# A Mathematical Study of a Fire in the Interaction Zone Between Flows with Different Velocities

David Katoshevski

• Department of Environmental Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

Revised: May 31, 2006
Accepted: May 31, 2006

Katoshevski, D (2006). A Mathematical Study of a Fire in the Interaction Zone Between Flows with Different Velocities. Aerosol Air Qual. Res. 6: 193-212. https://doi.org/10.4209/aaqr.2006.06.0007

## ABSTRACT

An analytical study is presented for describing a flame in a shear layer flow formed between a gaseous fuel stream and an oxidizer stream, moving at different velocities. The diffusion flamesheet approximation is addressed. It is shown how the shear layer flow-field driven by various ratios of free- flows velocities influences flame properties. The role of the “equivalence ratio for diffusion flames”, that is, the product of stoichiometric ratio and the concentration ratio of fuel/oxidizer at the outer flows, is analyzed, in terms of flame shape and location. Flame shapes regimes are described in terms of equivalence ratio and velocity ratio. A “turning point” is revealed in the shift of the flame location from one stream towards the other with increasing Schmidt number. The value of the corresponding “turning point” equivalence ratio, in which the flame shift changes direction, is found to be governed by the velocity profile and specifically by the free stream velocity ratio. Moreover, this ratio is shown to control also the sensitivity of the flame location to changes in the value of the Schmidt number. Downstream velocity deceleration is also addressed, with respect to flame location and flame shape, showing a shift of the flame towards the fuel stream and a change in flame curvature. This study of the location and shape of such a flame configuration elucidates the ways these flame characteristics may be manipulated. It also points out the general region of the main production of air-pollutants in related combustion cases which exist in industry and in the outdoor-atmosphere where fire is occurring between two flows of different chemical species moving at different velocities.

Keywords: Shear Flow; Flame; Analytical Solution

7.3
2022CiteScore

77st percentile

2022 Impact Factor: 4.0
5-Year Impact Factor: 3.4

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