Fire plumes

Fundamentals of Fire Phenomena James G. Quintiere 2006 John Wiley Sons, Ltd ISBN 0-470-09113-4 

Some of the foundational studies for turbulent fire plumes include the work of the following investigators  

The measurements of Rouse, Yih and Humphries (1952) [1] helped to generalize the temperature and velocity relationships for turbulent plumes from small sources, and established the Gaussian profile approximation as adequate descriptions for normalized vertical velocity (w) and temperature (7), e.g. 

The theoretical analysis by Morton, Taylor and Turner (1956) [2] established approximate similarity solutions for an idealized point source in a uniform and stably stratified atmosphere. 

Yokoi (1960) [3], singly produced a small book as a report, which carefully investigated point, line and finite heat sources with eventual applications to the hazard from house fire and window flame plumes. 

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The model is a straightforward extension of a pool-fire model developed by Steward (1964), and is, of course, a drastic simplification of reality. Figure 5.4 illustrates the model, consisting of a two-dimensional, turbulent-flame front propagating at a given, constant velocity S into a stagnant mixture of depth d. The flame base of width W is dependent on the combustion process in the buoyant plume above the flame base. This fire plume is fed by an unbumt mixture that flows in with velocity Mq. The model assumes that the combustion process is fully convection-controlled, and therefore, fully determined by entrainment of air into the buoyant fire plume. 

Example 3.4 A turbulent fire plume is experimentally found to bum with 10 times the required stoichiometric air up to the tip of the flame. It is also measured that 20 % of the chemical energy is radiated to the surroundings from the flame. The fuel is methane, which is supplied at 25 °C and burns in air which is also at 25 °C. Calculate the average temperature of the gases leaving the flame tip. Assume constant and equal specific heats and steady state. 

This is a realistic approximate average temperature at the flame tip for most fire plumes. 

At the instant of time shown, the entrainment of air into the fire plume is 300 g/s, the outflow of smoke through the door is 295 g/s and the liquid fuel evaporation rate of a spill burning on the floor is 10 g/s. What is the mass rate of smoke accumulation within the room ... 

Steward (1964) [4] and (1970) [5] presented a rigorous but implicit approximate analysis for both axisymmetric and two-dimensional strip fire plumes respectively, including combustion and variable density effects. 

Other measurements such as gas species and soot all have importance in fire plumes but will not be discussed here. As we have seen for simple diffusion flames, the mixture fraction plays a role in generalizing these spatial distributions. Thus, if the mixture fraction is determined for the flow field, the prospect of establishing the primary species concentration profiles is possible. 

As stated earlier, much has been written about fire plumes. Excellent reviews exist by Zukoski [8], Heskestad [9], Delichatsios [10] and McCaffrey [11]. The student is encouraged to read the literature since many styles of presentation exist, and one style might be more useful than another. We cannot address all here, but will try to provide some theoretical framework for understanding the basis for the many alternative correlations that exist. 

It is interesting to note some features of these ideal cases since they match the far-field data of large fire plumes. The velocity and temperature at the centerline of a point plume decreases with height and both are singular at the origin. Only the temperature has this behavior in the line plume, with the velocity staying constant along the centerline. A... 

Table 10.2 gives correlation results based on Gaussian profiles with [3 selected as 1 for the axisymmetric and line-fire plumes [12]. It is indeed remarkable that the local ... 

Figure 10.10 Centerline fire plume (a) temperature rise and (b) velocity (from McCaffrey [6])...

Table 10.4 Axisymmetric fire plume data for varying fuels and diameter taken from References [16], [17] and [19]...

Zukoski [8] claims that Cp can range from 3 to 6, and suggests a value from experiments by Turner [30] of 3.5. Recent results by Tanaka, Fujita and Yamaguchi [31] from rising fire plumes, shown in Figure 10.21, find a value of approximately 2. 

Figure 10.21 Rise time of starting fire plumes (from Tanaka, Fujita and Yamaguchi [31])...

Zukoski, E.E., Properties of fire plumes, in Combustion Fundamentals of Fire (ed. G. Cox), Academic Press, London, 1995. 

Heskestad, G., Fire plumes, in The SFPE Handbook of Fire Protection Engineering, 2nd edn, (eds P.J. DiNenno et all) Section 2, National Fire Protection Association, Quincy, Massachusetts, 1995, pp. 2-9 to 2-19. 

Heskestad, G., Virtual origins of fire plumes, Fire Safety J., 1983, 5, 109-14. 

Heskestad, G., Fire plume air entrainment according to two competing assumptions, Proc. Comb. Inst., 1986, 21, pp. 111-20. 

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