Concentration field and turbulent fluxes during the mixing of two buoyant plumes

In this work an experimental study of mixing of two identical plumes, carried out in a turbulent neutral boundary layer generated in a wind tunnel, is presented. Measurements have been performed with fast flame ionisation detectors (FFIDs) and a two-component Laser-Doppler Anemometer system. Results allow the study of both the average and the fluctuating concentration field, including the turbulent vertical and longitudinal mass fluxes, in single plumes and during the interaction of two identical plumes. This information gives insight into the details of the mixing phase of the two plumes. Results of trajectories and additional rise (due to plume interactions) have been compared with previous measurements carried out in laminar cross-flows, showing similar behaviour. Concentration distributions in plume cross-sections in turbulent cross-flows differ from those measured in laminar cross-flows. Average vertical and longitudinal velocity measurements into the plume core show the strength of the shielding effect of the upwind plume and some details of interaction between the counter-rotating vortex pairs (CVPs). For large values of the alignment angle φ, between the line joining the stacks and the cross-flow, an average negative vertical velocity is measured in the middle of the plume even if its centre of mass is rising. This downward velocity is induced by the slow interaction of the CVPs and generates a vertical stretching of the plume and negative rise enhancement. Vertical turbulent fluxes change sign on the plume centreline and are of opposite sign with respect to the longitudinal turbulent fluxes. Results indicate a good linearity between vertical turbulent fluxes and concentration gradients, with different proportionality for the top and bottom parts of the plume (especially in the near field) indicating that dispersion could be described by a gradient-transfer model.     

Validation of a Lagrangian model plume rise scheme using the Kincaid data set

Correct prediction of the initial rise of a plume due to momentum and buoyancy effects is an important factor in dispersion modelling. A new plume rise scheme, based upon conservation equations of mass, momentum and heat, for the Lagrangian model, NAME, is described. The conservation equations are consistent with the well-known analytical plume rise formulae for both momentum- and buoyancy-dominated plumes. The performance of the new scheme is assessed against data from the Kincaid field experiment. Results show that the new scheme adds value to the model and significantly outperforms the previous plume rise scheme. Using data from assessments of atmospheric dispersion models using the Kincaid data set, it is shown that NAME is comparable to other models over short ranges.     

A simple and fast model to compute concentration moments in a convective boundary layer

Recently, a modified meandering plume model for concentration fluctuations in a convective boundary layer has been formulated (Atmos. Environ. 34 (2000) 3599). This model is based on a hybrid Eulerian–Lagrangian approach and it accounts for the skewed and inhomogeneous turbulence characteristics of the convective flow. Using the same hypotheses, but eliminating the need for Lagrangian particle model, we propose a generalised approach, that only requires the knowledge of mean concentration field. The proposed model is independent from the method used to obtain the mean concentration field. The evaluation of the concentration fluctuation field needs a computational time of only few seconds on a standard PC. Therefore, the model is suitable for practical applications.     

Evaluation of a long-range lagrangian dispersion model with ETEX

Performance of a Lagrangian dispersion model was examined in connection with its dependency on the boundary layer modelling and the input data resolution. The European Tracer Experiment (ETEX) data were used as reference. According to the sensitivity analysis of the model performance, the long-range dispersion model with the sparse input data was not noticeably different from that with the finer resolution data. The assumption of the prescribed constant mixing depth did not largely degrade the prediction results as compared with the simulation results with the temporally changing boundary layer. It is, therefore, concluded that the model is practical, considering the limited input data in the operational mode. However, it was also pointed out that the parameterization for the horizontal and vertical diffusion processes used in the present model enhanced the growth of plume. The improvement of input data resolution in time and space caused further dispersion of tracer deterministically. These resulted in the underestimation of the maximum concentration and the unfocussed concentration distribution map although the mean concentration was predicted fairly well.     

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.     

Development and evaluation of the PRIME plume rise and building downwash model

A new Gaussian dispersion model, the Plume Rise Model Enhancements (PRIME), has been developed for plume rise and building downwash. PRIME considers the position of the stack relative to the building, streamline deflection near the building, and vertical wind speed shear and velocity deficit effects on plume rise. Within the wake created by a sharp-edged, rectangular building, PRIME explicitly calculates fields of turbulence intensity, wind speed, and streamline slope, which gradually decay to ambient values downwind of the building. The plume trajectory within these modified fields is estimated using a numerical plume rise model. A probability density function and an eddy diffusivity scheme are used for dispersion in the wake. A cavity module calculates the fraction of plume mass captured by and recirculated within the near wake. The captured plume is re-emitted to the far wake as a volume source and added to the uncaptured primary plume contribution to obtain the far wake concentrations. The modeling procedures currently recommended by the U.S. Environmental Protection Agency (EPA), using SCREEN and the Industrial Source Complex model (ISC), do not include these features. PRIME also avoids the discontinuities resulting from the different downwash modules within the current models and the reported overpredictions during light-wind speed, stable conditions. PRIME is intended for use in regulatory models. It was evaluated using data from a power plant measurement program, a tracer field study for a combustion turbine, and several wind-tunnel studies. PRIME performed as well as or better than ISC/SCREEN for nearly all of the comparisons.     

Development and Evaluation of the PRIME Plume Rise and Building Downwash Model

ABSTRACT

A new Gaussian dispersion model, the Plume Rise Model Enhancements (PRIME), has been developed for plume rise and building downwash. PRIME considers the position of the stack relative to the building, streamline deflection near the building, and vertical wind speed shear and velocity deficit effects on plume rise. Within the wake created by a sharp-edged, rectangular building, PRIME explicitly calculates fields of turbulence intensity, wind speed, and streamline slope, which gradually decay to ambient values downwind of the building. The plume trajectory within these modified fields is estimated using a numerical plume rise model. A probability density function and an eddy diffusivity scheme are used for dispersion in the wake. A cavity module calculates the fraction of plume mass captured by and recirculated within the near wake. The captured plume is re-emitted to the far wake as a volume source and added to the uncaptured primary plume contribution to obtain the far wake concentrations.

The modeling procedures currently recommended by the U.S. Environmental Protection Agency (EPA), using SCREEN and the Industrial Source Complex model (ISC), do not include these features. PRIME also avoids the discontinuities resulting from the different downwash modules within the current models and the reported overpredictions during light-wind speed, stable conditions. PRIME is intended for use in regulatory models. It was evaluated using data from a power plant measurement program, a tracer field study for a combustion turbine, and several wind-tunnel studies. PRIME performed as well as or better than ISC/SCREEN for nearly all of the comparisons.     

Stable plume rise in a shear layer

Solutions are given for plume rise assuming a power-law wind speed profile in a stably stratified layer for point and finite sources with initial vertical momentum and buoyancy. For a constant wind speed, these solutions simplify to the conventional plume rise equations in a stable atmosphere. In a shear layer, the point of maximum rise occurs further downwind and is slightly lower compared with the plume rise with a constant wind speed equal to the wind speed at the top of the stack. If the predictions with shear are compared with predictions for an equivalent average wind speed over the depth of the plume, the plume rise with shear is higher than plume rise with an equivalent average wind speed.     

Observations Less than the Analytical Limit of Detection: A New Approach

Abstract

Solutions are given for plume rise assuming a power-law wind speed profile in a stably stratified layer for point and finite sources with initial vertical momentum and buoyancy. For a constant wind speed, these solutions simplify to the conventional plume rise equations in a stable atmosphere. In a shear layer, the point of maximum rise occurs further downwind and is slightly lower compared with the plume rise with a constant wind speed equal to the wind speed at the top of the stack. If the predictions with shear are compared with predictions for an equivalent average wind speed over the depth of the plume, the plume rise with shear is higher than plume rise with an equivalent average wind speed.     

Assimilating concentration observations for transport and dispersion modeling in a meandering wind field

Assimilating concentration data into an atmospheric transport and dispersion model can provide information to improve downwind concentration forecasts. The forecast model is typically a one-way coupled set of equations: the meteorological equations impact the concentration, but the concentration does not generally affect the meteorological field. Thus, indirect methods of using concentration data to influence the meteorological variables are required. The problem studied here involves a simple wind field forcing Gaussian dispersion. Two methods of assimilating concentration data to infer the wind direction are demonstrated. The first method is Lagrangian in nature and treats the puff as an entity using feature extraction coupled with nudging. The second method is an Eulerian field approach akin to traditional variational approaches, but minimizes the error by using a genetic algorithm (GA) to directly optimize the match between observations and predictions. Both methods show success at inferring the wind field. The GA-variational method, however, is more accurate but requires more computational time. Dynamic assimilation of a continuous release modeled by a Gaussian plume is also demonstrated using the genetic algorithm approach.     

Pollutant dispersion in urban street canopies

The effects of building configurations on pollutant dispersion around street canopies were studied numerically. The dispersion of pollutants emitted from ground sources was simulated by continuously discharging large number of particles into the computation domain. The mean wind velocities at each time-step were firstly computed by solving the time-dependent incompressible Navier–Stokes equations, while the fluctuated velocities were determined using a statistical procedure. The trajectories of the discharged particles were obtained from a Lagrangian particle model. Three categories of numerical simulation were conducted to study the effect of different canopy geometries on the pollutant dispersion. The computed wind field data were consistent with the wind field characteristics described in the previous wind tunnel studies. A counter-clockwise vortex was found resulting in high pollutant concentration at the windward side of the downstream building of the street canopy and low pollutant concentration at the leeward side of the upstream building. The increase in height of the urban roughness buildings would facilitate the pollutant dispersion in urban street canopy under certain building configurations. Two or more vortices stacked vertically in a street canopy were found when height of the upstream and downstream buildings of a street canopy was increased, preventing pollutants from escaping out of the canopy.     

Boundary layer photochemistry simulated with a two-stream convection scheme

We explore the sensitivity of the simulation of photochemical smog to the turbulent mixing scheme, using two diffusion schemes and an original two-stream model (TSM) scheme, assuming in the column an updraft and a downdraft. In this latter scheme both updraft and downdraft concentrations are prognostic variables, unlike in previously proposed schemes. The comparisons are made using a one-dimensional column model, in a Eulerian or a Lagrangian mode. The diffusion schemes produce tilted concentration profiles for primary species, with higher concentrations near the surface and lower values at the top of the boundary layer, while TSM profiles yield more homogeneous concentrations in the planetary boundary layer (PBL). Ozone concentrations are also more homogeneous in the TSM PBL than in the diffusive PBL. Only deposition makes ozone concentrations slightly lower near the surface, while in diffusive case ozone is lower also due to titration by higher nitrogen oxide concentrations. The overall differences between the schemes remain small for ozone.Also, the development time and amplitude of an ozone city plume is not very sensitive to the choice of the mixing scheme. In the urban framework ozone build-up is slightly delayed by higher nitrogen oxide concentrations near the surface in the diffusive cases, but the plume development is similar to that of the TSM once the plume travels away from the emission area. Results also show that the sensitivity of ozone to nitrogen oxide and non-methane volatile organic compounds is itself not very sensitive to the mixing scheme.     

Improving Plume Rise Prediction Accuracy for Stable Atmospheres with Complex Vertical Structure

Accurately predicting the rise of a buoyant exhaust plume is difficult when there are large vertical variations in atmospheric stability or wind velocity. Such conditions are particularly common near shoreline power plants. Simple plume rise formulas, which employ only a mean temperature gradient and a mean wind speed, cannot be expected to adequately treat an atmosphere whose lapse rate and wind velocity vary markedly with height. This paper tests the accuracy of a plume rise model which is capable of treating complex atmospheric structure because it integrates along the plume trajectory. The model consists of a set of ordinary differential equations, derived from the fluid equations of motion, with an entralnment parameterization to specify the mixing of ambient air into the plume. Comparing model predictions of final plume rise to field observations yields a root mean square difference of 24 m, which is 9 % of the average plume rise of 267 m. These predictions are more accurate than predictions given by three simpler models which utilize variants of a standard plume rise formula, the most accurate of the simpler models having a 12% error.     

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.     

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.     

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.     

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.     

Concentration prediction for meandering plumes based on probability theory

A procedure is proposed for the calculation of the probability function of the concentration of gas in a pollutant plume that is meandering. As input, the velocity field must be known as well as the plume behaviour in the presence of turbulence but without meandering. It is assumed that the high-frequency turbulence and the low-frequency fluctuations that cause meandering are independent and can be superposed. Small-scale experiments are described which simulate meandering, in which these assumptions are verified. The concentration measurements in these experiments are also compared with the predictions using this calculation method. The agreement of the calculation with experiments shows the usefulness of this type of calculation.