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.     

A Theory of Plume Rise Compared with Field Observations

A theory for the rise of a plume in a horizontal wind is proposed in which it is assumed that, for some distance downwind of a high stack, the effects of atmospheric turbulence may be ignored in comparison with the effects of turbulence generated by the plume. The theory, an extension of the local similarity ideas used by Morton, Taylor, and Turner,¹ has two empirical parameters which measure the rate that surrounding fluid is entrained into the plume. Laboratory measurements of buoyant plume motion in laminar unstratified cross flow are used to estimate the empirical parameters. Using this determination of the parameters in the theory, the trajectories of atmospheric plumes may be predicted. To make such a prediction, the observed wind velocity and temperature as functions of altitude, and flow conditions at the stack orifice, are used in numerically integrating the equations. The resulting trajectories are compared with photographs, made by Leavitt, et al.,² of TVA, of plumes from 500 to 600 ft high stacks. Within 10 stack heights downwind of the stack, the root mean square discrepancy between the observed height of the trajectory above ground level and the theoretical value is 14%, which is about the uncertainty in the observed height. The maximum plume rise within the field of observation is within 15% of that predicted by the present theory.     

The Validity of Several Plume Rise Formulas

The ground level concentration of pollutants downwind of a tall chimney decreases as the effective height of the stack increases. The effective height of the stack is the actual height plus the rise of the plume center-line due to momentum and buoyancy of the effluent. Over twenty formulas to predict plume rise from stack and meteorological parameters have been proposed; none is uniformly accepted. In this paper, 711 plume rise observations were used to test the ability of fifteen of the published and commonly used formulas to predict plume rise. The plume rise data were obtained from single stacks whose heat emission rate varied over four orders of magnitude. None of the formulas tested was found to be significantly better than the others. Research was performed under the auspices of the U.S. Atomic Energy Commission.     

Integral model of dense gas plume dispersion

The injection of a dense gas stream at ground level into a flowing turbulent atmosphere produces a wide, flat plume that entrains air primarily through its upper surface. A quasi-one-dimensional flow model of an isothermal dense gas plume is developed for the purpose of comparing experiments in wind tunnels and water flumes and field tests in the atmosphere. Comparisons are made for plume width, including the width at the source, and centerline ground plane source gas concentration. All published data are used in this comparison, which cover a factor of about 100 in plume length scale and Reynolds number. Tests conducted by different experimenters were found not to be dynamically similar. Dimensionless model parameters, all of order unity, are selected to give the best agreement among all the experimental data. The dependence of entrainment rate on the plume Richardson number, a key feature of the model, is confirmed in the comparison. The entrainment rate parameter is found to be larger for the field tests than for the laboratory experiments, reflecting the much higher Reynolds number of the former.     

Maximum Ground-Level Concentrations with Downwash

Equations are derived from the Gaussian plume mode! and prescribe the critical downwind distance, wind speed, and plume rise values that result in maximum ground-level concentrations (MGLC) under downwash conditions. The derivations apply to bent-over plumes and encompass the Schulman-Scire and Huber-Snyder building downwash treatments.     

Theoretical study of the impact of particulate matter gravitational settling on ambient coarse particulate matter monitoring for agricultural emissions

The particle size distributions (PSDs) of particulate matter (PM) in the downwind plume from simulated sources of a cotton gin were analyzed to determine the impact of PM settling on PM monitoring. The PSD of PM in a plume varies as a function of gravitational settling. Gravitational settling has a greater impact on the downwind PSD from sources with PSDs having larger mass median diameters (MMDs). The change in PSD is a function of the source PSD of emitted PM, wind speed, and downwind distance. Both MMD and geometric standard deviation (GSD) in the downwind plume decrease with an increase in downwind distance and source MMD. The larger the source MMD, the greater the change in the downwind MMD and GSD. Also, the greater the distance from the source to the sampler, the greater the change in the downwind MMD and GSD. Variations of the PSD in the downwind plume significantly impact PM10 sampling errors associated with the U.S. Environmental Protection Agency (EPA) PM10 samplers. For the emission sources with MMD > 10 microm, the PM10 oversampling rate increases with an increase in downwind distance caused by the decrease of GSD of the PSD in the downwind plume. Gravitational settling of particles does not help reduce the oversampling problems associated with the EPA PM10 sampler. Furthermore, oversampling rates decrease with an increase of the wind speed.     

Dry Removal of Gaseous Fluorine Pollutants

The conservation equations governing buoyant plume rise are solved for the case of non-uniform wind conditions. A power law is selected to represent the actual wind profile. Analytical solutions are presented both for uniformly stable and neutral atmospheric conditions. These solutions are shown to be of the same form as those obtained in the simpler uniform case but with the plume rise now depending explicitly on the wind speed shear. A sensitivity analysis of the effects on plume rise of typical variation in wind shear and entrainment reveals that the two quantities have an almost equal effect therefore justifying the use of the present model. To simplify computations a “uniform wind” is introduced such that when used in conjunction with Briggs' equations the results become consistent with those of the present theory.     

Groundlevel concentration fluctuations from a buoyant and a non-buoyant source within a laboratory convectively mixed layer

With the use of mixed-layer scaling, the near-surface mean concentration and the concentration fluctuations at moderate distances downwind of a stack emitting a highly buoyant effluent are obtained and compared quantitatively with those from a non-buoyant source that is otherwise identical. The environment is a laboratory mixed layer in a state of free convection with mean wind simulated by towing the stack along a horizontal line. Although the buoyant effluent has a much smaller maximum mean groundlevel concentration occurring at a greater downwind distance than the non-buoyant effluent, the decay of mean concentration from that point downwind is found to be exceedingly slow in the buoyant case.The cumulative frequency distributions of sampled concentrations greater than zero for these same two cases are found to be log-normal in only a bimodal sense, with the weaker concentrations having a greater logarithmic range in amplitude than the stronger concentrations. The ratio of the root-mean-square (r.m.s.) concentration fluctuation to the mean concentration, in the central portion of the mean plume, is found to decay with downwind distance. Homogenization associated with both downstream and vertical mixing is believed responsible for the rapid decay observed.     

Performance Evaluation of Integral and Analytical Plume Rise Algorithms

The purpose of this study was to evaluate the performance of current regulatory algorithms for predicting plume rise for refinerytype sources (short stacks and a wide range of source conditions) and the performance of new or alternate algorithms which may provide better estimates. To meet the objectives, five plume rise algorithms were statistically evaluated against ten field and laboratory plume rise data bases. Two forms of the Briggs plume rise equations were tested because they are almost exclusively used in current EPA regulatory models. Two modified Briggs equations were tested to assess how simple modifications can Improve the accuracy of the estimates. The fifth algorithm was a numerical solution to the basic equations for conservation of mass, momentum, and energy often referred to as an Integral plume rise algorithm. This algorithm was selected because It handles the wide range of source and atmospheric boundary-layer conditions that affect trajectories of plumes from refinery stacks.

Ten independent plume rise data bases were assembled that covered a wide range of source and meteorological conditions. From the data bases, a total of 107 different data sets were obtained and each data set included plume rise observations versus downwind distance for one source and meteorological condition. Each model was run for each data set and the root-mean-square and mean error between model and observation was computed for use in statistically evaluating model performance.

The statistical evaluation of the algorithms showed that the rms error (considering all data bases) for the Integral plume rise algorithm was approximately 30 percent less than the errors for all other algorithms tested. This difference was significant at the 95 percent confidence level. The results suggest that improved plume rise estimates in regulatory models applied to refineries and other appropriate sources could be achieved to reduce costs and improve ambient air quality estimates through the use of an integral plume rise algorithm.     

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.     

A Correlation of Field Observations of Plume Rise

Data from 137 sets of plume observations, comprising nearly 1 500 data points, are correlated with two simple formulae. These formulae, one for the buoyancy-dominated rise region and the other for the stratification-dominated levelled-off region of a plume, represent an approximate form of the entrainment theory of Hoult, et al. (1968)¹ for the case of uniform atmospheric stratification and zero wind shear. The observations, which are those of the Tennessee Valley Authority and of Bringfelt (1968),⁶ were made of plumes whose source strengths ranged from 0.4 to 111 Mw and which were emitted from stacks of heights between 21 and 183 m. The two formulae are found to correlate the data equally well over all values of the stack exit and meteorological parameters, provided only that the bulk mean velocity of the stack gases exceeds the mean wind speed by at least 20%. The ratio of observed to calculated plume rise is found to be distributed log normally about the mean value.

The median rise at large distances downstream was found to differ insignificantly from that given by the effective stack height formula recommended recently¹¹ for large buoyant plumes. Based upon the correlation, two formulae are recommended for computing median plume rise at all distances downstream of the stack. The formulae include an estimate of the expected uncertainty in the predicted rise.     

Wind-tunnel study of entrainment in two-dimensional dense-gas plumes at the EPA's fluid modeling facility

This wind-tunnel study has been conducted as part of a collaborative effort to investigate the effect of large surface roughness on the entrainment of air from a neutrally stable simulated atmospheric boundary layer into a continuous dense-gas plume. The present study examined the entrainment rates of dense-gas plumes as they were transported over two surfaces with similar geometry but significantly different roughness lengths (factor of 6). Extensive measurements of the flow and plume structures over a wide range of source Richardson numbers (Ri*) are reported. Carbon dioxide was released from a two-dimensional source in order to obtain a plume with virtually constant Ri*. Over the small roughness, the plume depths were generally large compared with the element heights, whereas over the large roughness, plume depths were comparable with the element heights. Retardation of mean velocities in the lower levels of the dense plumes (with compensating increases in the upper levels) was observed, as well as strong suppression of turbulence over quite large fractions of the boundary-layer depth. These effects increased as Ri* increased. Propagation of dense gas was observed upstream of the source due to gravity spreading. The flow within the plumes was observed to become laminar at the larger Ri*. The primary measurements comprised longitudinal surface concentration profiles. Where the plumes were fully turbulent, the plots of inverse concentration versus downwind distance formed reasonably straight lines. The sought-after entrainment velocities are proportional to the slopes of these lines and were found to diminish quite rapidly with Ri*. More in-depth analyses and intercomparisons with the results of the other laboratories are contained in a companion paper in this same volume (Briggs et al., 2001, Atmospheric Environment 35, 2265–2284).     

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.     

Plume Dispersion in a Mountainous River Valley during Spring

The dispersion of hot plumes emitted from a smelter complex located In the Columbia River Valley, British Columbia, was evaluated under stable and neutral conditions during two mornings In spring. Spatial measurements of SO₂ and temperature within the plume were obtained by immersion probing using fast response helicopter and automobile mounted Instrumentation. In addition, meteorological measurements of vertical wind and temperature profiles at, and downwind from, the smelter were obtained from minisonde balloon releases. With weak down-valley winds, it was found that the plume axis elevations were generally lower during both stable and neutral conditions than would be predicted by Briggs plume-rise formulae. In contrast, plume dispersion, although confined in the horizontal by the steep valley walls during both stability regimes, was significantly enhanced by exceptionally good lateral mixing, particularly close to the source.     

Utilizing vortex behaviour to minimize drift

Abstract

The ULV spray emitted from a TBM flying in a cross wind was mapped by a scanning lidar system. The fate of the spray cloud for 2 min after release from the aircraft was followed as the material was transported downwind of the flight line. Vertical scans at 6 s intervals with 1 m^‐3 resolution provided detailed insight into the entrainment of the spray into the wing‐tip vortices and ultimate release to drift or deposit. Relative concentration, dosage and deposit profiles are presented for this cross‐wind case. Vortex lifetimes were found to be significantly different for the up‐wind and downwind vortices. The majority of the near field deposit was associated with the up‐wind vortex while the drift was linked to the down‐wind vortex.     

Pseudo-source parameters for flares: Derivation,implementation, and comparison

The United States Environmental Protection Agency (US EPA) flare pseudo-source parameters are over 30 years old and few dispersion modellers understand their basis and underlying assumptions. The calculation of plume rise from the user inputs of pseudo-stack diameter, temperature and velocity have the most influence on air dispersion model predictions of ground-level concentrations. Regulatory jurisdictions across Canada, the United States and around the world have adopted their own approach to pseudo-source parameters for flares; all relate buoyancy flux to the heat release rate, none consider momentum flux and flare tip downwash as adopted by the Alberta Energy Regulator (AER). This paper derives the plume buoyancy flux for flares burning a gas in terms of combustion variables readily known or calculated without simplifying assumptions. Dispersion model prediction sensitivity to flared gas composition, temperature and velocity, and ambient conditions are now correctly handled by the AER approach. The AER flare pseudo-source parameters are based on both the buoyancy and momentum flux, thus conserving energy and momentum. The AER approach to calculate the effective source height for flares during varying wind speeds is compared to the US EPA approach. Instead of a constant source for all meteorological conditions, multiple co-located sources with varying effective stack height and diameter are used. AERMOD is run with the no stack tip downwash option as flare stack tip downwash is accounted for in the effective stack height rather than the AERMOD model calculating the downwash incorrectly using the pseudo-source parameters. The modelling approaches are compared for an example flare. Maximum ground level predictions change, generally increasing near the source and decreasing further away, with the AER flare pseudo-source parameters. It's time to update how we model flares.

Implications: What are the implications of continuing to model flare source parameters using the overly simplified US EPA approach? First, the regulators perpetuate the myths that the flare source height, temperature, diameter and velocity are constant for all wind speeds and ambient temperatures. Second, that it is acceptable to make simplifying assumptions that violate the conservation of momentum and energy principles for the sake of convenience. Finally, regulatory decisions based on simplified source modelling result in predictions that are not conservative (or realistic). The AER regulatory approach for flare source parameters overcomes all of these shortcomings. AERflare is a publicly available spreadsheet that provides the “correct” inputs to AERMOD.     

Deposition and removal of fugitive dust in the arid southwestern United States: measurements and model results

This work was motivated by the need to better reconcile emission factors for fugitive dust with the amount of geologic material found on ambient filter samples. The deposition of particulate matter with aerodynamic diameter less than or equal to 10 microm (PM10), generated by travel over an unpaved road, over the first 100 m of transport downwind of the road was examined at Ft. Bliss, near El Paso, TX. The field conditions, typical for warm days in the arid southwestern United States, represented sparsely vegetated terrain under neutral to unstable atmospheric conditions. Emission fluxes of PM10 dust were obtained from towers downwind of the unpaved road at 7, 50, and 100 m. The horizontal flux measurements at the 7 m and 100 m towers indicated that PM10 deposition to the vegetation and ground was too small to measure. The data indicated, with 95% confidence, that the loss of PM10 between the source of emission at the unpaved road, represented by the 7 m tower, and a point 100 m downwind was less than 9.5%. A Gaussian model was used to simulate the plume. Values of the vertical standard deviation sigma(z) and the deposition velocity Vd were similar to the U.S. Environmental Protection Agency (EPA) ISC3 model. For the field conditions, the model predicted that removal of PM10 unpaved road dust by deposition over the distance between the point of emission and 100 m downwind would be less than 5%. However, the model results also indicated that particles larger than 10 microm (aerodynamic diameter) would deposit more appreciably. The model was consistent with changes observed in size distributions between 7 m and 100 m downwind, which were measured with optical particle counters. The Gaussian model predictions were also compared with another study conducted over rough terrain and stable atmospheric conditions. Under such conditions, measured PM10 removal rates over 95 m of downwind transport were reported to be between 86% and 89%, whereas the Gaussian model predicted only a 30% removal. One explanation for the large discrepancy between measurements and model results was the possibility that under the conditions of the study, the dust plume was comparable in vertical extent to the roughness elements, thereby violating one of the model assumptions. Results of the field study reported here and the previous work over rough terrain bound the extent of particle deposition expected to occur under most unpaved road emission scenarios.