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.     

Numerical and approximate solutions for plume rise

Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585–590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).     

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.     

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.     

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.     

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.     

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.     

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 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.     

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.     

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.     

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.     

A three-dimensional plume rise model for dry and wet plumes

We present a plume rise model which can be applied to situations with arbitrary wind fields and source exit directions and to both dry and wet plumes. The model is an integral model which considers plume properties averaged over the plume cross section. It is validated by means of water tank, wind tunnel, and field experiments (stacks and cooling towers).     

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.     

Factors controlling BTEX and chlorinated solvents plume length under natural attenuation conditions

Natural attenuation is presently used at numerous sites where groundwater is contaminated. In order to simulate this attenuation, reactive transport models are often used but they are quite complex and depend on both physical and chemical conditions in the aquifer. As complex numerical models cannot be used to study all possible cases, we develop here analytical solutions to draw general conclusions. Our strategy, called MIKSS (Mixed Instantaneous and Kinetics Superposition Sequence), allows the calculation of the concentrations of all reacting substances in a plume. It is an extension of the superimposition principle that is able to treat the case of joint kinetics and instantaneous reactions. The basic equations have been extended to treat different reactions that occur in the plume core and at its fringe. At first we consider one organic substance degraded under all oxidising conditions (toluene for instance). For this problem the size of the plume depends on the reduced source width and on the ratio of the organic substance concentration to the sum of the electron acceptors' concentrations. For several BTEX substances having different degradation behaviour the formulation is similar, but leads to quite different plume lengths for each substance. Contrary to the case of one substance, the plumes can be quite long and may not satisfy the target risk level. For chlorinated solvents we developed a specific approach to take under consideration all reactions and particularly the competition for hydrogen. A formula is given to assess the size of the plume core, i.e. the zone with highly reducing conditions. The factors influencing the core length are the same as for BTEX (source width, dispersivity, organic carbon content). The size of the TCE plume is calculated from the plume core length and the kinetic constant of TCE degradation. Using assumptions of degradation constants for DCE and VC it is also possible to calculate the longitudinal concentration profile of these substances. The degradation of moderately substituted solvents under oxic conditions reduces the size of their plumes but under these conditions TCE becomes the major threat. Among the conditions studied in this paper, very few chlorinated solvents sites can lead to a negligible risk at an acceptable distance from the source.     

A combined first-order closure/gaussian dispersion model

A dispersion model incorporating a large wind direction shear has been developed for an industrialized coastal area with an indented coastline and rough terrain. The model is based on a first-order closure solution for the vertical spread and a Gaussian profile for the lateral spread. Lateral spread is obtained by numerical integration of turbulent energy spectra. The model is verified against a large number of tracer experiments with near surface release within industrial complexes. The model is shown to correctly simulate shear-enhanced spread out to a distance of 10 km from the source. Part of the observed scatter is believed to be the result of an oversimplified plume rise calculation.     

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。