Instantaneous puff model

PasquiU Atmo.spheric Diffusion, Van Nostrand, 1962) recast Eq, (26-60) in terms of the dispersion coefficients and developed a number of useful solutions based on either continuous (plume) or instantaneous (puff) releases, Gifford Nuclear Safety, vol, 2, no, 4, 1961, p, 47) developed a set of correlations for the dispersion coefficients based on available data (see Table 26-29 and Figs, 26-54 to 26-57), The resulting model has become known as the Pasquill-Gifford model. 

The puff model describes near-instantaneous releases of material. The solution depends on the total quantity of material released, the atmospheric conditions, the height of the release above ground, and the distance from the release. The equation for the average concentration for this case is (Growl and Louvar, 1990, p, 143) ... 

Pasquill-Gifford puff model At a given downwind distance x, the maximum (average) concentration for a (instantaneous) passive puff from a point source is... 

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. 

Two types of dispersion models are used to describe these releases when the puff or plumes are neutrally or positively buoyant. When there is an instantaneous release or a burst of material, we make use of a puff model. In this model the puff disperses in the downwind, cross wind, and vertical directions simultaneously. Computer codes written for puff models usually have the capability of tracking multiple puff releases over a period of time. When the release rate is constant with time, the puff model can be mathematically integrated into a continuous model. In this case, dispersion takes place in the cross wind and vertical directions only. The mathematical expressions are those discussed in Section III. The dispersion coefflcients used, however, may differ from those described in Section IV. Plume rise equations from Section V for positively buoyant plumes may be used in conjunction with these dispersion models. The equations of current models indicate that they are well formulated, but the application of the models suffers from poor meteorological irrformation and from poorly defined source conditions that accompany accidental releases. Thus, performance of these models is not adequate to justify their use as the sole basis for emergency response planning, for example. 

The Gaussian model is based on analytical solutions of the general transport equation for a point source. Steady continuous and instantaneous releases (plumes and puffs) can be modeled. For time-varying continuous releases, time-integrated puff models should be used. For area sources, such as a liquid pool, two approaches are possible. In the first approach, an imaginary point source is assumed upwind of the actual source, so that the width of the cloud matches the source dimensions at the site of the actual source. The second approach is based on an area integration of the point source equations over the source area. 

The Gaussian dispersion model has several strengths. The methodology is well defined and well validated. It is suitable for manual calculation, is readily computerized on a personal computer, or is available as standard software packages. Its main weaknesses are that it does not accurately simulate dense gas discharges, validation is limited from 0.1 to 10 km, and puff models are less well estabUshed than plume models. The predictions relate to 10 min averages (equivalent to 10 min sampling times). While this may be adequate for most emissions of chronic toxicity, it can underestimate distances to the lower flammable limit where instantaneous concentrations are of interest. More discussion will follow. 

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. 

A rather significant amount of data and information is available for sources that emit continuously to the atmosphere. See Chapter 48 for more details. Unfortunately, little is available on instantaneous or puff sources. Other than computer models that are not suitable for classroom and/or illustrative example calculations, only Turner s Workbook of Atmospheric Dispersion Estimates, USEPA Publication No. AP-26, Research Triangle Park, NC, 1970 provides an equation that may be used for estimation purposes. Cases of instantaneous releases, as from an explosion, or shortterm releases on the order of seconds, are also and often of practical concern. 

Up to this point in this chapter we have developed the common theories of turbulent diffusion in a purely formal manner. We have done this so that the relationship of the approximate models for turbulent diffusion, such as the K theory and the Gaussian formulas, to the basic underlying theory is clearly evident. When such relationships are clear, the limitations inherent in each model can be appreciated. We have in a few cases applied the models obtained to the prediction of the mean concentration resulting from an instantaneous or continuous source in idealized stationary, homogeneous turbulence. In Section 18.7.1 we explore further the physical processes responsible for the dispersion of a puff or plume of material. Section 18.7.2 can be omitted on a first reading of this chapter that section goes more deeply into the statistical properties of atmospheric dispersion, such as the variances a (r), which are needed in the actual use of the Gaussian dispersion formulas. 

The Pasquill - Gifford model PUFF is suited for dispersion modeling in instantaneous outflow conditions. It is a dispersion model with normal (Gauss) distribution of concentrations and Lagrange approach, which consists in gas element move monitoring in wind field. The gas cloud spreads in the wind direction. At first the cloud grows and the gas concentration sinks. Later the cloud volume decreases, because more and more gas disperses in insignificant concentrations outside the cloud. 

Some of these limitations can be overcome by the use of other model types. For example, predictions of downwind concentrations from instantaneous releases or puff diffusion can be treated by reference to similarity theory. Shear fields can be introduced in the numerical solution of the deterministic model, and the statistical theory can assist in developing the Gaussian model itself... 

Box models are used to describe instantaneous heavy gas releases (puffs). Physical aspects of interest for a box model are ... 

Yet another complication arises if the diffusion process is triggered by a mass source. A puff of smoke emanating from a chimney, for example, constitutes such a source. If it lasts for only an instant, we speak of an instantaneous source. If the emanation persists, we speak of a continuous source. The existence of such sources must be incorporated into the Fickian model and leads to what we term solutions of source problems. Because of their importance, particularly in an environmental context, we address this topic separately in some detail. 

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