Karlovitz number explained

In combustion, the Karlovitz number is defined as the ratio of chemical time scale

t_F

t_η

, named after Béla Karlovitz.^[1] ^[2] ^[3] The number reads as

Ka=

	t_F
	t_η

In premixed turbulent combustion, the chemical time scale can be defined as

t_F=D_T/S

	2

	L

, where

D_T

is the thermal diffusivity and

S_L

is the laminar flame speed and the flame thickness is given by

\delta_L=D_T/S_L

, in which case,

Ka=

	2
\delta
	L

η²

where

is the Kolmogorov scale. The Karlovitz number is related to Damköhler number as

Ka=

	1
	Da

if the Damköhler number is defined with Kolmogorov scale. If

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.

Klimov–Williams criterion

In premixed turbulent combustion, the Klimov–Williams criterion or Klimov–Williams limit, named after A.M. Klimov^[4] ^[5] and Forman A. Williams,^[6] is the condition where

Ka=1

(assuming a Schmidt number of unity). When

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

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).

Notes and References

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