Flame stretch

In combustion, flame stretch ([math]\displaystyle{ K }[/math]) is a quantity which measures the amount of stretch of the flame surface due to curvature and due to the outer velocity field strain. The early concept of flame stretch was introduced by Karlovitz in 1953, although the correct definition was introduced two decades later by Forman A. Williams in 1975. [1][2][3] George H. Markstein studied flame stretch by treating the flame surface as a hydrodynamic discontinuity (known as flame front).[4] The flame stretch is also discussed by Bernard Lewis and Guenther von Elbe in their book.[5] All these discussions treated flame stretch as an effect of flow velocity gradients. The stretch can be found even if there is no velocity gradient, but due to the flame curvature. So, the definition required a more general formulation and its precise definition was first introduced by Forman A. Williams in 1975[6][7] as the ratio of rate of change of flame surface area to the area itself

[math]\displaystyle{ K = \frac{1}{A}\frac{dA}{dt}. }[/math]

When [math]\displaystyle{ K\gt 0 }[/math], the flame is stretched, otherwise compressed. Sometimes the flame stretch is defined as non-dimensional quantity

[math]\displaystyle{ \tilde K = \frac{\delta_L}{S_L} \frac{1}{A}\frac{dA}{dt} }[/math]

where [math]\displaystyle{ \delta_L }[/math] is the laminar flame thickness and [math]\displaystyle{ S_L }[/math] is the laminar propagation speed of unstretched premixed flame.

## See also

* Markstein number

## References

1. ↑ Karlovitz, B., Denniston Jr, D. W., Knapschaefer, D. H., & Wells, F. E. (1953, January). Studies on Turbulent flames: A. Flame Propagation Across velocity gradients B. turbulence Measurement in flames. In Symposium (international) on combustion (Vol. 4, No. 1, pp. 613-620). Elsevier.
2. ↑ Matalon, M. (1983). On flame stretch. Combustion Science and Technology, 31(3-4), 169-181.
3. ↑ Matalon, M., & Matkowsky, B. J. (1982). Flames as gasdynamic discontinuities. Journal of Fluid Mechanics, 124, 239-259.
4. ↑ Markstein, G. H. Non-steady flame Propagation,(1964). P22, Pergarmon, New York.
5. ↑ Lewis, B., & Von Elbe, G. (2012). Combustion, flames and explosions of gases. Elsevier.
6. ↑ Williams, F. A. (1975). Recent advances in theoretical descriptions of turbulent diffusion flames. In Turbulent mixing in nonreactive and reactive flows (pp. 189-208). Springer, Boston, MA.
7. ↑ Williams, F. A. (1975). " A Review of Some Theoretical Considerations of Turbulent Flame Structure." in analytical Numerical Methods for Investigation of Flow Fields with Chemical Reactions, Especially Related Fields to Combustion. In AGARD Conference Proceedings, 1975 (Vol. 164).

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