Markstein number

The Markstein number with respect to the unburnt gas mixture for a one step reaction in the limit of large activation energy asymptotics was derived by Paul Clavin and Forman A. Williams in 1982.[6] The Markstein number then is

${\displaystyle {\mathcal {M}}_{u}={\frac {1}{\alpha }}\ln {\frac {1}{1-\alpha }}+{\frac {\beta (\mathrm {Le} -1)}{2}}{\frac {1-\alpha }{\alpha }}\int _{0}^{\alpha /(1-\alpha )}{\frac {\ln(1+x)}{x}}\,dx}$

where

• ${\displaystyle \alpha }$ is the heat release parameter defined with density ratio,
• ${\displaystyle \beta }$ is the Zel'dovich number,
• ${\displaystyle {\rm {Le}}}$ is the Lewis number of the deficient reactant (either fuel or oxidizer)

and the Markstein number with respect to the burnt gas mixture is derived by Clavin (1985)[7]

${\displaystyle {\mathcal {M}}_{b}={\frac {1}{\alpha }}\ln {\frac {1}{1-\alpha }}+{\frac {\beta (\mathrm {Le} -1)}{2\alpha }}\int _{0}^{\alpha /(1-\alpha )}{\frac {\ln(1+x)}{x}}\,dx}$

In general, Markstein number for the curvature effects ${\displaystyle {\mathcal {M}}_{c}}$ and strain effects ${\displaystyle {\mathcal {M}}_{s}}$ are not same in real flames.[8] In that case, one defines a second Markstein number as

${\displaystyle {\mathcal {M}}_{2}={\mathcal {M}}_{c}-{\mathcal {M}}_{s}.}$

• G equation
• Prandtl number
• Schmidt number