Point-source model

For large downwind distances, the virtual distances will be negligible and the point source models are used directly. 

In reality, heat sources are seldom a point, a line, or a plane vertical surface. The most common approach to account for the real source dimensions is ro use a virtual source from which the airflow rates are calcu-lared " " see Fig. 7.64. The virtual origin is located along the plume axis at a distance on the other side of the real source surface. The adjustment of the point source model to the realistic sources using the virtual stmrce method gives a reasonable estimate of the airflow rate in thermal plumes. The weakness of this method is in estimating the location ol the virtual point source. 

Another design method uses capture efficiency. There are fewer models for capture efficiency available and none that have been validated over a wide range of conditions. Conroy and Ellenbecker - developed a semi-empirical capture efficiency for flanged slot hoods and point and area sources of contaminant. The point source model uses potential flow theory to describe the flow field in front of a flanged elliptical opening and an empirical factor to describe the turbulent diffusion of contaminant around streamlines. 

In the point-source model, it is assumed that a selected fraction (/) of the heat of combustion is emitted as radiation in all directions. The radiation per unit area and per unit time received by a target (q) at a distance (x) from the point source is, therefore, given by... 

The solid-flame model can be used to overcome the inaccuracy of the point-source model. This model assumes that the fire can be represented by a solid body of a simple geometrical shape, and that all thermal radiation is emitted from its surface. To ensure that fire volume is not neglected, the geometries of the fire and target, as well as their relative positions, must be taken into account because a portion of the fire may be obscured as seen from the target. 

Section 3.5 mentions two approaches, the point-source model and the solid-flame model. In the point-source model, it is assumed that a certain fraction of the heat of combustion is radiated in all directions. This fraction is the unknown parameter of the model. Values for fireballs are presented in Section 3.5.1. The point-source model should not be used for calculating radiation on receptors whose plane intercepts the fireball (see Figure 6.9B). 

The solid-flame model, presented in Section 3.5.2, is more realistic than the point-source model. It addresses the fireball s dimensions, its surface-emissive power, atmospheric attenuation, and view factor. The latter factor includes the object s orientation relative to the fireball and its distance from the fireball s center. This section provides information on emissive power for use in calculations beyond that presented in Section 3.5.2. Furthermore, view factors applicable to fireballs are discussed in more detail. 

Hymes (1983) presents a fireball-specific formulation of the point-source model developed from the generalized formulation (presented in Section 3.5.1) and Roberts s (1982) correlation of the duration of the combustion phase of a fireball. According to this approach the peak thermal input at distance L is given by... 

Alternative reproach point-source model. Another method of calculating the radiation received by an object relatively distant from the fireball is to use the point-source model. From this approach, the peak thermal input at distance L from the center of the fireball is... 

Ground Distance (m) Solid Flame Model Point Source Model... 

There were 311 major chemical manufacturing or consuming plants covered in this study. Because some major chemical plants were sources of more than one chemical, specific point source modeling was applied for 538 plants. Since there may be more than one source type in a plant, dispersion-dosage modeling was conducted for a total of 1819 individual point sources in this study. 

There were 62 source categories involved in the prototype modeling, each modeled in nine regions. Hence, the prototype point source modeling was conducted for a total of 558 prototype sources. 

Virtual sources As indicated above, the gaussian model was formulated for an idealized point source, and such an approach may be unnecessarily conservative (predict an unrealistically large concentration) for a real release. There are formulations for area sources, but such models are more cumbersome than the point source models above. For point source models, methods using a virtual source have been proposed in the past which essentially use the maximum concentration of the real source to determine the location of an equivalent upwind point source that would give the same maximum concentration at the real source. Such an approach will tend to overcompensate and unrealistically reduce the predicted concentration because a real source has lateral and along-wind extent (not a maximum concentration at a point). Consequently, the modeled concentration can be assumed to be bounded above, using the point source formulas in Eq. (23-78) or (23-79), and bounded below by concentrations predicted by using a virtual source approach. 

Because of the dominance of distributed sources over local single sources in the production of photochemical oxidants, point-source models are not discussed here. Related research regarding the measurement of diffusion or the development of atmospheric chemical submodels are not emphasized. Giapter 2 is devoted to the chemical processes that govern atmospheric transformation and removal, and this aspect of the models is not repeated here. 

The point source model assumes that the fire can be represented as a point that is radiating to a target at a distance, R, from the point. The model is most appropriate for calculating incident heat fluxes to targets where fluxes are in the range from 0 to 5 kW/m (SFPE, 1999). The point source model has been shown to be accurate for calculating the incident heat flux from a jet flame to a target outside the flame (Beyler, 2002). The literature contains more refined line or cylinder models (Beyler, 2002 SINTEF, 1997). 

Utilizing the point source model to estimate the incident flux on a target involves the following steps ... 

To estimate the impact of the jet fire on process equipment located 20 m from the source, the point source model can be used to determine the incident heat flux from the jet flame to the equipment. The incident heat flux per unit surface area of target, q" is calculated as follows. 

To estimate the impact of the pool fire on the nearby personnel, start with the point source model. Assuming a head height target, use a target point at a... 

Point source model—A thermal energy model based on representing the total heat release as a point source. 

The group was particularly asked to consider the modelling needs for regionalisation of the well monitoring data, including questions on the relevance of using mass balance models and non-point source models for nitrate. 

The model developed to account for the mixing under eithertype of stable layer employs the idea of complete reflection from the diffusion lid, as in the case for the plume contacting the ground. Now that the plume is trapped between lid and bottom, multiple reflections are allowed for in the model. Thus the continuous point source model becomes... 

Point-source models are generally less complex than the view-factor models. They are appropriate when the receptor is sufficiently separated from the fire that the specific shape and size of fhe Are is no longer important. In contrast, view-factor models allow the geometry of the flame, as well as the receptor configuration, to be taken into account in the estimation of thermal flux. These are therefore more applicable to cases where the receptor is close to the fire and/or when the geometric details of the fire are important (e g., wind effects, receptor orientation). 

Equations (2.58) and (2.61) are applicable to ideal point sources firom which the vapors are released. More complex formtilas for other types of sources can be found in Slade (1968). At the source, the simple point-source models have concentration values of infinity and therefore will greatly overpredict concentrations in the near field. To apply them to a real source with given dimensions, the concept of a virtual point source is introduced. The virtual source is located upwind from the real source such that if a plume were originated at die virtual source it would disperse and match the dimensions or concentration at the real source. However, to achieve this, a concentration at a centerline point directly downwind must be known. 

For the point source model, the surface emitted power per unit area is estimated using the radiation fraction method as follows ... 

While the point source model provides simplicity, the wide variability in the radiation fraction and the inability to predict it fundamentally detracts considerably from this approach. 

If the point source model is selected, then the received thermal flux is determined from the total energy rate from the combustion process ... 

The result from the solid plume radiation model is smaller than the point source model. This is most likely due to consideration of the radiation obscuration by the flame soot, a feature not treated direedy by the point source model. The differences between the two models might be greater at closer distance to the pool fire. 

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