Notes on the similarity of turbulent buoyant fire plumes with large density variations

A number of issues arise and are resolved from a discussion of similarity solutions for turbulent plumes of given convective heat release with large density variations (strong plumes). Similarity solutions are essential for understanding the physics, correlating experimental data and validating numerical simulations of turbulent free flows. We exploit results for plane plumes emphasizing, in particular, aspects of the plume sources, the plume width and the assumptions regarding the applicability of the ``turbulent'' boundary layer assumption (namely that the pressure variation normal to the axis is zero, dp/dy = 0). Although similarity solutions for the weak plumes can be extended to the source through similarity solutions for strong plumes, the latter show that a length scale additional to the distance from the origin (sufficient for weak plumes in the far field) is needed to characterize the flow near the source. Thus (a) a virtual point source of zero size does not exist and (b) the flow near the source must be elliptic being unable to be represented by a boundary layer approximation as extensively done. The additional length scale for plane plumes is proportional to (Q) over dot(2/3) where (Q) over dot is the rate of convected heat release per unit length of plume source. Similar results are obtained for axisymmetric plumes. For axisymmetric plumes, the length scale is proportional to (Q) over dot'(2/5) where the convected heat release rate is. These length scales seem to be the same as the flame heights in plane or axisymmetric fires. This apparent similarity is misleading because the proportionality coefficient for the flame heights depends on the properties of combustion in the flame region (e.g. flame temperature, stoichiometric ratio and radiant fraction) in contrast to the turbulent buoyant plumes where it depends only on the convective heat flow. For strong plumes with density variations greater than the air, the similarity solutions apply until the origin of zero plume width is reached. (C) 2006 Elsevier Ltd. All rights reserved.