Untitled - Aerobib - Universidad Politécnica de Madrid

298 CHAPTER 12. DIFFUSION FLAME
where R is the burner’s radius, and
t = L v , (12.48)
where v is the mean velocity of the jet between the base and the tip of the flame and L
the length of the same. Through elimination of t and z between (12.46), (12.47) and
(12.48) one obtains
L ∼ R2 v
2D . (12.49)
In laminar flames D depends only on the properties of the gases. Furthermore
R 2 v is proportional to the fuel flow rate G. Consequently, we have
in accordance with the result obtained by Burke-Schumann.
L ∼ G
2D , (12.50)
In a turbulent flame D is the turbulent diffusivity which has the form
When this value is substituted into (12.49) it results
D ∼ vR. (12.51)
L ∼ R, (12.52)
which as previously seen also agrees with experimental results.
References
[1] Burke, S. F. and Schumann, T. E. W.: Diffusion Flames. Industrial and Engineering
Chemistry, Vol. 20, October 1928, pp. 998-1004.
[2] Barr, J.: Diffusion Flames in the Laboratory. AGARD Memorandum No.
AG11/M7, 1954.
[3] Hottel, H. C. and Hawthorne, W.R.: Diffusion in Laminar Flame Jets. Third
Symposium (International) on Combustion, Williams and Wilkins Co., Baltimore,
1949, pp. 254-266.
[4] Barr, J.: Diffusion Flames. Fourth Symposium (International) on Combustion,
Williams and Wilkins Co., Baltimore, 1953, pp. 765-771.
[5] Barr, J.: Length of Cylindrical Laminar Diffusion Flames. Fuel, Jan. 1954,
pp. 51-59.
[6] Lewis, B. and von Elbe, G.: Combustion, Flames and Explosions of Gases.
Academic Press Inc. Publishers., New York, 1951.