Plume model, described

The plume model describes continuous release of material. The solution depends on the rate of release, the atmospheric conditions, the height of the release above ground, and the distance from the release. In this case, the wind is moving at a constant speed u in the x direction. The equation for the average concentration for this case is (Crowl and Louvar, 1990, p. 142) ... 

Two types of neutrally buoyant vapor cloud dispersion models are commonly used the plume and the puff models. The plume model describes the steady-state concentration of material released from a continuous source. The puff model describes the temporal concentration of material from a single release of a fixed amount of material. The distinction between the two... 

Dispersion models describe the airborne transport of toxic materials away from the accident site and into the plant and community. After a release the airborne toxic material is carried away by the wind in a characteristic plume, as shown in Figure 5-1, or a puff, as shown in Figure 5-2. The maximum concentration of toxic material occurs at the release point (which may not be at ground level). Concentrations downwind are less, because of turbulent mixing and dispersion of the toxic substance with air. 

The puff model can be used to describe a plume a plume is simply the release of continuous puffs. However, if steady-state plume information is all that is required, the plume model is recommended because it is easier to use. For studies involving dynamic plumes (for instance, the effect on a plume of a change in wind direction), the puff model must be used. 

The box model is closely related to the more complex airshed models described below in that it is based on the conservation of mass equation and includes chemical submodels that represent the chemistry more accurately than many plume models, for example. However, it is less complex and hence requires less computation time. It has the additional advantage that it does not require the detailed emissions, meteorological, and air quality data needed for input and validation of the airshed models. However, the resulting predictions are... 

The particle tracking-based advective control model described in this chapter is capable of solving two- and three-dimensional plume capture problems with multiple candidate wells and multiple particles in confined and unconfined aquifers. The formulation provides a direct approach to solving plume control problems and uses both forward and reverse particle tracking to exploit numerical characteristics of the two reference frames. 

Puff models such as that in Reference 5 use Gaussian spread parameters, but by subdividing the effiuent into discrete contributions, they avoid the restrictions of steady-state assumptions that limit the plume models just described. A recently documented application of a puff model for urban diffusion was described by Roberts et al, (19). It is capable of accounting for transient conditions in wind, stability, and mixing height. Continuous emissions are approximated by a series of instantaneous releases to form the puffs. The model, which is able to describe multiple area sources, has been checked out for Chicago by comparison with over 10,000 hourly averages of sulfur dioxide concentration. 

Murgai and Emmons [451] and Emmons and Ying [169] describe integral plume models, which are calibrated with experimental data. Satoh and Yang [559] used the UND-S AFE code with associated 3d, compressible, buoyant, and constant turbulent viscosity specifications. Ten cases were considered which included validation exercises and parameter sensitivity studies. 

Plume/oceanic plateau models This model is a variant of the basalt lower crust melting model described above, but in this case basalt melting takes place at the base of thick basaltic crust. Crust of this type may form through imbrication and stacking of normal-thickness oceanic crust or may form as initially thick crust in an oceanic plateau as the product of mantle plume-related magma-tism (Chapter 3, Section 3.1.5). 

These models describe a sharp ablation threshold and a logarithmic increase of the ablation crater depth with the number of laser pulses, but the Arrhenius tail is not accounted for [3,5,30,45,46]. A linear dependence can be described with models that consider the motion of the ablation front, but ignore the screen effects caused by the plasma plume. 

To model accidental releases of the kind described above requires both a source emission model and a transport and dispersion model. When an accidental source emission occurs, the initial emission and acceleration phase gives way to a regime in which the internal buoyancy of the puff or plume dominates the dispersion. This regime is followed by transition to a regime in which the internal turbulence dominates the dispersion. There is then a transition from dominance of internal buoyancy to dominance of ambient turbulence. Models describing source emissions are beyond the scope of this article. This article will describe only the transport and dispersion models where ambient turbulence dominates. 

The steady plume models cannot describe instantaneous releases because the initial slumping phase... 

The well-known Gaussian models describe the behavior of neutrally buoyant gas released in the wind direction at the wind speed. Dense gas releases will mix and be diluted with fresh air as the gas travels downwind and eventually behave as a neutrally buoyant cloud. Thus, neutrally buoyant models approximate the behavior of any vapor cloud at some distance downwind from its release. Neutrally or positively buoyant plumes and puffs have been studied for many years using Gaussian models. These studies have included especially the dispersion modeling of power station emissions and other air contaminants used for air pollution studies. Gaussian plumes are discussed in more detail in Section 2.3.1. 

We now are in something of a quandary. We have a good diffusion model in Eq. 4.1-1 that explains most of the qualitative features of the plume, but this model grossly underpredicts the effects. To resolve this, we assume that mass transport in the plume is described by the flux equation... 

The dispersion model is typically used to determine the downwind concentrations of released materials and the total area affected. Two models are available the plume and the puff. The plume describes continuous releases the puff describes instantaneous releases. 

One of these models the plume itself, attempting to provide a predictive capability for describing the characteristics of the plume in a measured environment. Knowing the motion characteristics of the medium—air or water—the models seek to predict the concentration and dimensions of the plume at distances downstream. Of course, the nature of the problem quickly leads to use of statistical descriptions. This provides a model quite adequate for constructing tracking algorithms. 

As described above, the plume becomes wider and more dilute as it evolves in the streamwise direction, thus ccenteriine and a are changing with x. The decrease of the time-averaged concentration along the centerline of the plume follows a v 1 profile for x/H > 2 (Fig. 5.8). This power law decrease agrees well with the time-averaged concentration field predicted by modeling efforts that assume... 

---