The spill plume in smoke control design

Using recent data, obtained by Morgan, Poreh and colleagues, we produce correlations for the mass flow of a two-dimensional plume emerging normal to the straight edge of a flat horizontal surface—the balcony—and rising up into a uniform atmosphere (the spill plume). A comparison is made with an earlier correlation of the same data by Poreh et al. which required values of the layer depth, D_B, in addition to those of the layer flow per unit length of line plume, M^′_B. The treatment of Poreh et al. followed others assuming the linear relationship typical of far-field line plumes between the mass flow M^′ and the height z with a correction Δ—the virtual source. This linearity is a theoretical consequence of self-similarity (and a constant entrainment coefficient) in the velocity and temperature profiles across the plume, but recent, as yet unpublished, studies including some by computational fluid dynamics (CFD) cast doubt on the existence of self-similarity for these plumes at the low heights relevant in practice. However, a dimensional analysis of the flow does not require the assumption of self-similarity and we have demonstrated the linearity as a conclusion and not an assumption. The effective entrainment coefficient is, as found by Poreh et al., less than the value 0·16 found by Lee and Emmons and used in early work by Morgan and Marshall. The lower figure of 0·11 is consistent with other recent work on line plumes. The experimental values of D_B, the layer depth reported by Poreh et al., are in reasonable agreement with theoretical values for small increases in temperatures only. Experiments in model atria by Hansell, Morgan and Marshall which are not fully two-dimensional are discussed. Our correlation of them can be reconciled with that obtained by Law and subsequently used by the Chartered Institution of Building Service Engineers (CIBSE).