Transient Aspects of Fire Plumes

For simplicity let us consider an idealized point (or line) transient plume. Then by an extension of Equation (10.27), it can be shown that the plume dimensionless variables would depend on the axial position and time as 

One approach is to approximate the unsteady solution by a quasi-steady solution where Q(t) is a function of time and time is adjusted. This can be approximated by determining the transport time (fD) from the origin to position z by 

More specific results are beyond the scope of our limited presentation for plumes. However, we will examine some gross features of transient plumes namely (a) the rise of a starting plume and (b) the dynamics of a fire ball due to the sudden release of a finite burst of gaseous fuel. Again, our philosophy here is not to develop exact solutions, but to represent the relevant physics through approximate analyses. In this way, experimental correlations for the phenomena can be better appreciated. 

---