Turbulent Karlovitz number

The concept of turbulent flame stretch was introduced by Karlovitz long ago in [15]. The turbulent Karlovitz number (Ka) can be defined as the ratio of a turbulent strain rate (s) to a characteristic reaction rate (to), which has been commonly used as a key nondimensional parameter to describe the flame propagation rates and flame quenching by turbulence. For turbulence s >/ />, where the dissipation rate e and u, L and v... 

The classification of flames depends on the mixture characteristics of the fuel and oxidizer, and on the interaction between the flow properties and the chemistry. This classification is done by means of dimensionless quantities, namely, the mrbulent Reynolds number, the turbulent Damkohler number, and the turbulent Karlovitz number, respectively defined by... 

In any circumstances, it can be expected that and (5x are algebraic functions of turbulence length scale and kinetic energy, as well as chemical and molecular quantities of the mixture. Of course, it is expedient to determine these in terms of relevant dimensionless quantities. The simplest possible formula, in the case of very fast chemistry, i.e., large Damkohler number Da = (Sl li)/ SiU ) and large Reynolds Re = ( Ij)/ (<5l Sl) and Peclet numbers, i.e., small Karlovitz number Ka = sjRej/Da will be Sj/Sl =f(u / Sl), but other ratios are also quite likely to play a role in the general case. 

In particular, Bradley and co-authors [40-45] have collected more than 1,600 experimental data sets on 5t, normalized to the laminar burning velocity The data interrelate Sj/Su with the curvature factor that includes the effective mean-square normalized pulsation velocity u /Sj in cold premixed gases and the Karlovitz factor K multiplied by the Lewis number Le. The diagrammatic presentation of the aforementioned data shows the Re/Le parameter effect, where Re is the turbulent Reynolds number. These experimental data are the source for verification of turbulent combustion models including a laminar flamelet approach [46, 47]. 

However, in region n, which boundary corresponds to the Karlovitz turbulence number Kax = 1, the reaction zone thickness is equal to that of region 1. It means that the chemical reaction is completed within tc, a negligibly small value in comparison with the characteristic time of the turbulent mixing t. The txAc ratio is called the Damkohler number Dax. 

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