2000 Progress Report: Buoyant Plume Dispersal in the Convective Boundary Layer: Analysis of Experimental Data and Lagrangian ModelingEPA Grant Number: R826160
Title: Buoyant Plume Dispersal in the Convective Boundary Layer: Analysis of Experimental Data and Lagrangian Modeling
Investigators: Weil, Jeffrey C.
Institution: University of Colorado at Boulder
EPA Project Officer: Shapiro, Paul
Project Period: February 3, 1998 through February 2, 2001 (Extended to February 2, 2003)
Project Period Covered by this Report: February 3, 2000 through February 2, 2001
Project Amount: $244,000
RFA: Exploratory Research - Physics (1997) RFA Text | Recipients Lists
Research Category: Water , Land and Waste Management , Air , Engineering and Environmental Chemistry
The objective of this research project is to improve our knowledge and predictive capability of buoyant plume dispersion from elevated sources in the convective boundary layer (CBL). The focus is on modeling of the mean and root-mean-square (rms) concentration fields due to such sources. The specific objectives are to: (1) increase understanding of highly buoyant plumes that loft or remain near the CBL top and disperse downwards slowly, including development of an improved gravity current model for the lofting plume spread; (2) enhance a hybrid Lagrangian dispersion model for predicting concentrations in buoyant plumes by including the gravity current model and other new features; and (3) further develop a simple analytical probability density function (PDF) model for the mean and rms concentration fields.
During the first year of the project, we modified our model of a buoyant plume lofting near the CBL capping inversion based on dispersion data from laboratory experiments. In the new model, the elevated plume was assumed to be embedded within the entrainment layer capping the CBL and spreading laterally as gravity current. The plume was assumed to lose buoyancy and pollutant mass due to entrainment by the CBL turbulence. Estimates of the entrainment velocity obtained from the plume data showed that it decreased inversely with the source buoyancy; an empirical relationship deduced from the data agreed with previous experiments on heat entrainment at the CBL top.
For the lateral spread, we adopted a gravity current model, which predicts the advancement of one fluid into another, due to the density difference between them. For a plume with a conserved buoyancy flux, an equation for the lateral spread led to a simple power law dependence of spread on distance. For a lofting plume that was slowly eroded by the CBL turbulence from below, we accounted for the buoyancy loss. Comparisons between the modeled lateral dispersion and the laboratory data showed that the predicted spread followed the data trends with consistency. The results with the buoyancy loss model were more favorable than those for the constant buoyancy model.
During the second year of the project, we modified the hybrid Lagrangian model to: (1) treat dispersion by the motion of buoyant "particles" rather than by a "meandering" plume, as used earlier; (2) account for environmental turbulence effects on plumes through detrainment (or removal) of plume material by the ambient turbulence; and (3) incorporate the gravity current plume spreading at the CBL capping inversion. The treatment of dispersion by a large number of buoyant particles was included to improve the modeling of the plume interaction with the elevated inversion.
In the modified model, particles were tracked by superposing the plume rise velocity and the local ambient turbulence velocity, which was treated stochastically. The plume properties were obtained using equations for mass, momentum, and buoyancy conservation. The detrainment concept was supported by plume snapshots from convection tank experiments. A preliminary evaluation was made by comparing model predictions of the mean plume height and crosswind-integrated concentration (CWIC) distribution with dispersion data from convection tank experiments. Our initial focus on a non-buoyant plume showed consistency with the laboratory data.
During the third year of the project, we further developed the hybrid model by establishing consistency between the plume rise/entrainment model and the particle model. This was achieved by requiring that the number of particles detrained from the "active" plume core be consistent with the equations governing the plume fluxes. For the plume sections in the mixed layer, the total probability of particles remaining in the plume at any distance was estimated from the plume momentum flux with and without considering detrainment. For the lofting plume, the probability was estimated from an integral of the entrainment velocity over distance.
A comparison of the model with laboratory data showed that the mean plume height and the vertical dispersion were consistent with the data, both as a function of distance and plume buoyancy. The maximum predicted plume heights were somewhat less than the laboratory data, a result attributed to the neglect of wind speed fluctuations in the model. One of the significant improvements of the modified Lagrangian model over the earlier model was the shape of the vertical concentration or CWIC profile. The profile showed a peak CWIC near the CBL top. The peak was maintained over a considerable distance downstream consistent with the laboratory data. However, for large distances, the model overestimated the concentrations in the mixed layer due to a deficiency in the entrainment velocity for the lofting plume. Finally, the predicted surface CWIC, which is of much practical interest and value, exhibited consistency with the laboratory data.
A 1-year no-cost project extension was requested and granted to complete several modeling aspects requiring further attention. These include modifications to: (1) incorporate the effects of longitudinal wind fluctuations; (2) improve the modeling of the plume interaction with the CBL top and stable layer interface; and (3) revise/enhance the entrainment velocity formulation for the lofting plume. Furthermore, we plan to enhance the PDF model by including the gravity current approach for lofting plumes. We also plan to prepare papers for journal publication.