Markstein number

In combustion engineering and explosion studies, the Markstein number (named after George H. Markstein who first proposed the notion in 1951[1]) characterizes the effect of local heat release of a propagating flame on variations in the surface topology along the flame and the associated local flame front curvature. The dimensionless Markstein number is defined as:

where is the Markstein length, and is the characteristic laminar flame thickness. The larger the Markstein length, the greater the effect of curvature on localised burning velocity. George H. Markstein (1911—2011) showed that thermal diffusion stabilized the curved flame front and proposed a relation between the critical wavelength for stability of the flame front, called the Markstein length, and the thermal thickness of the flame.[2] Phenomenological Markstein numbers with respect to the combustion products are obtained by means of the comparison between the measurements of the flame radii as a function of time and the results of the analytical integration of the linear relation between the flame speed and either flame stretch rate or flame curvature.[3][4][5] The burning velocity is obtained at zero stretch, and the effect of the flame stretch acting upon it is expressed by a Markstein length. Because both flame curvature and aerodynamic strain contribute to the flame stretch rate, there is a Markstein number associated with each of these components.[6]

  1. ^ Markstein, G. H. (1988). Experimental and theoretical studies of flame-front stability. In Dynamics of curved fronts (pp. 413-423). Academic Press.
  2. ^ Oran E. S. (2015). "A tribute to Dr. George H. Markstein (1911–2011)". Combustion and Flame. 162 (1): 1–2. Bibcode:2015CoFl..162....1O. doi:10.1016/j.combustflame.2014.07.005.
  3. ^ Karpov V. P.; Lipanikov A. N.; Wolanski P. (1997). "Finding the markstein number using the measurements of expanding spherical laminar flames". Combustion and Flame. 109 (3): 436. Bibcode:1997CoFl..109..436K. doi:10.1016/S0010-2180(96)00166-6.
  4. ^ Chrystie R.S.M.; Burns I.S.; Hult J.; Kaminski C.F. (2008). "On the improvement of two-dimensional curvature computation and its application to turbulent premixed flame correlations". Measurement Science and Technology. 19 (12): 125503. Bibcode:2008MeScT..19l5503C. doi:10.1088/0957-0233/19/12/125503. S2CID 21642877.
  5. ^ Chakraborty N, Cant RS (2005). "Influence of Lewis number on curvature effects in turbulent premixed flame propagation in the thin reaction zones regime". Physics of Fluids. 17 (10): 105105–105105–20. Bibcode:2005PhFl...17j5105C. doi:10.1063/1.2084231.
  6. ^ Haq MZ, Sheppard CG, Woolley R, Greenhalgh DA, Lockett RD (2002). "Wrinkling and curvature of laminar and turbulent premixed flames". Combustion and Flame. 131 (1–2): 1–15. Bibcode:2002CoFl..131....1H. doi:10.1016/S0010-2180(02)00383-8.