Puff with Wind

4Frank P. Lees, Loss Prevention in the Process Industries, 2d ed. (London Butterworths, 1996), p. 15/106. 

The solution to this problem is found by a simple transformation of coordinates. The solution to case 5 represents a puff fixed around the release point. If the puff moves with the wind along the x axis, the solution to this case is found by replacing the existing coordinate x by a new coordinate system, x — ut, that moves with the wind velocity. The variable t is the time since the release of the puff, and u is the wind velocity. The solution is simply Equation 5-29, transformed into this new coordinate system  

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Figure 5-8 Puff with wind. After the initial instantaneous release, the puff moves with the wind.

Case 5 Puff with No Wind and Eddy Diffusivity Is a Function of Direction... 

Case 8 Puff with No Wind and with Source on Ground... 

Case 11 Puff with Instantaneous Point Source at Ground Level, Coordinates Fixed at Release Point, Constant Wind Only in x Direction with Constant Velocity u... 

Further work for comparing different models with wind tunnel experiments and their improvement is required. The main weak point of all the above mentioned simple models is that the models wind flow does not follow building structure. Therefore, the canalling effects (a very important for street canyons) are not reproduced in the models. Instead for the building effects they use an extra dispersion and porosity (e.g., dispersion coefficient corrections and puff splitting) approach, which is very limited. As seen from Figure 9.19, the plume penetrates the buildings, but does not flow round them. Besides, urban sub-layer wind profiles and fluxes are not considered in most of these models. 

Since microscopic samples are much smaller than the infrared transparent window upon which they sit, they are sometimes difficult to locate. A probe or tweezers can be used to place an identilying scratch on the window near the sample. Once the window is placed in the microscope the scratch can easily be found, and moving the field of view along the saatch will lead to the sample. Another problem with microscopic samples is that they can be easily blown away by a sneeze or a puff of wind, such as from a door opening, a ventilation system turning on, or by someone walking past A way around this problem is to flatten the sample into the surface of the infrared transparent window, thereby embedding it. This works because KBr... 

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 third level of complexity in airshed modeling involves the solution of the partial differential equations of conservation of mass. While the computational requirements for this class of models are much greater than for the box model or the plume and puff models, this approach permits the inclusion of chemical reactions, time-varying meteorological conditions, and complex source emissions patterns. However, since this model consists only of the conservation equations, variables associated with the momentum and energy equations—e.g., wind fields and the vertical temperature structure—must be treated as inputs to the model. The solution of this class of models will be examined here. 

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. 

The dispersion coefficients above are not necessarily those evaluated with respect to the dispersion of a continuous source at a fixed point in space. (See Chapter 48 for more details.) This equation can be simplified for centerline concentrations and ground-level emissions by setting y — 0 and H = 0, respectively. The dispersion coefficients in the above equation refer to dispersion statistics following the motion of the expanding puff. The is the standard deviation of the concentration distribution in the puff in the downwind direction, and t is the time after release. Note that there is essentially no dilution in the downwind direction by wind speed. The speed of the wind mainly serves to give the downwind position of the center of the puff, as shown by examination of the exponential term involving In general, one should expect the (7 value to be about the same as... 

To complete the computation of the concentration field of the puff in Eulerian coordinates, the position of the puff centroid must be updated based on the wind field velocity at the puff centroid the entire (Lagrangian) puff is then assumed to translate affinely with the centroid. A puff-splitting algorithm may be used to overcome the inaccuracies that arise as the puff dimensions become sufficiently large that the approximation inherent in assuming constant wind velocities throughout the puff becomes invalid (Sykes and Henn 1995). 

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. 

The physical picture of a smoke plume can be developed by considering first a puff of smoke emitted as a point somce. The puff is made up of a gas or small particles which follow the direction of the wind with the speed of the wind. Small eddies caitse dilution and expansion of the puff about the centerline of its path by pitmping fresh air into the puff. Large eddies buffet the puff about and transport it downwind. Linking together an infinity of puffs results-in the formation of continnons release from a point. 

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. 

Here Qr represents the total mass of the release, the a s refer to dispersion coefficients following the motion of the expanding puff, and the 2 in the numerator accounts for assumed ground reflection, which is consistent with the continuous plume models. Note that there is no dilution in the downwind direction by the wind. The wind serves to move the centerline of the puff in the downwind direction. This motion is accounted for by the product u t term in the exponential involving a. In the term u t, t is the time after release and u is the average wind speed in the X direction. Thus, m t is the distance down wind the puff has traveled after release. 

Assuming that the puff passes rapidly oveihead, oy and will be constant during the integration. Furthermore, diffusion along the x-axis is neglected by comparison with the mean wind resulting in... 

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. 

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