# 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 wrinked flamelets, otherwise into the thin reaction zone or broken reaction zone flames.

## Klimov-Williams criterion

In premixed turbulent combustion, Klimov-Williams criterion or Klimov-Williams limit is the condition where ${\displaystyle \mathrm {Ka} =1}$, named after A.M. Klimov[4][5] and Forman A. Williams.[6] When ${\displaystyle \mathrm {Ka} <1}$, the flame thickness is smaller than the Kolmogorov scale, thus the flame burning velocity is not affected by the turbulence field. Here, the burning velocity is given by the laminar flame speed and these laminar flamelets are called as wrinkled flamelets or corrugated flamelets, depending on the turbulence intensity. When ${\displaystyle \mathrm {Ka} >1}$, the turbulent transport penetrates into the preheat zone of the flame (thin reaction zone) or even into the reactive-diffusive zone (distributed flames).

## References

1. ^ Peters, N. (2000). Turbulent combustion. Cambridge university press.
2. ^ Libby, P. A., & Williams, F. A. (1980). Turbulent reacting flows. Turbulent reacting flows.
3. ^ Williams, F. A. (2018). Combustion theory. CRC Press.
4. ^ Klimov, A. M. (1963). Laminar ame in a turbulent ow. Zhur. Prikl. Mekh. Tekh. Fiz, 3, 4958.
5. ^ Klimov, A. M. (1988). Laminar flame in a turbulent flow (No. FTD-ID (RS) T-0642-88). FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OH.
6. ^ 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).