Grantee Research Project Results
Final Report: Lagrangian Modeling of Plume Dispersal in the Urban Boundary Layer
EPA Grant Number: R828178Title: Lagrangian Modeling of Plume Dispersal in the Urban Boundary Layer
Investigators: Weil, Jeffrey C.
Institution: University of Colorado at Boulder , Cooperative Institute for Research in Environmental Sciences
EPA Project Officer: Hahn, Intaek
Project Period: September 1, 2000 through August 31, 2002
Project Amount: $172,773
RFA: Exploratory Research - Engineering, Chemistry, and Physics) (1999) RFA Text | Recipients Lists
Research Category: Water , Land and Waste Management , Air , Safer Chemicals
Objective:
The overall goal of this research project was to improve our knowledge and predictive capability of buoyant plume dispersion in urban areas during nighttime. The specific objectives of this research project were to: (1) increase our understanding of the depth, vertical structure, and other features of the nocturnal urban boundary layer (UBL) and adapt models for a thermal internal boundary layer (TIBL) to the UBL; (2) couple a TIBL model with a Lagrangian particle model for the dispersion of highly buoyant lofting plumes in the UBL; (3) further our understanding of plume fumigation into the nocturnal UBL because of plumes from sources upwind of an urban area (this was addressed with a Lagrangian particle model coupled with large-eddy simulations [LESs] of the TIBL); and (4) further develop a probability density function (PDF) model for dispersion in the nighttime UBL by coupling a simplified lofting approach with the TIBL model.
Summary/Accomplishments (Outputs/Outcomes):
The model developments, results, and their significance are presented below with a focus on the first three objectives. The Lagrangian model is a statistical or stochastic approach in which one follows plume "particles" given the ambient turbulence and source conditions. At night, the UBL has characteristics similar to a daytime convective boundary layer (CBL), albeit with smaller turbulence scales. Plume material that reaches the surface either originates from the rising plume within the UBL or from plume material lofting at the UBL top.
The degree of plume buoyancy is characterized by the dimensionless buoyancy flux F* = Fb/(U w* 2zi), where Fb is the source buoyancy flux, U is the mean wind speed, w* is the convective velocity scale, and zi is the UBL or CBL depth. The w* and zi characterize the turbulence velocity and length scales. The source buoyancy can be divided into three ranges: low buoyancy for F* 0.05; moderate buoyancy for 0.05 F* 0.1; and high buoyancy for F* > 0.1, which corresponds to plume lofting.
Models for Nocturnal UBL Properties. Models for the height, wind speed, and turbulence in the nighttime UBL are required for the Lagrangian dispersion modeling. The models are used repeatedly in the particle trajectory computations, and thus the chosen models are of simple analytical forms, but forms that capture the essential physics.
For the UBL height zi(x) as a function of distance x from the leading edge of a city, we adopted a model for a TIBL, which typically forms during daytime near coastlines. At nighttime above an urban area, a TIBL forms primarily because of the heating of the cool, rural air as it flows over the warm, urban surface. The TIBL model adopted includes an entrainment heat flux at the TIBL top in addition to the surface heat flux.
The model was derived for the time variation of the CBL height zi(t) during daytime, but is applied to a TIBL by replacing the travel time t by x/U. For a TIBL or UBL dominated by surface heating, the UBL height varies as zi x1/2. A well-mixed UBL also can be produced by mechanical mixing resulting from the wind flow over the rough surface. In this case, the turbulent energy input causing the mixing is proportional to u*3, where u* is the surface friction velocity and zi(x) x1/3.
A nocturnal well-mixed UBL also can exist in the limit of a zero wind or a "calm." Warm rising air over the city drives a local circulation that induces a near-surface inflow of cool air from the surroundings. We developed a simple thermodynamic model for the unsteady UBL depth zi and radius R, which encloses the air affected by the urban heating. The R(t) is determined independently of zi(t) by one of two approaches: (1) a gravity current model with R t3/4 at large times; and (2) a turbulent diffusion model with R t1/2 at long times. The diffusion model leads to a constant zi at large times and should be an upper bound on zi.
The mean wind U is estimated from the vertical average over the UBL and requires u*. For wind measurements available only in the upwind rural area, we developed a method for estimating the urban u* by considering advection effects and accounting for the roughness and heat flux change at the rural/urban boundary.
Lagrangian Modeling of Lofting Plumes in the Nocturnal UBL. The modeling of highly buoyant lofting plumes in the nocturnal UBL is similar to that for the CBL. However, the time dependence of zi and the turbulence properties must be included in the UBL. The overall model includes three components: (1) a lofting model that accounts for the buoyant plume interaction with the UBL top, (2) a Lagrangian particle model modified to include the time-dependent UBL variables, and (3) models for the UBL variables.
The lofting model was developed under another U.S. Environmental Protection Agency (EPA) research project and predicts the lateral (ry) and vertical (rz) plume dimensions, the plume density deficit, and the removal rate of plume material by the CBL or UBL turbulence. There are three equations for the three variables ry, rz, and the "reduced" gravitational acceleration g'. Analysis of the equation shows that: (1) rz decreases with time; (2) the plume density deficit and g' remain constant; and (3) the species concentration in the plume is constant. The second point is important because maintenance of the density deficit enables the plume to remain aloft and resist detrainment. The equations are solved numerically for ry, rz, and g' and are coupled with the dispersion model.
The Lagrangian dispersion model developed earlier (Weil, 2004a) was modified to include the UBL time-dependent zi(t) and turbulence. The main model features are: (1) it treats dispersion by the motion of buoyant particles; (2) it accounts for environmental turbulence effects on plumes through detrainment of plume material by the ambient turbulence; and (3) it incorporates the gravity current plume spreading in the UBL entrainment layer by including the lofting model. The particles are tracked by superposing the plume rise velocity and the local ambient turbulence velocity, which is treated stochastically. A particle is assumed to behave as "passive" material—without the effects of buoyancy or momentum—once it has been removed from the plume.
Modifications to account for the time variation in the UBL turbulence were accomplished using Thomson's (1987) formulation. The properties (e.g., variance) were assumed to follow a similarity profile, but with a time-dependent zi and w*. An additional term accounted for the zi/t explicitly following Weil (1992).
Computations of the crosswind-integrated concentration (CWIC) field resulting from a stack source in a shallow nocturnal UBL were conducted for a large city (25 km), a small surface heat flux (20 W/m2), and a light wind (3 m/s). The average UBL (or TIBL) height over the city was 167 m, and the average w* or * corresponding to the was 0.5 m/s. The CWIC calculations and results were investigated as a function of the source buoyancy flux (or F*) and two stack heights (25 m and 50 m); results were obtained for F* = 0.2, 0.4, and 0.8, which placed the plume in the highly buoyant or lofting category. Comparison of the surface CWIC values for the three F* cases showed that: (1) the results exhibited a systematic increase in the CWIC with decreasing F*, as would be expected; and (2) the CWIC (Cy) varied systematically with distance (x) with a generally small rate of increase in the Cy with X = *x/(U). The dimensionless CWIC (CyU/Q) was relatively low and did not exceed the well-mixed concentration CyU/Q = 1. This resulted from: (1) plume lofting and the slow entrainment of material by the UBL turbulence; and (2) the growth of the TIBL beyond its average value . The approach to the well-mixed state was rather slow, requiring about 7 and 10 eddy turnover times (/*) for F* = 0.2 and 0.4, respectively. Overall, the combination of the Lagrangian particle model with a TIBL or UBL height model has established a sound basis for computing dispersion and concentration fields for highly buoyant lofting plumes in the nocturnal UBL.
Lagrangian Modeling of Plume Fumigation in a TIBL. We investigated the fumigation process in which a plume initially lying above a CBL or a TIBL is entrained into the CBL or TIBL by convective turbulence. A time-dependent fumigation process was modeled, which can be converted to fumigation into a UBL or TIBL by assuming Taylor's hypothesis, t = x/U. We used a Lagrangian particle dispersion model (LPDM) coupled with LESs of a growing CBL with time to model dispersion, that is, by tracking a large number of particles using the random, turbulent LES velocity fields. The specific objectives were to determine the dependence of fumigation on the entrainment or growth rate of the CBL, the initial plume height, and the initial vertical plume dimension. This was a collaborative effort with a postdoctoral researcher (S.-W. Kim) and scientists (C.-H. Moeng and M. Barth) at the National Center for Atmospheric Research.
The calculations were conducted for two LESs with dimensionless entrainment rates we/w*o = 0.015 (slow entrainment) and 0.042 (fast entrainment), which were comparable to those in laboratory experiments; w*o is the w* at the start of the experiment. Results showed that for slow entrainment, the CWIC contours were shifted to greater downstream distances than for fast entrainment, in agreement with the experimental data. Calculations were made for a series of dimensionless source heights zs/zio ranging from 0.91 to 1.30 to investigate the effect of zs and the "starting time" of fumigation on the surface CWIC downstream. The results showed that the time-shifted surface CWICs collapsed to nearly universal curves for "fumigation cases"—those with zs/zio 1.15—indicating a similarity of the dispersion process once material entered the CBL. However, for entrainment layer source heights—0.91 zs/zio 1.09—such a collapse did not occur. The results and their agreement with the laboratory data demonstrated that the combined LPDM/LES approach is a useful technique for fumigation investigations for a TIBL or UBL.
PDF Dispersion Model. The PDF model, including buoyancy effects, was developed under an earlier program and demonstrated generally good agreement with field observations. A somewhat deficient case was found for highly buoyant lofting plumes. However, because of the extensive efforts required for the development of the Lagrangian model for the nocturnal UBL, there was insufficient time to include the lofting and TIBL models in the PDF approach. This will be pursued in the future because an improved PDF model for the UBL and TIBL would be very worthwhile for applied dispersion modeling and regulatory applications.
Significance and Use of Results. The scenario addressed above—lofting plumes in the nocturnal UBL—has been a longstanding scientific issue in dispersion modeling because lofting plumes do not fit into the standard frameworks of most air quality models. The lofting situation is problematic for short to moderately tall stacks in or near urban areas. Plumes from such sources can become trapped in shallow UBLs, driven by anthropogenic surface heating, and produce high surface concentrations. The model results fill an important void for the treatment of buoyant plumes interacting with elevated inversions in the UBL, TIBL, or CBL. The combined lofting, TIBL, and Lagrangian dispersion models could be used by regulatory agencies (U.S. EPA and state agencies), private sector groups, urban planners, power plant siting agencies, etc. for predicting dispersion in urban areas. Principal uses of the model would be determining the source emission limits for the protection of human health and welfare and assessing environmental risk.
Journal Articles on this Report : 1 Displayed | Download in RIS Format
Other project views: | All 1 publications | 1 publications in selected types | All 1 journal articles |
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Type | Citation | ||
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Kim SW, Moeng CH, Weil JC, Barth MC. Lagrangian particle dispersion modeling of the fumigation process using large-eddy simulation. Journal of the Atmospheric Sciences 2005;62(6):1932-1946. |
R828178 (Final) |
not available |
Supplemental Keywords:
air, ambient air, atmosphere, atmospheric dispersion, buoyant plumes, chemicals, engineering, exposure, Lagrangian stochastic modeling, mean concentrations, modeling, physics, risk assessment, toxics, urban air quality, large-eddy simulations, LES, thermal internal boundary layer, TIBL, urban boundary layer, UBL, convective boundary layer, CBL, probability density function, PDF., RFA, Scientific Discipline, Air, Ecosystem Protection/Environmental Exposure & Risk, Physics, Environmental Chemistry, Monitoring/Modeling, Environmental Monitoring, Engineering, Chemistry, & Physics, atmospheric dispersion models, urban air footprint modeling, air modeling, Langraian modeling, chemical transport modeling, mean and fugitive concentrations, stochiometry, chemical transport models, lagrangian modeling, ground-level concentrations, thermal properties, pollution dispersion models, urban boundry layer, aerosol analyzers, plume dispersal, atmospheric modelsProgress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.