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International Journal of Chemical Engineering
Volume 2008, Article ID 178292, 10 pages
Research Article

Scaling Analysis on Pulsating Flame Spread over Liquids

1Department of Intelligent Machines and System Engineering, Hirosaki University, Hirosaki 036-8561, Japan
2Department of Mechanical Engineering, Oita National College of Technology, Oita 879-0152, Japan
3Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USA

Received 16 February 2008; Accepted 12 May 2008

Academic Editor: Adrian Schumpe

Copyright © 2008 Kozue Takahashi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Scaling analyses based on subsurface layer instability were performed to explore the role of three independent (surface tension, gravity, and viscosity) influences on the mechanism of pulsating flame spread under normal and microgravity conditions. These three influences form two independent pi-numbers: the Marangoni (Ma) number and Grashof (Gr) number, which include the characteristic length scale ratio (depth of subsurface circulation)/(horizontal length of preheated liquid surface). The Prandtl (Pr) number was introduced to compensate for the different thermal diffusivity and kinematic viscosity of different liquids. Also a nondimensional flame spread rate, (= , where is the quenching distance and is the diffusivity of fuel vapor) was introduced. Using these nondimensional parameters, the flame spread mechanism was divided into two separate regimes: for the shallow liquid pool the nondimensional flame spread rate was correlated with , while for the deep liquid pool it was correlated with .