Plume Rise Determination-A New Technique Without Equations

Information on plume rise is important in determining the resulting concentrations of a pollutant on the ground. Practical use of plume rise values may be made in connection with stack design, the use of urban air pollution models, and in evaluating the hazards to a population complex.

This paper presents a new equationless technique for estimating plume rise as well as a comparison of seventeen commonly used plume rise formulas. Data from 10 sets of experiments, involving 615 observations and 26 different stacks, were used to study the relation between plume rise and related meteorological and stack parameters.

An independent data set was used to test the derived methods for determining plume rise. These data were obtained by Bringfelt of Sweden and contained measurements from stacks smaller than that at the Argonne National Laboratory to those approaching the TVA stacks.

A significant improvement in the prediction of plume rise from meteorological and stack parameters resulted from the use of a new technique called the Tabulation Prediction Technique. This is a method whereby an estimate of the value of a dependent variable may be obtained from information on the independent variables. Combinations of the independent variables—wind speed, heat emission rate, momentum rate, and stability—are arranged in an ordered sequence. For each combination of independent variables, the cumulative percentile frequency distribution of the dependent variable based on past measurements is given along with other statistics such as the mean, standard deviation, and interquartile range, i.e., the difference in plume rise between the 75th and 25th percentile values. Thus, one may look up the combination of independent variables just as one looks up words in a dictionary to obtain the percentile frequency distribution of the dependent variable. The mean, for each combination of independent variables may be considered as the best estimate for the given conditions.     

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.     

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.     

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.     

Lidar Observations of the Diurnal Behavior of the Cumberland Power Plant Plume

Mobile lidar observations were made downwind of TVA’s Cumberland (Tennessee) power plant as part of the STATE (Sulfur Transport and Transformation in the Environment) program. Vertical profiles of aerosol backscatter have been processed and displayed to show plume structure as an intensity-modulated TV presentation. Available meteorological data, especially the pilot balloon and radiosonde measurements collected during the STATE experiment, have been used to aid in the interpretation of the lidar display. The data show: ? Well defined nighttime plumes, which often tilt or display a layered structure in the shape of a “>”.

? Late morning convective breakup of the plume.

? Well mixed convective plumes during the day.

? Reformation of the layered nighttime plume during the late afternoon.

It appears that the nighttime plume behavior can be related qualitatively to the strong directional shear of the wind with height that often accompanies the stable nighttime atmosphere. The nighttime plume shapes frequently differ markedly from the oval shape one expects of a gaussian plume. Daytime plumes are in better conformance to the expected shape except when constricted by the surface or the top of the mixing layer     

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.     

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.     

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.     

Turbulent Plume in a Turbulent Cross Flow: Comparison of Wind Tunnel Tests with Field Observations

Plume rise downwind of a large stationary gas turbine was measured in the field and the conditions were then scaled in the laboratory. For the laboratory, the plume exit conditions, wind velocity and temperature profiles, and wind direction were matched. It was found that for high temperature exhaust, the buoyancy is best matched by calculating a dimensionless density difference. With properly calculated buoyancy length scales, the plume trajectories were compared and were found to agree quite well. The probability distributions of the entrainment constant and the average values of the entrapment constant with downwind distance were compared. The field data showed about 15% greater plume rise. The median entrainment constant was about 10% greater for the lab test and the shape of the probability distribution matched very closely.     

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.     

Performance of a time-dependent dispersion model in elevated terrain

A study was conducted to evaluate the ability of the TVA quasi-steady model (QSM) to simulate plume dispersion over high terrain. QSM is a time-dependent, plume-segment model. The modeling results are compared with measured data obtained from a field study conducted at the Tennessee Valley Authority's (TVA) Widows Creek Steam Plant. Also, the results obtained using a steady-state Gaussian model are compared to give an indication of the advantages of a time-dependent method compared to a steady-state method.Although the results from both models agree well with the measured values, QSM, which provides better temporal and spatial resolution, more successfully modeled inversion-breakup and plume-impingement conditions.     

Modelling plume rise and dispersion from pool fires

This paper describes an investigation into the behaviour of smoke plumes from pool fires, and the subsequent generation of empirical models to predict plume rise and dispersion from such a combustion source. Synchronous video records of plumes were taken from a series of small-scale (0.06–0.25m²) outdoor methanol/toluene pool fire experiments, and used to produce sets of images from which plume dimensions could be derived. Three models were used as a basis for the multiple regression analysis of the data set, in order to produce new equations for improved prediction. Actual plume observations from a large (20.7 m×14.2 m) aviation fuel pool fire were also used to test the predictions. The two theoretically based models were found to give a better representation of plume rise and dispersion than the empirical model based on measurements of small-scale fires. It is concluded that theoretical models tested on small-scale fires (heat output ≈70 kW) can be used to predict plume behaviour from much larger combustion sources (heat output ≈70 MW) under near neutral atmospheric conditions.     

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.     

Development of the ClearSky smoke dispersion forecast system for agricultural field burning in the Pacific Northwest

The post-harvest burning of agricultural fields is commonly used to dispose of crop residue and provide other desired services such as pest control. Despite careful regulation of burning, smoke plumes from field burning in the Pacific Northwest commonly degrade air quality, particularly for rural populations. In this paper, ClearSky, a numerical smoke dispersion forecast system for agricultural field burning that was developed to support smoke management in the Inland Pacific Northwest, is described. ClearSky began operation during the summer through fall burn season of 2002 and continues to the present. ClearSky utilizes Mesoscale Meteorological Model version 5 (MM5v3) forecasts from the University of Washington, data on agricultural fields, a web-based user interface for defining burn scenarios, the Lagrangian CALPUFF dispersion model and web-served animations of plume forecasts. The ClearSky system employs a unique hybrid source configuration, which treats the flaming portion of a field as a buoyant line source and the smoldering portion of the field as a buoyant area source. Limited field observations show that this hybrid approach yields reasonable plume rise estimates using source parameters derived from recent field burning emission field studies. The performance of this modeling system was evaluated for 2003 by comparing forecast meteorology against meteorological observations, and comparing model-predicted hourly averaged PM_2.5 concentrations against observations. Examples from this evaluation illustrate that while the ClearSky system can accurately predict PM_2.5 surface concentrations due to field burning, the overall model performance depends strongly on meteorological forecast error. Statistical evaluation of the meteorological forecast at seven surface stations indicates a strong relationship between topographical complexity near the station and absolute wind direction error with wind direction errors increasing from approximately 20° for sites in open areas to 70° or more for sites in very complex terrain. The analysis also showed some days with good forecast meteorology with absolute mean error in wind direction less than 30° when ClearSky correctly predicted PM_2.5 surface concentrations at receptors affected by field burns. On several other days with similar levels of wind direction error the model did not predict apparent plume impacts. In most of these cases, there were no reported burns in the vicinity of the monitor and, thus, it appeared that other, non-reported burns were responsible for the apparent plume impact at the monitoring site. These cases do not provide information on the performance of the model, but rather indicate that further work is needed to identify all burns and to improve burn reports in an accurate and timely manner. There were also a number of days with wind direction errors exceeding 70° when the forecast system did not correctly predict plume behavior.     

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.     

高架连续点源落地浓度预测中风速的确定

高架连续点源污染物排放落地浓度是大气环境影响预测的主要内容。由于大气污染物扩散明显受气象条件尤其是风速的影响,而现有预测模型中对于风速的取值都是按经验值来确定的。通过分析在不同气象和烟源条件下,平均风速的计算方法对烟羽抬升高度以及最大落地浓度产生的影响,与实测值相比较确定了风速取值的合理方法,缩小了预测偏差。     

Control of Asphaltic Concrete Plants in Los Angeles County

Characteristics of maximum short-term ground level concentrations from an elevated point source, namely, the effective plume height, the critical wind speed, the distance to the point of maximum concentration, and the maximum concentration, are derived from the gaussian plume model. Both phases of plume development—before and after it has reached its final height—are considered. The plume rise treatment includes both thermal buoyancy and momentum effects. Certain limitations on critical wind speed are discussed. The dispersion model whose basis is established in this paper should be especially useful in applications where on site meteorological data are unavailable.     

Adherence of Sulfur Dioxide Concentrations in the Vicinity of a Steam Plant to Plume Dispersion Models

Air monitoring data for a calendar year at one of the TVA power plants has been used to evaluate the appropriateness of the Sutton, the Bosanquet and Pearson, and the USPHS-TVA atmospheric dispersion models to predict ground level concentrations of sulfur dioxide from emission and meterological data. Aerometric data included one half hourly average sulfur dioxide concentrations, recorded by four Thomas autometers, and the necessary meterological parameters for the solving of atmospheric dispersion models. Based on these meterological parameters and observed plume rise data, over 4000 one half hourly average maximum and minimum expected ground line sulfur dioxide concentrations were predicted for each of the above dispersion models by the use of computer techniques. The plant is a line source; however, an empirical correction was applied to emission data to reduce them to emissions for an equivalent point source. The predicted sulfur dioxide levels for each of the dispersion models were compared to the measured levels throughout the year. Three different sets of diffusion coefficients were applied to the Sutton model and successful predictions, according to a criterion utilizing an acceptable range of concentration, varied from 66 to 93%. The Bosanquet and Pearson model produced successful predictions 90% of the time, while the USPHS-TVA model was successful 94% of the time.Unsuccessful predictions were primarily overestimates.