Comparison of a new Eulerian model with a modified Lagrangian approach for particle distribution and deposition indoors

Understanding of aerosol dispersion characteristics has many scientific and engineering applications. It is recognized that Eulerian or Lagrangian approach has its own merits and limitations. A new Eulerian model has been developed and it adopts a simplified drift–flux methodology in which external forces can be incorporated straightforwardly. A new near-wall treatment is applied to take into account the anisotropic turbulence for the modified Lagrangian model. In the present work, we present and compare both Eulerian and Lagrangian models to simulate particle dispersion in a small chamber. Results reveal that the standard k–ε Lagrangian model over-predicts particle deposition compared to the present turbulence-corrected Lagrangian approach. Prediction by the Eulerian model agrees well with the modified Lagrangian model.     

An efficient Lagrangian stochastic model of vertical dispersion in the convective boundary layer

We consider the one-dimensional case of vertical dispersion in the convective boundary layer (CBL) assuming that the turbulence field is stationary and horizontally homogeneous. The dispersion process is simulated by following Lagrangian trajectories of many independent tracer particles in the turbulent flow field, leading to a prediction of the mean concentration. The particle acceleration is determined using a stochastic differential equation, assuming that the joint evolution of the particle velocity and position is a Markov process. The equation consists of a deterministic term and a random term. While the formulation is standard, attention has been focused in recent years on various ways of calculating the deterministic term using the well-mixed condition incorporating the Fokker–Planck equation. Here we propose a simple parameterisation for the deterministic acceleration term by approximating it as a quadratic function of velocity. Such a function is shown to represent well the acceleration under moderate velocity skewness conditions observed in the CBL. The coefficients in the quadratic form are determined in terms of given turbulence statistics by directly integrating the Fokker–Planck equation. An advantage of this approach is that, unlike in existing Lagrangian stochastic models for the CBL, the use of the turbulence statistics up to the fourth order can be made without assuming any predefined form for the probability distribution function (PDF) of the velocity. The main strength of the model, however, lies in its simplicity and computational efficiency. The dispersion results obtained from the new model are compared with existing laboratory data as well as with those obtained from a more complex Lagrangian model in which the deterministic acceleration term is based on a bi-Gaussian velocity PDF. The comparison shows that the new model performs well.     

A fluctuating plume model for concentration fluctuations in a plant canopy

A one-particle Lagrangian model for continuous releases in the non-Gaussian inhomogeneous turbulence of a canopy layer is derived based on the fluctuating plume model of Franzese [2003. Lagrangian stochastic modeling of a fluctuating plume in the convective boundary layer. Atmos. Environ. 37, 1691–1701.]. The model equations are filtered by a time-dependent low-pass filter applied to the turbulent kinetic energy in order to obtain a fluctuating plume model able to simulate the vertical meandering of the cloud centroid through non-stationary Lagrangian equations. The model satisfies the well-mixed condition. The relative dispersion of particles and the concentration fluctuation statistics of a passive tracer inside a modeled vegetal canopy are studied. The probability density function of the concentration relative to the plume centroid is parameterized and the mean and variance fields of concentration are simulated and compared with wind-tunnel data and numerical simulations. A skewed, reflected probability density function for the vertical position of the plume centroid is considered.     

Modelling dispersion of traffic pollution in a deep street canyon: Application of CFD and operational models

In this study, numerical modelling of the flow and concentration fields has been undertaken for a deep street canyon in Naples (Italy), having aspect ratio (i.e. ratio of the building height H to the street width W) H/W = 5.7. Two different modelling techniques have been employed: computational fluid dynamics (CFD) and operational dispersion modelling. The CFD simulations have been carried out by using the RNG k–? turbulence model included in the commercial suite FLUENT, while operational modelling has been conducted by means of the WinOSPM model. Concentration fields obtained from model simulations have been compared with experimental data of CO concentrations measured at two vertical locations within the canyon. The CFD results are in good agreement with the experimental data, while poor agreement is observed for the WinOSPM results. This is because WinOSPM was originally developed and tested for street canyons with aspect ratio H/W ≌ 1. Large discrepancies in wind profiles simulated within the canyon are observed between CFD and OSPM models. Therefore, a modification of the wind profile within the canyon is introduced in WinOSPM for extending its applicability to deeper canyons, leading to an improved agreement between modelled and experimental data. Further development of the operational dispersion model is required in order to reproduce the distinct air circulation patterns within deep street canyons.     

A statistical approach for estimating uncertainty in dispersion modeling: An example of application in southwestern USA

A method based on a statistical approach of estimating uncertainty in simulating the transport and dispersion of atmospheric pollutants is developed using observations and modeling results from a tracer experiment in the complex terrain of the southwestern USA. The method takes into account the compensating nature of the error components by representing all terms, except dispersion error and variance of stochastic processes. Dispersion error and the variance of the stochastic error are estimated using the maximum likelihood estimation technique applied to the equation for the fractional error. Mesoscale Model 5 (MM5) and a Lagrangian random particle dispersion model with three optional turbulence parameterizations were used as a test bed for method application. Modeled concentrations compared well with the measurements (correlation coefficients on the order of 0.8). The effects of changing two structural components (the turbulence parameterization and the model grid vertical resolution) on the magnitude of the dispersion error also were examined. The expected normalized dispersion error appears to be quite large (up to a factor of three) among model runs with various turbulence schemes. Tests with increased vertical resolution of the atmospheric model (MM5) improved most of the dispersion model statistical performance measures, but to a lesser extent compared to selection of a turbulence parameterization. Method results confirm that structural components of the dispersion model, namely turbulence parameterizations, have the most influence on the expected dispersion error.     

CFD modelling of small particle dispersion: The influence of the turbulence kinetic energy in the atmospheric boundary layer

When considering the modelling of small particle dispersion in the lower part of the Atmospheric Boundary Layer (ABL) using Reynolds Averaged Navier Stokes simulations, the particle paths depend on the velocity profile and on the turbulence kinetic energy, from which the fluctuating velocity components are derived to predict turbulent dispersion. It is therefore important to correctly reproduce the ABL, both for the velocity profile and the turbulence kinetic energy profile.For RANS simulations with the standard k–ε model, Richards and Hoxey (1993. Appropriate boundary conditions for computational wind engineering models using the k–ε turbulence model. Journal of Wind Engineering and Industrial Aerodynamics 46–47, 145–153.) proposed a set of boundary conditions which result in horizontally homogeneous profiles. The drawback of this method is that it assumes a constant profile of turbulence kinetic energy, which is not always consistent with field or wind tunnel measurements. Therefore, a method was developed which allows the modelling of a horizontally homogeneous turbulence kinetic energy profile that is varying with height.By comparing simulations performed with the proposed method to simulations performed with the boundary conditions described by Richards and Hoxey (1993. Appropriate boundary conditions for computational wind engineering models using the k–ε turbulence model. Journal of Wind Engineering and Industrial Aerodynamics 46–47, 145–153.), the influence of the turbulence kinetic energy on the dispersion of small particles over flat terrain is quantified.     

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.     

Evaluation of a Gaussian and a Lagrangian model against a roadside data set,with emphasis on low wind speed conditions

The evaluation of the high percentiles of concentration distributions is required by most national air quality guidelines, as well as the EU directives. However, it is problematic to compute such high percentiles in stable, low wind speed or calm conditions. This study utilizes the results of a previous measurement campaign near a major road at Elimäki in southern Finland in 1995, a campaign specifically designed for model evaluation purposes. In this study, numerical simulations were performed with a Gaussian finite line source dispersion model CAR-FMI and a Lagrangian dispersion model GRAL, and model predictions were compared with the field measurements. In comparison with corresponding results presented previously in the literature, the agreement of measured and predicted data sets was good for both models considered, as measured using various statistical parameters. For instance, considering all NO_x data (N=587), the so-called index of agreement values varied from 0.76 to 0.87 and from 0.81 to 1.00 for the CAR-FMI and GRAL models, respectively. The CAR-FMI model tends to slightly overestimate the NO_x concentrations (fractional bias FB=+14%), while the GRAL model has a tendency to underestimate NO_x concentrations (FB=−16%). The GRAL model provides special treatment to account for enhanced horizontal dispersion in low wind speed conditions; while such adjustments have not been included in the CAR-FMI model. This type of Lagrangian model therefore predicts lower concentrations, in conditions of low wind speeds and stable stratification, in comparison with a standard Lagrangian model. In low wind speed conditions the meandering of the flow can be quite significant, leading to enhanced horizontal dispersion. We also analyzed the difference between the model predictions and measured data in terms of the wind speed and direction. The performance of the CAR-FMI model deteriorated as the wind direction approached a direction parallel to the road, and for the lowest wind speeds. However, the performance of the GRAL model varied less with wind speed and direction; the model simulated better the cases of low wind speed and those with the wind nearly parallel to the road.     

An Atmospheric Dispersion Model for the Environmental Impact Assessment of Thermal Power Plants in Japan—A Method for Evaluating Topographical Effects

Abstract

An atmospheric dispersion model was developed for the environmental impact assessment of thermal power plants in Japan, and a method for evaluating topographical effects using this model was proposed. The atmospheric dispersion model consists of an airflow model with a turbulence closure model based on the algebraic Reynolds stress model and a Lagrangian particle dispersion model (LPDM). The evaluation of the maximum concentration of air pollutants such as SO₂, NO_x, and suspended particulate matter is usually considered of primary importance for environmental impact assessment. Three indices were therefore estimated by the atmospheric dispersion model: the ratios (α and β, respectively) of the maximum concentration and the distance of the point of the maximum concentration from the source over topography to the respective values over a flat plane, and the relative concentration distribution [γ(x)] along the ground surface projection of the plume axis normalized by the maximum concentration over a flat plane. The atmospheric dispersion model was applied to the topography around a power plant with a maximum elevation of more than 1000 m. The values of α and β evaluated by the atmospheric dispersion model varied between 1 and 3 and between 1 and 0.4, respectively, depending on the topographical features. These results and the calculated distributions of γ(x) were highly similar to the results of the wind tunnel experiment. Therefore, when the slope of a hill or mountain is similar to the topography considered in this study, it is possible to evaluate topographical effects on exhaust gas dispersion with reasonable accuracy using the atmospheric dispersion model as well as wind tunnel experiments.     

Large-eddy simulation of pollution dispersion in an urban street canyon—Part II: idealised canyon simulation

Three-dimensional large-eddy simulations are performed with the dynamic sub-grid scale model for an idealised urban canyon with pollution modelled as a passive scalar. In addition to concentration distributions, turbulence statistics for the canyon are presented. Higher turbulence intensities are predicted in the core of the vortex compared to the widely used k–ε model. This results in a more homogeneous distribution of pollutants, in agreement with experimental studies reported in the literature. Regions of enhanced turbulence are also observed near the walls leading to a lateral dispersion of pollutants along the canyon. The centre of the vortex is observed to precess around the canyon and also meanders along the length of the canyon. Puffs of pollution are ejected from the top of canyons intermittently rather than smoothly, with a characteristic time scale of the order of 30–60 s.     

Monte Carlo simulation of nitrogen oxides dispersion from a vehicular exhaust plume and its sensitivity studies

The pollutant dispersion behavior from the vehicular exhaust plume has a direct impact on human health, particularly to the drivers, bicyclists, motorcyclists, pedestrians, people working nearby and vehicle passengers. A two-dimensional pollutant dispersion numerical model was developed based on the joint-scalar probability density function (PDF) approach coupled with a k–ε turbulence model to simulate the initial dispersion process of nitrogen oxides, temperature and flow velocity distributions from a vehicular exhaust plume. A Monte Carlo algorithm was used to solve the PDF transport equations in order to obtain the dispersion distribution of nitrogen oxides concentration. The model was then validated by a series of sensitivity experimental studies in order to assess the effects of vehicular exhaust tailpipe velocities, wind speeds and chemistry on the initial dispersion of NO and NO₂ mass concentrations from the vehicular exhaust plume. The results show that the mass concentrations of nitrogen oxides decrease along the centerline of the vehicular exhaust plume in the downstream distance. The dispersion process can be enhanced when the vehicular exhaust tailpipe velocity is much larger than the wind speed. The oxidation reaction of NO plays an important role when the wind speed is large and the vehicular exhaust exit velocity is small, which leads to chemical reduction of NO, and the formation and accumulation of NO₂ in the exhaust plume. It is also found that the effect of vehicular exhaust-induced turbulence in the vicinity of the exhaust tailpipe exit is more dominant than the effect of wind turbulence, while the wind turbulence gradually shows a significant role for the dispersion of nitrogen oxides along with the development of exhaust plume. The range of dispersion of nitrogen oxides in the radial direction is increased along with the development of vehicular exhaust plume.     

Numerical simulation of flow and dispersion around an isolated cubical building: The effect of the atmospheric stratification

The aim of this work is to investigate atmospheric flow and dispersion of contaminants in the vicinity of single buildings under different stability conditions. The mathematical model used is based on the solution of equations of conservation of mass, linear momentum and energy with the use of a non-standard κ–? turbulence model. The modifications proposed in the κ–? model are the inclusion of the Kato and Launder correction in the production of turbulent kinetic energy and the use of a modified wall function. Results are presented of numerical simulations of dispersion around a cubical obstacle, under neutral, stable and unstable atmospheric conditions. Experimental data from wind tunnel and field trials obtained by previous authors are used to validate the numerical results. The numerical simulation results show a reasonable level of agreement with field and wind tunnel concentration data. The deviation between model results and field experimental data is of the same order as the deviation between field and wind tunnel data.     

Numerical modeling on air quality in an urban environment with changes of the aspect ratio and wind direction

Due to heavy traffic emissions within an urban environment, air quality during the last decade becomes worse year by year and hazard to public health. In the present work, numerical modeling of flow and dispersion of gaseous emissions from vehicle exhaust in a street canyon were investigated under changes of the aspect ratio and wind direction. The three-dimensional flow and dispersion of gaseous pollutants were modeled using a computational fluid dynamics (CFD) model which was numerically solved using Reynolds-averaged Navier–Stokes (RANS) equations. The diffusion flow field in the atmospheric boundary layer within the street canyon was studied for different aspect ratios (W/H?=?1/2, 3/4, and 1) and wind directions (θ?=?90°, 112.5°, 135°, and 157.5°). The numerical models were validated against wind tunnel results to optimize the turbulence model. The numerical results agreed well with the wind tunnel results. The simulation demonstrated that the minimum concentration at the human respiration height within the street canyon was on the windward side for aspect ratios W/H?=?1/2 and 1 and wind directions θ?=?112.5°, 135°, and 157.5°. The pollutant concentration level decreases as the wind direction and aspect ratio increase. The wind velocity and turbulence intensity increase as the aspect ratio and wind direction increase.     

Use of an inverse dispersion technique for estimating ammonia emission from surface-applied slurry

Ammonia (NH₃) emission from land application of manure is typically measured using the integrated horizontal flux (IHF) micrometeorological method. However, there are some situations in which alternative techniques (such as an inverse dispersion modelling technique) might be preferable, for example when measuring from large or irregularly shaped source areas. In this study, an inverse dispersion technique using the backward Lagrangian stochastic (bLS) model, with 2 different experimental configurations, was compared with the Integrated Horizontal Flux method (i.e. IHF), which was used as reference technique. Pig slurry was surface-applied at 125 kg N ha^?1 to bare soil on a large plot (80 × 125 m). Cumulative emissions were 19.3, 21.2 and 18.4 kg N ha^?1 from the IHF and the bLS technique (experimental configurations I and II), respectively. Mean flux within each sampling period as estimated by the two techniques compared extremely well, with a slope not significantly different from 1 and r² of 0.99. Although limited in extent, this dataset agree with a previous study in demonstrating the use of the bLS technique with longer period time-averaged concentration measurements.     

Flow and dispersion in an urban cubical cavity

Flow and dispersion in an urban cubical cavity are numerically investigated using a Reynolds-averaged Navier–Stokes equations (RANS) model with the renormalization group (RNG) k–? turbulence closure model. The urban cubical cavity is surrounded by flank walls that are parallel to the streamwise direction, called end-walls, as well as upstream and downstream walls. A primary vortex and secondary vortices including end-wall vortices are formed in the cavity. Because of the end-wall drag effect, the averaged mean-flow kinetic energy in the cavity is smaller than that in an urban street canyon that is open in the along-canyon direction. A trajectory analysis shows that the end-wall vortices cause fluid particles to move in the spanwise direction, indicating that flow in the cavity is essentially three-dimensional. The iso-surfaces of the Okubo–Weiss criterion capture cavity vortices well. The pollutant concentration is high near the bottom of the upstream side in the case of continuous pollutant emission, whereas it is high near the center of the primary vortex in the case of instantaneous pollutant emission. To get some insight into the degree of pollutant escape from the cavity according to various meteorological factors, extensive numerical experiments with different ambient wind speeds and directions, inflow turbulence intensities, and cavity-bottom heating intensities are performed. For each experiment, we calculate the time constant, which is defined as the time taken for the pollutant concentration to decrease to e^?1 of its initial value. The time constant decreases substantially with increasing ambient wind speed, and tends to decrease with increasing inflow turbulence intensity and cavity-bottom heating intensity. The time constant increases as the ambient wind direction becomes oblique. High ambient wind speed is found to be the most crucial factor for ventilating the cavity, thus improving air quality in an urban cubical cavity.     

Large-eddy simulation of pollution dispersion in an urban street canyon—Part I: comparison with field data

Large-eddy simulations (LESs) are applied to the problem of pollution dispersion within the urban canopy layer, specifically street canyons. The objective is to study the turbulence structure and hence the physical dispersion mechanisms of pollutants. LESs are implemented by incorporating the dynamic sub-grid scale stress model into the commercial computational fluids dynamics code CFX. To gain confidence in the approach, simulations are performed for a canyon-like geometry (roof garden) for which experimental measurements were also made. The experimental campaign consisted of using sonic anemometers to measure mean flow and turbulence intensities at a high sample rate of 60 Hz. Good agreement between simulations and experimental data are obtained. Real geometric features, such as non-uniform wall heights, result in a very much three-dimensional flow distribution. Comparisons with the k–ε model show that LESs are able to predict more accurately the turbulence statistics of the flow.     

Applied dispersion modelling based on meteorological scaling parameters

A method for calculating the dispersion of plumes in the atmospheric boundary layer is presented. The method is easy to use on a routine basis. The inputs to the method are fundamental meteorological parameters, which act as distinct scaling parameters for the turbulence. The atmospheric boundary layer is divided into a number of regimes. For each scaling regime we suggest models for the dispersion in the vertical direction. The models directly give the crosswind-integrated concentrations at the ground, x_y, for nonbuoyant releases from a continuous point source. Generally the vertical concentration profile is proposed to be other than Gaussian. The lateral concentration profile is always assumed to be Gaussian, and models for determining the lateral spread σ_y are proposed. The method is limited to horizontally homogeneous conditions and travel distances less than 10km. The method is evaluated against independent tracer experiments over land. The overall agreement between measurements and predictions is very good and better than that found with the traditional Gaussian plume model.     

A numerical experiment of roadside diffusion under traffic-produced flow and turbulence

Roadside air pollution due to heavy traffic is one of the unsettled issues in the atmospheric environment in urban areas. As a practical application of a Computational Fluid Dynamics (CFD) model, a coupled mesoscale-CFD model was applied to the Ikegamicho area of Kawasaki City, Japan. For this study, the effects of traffic-produced flow and turbulence (TPFT) on the dispersion of the pollutants near the heavy traffic road were mainly investigated in an actual urban area. First, a series of preliminary CFD calculations was conducted for a road tunnel field experiment to obtain a fitting parameter for the traffic-produced flow. The calculation was then performed for 24 h in December 2005 around Ikegamicho, and the results were compared with the data at a roadside monitoring post in the area, located 10 m from the boundary of the ground road. In general, the effect of traffic-produced flow and turbulence was limited at the downstream side of the roads. The maximum concentration of NO_x was reduced and smoothed out along the traffic flow by the traffic-produced flow and turbulence on the road. The effects of traffic-produced turbulence on the dispersion of pollutants were greater than those of traffic-produced flow; however, the effects of traffic-produced flow were not negligible. The concentration of pollutants was not particularly dependent on the turbulent Schmidt number because most of the emission sources were introduced as volume sources in the present calculations, and the effect caused by differences in the material diffusion coefficient was not particularly significant at the outside of the road.     

Comparison of PDFs, closure schemes and turbulence parameterisations in Lagrangian stochastic models

Six one-dimensional models, based on the Ito-type stochastic equation, are presented and compared. Four of these take into account up to the fourth order moment of vertical velocity fluctuations, and two up to the third order moment. Four models make use of a bi-Gaussian probability density function (PDF) and the other two are based on a Gram-Charlier series expansion truncated to the third or fourth order. All the models were run with a parameterisation of input turbulence (i.e. w², w³, and τ profiles). Concerning the fourth order moment w⁴, two different parameterisations were considered. Comparisons are made between ground-level concentrations, plume height and plume width observed in the Willis and Deardorff water tank experiments and those predicted by the different models here considered. The goal of this study was to find the models that give greater confidence in their applicability in dispersion studies and to verify the importance of considering the fourth order moment. The main conclusions are: simulation results largely depend on the turbulence parameterisation chosen; the Gram-Charlier PDF gives the best agreement with observations; some combinations of models and turbulence parameterisations perform well in simulating the shape of the ground-level concentration (g.1.c.) trend but fail in correctly simulating the form of the plume (plume height and vertical width); in the case of the Gram-Charlier PDF, the fourth order model reproduced the vertical plume width better than the third order one, whereas the two schemes yielded similar g.1.c. distributions.