic and transport models to simulate tidal and subtidal circulation, flushing times, local residence times, and the distributions of conservative constituents over individual embayments. Preliminary results for a subset of the systems compare favorably with published values. The full set of results reveals relationships between flushing times and physical properties of the embayments. A set of relationships to estimate flushing and maximum residence times from the length and surface area of embayments in southern New England is also presented.

In-situ diffusion of HTO, 22Na+, Cs+ and I- in Opalinus Clay at the Mont Terri underground rock laboratory

Summary The diffusion properties of the Opalinus Clay were studied in the underground research laboratory at Mont Terri (Canton Jura, Switzerland) and the results were compared with diffusion data measured in the laboratory on small-scale samples. The diffusion of HTO, 22Na+, Cs+ and I- were investigated for a period of 10 months. The diffusion equipment used in the field experiment was designed in such a way that a solution of tracers was circulated through a sintered metal screen placed at the end of a borehole drilled in the formation. The concentration decrease caused by the diffusion of tracers into the rock could be followed with time and allowed first estimations of the effective diffusion coefficient. After 10 months, the diffusion zone was overcored and the tracer profiles measured. From these profiles, effective diffusion coefficients and rock capacity factors could be extracted by applying a two-dimensional transport model including diffusion and sorption. The simulations were done with the reactive transport code CRUNCH. In addition, results obtained from through-diffusion experiments on small-sized samples with HTO, 36Cl- and 22Na+ are presented and compared with the in situ data. In all cases, excellent agreement between the two data sets exists. Results for Cs+ indicated five times higher diffusion rates relative to HTO. Corresponding laboratory diffusion measurements are still lacking. However, our Cs+ data are in qualitative agreement with through-diffusion data for Callovo–Oxfordian argillite rock samples, which also indicate significantly higher effective diffusivities for Cs+ relative to HTO.

Modulation of Cosmic‐Ray Electrons in a Nonspherical and Irregular Heliosphere

With the Voyager 1 spacecraft approaching the solar wind termination shock, much emphasis is put on numerical models to simulate the physical parameters that can be expected at and beyond the shock. This work emphasizes the modulation of cosmic-ray electrons in a realistic, nonspherical heliosphere; e.g., the effects on electron modulation of a poleward elongation of the heliospheric boundary and shock, as well as an irregular shock geometry, are studied. To achieve this, a new two-dimensional time-dependent transport model is developed including the major modulation mechanisms with a realistic, asymmetric heliosheath and heliopause. Because the mutual interaction of the solar wind plasma and the interstellar medium defines the geometry of the heliosphere, a 3-fluid two-dimensional hydrodynamic model is used to calculate the geometry of the heliosphere (location of the termination shock and heliopause) as input to the transport model. We find that changes in the geometry of the heliosphere caused by solar cycle-related changes in the solar wind speed influence the electron distribution significantly close to the shock and to a lesser extent in the heliosheath and inner heliosphere, but only if there is a significant amount of particle drift present. These effects decrease toward solar maximum when the heliosphere is expected to be diffusion dominated and also for low-energy (<30 MeV) electrons, where drift is not important. The model is also utilized to study the effect of possible nonspherical, irregular incursions in the termination shock geometry on the distribution of cosmic-ray electrons in the shock's vicinity. It is shown that these incursions only affect the electron distribution close to the termination shock and to a lesser extent in the heliopause and are highly dependent on drift. Furthermore, a time dependence and/or incursions in the shock geometry could account for the sudden increase by up to a factor of ~4 in the low-energy electron intensities measured by Voyager 1 with the spacecraft still, e.g., ~2 AU away from the shock.

Mixing of Hillslope, River, and Alluvial Ground Waters in Lowland Floodplains

AbstractIn this paper, we develop and apply a two‐dimensional flow and transport model to simulate the mixing of variously sourced water within a fluvial floodplain during one in‐bank and one out‐of‐bank flood event. The model is applied to two 120 m long transects through the floodplain of the River Severn, Shropshire, United Kingdom, which run to the river from the hillslope bordering the floodplain. For this site, hourly piezometric, river stage, and rainfall data are used to parameterize and validate the flow component of the model. Simulation of the movement of hypothetical conservative tracers driven by these hydrodynamic conditions is then undertaken to confirm and refine an evolving conceptual model of floodplain hydrology. This is based on the bank storage concept, and extended to include the impact of hillslope contributions to the floodplain/riparian zone and the impact of out‐of‐bank inundation on subsurface flow processes. The paper demonstrates that the role of the unsaturated zone has been underestimated in our previous investigations at this site and, in addition, that there is a potentially high residence time for solutes which remain in the unsaturated zone at the end of the flood event. In general, flood events in lowland plain systems are shown to be times of great hydrological and chemical activity. Lastly, the results confirm the complexity of interactions between surface and ground water flows in lowland plain settings and highlight the need for correct treatment of both dynamic boundary conditions and unsaturated zone processes.

Hydrodynamics and Mass Transport in Wall-Tube and Microjet Electrodes: An Experimental Evaluation of Current Theory

The application of steady-state and fast-scan linear sweep voltammetry to a high-speed wall-tube electrode (HWTE) is reported in different solvents to investigate the response of the HWTE over a wide range of Reynolds' numbers (Re). Experiments are reported for the oxidation of N,N,N‘,N‘-tetramethyl-p-phenylenediamine (TMPD) in propylene carbonate (PC), water, butyronitrile (BN), acetonitrile (AN), and acetonitrile−water mixture solutions containing 0.10 M supporting electrolyte for a 24 μm radius platinum microdisk electrode housed within the HWTE using a range of average flow jet velocities from 0.03 to 19.8 m s-1 (corresponding to volume flow rates of 0.003−0.25 cm3 s-1 and center-line jet velocities from 0.05 to 39.5 m s-1). Fast scan linear sweep voltammetry is presented for the oxidation of TMPD in PC and of 9,10-diphenylanthracene (DPA) in AN. Theoretical results are derived using finite element methods for both one- and two-dimensional mass transport models. It is found that, for solvents with a k...

Effects of flow distributor geometry and diffusion layer porosity on reactant gas transport and performance of proton exchange membrane fuel cells

A study has been conducted on the effects of flow distributor and diffusion layer geometries and morphologies on the transport phenomena of reactant gas from flow channels to gas diffuser, and on the performance of a proton exchange membrane fuel cell. The emphasis of the analysis is placed on the effects of the cross-section of the channel of the anode flow distributor and the porosity of the gas-diffusion layer. By applying a two-dimensional mass transport model, the effects of the channel width fraction, λ=lc/lb, the channel number, N, the porosity of the diffuser layer, e, and the surface overpotential of the catalyst layer, η, on the resultant current density are investigated. The cell performance is evaluated by the predicted voltage–current density curves. It is disclosed that an increase in either λ, N or e may lead to a better cell performance. At relatively low overpotential, better uniformity in current density distribution along the width of the cell (x-direction) can be attained. Based on the present results, a correlation of overpotentials is proposed, namely, ηcr=0.165λ0.0935N0.2033e0.0856, which may serve as a guideline to justify the validity of a simplified one-dimensional model.

Predicting fine sediment dynamics along a pool-riffle mountain channel

Fine sediment dynamics in mountain rivers are of concern because of implications for aquatic habitat, channel stability, and downstream sediment yields. Many mountain river systems have episodic fine sediment transport because of infrequent, point-source sediment inputs from landslides; basin instability triggered by land uses such as logging; or infrequent mobilization of the coarse surface layer in channels. Dam removal, which is now more likely along mountain rivers, may also provide a substantial fine sediment input to downstream channel reaches. Fine sediment storage in the interstices of spawning gravels and within pools along mountain rivers is of particular interest because of impacts to aquatic organisms. In this study we focus on sediment dynamics within pools of the North Fork Poudre River in Colorado as an example of the processes controlling fine sediment deposition, storage, and transport within laterally constricted pools. The 1996 release of ∼7000 m 3 of silt-to gravel-sized sediment from a reservoir on the North Fork provided an opportunity to develop a field data set of fine sediment dynamics and to test the predictions of three different one- or two-dimensional sediment transport and hydraulic models against the field observations. The models were calibrated against quantitative measurements of pool scour and fill. One-dimensional HEC-6 results indicate that robust simulations yield the greatest agreement between predicted and measured pool bed elevation change. Model calibration on two pools and validation on one pool indicate that at least 58% of observed bed changes after the sediment release were predicted by HEC-6. Modeling accuracy using quasi-two-dimensional GSTARS 2.0 was considerably more variable, and no pool-wide trends were obtained. The two-dimensional model RMA2 substantially improved the representation of eddy pool hydraulics within a compound pool of the North Fork. Results from the hydraulic modeling, coupled with bed load and total load computations, delineate areas of scour and deposition which are consistent with observations in the field. A conceptual model of sediment delivery and storage for laterally confined pools suggests that persistent deposition of fine sediment within eddies distal from the sediment source may result from sediment releases. The original loss of channel capacity facilitated additional deposition within eddies as sediment within upstream proximal pools became mobilized. At high discharges, the development of a strong shear zone prevents degradation of sediment deposits within the eddy. Central portions of these proximal pools may clear according to existing models, whereas deposition within recirculating zones may be long-term. Water managers could use these models to estimate minimum pool volume for overwinter habitat and residence time of pool sediment.

Determination of free carrier bipolar diffusion coefficient and surface recombination velocity of undoped GaN epilayers

Time-resolved nondegenerate four-wave mixing experiments were performed on 2.6-μm-thick GaN epilayers grown by metalorganic chemical-vapor deposition using picosecond pulses at 355 and 1064 nm for grating recording and probing, respectively. Measurements of free carrier grating kinetics at various grating periods Λ in range from 3 to 10 μm allowed determination of nonequilibrium carrier bipolar diffusion coefficient D=1.7 cm2/s at 300 K. Substitution of the D value into two-dimensional carrier transport model allowed fitting of the whole set of grating kinetics at various Λ varying surface recombination velocity S and linear recombination time τR. This procedure provided us a value of S=5×104 cm/s as well as carrier lifetime of ∼1 ns.

Modeling dissolution and volatilization of LNAPL sources migrating on the groundwater table

A vertically averaged two-dimensional model was developed to describe areal spreading and migration of light nonaqueous-phase liquids (LNAPLs) introduced into the subsurface by spills or leaks from underground storage tanks. The NAPL transport model was coupled with two-dimensional contaminant transport models to predict contamination of soil gas and groundwater resulting from a LNAPL migrating on the water table. Numerical solutions were obtained by using the finite-difference method. Simulations and sensitivity analyses were conducted with a LNAPL of pure benzene to study LNAPL migration and groundwater contamination. The model was applied to subsurface contamination by jet fuel. Results indicated that LNAPL migration were affected mostly by volatilization. The generation and movement of the dissolved plume was affected by the geology of the site and the free-product plume. Most of the spilled mass remained as a free LNAPL phase 20 years after the spill. The migration of LNAPL for such a long period resulted in the contamination of both groundwater and a large volume of soil.

On the estimation of impact of vehicular emissions

It is suggested a method for estimating the carbon monoxide (CO) concentration levels in various zones of an urban area caused by vehicular emissions. The method is based on using the adjoint operator and adjoint transport equation and can be used by any pollution transport model. It is illustrated here with a simple two-dimensional pollution transport model and its adjoint applied to Guadalajara City. The car emissions are described by linear sources located along the main city roadways. Each of the models is well posed, that is, has unique solution continuously depending on the CO emission rates and initial CO distribution in the area. Two equivalent (direct and adjoint) mean CO concentration estimates in an ecologically important zone are given. The sensitivity of these estimates with respect to vehicular emission rates along the main city roads, as well as to the wind and initial CO distribution is examined. Compatible, balanced, and absolutely stable second-order finite-difference schemes based on the splitting method are used to simulate CO transport in the Guadalajara City Metropolitan Area (GCMA). It is shown that the adjoint model solutions serve as influence (Green) functions providing valuable information on the contribution of various parts of the roadways in polluting the zone selected.

An investigation of spatial and temporal weighting schemes for use in unstructured mesh control volume finite element methods

In this work the control volume finite element (CVFE) method is used to discretise a two-dimensional non-linear transport model on an unstructured mesh. First and second order temporal weighting, combined with various flux limiting techniques (spatial weighting) are analysed in order to identify the most accurate and efficient numerical scheme. An inexact Newton method is used to resolve the underlying discrete non-linear system. In computing the Newton step the performance of the preconditioned iterative solvers BiCGSTAB and GMRES, in conjunction with a two-node Jacobian approximation is also examined. A linear benchmark problem that admits an analytical solution is used to assess the accuracy and computational efficiency of the numerical model. The results show that the flux limited second order temporal scheme substantially reduce numerical diffusion on relatively coarse meshes. The low temperature wood drying non-linear case study highlights that the first order temporal scheme combined with flux limiting achieves good accuracy on a relatively coarse mesh and improves the overall computational efficiency.

TACK—a program coupling chemical kinetics with a two-dimensional transport model in geochemical systems

The Transport And Chemical Kinetics (TACK) program has been designed to make predictions of the chemistry in the vicinity of a planned repository for nuclear waste, i.e. SFL 3-5, where SFL is the Swedish abbreviation for “Swedish repository for long-lived waste”. This implies modelling transport and chemistry in fractured rock. The system concerned in the modelling of SFL is leaching water from decommissioning waste in concrete. The concrete will raise the pH in the water to between 12 and 13.5. So far, only a few calculations have been made on such systems. Coupled transport and chemical reaction programs should be used, since the system is important for safety assessments of the repository. At least two of programs can be used for this kind of problem, for example OS3D/GIMRT and PHAST. As it is also important to consider the uncertainty of the model, the TACK program fills an important purpose here. A slightly different approach to the problem may give significantly different results. Because validation is generally not possible, using several programs is the only key to identifying conceptual uncertainties. To illustrate this point, comparative calculations have been made between TACK and the PHAST program. The calculations gave qualitatively similar result but quantitatively somewhat differing results. The TACK program couples the well known PHREEQC geochemical program with a two-dimensional transport model. The PHREEQC calculations include speciation of solutions and mineral reactions involving kinetics. The reasons for choosing this program are that it is quite a general one and is relatively stable at the high pH values present in the systems used. The transport phenomena taken into account in the model are advection, diffusion and dispersion in two dimensions.

Flow velocity retardation and sediment retention in two constructed wetland–ponds

Hydraulic properties of two constructed wetland–ponds in agricultural watersheds in southern Finland were examined by simulations with two-dimensional hydrodynamic and water quality transport models. Hydraulic efficiency was determined for the existing and hypothetical layouts of both wetlands to find out the effects of different design options. Suspended sediment retention in the wetlands was simulated with a two-dimensional model for sediment transport. Hydraulic efficiency was found to be highly improved by baffles that direct the main flow to optimally exploit the wetland acreage. Also, an elongated shape of wetland appeared beneficial; hydraulic efficiency was high regardless of the size or position of the inlet. As for suspended sediment retention, the wetland area in relation to its watershed proved to be an essential factor. According to water quality observations, the wetland which occupied 5% of its watershed area was capable of reducing the inflow of total suspended solids (TSS) concentrations during flood events by 43–72%, whereas the reduction varied between −7 and 5% in the other wetland with a corresponding ratio of 0.5%. Model simulations of the same flood events plausibly predicted the output TSS concentrations, even though with wider ranges of the reductions (26 to 74 and −13 to 43%, respectively).

Effect of soil parameters on radon entry into a building by means of the transrad numerical model.

High indoor radon concentration means an increased risk of developing lung cancer. When high radon levels are present in a dwelling, the major source is normally the soil. Therefore, it is useful to know the radon concentration field in the soil underneath a building. A steady-state two-dimensional radon transport model has been used to calculate the effect of a reference building on the soil radon concentration, and the influence of soil parameters on radon entry through a single crack in the basement. Both advective and diffusive flows are considered. Away from the building, the well-known undisturbed soil radon concentration profile has been obtained, while under the house the radon level is increased. A variability analysis around the reference site has shown that the most relevant soil parameters on the radon flux at the top of the crack are, in this case, effective diffusion coefficient, soil gas-permeability and deep soil radon concentration.

Numerical modelling and hydrochemical characterisation of a fresh-water lens in the Belgian coastal plain

The distribution of fresh and salt water in coastal aquifers is influenced by many processes. The influence of aquifer heterogeneity and human interference such as land reclamation is illustrated in the Belgian coastal plain where, around A.D. 1200, the reclamation of a tidally influenced environment was completed. The aquifer, which was filled with salt water, was thereafter freshened. The areal distribution of peat, clay, silt and sand influences the general flow and distribution of fresh and salt water along with the drainage pattern and results in the development of fresh-water lenses. The water quality in and around the fresh-water lenses below an inverted tidal channel ridge is surveyed. The hydrochemical evolution of the fresh water lens is reconstructed, pointing to cation exchange, solution of calcite and the oxidation of organic material as the major chemical reactions. The formation and evolution of the fresh water lens is modelled using a two-dimensional density-dependent solute transport model and the sensitivity of drainage and conductivities are studied. Drainage level mainly influences the depth of the fresh-water lens, whereas the time of formation is mainly influenced by conductivity.

Ion partitioning among soil and plant components under drip, furrow, and sprinkler irrigation regimes: field and modeling assessments.

Soil and water resources can be severely degraded by salinity when total salt input exceeds output in irrigated agriculture. This study was conducted to examine partitioning of Ca2+, Na+, and Cl- between soil and soybean [Glycine max (L.) Merr.] plants under different irrigation regimes with both field and modeling assessments. In drip and sprinkler treatments, the irrigation water was salinized with NaCl and CaCl2 salts to simulate a Cl- and Na+ dominant saline drainage water. In the furrow irrigation treatment, the soil was salinized, prior to planting, with NaCl and CaCl2 salts to simulate a Cl- and Na+ dominant saline soil. A total of 756 soil and 864 plant samples were collected and analyzed for the salt ions to obtain ion partitioning and mass balance assessments. Modeling of salt ion uptake by plants and distribution in the soil profile was performed with a two-dimensional solute transport model for the three irrigation regimes. Results indicated that about 20% of the applied Ca2+ was recovered in harvested soybean biomass in all treatments. Plant uptake of either Na+ or Cl- was less than 0.5% in the drip and furrow, and about 2% in the sprinkler irrigation treatment. Significant increases in soil salinity were found in the sprinkler plot that received the highest cumulative amount of salts. Simulated ion distributions in the soil were comparable with the measurements. Compared with the total seasonal salt input, mass balances between 65 and 108% were obtained. Most salt inputs accumulate in the soil, and need to be removed periodically to prevent soil salinization.

Two-dimensional self-consistent radiation transport model for plasma display panels

A two-dimensional radiation transport model is coupled with a fluid simulation to incorporate the resonance radiation trapping effect in a plasma display panel cell. Compared with the conventional trapping factor approach, this model has an advantage in describing the spatial evolution of the radiative excited-state density. Compared with a Monte Carlo model, it also takes advantage of its fast computation to couple the radiation transport self-consistently with the time-dependent fluid model. The effect of the spatial evolution of the resonant excited state on the light emission is investigated for the variations of system sizes and the gas mixture ratio, and the results are compared with those of the conventional trapping factor approach. The discrepancy between the two methods increases as the gap size between the dielectrics increases, but does not change significantly for the variation of the gas mixture ratio.

Modeling Enhanced In Situ Denitrification in Groundwater

A two-dimensional numerical solute transport model was developed for simulating an enhanced in situ denitrification experi- ment performed in a nitrate-contaminated aquifer on Cape Cod, Massachusetts. In this experiment, formate ~HCOO 2 ! was injected for a period of 26 days into the carbon-limited aquifer to stimulate denitrification. Calibration of the vertical-profile site model was demon- strated through error analysis and comparison with formate, nitrate, and nitrite concentration data monitored along a transect of three multilevel groundwater sampling wells for 75 days after initial injection. Formate utilization rates were approximately 142 and 38 mM/day for nitrate and nitrite reduction, respectively. Nitrate and nitrite utilization rates were approximately 29 and 8 mM/day, respectively. Nitrate utilization rates under enhanced conditions were 1 order of magnitude greater than previously reported naturally occurring rates. The nitrite production rate was approximately 29 mM/day. Persistence of nitrite was attributed to a combination of factors, including electron donor ~formate! limitation late in the experiment, preferential utilization of nitrate as an electron acceptor, and greater nitrite production relative to nitrite utilization.

Impurity transport in edge plasmas with application to liquid walls

The transport of impurity ions in a magnetically confined plasma is studied in the region between their origin at a material surface and the core plasma as defined by closed magnetic flux surfaces. The focus is physics understanding of the results of two-dimensional (2-D) transport modeling of the plasma and neutrals. A simple one-dimensional model is introduced to identify key processes and illustrate how such processes affect the core-edge impurity level. The 2-D simulation gives detailed results of scaling of the impurity level with parameters such as anomalous radial diffusion, hydrogen–plasma recycling, core power flux, and core-edge density. The results are obtained for a slab model of a tokamak, but by changing the magnetic connection length, scaling to other types of devices can be inferred. Lithium and fluorine impurities are considered explicitly as examples with low and moderate charge-state number, Z, for liquid wall materials; trends found for these cases provide guidance to the behavior of other impurities. The tolerable amount of impurity influx can be closely associated with the partial thermal collapse of the edge plasma. The results are used to provide a physics picture of previous results on the acceptable evaporative impurity flux from different types of liquid wall materials, and to show how these results can be expected to scale with parameters.