Karlovitz number

In combustion, the Karlovitz number is defined as the ratio of chemical time scale ${\displaystyle t_{F}}$ to Kolmogorov time scale ${\displaystyle t_{\eta }}$, named after Béla Karlovitz.^[1][2][3] The number reads as

${\displaystyle \mathrm {Ka} ={\frac {t_{F}}{t_{\eta }}}}$.

In premixed turbulent combustion, the chemical time scale can be defined as ${\displaystyle t_{F}=D_{T}/S_{L}^{2}}$, where ${\displaystyle D_{T}}$ is the thermal diffusivity and ${\displaystyle S_{L}}$ is the laminar flame speed and the flame thickness is given by ${\displaystyle \delta _{L}=D_{T}/S_{L}}$, in which case,

${\displaystyle \mathrm {Ka} ={\frac {\delta _{L}^{2}}{\eta ^{2}}}}$

where ${\displaystyle \eta }$ is the Kolmogorov scale. The Karlovitz number is related to Damköhler number as

${\displaystyle \mathrm {Ka} ={\frac {1}{\mathrm {Da} }}}$

if the Damköhler number is defined with Kolmogorov scale. If ${\displaystyle \mathrm {Ka} <1}$, the premixed turbulent flame falls into the category of corrugated flamelets and wrinkled flamelets, otherwise into the thin reaction zone or broken reaction zone flames.