A numerical study of interacting buoyant cooling-tower plumes

The compact design of mechanical cooling towers necessitates that the plumes are issued into the cross-wind in close proximity. An improved understanding of the interaction of adjacent plumes is therefore required for better design of such cooling towers, which may lead to a reduction in their environmental impact. This paper presents the results of a numerical investigation into the interaction of two adjacent plumes in a cross-flow. The numerical model simulates small-scale wind tunnel experiments of a cooling tower arrangement. The computations are performed for three-dimensional, turbulent, buoyant and interacting plumes, and for a single plume for comparison. Two double-source arrangements, namely, tandem and side-by-side, with respect to the oncoming atmospheric boundary layer are considered. A low Reynolds number k–ε turbulence model is used with two discretisation schemes, hybrid and QUICK, and the results are compared. Comparisons are also made with the experimental results. The results show that the interaction of side-by-side plumes is dominated by the interaction of the rotating vortex pairs within the plumes. A tandem source arrangement leads to early merging and efficient rise enhancement. Comparisons of the predicted results with experimental data show good agreement for the plume rise.     

Numerical experiments and field results on the size of steady state plumes

Contaminated groundwater poses a serious risk for drinking water supplies. Under certain conditions, however, groundwater contamination remains restricted to a tolerable extent because of natural attenuation processes. We present an innovative approach to evaluate the size of these so-called steady-state plumes by 2-D and 1-D modelling in homogeneous aquifers. If longitudinal mixing is negligible, scenarios can be modelled in a simplified way using a 1-D domain vertical to the direction of flow. We analysed the sensitivity of the plume length with respect to biodegradation kinetics, flow velocity, transverse vertical dispersivity alphat, the source and aquifer geometry and reaction stoichiometry. Our findings indicate that for many readily biodegradable compounds transverse-dispersive mixing rather than reaction kinetics is the limiting factor for natural attenuation. Therefore, if alphat, aquifer and source geometry and concentrations of electron acceptors and donors are known, the length of the steady state contaminant plume can be predicted. The approach is validated under field conditions for an ammonium plume at a former landfill site in SW Germany.     

On plume meandering in unstable stratification

Vertical plume meandering of gaseous pollutant is commonly experienced in the daytime atmospheric boundary layer (also know as convective boundary layer, CBL) that arose from the complicated interaction between buoyancy-generated turbulence and gravitational force. It leads to rapid pollutant mixing that cannot be accurately modeled by conventional Gaussian plume model. In the light of explaining the mechanism of plume rises and descents in CBLs, this study employs a direct numerical simulation (DNS) technique to compute the plume behaviors for pollutant emitted from line sources placed parallel to the spanwise direction in an unstably stratified turbulent open channel flow. The DNS results show that the plume meandering is due to the domination of uni-directional mean vertical pollutant fluxes above and below the mean plume height.     

Water tank measurements of buoyant plume rise and structure in neutral crossflows

In this paper, an experimental study of the rise and development of a single buoyant plume and a pair of in-line buoyant plumes is presented. The investigations were carried out at small scale in a water filled towing tank using both quantitative flow visualisation and local concentration measurements. The measured plume trajectories for a single plume were compared with the Briggs plume rise equation and predictions from a numerical integral model. Plume trajectories were studied for twin in-line plumes, with particular attention to changes in the plume trajectory, especially any additional rise that resulted from the interaction between the two plumes. Concentration field distributions in cross-sections through both single and interacting twin plumes were obtained from the local concentration measurement system. These showed how the interaction affected the plume structure, notably the double vortex system that occurs in a fully developed plume.     

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).     

Experiments on vertical transverse mixing in a large-scale heterogeneous model aquifer

Vertical transverse mixing is known to be a controlling factor in natural attenuation of extended biodegradable plumes originating from continuously emitting sources. We perform conservative and reactive tracer tests in a quasi two-dimensional 14 m long sand box in order to quantify vertical mixing in heterogeneous media. The filling mimics natural sediments including a distribution of different hydro-facies, made of different sand mixtures, and micro-structures within the sand lenses. We quantify the concentration distribution of the conservative tracer by the analysis of digital images taken at steady state during the tracer-dye experiment. Heterogeneity causes plume meandering, leading to distorted concentration profiles. Without knowledge about the velocity distribution, it is not possible to determine meaningful vertical dispersion coefficients from the concentration profiles. Using the stream-line pattern resulting from an inverse model of previous experiments in the sand box, we can correct for the plume meandering. The resulting vertical dispersion coefficient is approximately approximately 4 x 10(-)(9) m(2)/s. We observe no distinct increase in the vertical dispersion coefficient with increasing travel distance, indicating that heterogeneity has hardly any impact on vertical transverse mixing. In the reactive tracer test, we continuously inject an alkaline solution over a certain height into the domain that is occupied otherwise by an acidic solution. The outline of the alkaline plume is visualized by adding a pH indicator into both solutions. From the height and length of the reactive plume, we estimate a transverse dispersion coefficient of approximately 3 x 10(-)(9) m(2)/s. Overall, the vertical transverse dispersion coefficients are less than an order of magnitude larger than pore diffusion coefficients and hardly increase due to heterogeneity. Thus, we conclude for the assessment of natural attenuation that reactive plumes might become very large if they are controlled by vertical dispersive mixing.     

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 wind tunnel study of dense gas dispersion in a neutral 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 neutral boundary layer conditions in the EnFlo wind tunnel at the University of Surrey; a companion paper treats the stable boundary layer case. Entrainment velocities, W_E, were 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^*. Results for Richardson numbers in the range Ri^*<15 were found to be well fitted by the empirical expression: W_E/u^*=0.65/(1+0.2Ri^*). Flow visualisation studies showed layered plume structures with a sharp upper interface at higher Richardson numbers and in this regime turbulent motion below the interface became progressively more intermittent as Ri^* increased. Measured turbulence levels collapsed within such high Richardson number plumes and flow and dispersion were significantly affected by molecular processes. Up-welling above the source was observed when the emission speed exceeded the approach flow friction velocity, though there was no clear evidence that this affected plume behaviour away from the immediate vicinity of the source.     

Theoretical analysis of deviations from local equilibrium during sorbing solute transport through idealized stratified aquifers

This paper studies the spreading characteristics of reactive solute plumes in idealized stratified aquifers. The aquifer consists of two layers having different permeabilities with flow parallel to the stratification. The solute is assumed to adsorb onto the aquifer solids according to a first-order reversible kinetic rate law; the adsorption parameters are spatially uniform. We use the Aris moment method to examine analytically the time evolution of the lower-order spatial moments of the depth-averaged contaminant plume for an instantaneous input of mass. The results demonstrate that sorption kinetics cause the total dissolved mass and average velocity of the contaminant plume to decrease with increasing travel time. The plume variance is shown to depend upon three factors: intra-layer longitudinal dispersion, intra-layer kinetics, and vertical averaging. The results indicate that the relative importance of sorption kinetics diminishes as the permeability contrast between the layers increases. We present a simple criterion that can be used to assess the applicability of the local equilibrium assumption in idealized stratified systems.     

Water flume study of the enhancement of buoyant rise in pairs of merging plumes

When multiple stacks are grouped or ganged together at a site, the effluent plumes are often observed to merge downwind, forming a single buoyant plume whose rate of rise is enhanced relative to the rise of the plumes individually. The magnitude of this rise enhancement depends on many factors, and the few available models for rise enhancement do not always agree with one another. In the present study the rise behaviour of pairs of merging, buoyant plumes was studied by physical modelling in a water flume at 1:500 scale. The experiments were conducted at several stack separation distances and various exit velocity ratios for stack pairs aligned with, or perpendicular to, the ambient flow. Limited experiments were also done with the stacks aligned at other angles to the flow. The stack releases were made buoyant by heating the source water, and the resulting plumes were measured with an array of sensitive temperature probes. From these measurements it was possible to determine the plume structure and rise rates. For small stack separations when the stacks are aligned with the ambient flow, the experimental results show that the enhanced rise is close to, and sometimes above, the maximum theoretical rise enhancement factor of 2^1/3. For the perpendicular orientation there is little or no rise enhancement. The rise enhancement for other stack orientations is somewhere between these two extremes. A plausible physical explanation for the observed behaviour is given, based on initial momentum shielding and line vortex dynamics in the merging plumes.     

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.     

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-assisted measurement of PM10 emissions from agricultural tilling in California's San Joaquin Valley – Part I: lidar

Vertical profiling with point samplers is an accepted method for quantifying the fluxes of PM₁₀ from non-point fugitive dust sources, but is limited by uncertainty in estimates of the actual height of the dust plume, especially for plumes that exceed the highest sampling height. Agricultural land preparation operations in the San Joaquin Valley were monitored using upwind–downwind vertical PM₁₀ profiles and data collected during the first successful experiment to include light detection and ranging (lidar), in 1998, were analyzed to provide modeling criteria for the 1996 and 1997 data. A series of six comprehensive PM₁₀ tests with concurrent lidar data was examined to: (a) develop a framework for analyzing upwind–downwind point PM₁₀ concentration profiles of land preparation operations (disking, listing, root cutting, and ripping) and (b) identify conditions under which the field sampling strategies affect the reproducibility of PM₁₀ concentration measurements. Lidar data were used to verify that the plume heights and shapes extrapolated from the point sampler vertical profiles adequately described the plumes. The shortcomings of the vertical profiling technique and lidar methods are discussed in the light of developing efficient robust methods for accurate PM₁₀ emissions quantification from complex non-point sources.     

Split-level Plumes

Two recent power plant plume studies by mobile, ground-based and airborne lidar have recorded cross-section images of plumes with sharply-defined layered and connected bands of aerosol in the vertical. Of the external parameters considered, wind direction and speed changes in the vertical were found to be associated most with these plume types. Statistical analyses indicate that both direction and speed shear are highly correlated with the layered plumes.     

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.     

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