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.     

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.     

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.     

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.     

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.     

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.     

Plume rise in a shear layer with neutral stability

Several solutions have been published to predict the rise of buoyant plumes in a shear layer with a power-law velocity profile. Each of these solutions is either a special case or is based on oversimplifying assumptions. In this paper, solutions to the plume-rise equations are given for buoyant and nonbuoyant plumes with initial vertical momentum. Solutions are given for both point sources and sources with a finite initial size under neutral stability. For a constant wind speed, these solutions simplify to the conventional plume-rise equations.     

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.     

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.     

Predictions of Maximum Ground-Level H2S Concentrations Resulting from Two Sour Gas Well Blowouts

Alberta has recently experienced two sour gas well blowouts: Lodgepole and Claresholm. Sulphur emissions associated with the blowouts were about 1400 and 2 tonnes per day, respectively. The Lodgepole blowout was not only of much greater magnitude but also lasted significantly longer than the Claresholm blowout (67 vs. 4 days). Special air quality monitoring with respect to H₂S was conducted to assess impacts of the blowouts. Monitoring was especially extensive for the Lodgepole incident. Maximum observed ground-level H₂S concentrations were compared to predictions obtained using a Gaussian model which makes allowance for the effects of sonic exit velocity on plume spread and the effects of wind shear on plume transport. There was appreciable agreement between predicted and observed values.     

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.     

Remote sampling of a CO2 point source in an urban setting

High frequency CO₂ and wind speed measurements were used to examine the urban baseline eddy covariance CO₂ flux and analyse the CO₂ rich plume from a local power station. A reliable relationship between high frequency CO₂ maxima and the rate of CO₂ emission at the power station was established. This relationship was shown to be highly dependant on wind speed. The ensemble mean plume was found to be Gaussian in horizontal profile with a width dependant on wind speed. The relationship between peak CO₂ mixing ratio and averaging time was shown to be a simple power law with a time exponent of approximately 0.5. The large, short pulses in CO₂ mixing ratio in the power plant plume were found to have an approximately Lorentzian shape. These pulses generated negative vertical eddy flux measurements so data from the plume sector were necessarily excluded from the flux baseline results. The plume-excluded flux had a similar magnitude and variability to those reported in other urban CO₂ flux studies despite this site not being ideal due to the proximity of roughness elements to the measurement point.     

Full-Scale Study of Plume Rise At Large Coal-Fired Electric Generating Stations

This paper reports on the plume rise research project conducted by TVA under sponsorship of the U. S. Public Health Service. Plume rise data were collected at six coal-fired, steam-electric generating stations within the TVA system over a 2-year period. Unit ratings ranged from 173 to 704 Mw with stack heights varying from 250 to 600 ft. An instrumented helicopter and special photographic equipment were used to obtain 1580 separate plume observations and significant related meteorological parameters during stable, neutral, and slightly unstable conditions. The 1580 observations were resolved and consolidated into 133 composite observation periods covering 30 to 120 min. Meteorological parameters and other compiled input data were entered into four principal equations for calculation of plume rise, and calculated plume rise values were compared with observed values. Most equations overestimated plume rise in low wind speed. For moderately high wind speeds, the Carson and Moses and the Concawe equations gave best fit.     

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 Short-Term Air Quality Model for Sulfur Dioxide in Louisville,Kentucky

The conventional gausslan plume equation for ground level concentrations was used to estimate hourly average sulfur dioxide concentrations at selected points in Louisville, KY, on specific days during 1973. Area emission sources were not included in the model since they are not substantial. The trajectory of the emissions from each continuous point source was calculated by a procedure that allowed for spatial variability in wind direction. All other meteorological parameters were held constant during each hour. The twenty-four individual hourly estimates at each location for a given day were arithmetically averaged yielding a daily mean. The model predictions were compared to actual measurements conducted by Jefferson County Air Pollution Control District personnel using the West-Gaeke sampling procedure. The sample correlation coefficient for all predictions was low, but after only about 30% of the predictions were eliminated on statistical grounds, the sample correlation coefficient was increased to 0.72. The statistical analysis appeared to discard a reasonable number of predictions on the basis of observed variability in the measured air quality.     

A wind tunnel study of dense gas dispersion in a stable boundary layer over a rough surface

Measurements of the vertical entrainment velocity into two-dimensional dense gas plumes over fully rough surfaces were carried out as part of a co-operative research programme with wind tunnel facilities in the USA. This paper presents results obtained for stable boundary layer conditions in the EnFlo wind tunnel at the University of Surrey; a companion paper treats the neutral boundary layer case. Mean velocity and temperature, turbulent normal and shear tresses, temperature fluctuations and heat fluxes were measured and used to demonstrate that a moderately stable atmospheric boundary layer had been successfully simulated in the tunnel. Entrainment velocities, W_E, were then deduced from the streamwise development of the concentration field, non-dimensionalised with respect to the friction velocity in the undisturbed flow, u^*, and correlated with the plume Richardson number, Ri^*. Higher non-dimensional entrainment speeds, W_E/u^*, were observed for Ri^*>5 in the stable boundary layer than in the neutral boundary layer, the difference growing with increasing Richardson number. Emission velocity ratios, W₀/u^*, were however larger in the stable experiments, and exceeded one at about Ri^*=18. Entrainment in the stable boundary layer appeared therefore to be more sensitive to emission velocity ratio than in the neutral case. Entrainment behaviour for Ri^*⩽5 followed that found in the neutral boundary layer. In this regime, use of the neutral boundary layer entrainment speed correlation is unlikely to lead to the over-prediction of plume dilution rates in moderately stable boundary layers.     

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     

Maximum Ground-Level Concentrations with Downwash: The Urban Stability Mode

Abstract

Gaussian model-based equations for critical downwind distance, wind speed, and plume height that result in maximum ground-level concentrations (MGLC) under downwash conditions for the rural stability mode were presented in a previous paper. This paper presents general equations for the critical downwind distance xc for the urban stability mode. Specific examples are presented for Schulman-Scire and Huber-Snyder downwash treatments for building-enhanced and regular sigmas.