Lagrangian Stochastic Particle Model Research Articles

A 3D Lagrangian stochastic particle model for the concentration variance dispersion

A new scheme for the concentration variance calculation is assessed using field experiment data. The scheme is introduced in a Lagrangian stochastic particle model. The model provides run-time mean concentrations and concentrations’ variance 3D fields; thus, it does not need any off-line post-processing. The model is tested against the FFT-07 field experiment which involves a series of tracer releases. It is a short-range (500 m) highly instrumented experiment. In this work, measurement of tracer concentrations, emitted from a ground level point source is used to assess the ability of the new model in predicting the mean concentration, concentration variance, and the concentration fluctuation intensity at the ground level with a high spatial resolution. The results of the intercomparison are shown and discussed in terms of statistical plots and indices.

A Stochastic Single-Particle Lagrangian Model for the Concentration Fluctuations in a Plume Dispersing Inside an Urban Canopy

A new approach for estimating concentration fluctuations intensity in dense built-up environments using a Lagrangian stochastic (LS) particle model is described. Following past success in modelling the dynamics of concentration variance as a diffusion-advection process, the ensemble-averaged concentration variance is represented by particles that advect and diffuse throughout the computational domain. The calculation of the concentration variance is addressed by assuming an appropriate distribution of effective variance sources for a given mean concentration field. Dissipation is treated by allowing the variance carried by every particle to decay exponentially with a locally-estimated decay time. The approach has the benefit of easily handling complex boundary conditions. It can also be easily and naturally implemented as an extension to an existing LS model, which is used for mean concentration estimations. The method differs from existing two-particle methods that demand knowledge of the structure function of the flow. It is also more computationally efficient than micro-mixing approaches that involve maintaining high population levels of particles in every grid volume. The model is compared with high frequency concentration measurements, taken as part of the JU2003 (Joint Urban 2003) experiment that was carried out in Oklahoma City. Good agreement is observed.

First-Order Inconsistencies Caused by Rogue Trajectories

A theoretical requirement of the Interaction by Exchange with the Conditional Mean (IECM) micromixing model is that the mean concentration field produced by it must be consistent with the mean concentration field produced by a traditional Lagrangian stochastic (LS) marked particle model. We examine the violation of this requirement that occurs in a coupled LS-IECM model when unrealistically high particle velocities occur. No successful strategy was found to mitigate the effects of these rogue trajectories. It is our hope that this work will provide renewed impetus for investigation into rogue trajectories and methods to eliminate them from LS models.

Turbulent dispersion of a gas tracer in a nocturnal atmospheric flow

A Lagrangian turbulent dispersion model has been coupled with the Regional Atmospheric Modelling System (RAMS) to predict the transport, dispersion and concentration of a gas tracer released into a stable atmosphere (nocturnal drainage flow) of the Anderson Springs Valley near San Francisco, California. The mean wind velocities governed by the topography of the region and the surface layer fluxes of momentum and heat into the stable atmosphere, were calculated by the RAMS code. The atmospheric transport and dispersion of a gas tracer was simulated in non-homogeneous turbulence conditions by using a Lagrangian Stochastic Particle Model. A Moving Least Squares technique was used to calculate the tracer gas concentration. The vertical profiles of the mean wind speed and the wind direction, as well as the tracer gas concentration, were compared with the field measurements for the fourth night of the ASCOT experiment (the night between 19 and 20 September 1980) carried out in the Anderson Springs Valley, California, USA The computed profiles for wind direction and wind speed agreed well with the field data. Although at some locations the model predicted strong winds which transported the particle to larger distances downwind, the overall pattern of concentration distribution generated by the model compared quite well with the observations. It was concluded that the concentration patterns tend to follow the topography when the synoptic winds are weak.

Difusão de contaminantes em condições de vento fraco empregando um modelo estocástico Lagrangeano

Um modelo estocástico Lagrangeano é utilizado para simular a dispersão e o transporte de contaminantes, sob condições estáveis, com velocidade do vento fraco, no experimento traçante realizado no Idaho National Engineering Laboratory (INEL). Neste trabalho é testada uma nova parametrização dos parâmetros que representam as freqüências associadas ao fenômeno de meandro do vento, presentes nas equações de Langevin para as componentes do vento horizontal. Esta nova parametrização é descrita em termos de uma quantidade adimensional que controla a freqüência de oscilação de meandro do vento e da escala de tempo, associada às estruturas coerentes em uma turbulência bem desenvolvida. As simulações demonstram que o modelo Lagrangeano considerado, incorporando esta nova parametrização, reproduz corretamente a difusão de escalares passivos em uma camada limite atmosférica estável com velocidade do vento fraco.

Simulation of atmospheric dispersion of radionuclides using an Eulerian–Lagrangianmodelling system

In this paper we present an atmospheric dispersion scenario for a proposed nuclear powerplant in Pakistan involving the hypothetical accidental release of radionuclides. Forthis, a concept involving a Lagrangian stochastic particle model (LSPM) coupledwith an Eulerian regional atmospheric modelling system (RAMS) is used. Theatmospheric turbulent dispersion of radionuclides (represented by non-buoyantparticles/neutral traces) in the LSPM is modelled by applying non-homogeneousturbulence conditions. The mean wind velocities governed by the topography of the regionand the surface fluxes of momentum and heat are calculated by the RAMS code.A moving least squares (MLS) technique is introduced to calculate the concentration ofradionuclides at ground level. The numerically calculated vertical profiles of wind velocityand temperature are compared with observed data. The results obtained demonstrate thatin regions of complex terrain it is not sufficient to model the atmospheric dispersion ofparticles using a straight-line Gaussian plume model, and that by utilising a Lagrangianstochastic particle model and regional atmospheric modelling system a much more realisticestimation of the dispersion in such a hypothetical scenario was ascertained. The particledispersion results for a 12 h ground release show that a triangular area of about400 km2 situated in the north-west quadrant of release is under radiological threat. The particledistribution shows that the use of a Gaussian plume model (GPM) in such situations willyield quite misleading results.

Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation

A Lagrangian stochastic (LS) model, which is embedded into a parallelised large-eddy simulation (LES) model, is used for dispersion and footprint evaluations. For the first time an online coupling between LES and LS models is applied. The new model reproduces concentration patterns, which were obtained in prior studies, provided that subgrid-scale turbulence is included in the LS model. Comparisons with prior studies show that the model evaluates footprints successfully. Streamwise dispersion leads to footprint maxima that are situated less far upstream than previously reported. Negative flux footprints are detected in the convective boundary layer (CBL). The wide range of applicability of the model is shown by applying it under neutral and stable stratification. It is pointed out that the turning of the wind direction with height leads to a considerable dependency of source areas on height. First results of an application to a heterogeneously heated CBL are presented, which emphasize that footprints are severely affected by the inhomogeneity.

Particle simulations of dispersion using observed meandering and turbulence

A Lagrangian stochastic particle model driven by observed winds from a network of 13 sonic anemometers is used to simulate the transport of contaminates due to meandering of the mean wind vector and diffusion by turbulence. The turbulence and the meandering motions are extracted from the observed velocity variances using a variable averaging window width. Such partitioning enables determination of the separate contributions from turbulence and meandering to the total dispersion. The turbulence is described by a Markov Chain Monte Carlo process based on the Langevin equation using the observed turbulence variances. The meandering motions, not the turbulence, are primarily responsible for the 1-h averaged horizontal dispersion as measured by the travel time dependence of the particle position variances. As a result, the 1-h averaged horizontal concentration patterns are often characterized by streaks and multi-modal distributions. Time series of concentration at a fixed location are highly nonstationary even when the 1-h averaged spatial distribution is close to Gaussian. The results show that meandering dominates the travel-time dependence of the horizontal dispersion under all atmospheric conditions: weak and strong winds, and unstable and stable stratification.

Efficiently characterizing the origin and decay rate of a nonconservative scalar using probability theory

We present a methodology for estimating parameters which describe the source location and strength, as well as the rate of transformation, of a passive, nonconservative scalar released into (or already present in) the atmosphere. A finite number of uncertain (noisy) concentration measurements is the primary source of information for the source reconstruction, which implies that the problem is ill-posed and must be solved using a Bayesian probabilistic inferential framework. All parameters are estimated simultaneously and the model describing the forward problem (prediction of the dispersion of a contaminant given its source and rate of decay) is computationally demanding, so the capability to efficiently calculate the solution to the inverse problem is crucial. It is demonstrated how a backward Lagrangian stochastic particle model facilitates the rapid characterization of the source location and strength, while by monitoring the statistical properties of the particle travel times, the rate of transformation of the agent can be efficiently estimated. Markov chain Monte Carlo is used to sample from the multi-dimensional domain of definition of the posterior probability density function that results from applying Bayes’ theorem. The overall methodology is validated in two stages. First, the source reconstruction approach is tested using concentration data measured during an experiment in which a conservative scalar was continuously released from a point source into a statistically stationary flow in a horizontally homogeneous and neutrally stratified atmospheric surface layer (Project Prairie Grass). Next, the reconstruction approach is applied to synthetic concentration data generated using a Lagrangian stochastic model operating under the same atmospheric conditions, with decay of particle mass being modelled by a straightforward first-order mechanism.

Derivation of a decorrelation timescale depending on source distance for inhomogeneous turbulence in a convective boundary layer

Considering the convective boundary layer physical structure and their characteristics, a derivation for the Lagrangian decorrelation timescales to be used in Lagrangian stochastic particle models has been developed. That is, expressions for the Lagrangian decorrelation timescales depending on source distance for inhomogeneous turbulence are proposed. The classical statistical diffusion theory, the observed spectral properties and observed characteristics of energy-containing eddies are used to estimate these parameters. In addition, these decorrelation timescales were introduced in an Lagrangian stochastic particle model and validated with the data of Copenhagen experiments. The results of this new method are shown to agree very well with the measurements of Copenhagen. Furthermore, the present study suggests that the inclusion of the memory effect, important in near regions from an elevated continuous point source, improves the description of the turbulent transport process of atmospheric contaminants. The major advance shown in this paper is the necessity of including the downwind distance-dependent decorrelation timescales in air quality modeling, and it is demonstrated that such theory would suggest that it should yield better results than the asymptotic solution alone. It in fact does yields better results in the near and intermediate fields.

Parameterization of meandering phenomenon in a stable atmospheric boundary layer

Accounting for the current knowledge of the stable atmospheric boundary layer (ABL) turbulence structure and characteristics, a new formulation for the meandering parameters to be used in a Lagrangian stochastic particle turbulent diffusion model has been derived. That is, expressions for the parameters controlling the meandering oscillation frequency in low wind speed stable conditions are proposed. The classical expression for the meandering autocorrelation function, the turbulent statistical diffusion theory and ABL similarity theory are employed to estimate these parameters. In addition, this new parameterization was introduced into a particular Lagrangian stochastic particle model, which is called Iterative Langevin solution for low wind, validated with the data of Idaho National Laboratory experiments, and compared with others diffusion models. The results of this new approach are shown to agree with the measurements of Idaho experiments and also with those of the other atmospheric diffusion models. The major advance shown in this study is the formulation of the meandering parameters expressed in terms of the characteristic scales (velocity and length scales) describing the physical structure of a turbulent stable boundary layer. These similarity formulas can be used to simulate meandering enhanced diffusion of passive scalars in a low wind speed stable ABL.

A heuristic Lagrangian stochastic particle model of relative diffusion: model formulation and preliminary results

A new method is proposed to calculate two-particle statistics of turbulent diffusion in complex flows. The method is a combination of a single-particle Lagrangian stochastic model and a two-particle model applicable to isotropic turbulence. An encouraging preliminary evaluation of the method is presented.

Computation of Particle-Laden Turbulent Gas Flows Using Two Dispersion Models

Ahybrid Eulerian‐ Lagrangianmodelwasused tostudy thesolidparticles,witha meandiameterof49 :3πmand a standard deviation of 4 :85πm, dispersing from a turbulent wall-adjacent gaseous jet. Two Lagrangian particle dispersion models, the conventional stochastic discrete delta function model and a recently developed stochasticprobabilistic efe ciency-enhanced dispersion (SPEED) model, were used to account for the particle dispersion induced by gas turbulence. The present work also investigated theeffects of two different methods for determining the particle‐ eddy interaction time on the predicted particle property. Numerical predictions obtained with the different models using the conventional and modie ed particle‐ eddy interaction timescales were compared with each other and with experimental measurements. It was found that betteragreementwith experimental data could be achieved by using the modie ed particle‐ eddy interaction timescale. Moreover, it was demonstrated that the SPEED model could not only signie cantly improvethe computational efe ciency of the trajectory solver by a factor of 10 for the present e ow considered but also yield smoother proe les and better agreement with the measurements than could the conventional Lagrangian stochastic discrete particle model.

Lagrangian stochastic particle model simulations of turbulent dispersion around buildings

Abstract This paper describes a numerical modeling approach that can be used to provide estimates of air concentrations due to emissions at industrial sites or other sites where buildings may have an important impact on the dispersion patterns. The procedure consists of two sequential steps: (i) Prediction of mean flow and turbulence fields via a turbulent flow model; and, (ii) Employment of the calculated flow and turbulence fields to drive a Lagrangian stochastic particle model. Two flow scenarios are used as input to a Lagrangian model; the scenarios assume neutral atmospheric conditions and incoming winds that are from 270 and 240°. The problem configuration for the first calculation is based on an earlier transport and diffusion simulation that employed an existing particle-in-cell flux-gradient dispersion model. The second simulation is used to demonstrate the strong spatial variations that the concentration field exhibit within the highly complex separation zones of building wakes. The relationship between concentration levels and toxic load are discussed for the case of a chemical spill.