Performance of various sub-grid scale models in large-eddy simulations of turbulent flow over complex terrain

Turbulent flow over a two-dimensional steep hill was analyzed by large-eddy simulations (LES). Here, six LES computations were carried out using four different sub-grid scale (SGS) models and two different ground surface conditions. The accuracy of these computations was assessed by comparing the results with those from an experiment by Ishihara et al. (An experimental study of turbulent boundary layer over a steep hill, Proceedings of the 15th National Symposium on Wind Engineering, 1998, pp. 61–66; J. Wind Eng. 89 (2001) 573). The results of the dynamic SGS models were in very poor agreement with those of the experiment. The poor prediction accuracy was mainly caused by the inaccurate estimation of the model coefficient near the ground surface. In order to improve the prediction accuracy of the dynamic SGS models, a hybrid SGS model, i.e., a combination of the standard Smagorinsky model and the dynamic Smagorinsky model, was introduced. The hybrid model provided very accurate predictions and produced the best results of the four SGS models compared here.     

A Lagrangian stochastic model for predicting concentration fluctuations in urban areas

A combined Lagrangian stochastic model with a micromixing sub-model is used to estimate the fluctuating concentrations observed in two wind tunnel experiments. The Lagrangian stochastic model allows fluid trajectories to be simulated in the inhomogeneous flow, while the mixing model accounts for the dissipation of fluctuations using the interaction by exchange with the mean (IEM) mechanism. The model is first tested against the open terrain, wind tunnel data of Fackrell, J.E. and Robins, A.E. [1982. Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary layer. Journal of Fluid Mechanics 117, 1–26] and shows good agreement with the observed mean concentrations and fluctuation intensities. The model is then compared with the wind tunnel simulation of a two-dimensional street canyon by Pavageau, M. and Schatzmann, M. [1999. Wind tunnel measurements of concentration fluctuations in an urban street canyon. Atmospheric Environment 33, 3961–3971]. Despite the limitations of the k–ε turbulence scheme and the IEM mixing mechanism, the model reproduces the fluctuation intensity pattern within the canyon well. Overall, the comparison with both sets of wind tunnel experiments are encouraging, and the simplicity of the model means that predictions in a complex, three-dimensional geometry can be produced in a practicable amount of time.     

Evidence of one-dimensional scale-dependent fractional advection-dispersion

A semi-analytical inverse method and the corresponding program FADEMain for parameter estimation of the fractional advection-dispersion equation (FADE) were developed in this paper. We have analyzed Huang et al.'s [Huang, K., Toride, N., van Genuchten, M.Th., 1995. Experimental investigation of solute transport in large homogeneous and heterogeneous saturated soil columns. Trans. Porous Media 18, 283-302.] laboratory experimental data of conservative solute transport in 12.5-m long homogeneous and heterogeneous soil columns to test the non-Fickian dispersion theory of FADE. The dispersion coefficient was calculated by fitting the analytical solution of FADE to the measured data at different transport scales. We found that the dispersion coefficient increased exponentially with transport scale for the homogeneous column, whereas it increased with transport scale in a power law function for the heterogeneous column. The scale effect of the dispersion coefficient in the heterogeneous soil was much more significant comparing to that in the homogeneous soil. The increasing rate of dispersion coefficient versus transport distance was smaller for FADE than that for the advection-dispersion equation (ADE). Finite difference numerical approximations of the scale-dependent FADE were established to interpret the experimental results. The numerical solutions were found to be adequate for predicting scale-dependent transport in the homogeneous column, while the prediction for the heterogeneous column was less satisfactory.     

Examination of a subgrid-scale parameterization for the transport of pollutants in a nonprecipitating cumulus cloud ensemble

The mass flux based subgrid-scale parameterization technique of Gidel (1983, J. geophys. Res.88, 6587–6599) is re-examined for use in Eulerian long-range transport models. Specifically, the parameterization scheme is incorporated into the STEM-II Eulerian transport/transformation/removal model and the model is used to investigate pollutant transport in a nonprecipitating cumulus cloud ensemble. The effects of entrainment, detrainment, evaporation and the transport by subsidence, updrafts and turbulent diffusion are included in the analysis. Presented simulation results indicate that the parameterization is able to treat the rapid vertical transport by cloud updrafts, enables the calculation of reaction rates based on subgrid-scale concentrations, and is readily adopted by Eulerian models.     

Computational Fluid Dynamics (CFD) Simulations on the Effect of Rough Surface on Atmospheric Turbulence Flow Above Hilly Terrain Shapes

The behavioral distribution of the atmospheric turbulence flow over the terrain with changes in a rough surface has become one of the most important topics of air pollution research, among such other topics as transportation and dispersion pollutants. In this study, a computational model on atmospheric turbulence flow over a terrain hill shaped with rough surface was investigated under neutral atmospheric conditions. The flow was assumed to be 2D and modeled using computational fluid dynamics (CFD) models, which were numerically solved using Reynolds-averaged Navier-Stokes equations. Rough surface conditions were modeled using a number of windbreak fences regularly spaced on the hill. The mean velocity and turbulent structures such as turbulence intensity and turbulent kinetic energy were investigated in the upwind and downwind regions over the hill, and the numerical models were validated against the wind-tunnel results to optimize the turbulence model. The computational results agreed well with the results obtained from the wind tunnel experiments. The computational results indicate that the mean velocity was observed to increase dramatically around the crest of the upwind slope of the hill. A thick internal boundary layer was observed with a fence on the crest and downwind region of the hill. The reversed flow and recirculation zone were formed in the wake region behind the hill. It was thus determined that turbulent kinetic energy decreases as the mean velocity increases.     

Sensitivity of the DERMA long-range Gaussian dispersion model to meteorological input and diffusion parameters

The Danish Emergency Response Model of the Atmosphere (DERMA) is described and applied to the first ETEX experiment. By using analysed low-resolution numerical weather-prediction data from the global model of the European Centre for Medium-range Weather Forecast (ECMWF) as well as higher-resolution data from two versions of the High Resolution Limited Area Model (HIRLAM), which are operational at the Danish Meteorological Institute (DMI), the sensitivity of DERMA to the resolution of meteorological data is analysed by comparing DERMA results with concentration measurements. Furthermore, the sensitivity to boundary-layer height and diffusion parameters is studied. These parameters include the critical bulk Richardson number, which is used to estimate the atmospheric boundary-layer height, the horizontal eddy diffusivity and the Lagrangian turbulence time scale. The parameters, which provide the best performance of DERMA, are 0.25 for the critical bulk Richardson number, 6×10³ m² s^-1 for the horizontal eddy diffusivity, and 3 h for the Lagrangian time scale. DERMA is much more sensitive to boundary-layer parameters when using high-resolution DMI-HIRLAM data than when using data of lower resolution from the ECMWF. Finally, the bulk Richardson number method of boundary-layer height calculation applied to DMI-HIRLAM data is verified directly against routine radiosondes released under the tracer gas plume. The boundary-layer height estimates based on analysed NWP model data agree well with observations, and the agreement deteriorates as a function of forecast length.     

An interpretation of potential scale dependence of the effective matrix diffusion coefficient

Matrix diffusion is an important process for solute transport in fractured rock, and the matrix diffusion coefficient is a key parameter for describing this process. Previous studies have indicated that the effective matrix diffusion coefficient values, obtained from a large number of field tracer tests, are enhanced in comparison with local values and may increase with test scale. In this study, we have performed numerical experiments to investigate potential mechanisms behind possible scale-dependent behavior. The focus of the experiments is on solute transport in flow paths having geometries consistent with percolation theories and characterized by multiple local flow loops formed mainly by small-scale fractures. The water velocity distribution through a flow path was determined using discrete fracture network flow simulations, and solute transport was calculated using a previously derived impulse-response function and a particle-tracking scheme. Values for effective (or up-scaled) transport parameters were obtained by matching breakthrough curves from numerical experiments with an analytical solution for solute transport along a single fracture. Results indicate that a combination of local flow loops and the associated matrix diffusion process, together with scaling properties in flow path geometry, seems to be an important mechanism causing the observed scale dependence of the effective matrix diffusion coefficient (at a range of scales).     

Development of Artificial Neural Network Based Metamodels for Inactivation of Anthrax Spores in Ventilated Spaces Using Computational Fluid Dynamics

ABSTRACT

Linear, quadratic, and artificial neural network (ANN)-based metamodels were developed for predicting the extent of anthrax spore inactivation by chlorine dioxide in a ventilated three-dimensional space over time from computational fluid dynamics model (CFD) simulation data. Dimensionless groups were developed to define the design space of the problem scenario. The Hammersley sequence sampling (HSS) method was used to determine the sampling points for the numerical experiments within the design space. A CFD model, comprised of multiple submodels, was applied to conduct the numerical experiments. Large eddy simulation (LES) with the Smagorinsky subgrid-scale model was applied to compute the airflow. Anthrax spores were modeled as a dispersed solid phase using the Lagrangian treatment. The disinfectant transport was calculated by solving a mass transport equation. Kinetic decay constants were included for spontaneous decay of the disinfectant and for the reaction of the disinfectant with the surfaces of the three-dimensional space. To enhance the mixing of the disinfectant with the room air, a momentum source was included in the simulation. An inactivation rate equation accounted for the reaction between the spores and the disinfectant. The ANN-based metamodels were most successful in predicting the number of viable bioaerosols remaining in an arbitrary enclosed space. Sensitivity analysis showed that the mass fraction of the disinfectant, inactivation rate constant, and contact time had the most influence on the inactivation of the spores.

IMPLICATIONS This investigation presents a framework for the development of user-friendly models; metamodels for the prediction of the number of viable spores remaining in an indoor room during disinfection from accurate but time-consuming CFD studies. During any decontamination event, to know when to stop pumping in the disinfectant and to know what level of log reduction of the spores have been achieved before even starting decontamination would provide valuable guidance. The neural network based metamodels can be applied to obtain quick and relatively accurate answers. This would be necessary when immediate information is required during emergencies.     

Design of aquifer remediation systems: (1) describing hydraulic structure and NAPL architecture using tracers

Aquifer heterogeneity (structure) and NAPL distribution (architecture) are described based on tracer data. An inverse modelling approach that estimates the hydraulic structure and NAPL architecture based on a Lagrangian stochastic model where the hydraulic structure is described by one or more populations of lognormally distributed travel times and the NAPL architecture is selected from eight possible assumed distributions. Optimization of the model parameters for each tested realization is based on the minimization of the sum of the square residuals between the log of measured tracer data and model predictions for the same temporal observation. For a given NAPL architecture the error is reduced with each added population. Model selection was based on a fitness which penalized models for increasing complexity. The technique is demonstrated under a range of hydrologic and contaminant settings using data from three small field-scale tracer tests: the first implementation at an LNAPL site using a line-drive flow pattern, the second at a DNAPL site with an inverted five-spot flow pattern, and the third at the same DNAPL site using a vertical circulation flow pattern. The Lagrangian model was capable of accurately duplicating experimentally derived tracer breakthrough curves, with a correlation coefficient of 0.97 or better. Furthermore, the model estimate of the NAPL volume is similar to the estimates based on moment analysis of field data.     

Design of aquifer remediation systems: (1) Describing hydraulic structure and NAPL architecture using tracers

Aquifer heterogeneity (structure) and NAPL distribution (architecture) are described based on tracer data. An inverse modelling approach that estimates the hydraulic structure and NAPL architecture based on a Lagrangian stochastic model where the hydraulic structure is described by one or more populations of lognormally distributed travel times and the NAPL architecture is selected from eight possible assumed distributions. Optimization of the model parameters for each tested realization is based on the minimization of the sum of the square residuals between the log of measured tracer data and model predictions for the same temporal observation. For a given NAPL architecture the error is reduced with each added population. Model selection was based on a fitness which penalized models for increasing complexity. The technique is demonstrated under a range of hydrologic and contaminant settings using data from three small field-scale tracer tests: the first implementation at an LNAPL site using a line-drive flow pattern, the second at a DNAPL site with an inverted five-spot flow pattern, and the third at the same DNAPL site using a vertical circulation flow pattern. The Lagrangian model was capable of accurately duplicating experimentally derived tracer breakthrough curves, with a correlation coefficient of 0.97 or better. Furthermore, the model estimate of the NAPL volume is similar to the estimates based on moment analysis of field data.     

Interregional Exchanges of Air Pollution: Model Types and Applications

Regional scale air quality simulation models covering spatial scales of thousands of kilometers are finding increasing applications in studies of acid deposition and other air pollution problems. The purpose of this paper is to familiarize the nonexpert with the characteristics of the major types of interregional air quality models currently in use: Eulerian grid, statistical trajectory, and Lagrangian trajectory. The basic features, advantages, and disadvantages of each of these modeling approaches are summarized, as are the important limitations and problems associated with interregional modeling in general. Typical applications are illustrated using examples from the use of a representative Lagrangian trajectory model, ENAMAP, over the eastern North American area.     

Analytical solutions for reactive transport under an infiltration-redistribution cycle

Transport of reactive solute in unsaturated soils under an infiltration-redistribution cycle is investigated. The study is based on the model of vertical flow and transport in the unsaturated zone proposed by Indelman et al. [J. Contam. Hydrol. 32 (1998) 77], and generalizes it by accounting for linear nonequilibrium kinetics. An exact analytical solution is derived for an irreversible desorption reaction. The transport of solute obeying linear kinetics is modeled by assuming equilibrium during the redistribution stage. The model which accounts for nonequilibrium during the infiltration and assumes equilibrium at the redistribution stage is termed partial equilibrium infiltration-redistribution model (PEIRM). It allows to derive approximate closed form solutions for transport in one-dimensional homogeneous soils. These solutions are further applied to computing the field-scale concentration by adopting the Dagan and Bresler [Soil Sci. Soc. Am. J. 43 (1979) 461] column model. The effect of soil heterogeneity on the solute spread is investigated by modeling the hydraulic saturated conductivity as a random function of horizontal coordinates. The quality of the PEIRM is illustrated by calculating the critical values of the Damk?hler number which provide the achievable accuracy in estimating the solute mass in the mobile phase. The distinguishing feature of transport during the infiltration-redistribution cycle as compared to that of infiltration only is the finite depth of solute penetration. For irreversible desorption, the maximum solute penetration W/theta(r) is determined by the amount of applied water W and the residual water content theta(r). For sorption-desorption kinetics, the maximum depth of penetration z(r)(e, infinity ) also depends on the ratio between the rate of application and the column-saturated conductivity. It is shown that z(r)(e, infinity ) is bounded between the depths W/(theta(r)+K(d)) and W/theta(r) corresponding to the maximum solute penetration for equilibrium transport and for irreversible desorption, respectively. This feature of solute penetration explains the unusual phenomena of plume contraction after an initial period of spreading [Lessoff, S.C., Indelman, P., Dagan, G., 2002. Solute transport in infiltration-redistribution cycles in heterogeneous soils. In Raats, P.A.C., Smiles, D.,Warrick, A.W. (Eds), Environmental Mechanics: Water, Mass and Energy Transport in the Biosphere. American Geophysical Union, pp. 133-144]. Unlike transport under equilibrium conditions, when the solute is completely concentrated at the front, the solute under nonequilibrium conditions is spread out behind the front. Heterogeneity leads to additional spreading of the plume.     

Kinetics of the reduction of hexavalent chromium with the brown seaweed Ecklonia biomass

The dead biomass of the brown seaweed, Ecklonia sp., is capable of reducing toxic Cr(VI) into less toxic or nontoxic Cr(III). However, little is known about the mechanism of Cr(VI) reduction by the biomass. The objective of this work was to develop a kinetic model for Cr(VI) biosorption, for supporting our mechanism. The reduction rate of Cr(VI) increased with increasing total chromate concentration, [Cr(VI)], and equivalent concentration of organic compounds, [OCs], and decreasing solution pH. It was found that the reduction rate of Cr(VI) was proportional to [Cr(VI)] and [OCs], suggesting the simple kinetic equation -d[Cr(VI)]/dt=k[Cr(VI)][OCs]. When considering the consumption of organic compounds due to the oxidation by Cr(VI), an average rate coefficient of 9.33 (+/-0.65)microM(-1)h(-1) was determined, at pH 2. Although the function of the pH could not be expressed in a mechanistic manner, an empirical model able to describe the pH dependence was obtained. It is expected that the developed rate equation could likely be used for design and performance predictions of biosorption processes for treating chromate wastewaters.     

Estimation of local scale dispersion from local breakthrough curves during a tracer test in a heterogeneous aquifer: the Lagrangian approach

The local scale dispersion tensor, Dd, is a controlling parameter for the dilution of concentrations in a solute plume that is displaced by groundwater flow in a heterogeneous aquifer. In this paper, we estimate the local scale dispersion from time series or breakthrough curves, BTCs, of Br concentrations that were measured at several points in a fluvial aquifer during a natural gradient tracer test at Krauthausen. Locally measured BTCs were characterized by equivalent convection dispersion parameters: equivalent velocity, v(eq)(x) and expected equivalent dispersivity, [lambda(eq)(x)]. A Lagrangian framework was used to approximately predict these equivalent parameters in terms of the spatial covariance of log(e) transformed conductivity and the local scale dispersion coefficient. The approximate Lagrangian theory illustrates that [lambda(eq)(x)] increases with increasing travel distance and is much larger than the local scale dispersivity, lambda(d). A sensitivity analysis indicates that [lambda(eq)(x)] is predominantly determined by the transverse component of the local scale dispersion and by the correlation scale of the hydraulic conductivity in the transverse to flow direction whereas it is relatively insensitive to the longitudinal component of the local scale dispersion. By comparing predicted [lambda(eq)(x)] for a range of Dd values with [lambda(eq)(x)] obtained from locally measured BTCs, the transverse component of Dd, DdT, was estimated. The estimated transverse local scale dispersivity, lambda(dT) = DdT/U1 (U1 = mean advection velocity) is in the order of 10(1)-10(2) mm, which is relatively large but realistic for the fluvial gravel sediments at Krauthausen.     

Prediction of atmospheric dispersion of pollutants in an airport environment

In this article we discuss the development of a methodology to predict atmospheric turbulent dispersion of pollutants generated from air traffic in an airport. It is based on the Lagrangian stochastic model (LSM), developed by Das and Durbin [2005. A Lagrangian stochastic model for dispersion in stratified turbulence, Physics of Fluids 17, 025109]. The approach is via the backward trajectory formulation of the model. The sources and receptors in an airport type problem are modeled as spheres and procedures have been derived for concentration calculation by both forward and backward trajectory methods. Some tests are performed to highlight certain features of the method. The turbulence statistics that are required as input are provided in terms of similarity profiles. The airport domain is partitioned to make the required search algorithms efficient. Pollutant concentration profiles are calculated over a range of meteorological data.     

Sorption of hydrophobic organic pollutants in saturated soil systems

Sorption equilibria and rates were characterized for a matrix of four aquifer sands and two slightly to moderately hydrophobic organic solutes (nitrobenzene and lindane), and the effects of sorption on the behavior of these solutes in saturated systems of the soils were determined. Experimental data were used to test and evaluate a variety of mathematical models for predicting contaminant fate and transport in groundwater systems.Observed equilibrium relationships between soil and solution phase solute concentrations were found to be described best by the nonlinear Freundlich isotherm model. It was further determined that the sorption process in the systems tested is rate controlled, requiring several days to approach equilibrium in completely mixed batch reactors. Subsequent modeling of solute transport in continuous flow soil column reactors was found to be most successful when rate-controlled models were used, the best results were obtained with a dual-resistance model incorporating the coupled mass transport steps of boundary-layer and intraparticle diffusion.     

Notes on the models of cadmium kinetics

This paper identifies several drawbacks in the models of absorption and desorption of cadmium presented by [Garcia-Gomez, C., Carbonell, G., 2004. Modelling the absorption and desorption of cadmium on paper pulp using kinetic approaches. Chemosphere 55, 869-878]. It then provides suggestions on improving the effectiveness of the model.