Modelling of the plume rise phenomenon due to warehouse or pool fires considering penetration of the mixing layer
Introduction
Smoke plumes containing toxic combustion products resulting from warehouse or pool fires, will initially rise due to the density difference between the hot combustion products and the ambient air. This density difference is caused by the fact that the temperature of the plume is significantly higher than the temperature of ambient air. The theory behind this plume rise phenomenon foresees that there will be a height at which the released material will be in equilibrium with the density of the air at that height, leading to a maximum plume height. The trajectory of the plume and the hazard distances to specific concentration threshold levels will be mainly influenced by the windspeed, atmospheric stability class and the fire's convective heat production, where the combination of these parameters lead to potential penetration of, or even reflection by the mixing layer.
Typical models that describe the mathematics behind rising of hot plumes include the effects of atmospheric turbulence, as described by the Pasquill stability class, such as those described by Briggs (1969). However, the plume's potential penetration of the mixing layer should also be considered. The importance of the plume penetration is that all mass that has risen above the mixing layer, will never disperse back into the mixing layer. Therefore, toxic combustion products will be trapped above the mixing layer height and will never create chemical exposure at ground level. The reason for this is that at the boundary of the mixing layer (at the temperature inversion height) there is no vertical turbulence. Only the stronger chimney emissions are likely to penetrate upwards due to their greater buoyancy forces. Apart from penetration of the mixing layer height, the potential reflection of the plume should also be considered, which can play a role for plumes that remain below the mixing layer height. Fig. 1 shows the penetration and reflection phenomenon in smoke plumes.
The present study has led to the implementation of a dedicated model, implemented in Gexcon's software package EFFECTS, to simulate the plume rise phenomenon due to warehouse or pool fires. This model calculates the maximum height and plume path of the plume and includes reporting of a ‘penetration fraction’, which is a calculated parameter that expresses the amount of plume penetrating the mixing layer. Additionally, the reflection phenomenon is also considered. The model also presents concentration threshold contours of toxic combustion products at any height level. Dry and wet deposition are not accounted for in the model.
The model provides safety professionals with valuable information for hazard identification, safety analysis and emergency planning. For instance, if a warehouse fire has enough convective heat production, a toxic smoke plume may rise high enough and even penetrate the mixing layer, not providing any danger at ground level. Trying to extinguish the fire, would decrease the heat production, leading to more danger of toxic exposure at ground level, although other factors should also be taken into consideration such as potential escalation to a bigger and prolonged fire.
Because harmful concentrations may reach very large distances, where the assumption of a homogeneous wind-field is no longer realistic, the plume rise model has also been extended to account for the meandering of the plume (due to time and location dependent meteorological conditions). This model extension uses real-time meteorological data retrieved from the internet, which results in time dependent concentration contours of the plume and a real time view of the meandering plume path. This extension has not been made commercially available but could – when properly integrated into control rooms – provide valuable information to emergency services during interventions.
Section snippets
Plume rise modelling
The “plume rise from warehouse or pool fires model” as implemented in the software package EFFECTS is based on Briggs' study of the plume rise phenomenon (Briggs, 1969), the theory of the Yellow Book (Yellow Book, 1992) and uses Mill's correction for burning fires (Mills, 1987).
Validation
The validation of the “plume rise from warehouse or pool fires model” is performed by comparing the results given with EFFECTS with measurements from field experiments and with other already validated mathematical models. The validation includes a description of each validation experiment and a detailed discussion of the results obtained from a statistical and graphical comparison against the field data.
Each experiment set is statistically evaluated to determine the accuracy and precision of
Results
In this chapter the results obtained with the “plume rise from warehouse or pool fires model” as implemented in the software package EFFECTS are presented. For all the figures included in this chapter, the black dashed line corresponds to the mixing layer height, the red line corresponds to the centerline of the rising plume and the dark green line (the outermost contour) corresponds to the side view contour for a threshold concentration of 1 mg/m3. The dark blue line (first central contour),
Conclusions
The “plume rise from warehouse or pool fires model” is a model implemented in the software package EFFECTS to calculate the plume rise phenomenon due to warehouse or pool fires. The model is based on the theory presented on Briggs' study (Briggs, 1969), the theory in the Yellow Book (Yellow Book, 1992) and corrected with Mill's correction for burning fires (Mills, 1987).
A mathematical approach for the calculation of the potential penetration of the plume through the atmospheric mixing layer has
CRediT authorship contribution statement
Hans Boot: Conceptualization, Software, Supervision, Project administration. Sonia Ruiz Pérez: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Writing - review & editing, Visualization.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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