Markstein length

In the case of spherical flames, additional characteristics, such as the Karlovitz stretch factor [2] and the Markstein length [3, 4], are used to describe real curved flames. 

Most real flames are subjected to local surface hydrodynamic deformation including the one that causes changing of the local curvature. It affects the velocity of the flame front propagation (further referred to as flame velocity ) and it is called a stretch or a stretch effect. 

The Karlovitz stretch factor K denotes the rate of a flame front area change dAldt with respect to the whole flame surface area [5] 

The K factor has dimensionality s, it can be expressed in terms of a flame front radius ty for a spherical flame  

Gelfand et al., Thermo-Gas Dynamics of Hydrogen Combustion and Explosion, Shock Wave and High Pressure Phenomena, 

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The proportionality constant, L, is called the Markstein length [97]. Equation (7.2) can be written, in dimensionless form, as... 

D. Bradley, P.H. Gaskell and X.J. Gu, Burning Velocities, Markstein Lengths, and Flame Quenching for Spherical Methane-Air Flames A Computational Study, Comb, and Flame 104 (1996) 176. 

Bechtold, J.K., and M. Matalon. 2001. The dependence of the Markstein length on stoichiometry. Combustion Flame 127 1906. 

Quantitative description of the stretch is a key problem for both laminar and turbulent combustion. Experimental data obtained for the stretch effect on a premixed flame have been proven by theory and by detailed computer simulation [7-14]. It has been found that when the stretch value is small, its effect on the flame velocity is linear. The change in the burning velocity can be expressed by the so called Markstein length [3, 4, 11, 12] found from the equation ... 

The Markstein length - is a quantitative measure of the flame response to the stretch. Here - curved flame velocity, - flat flame velocity, Lm - Markstein length, K - Karlovitz stretch factor. 

The characteristic dimensional parameter Lm takes into account the flame curvature effect on the burning velocity. The higher its absolute value, the stronger the curvature effect is. The Markstein length relation to the laminar flame thickness S = dSu, where - the laminar flame velocity, is known as the Markstein number Ma = Lyild. Table 1.1 [15] presents the Markstein length for hydrogen-air mixtures at 298 K and 0.1 MPa... 

Figure 1.2 illustrates the change in the Markstein length for H2 + Air mixture in relation to the stoichiometric ratio value. 

Fig. 1.2 The Markstein lengths found experimentally for spherically divergent flames in H2 + air mixture at room temperature and atmospheric pressure [15, 50]...

The flame stretch-effect influences a laminar flame velocity due to the thermal and mass selective diffusion [7-12]. This effect may cause a flame front instability depending on the sign of the Markstein length. When a Markstein length is negative, the flame laminar velocity increases with the stretch growth. 

The flame front concavity (bulging) with respect to the combustion products possess a positive (negative) stretch, and their growth makes the flame unstable. At a positive Markstein length, the flame laminar velocity falls with the stretch increase and the flame surface curvatures reduce, which indicates flame stability. 

M.J. Brown, I.C. McLean, D.B. Smith, S.C. Taylor, Markstein lengths of CO/H2/air flames, using expanding spherical flames. Proc. Combust. Inst. 26, 875-881 (1996)... 

Markstein length Characteristic dimensional parameter Lm taking into account a flame curvature effect on a combustion velocity. The greater is an absolute value of this parameter, the more the curvature effect is. A ratio of a Markstein length Lm to a laminar flame thickness d = alS, where -combustion laminar velocity, is called the Markstein number Ma = Lm/S. 

Diffusion flame body length Markstein length (scale)... 

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