Turbulent Karlovitz

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... 

Karlovitz, B. 1951. Investigation of turbulent flames. /. Chem. Phys. 19 541-547. 

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. 

B. Karlovitz, J.W Denniston, D.IT. Knapschaefer, and RE. Wells 1953, Studies on turbulent flames, Proc. Combust. Inst. 4 613-620. 

CA 42, 5229(1948)(Theory of propagation of flame. States conditions in an expl chem reaction necesssry for propagation of the flame at a const rate. Calcs this rate for a definite relationship between diffusion and heat conductance. Evaluates the effect of chain reactions on the propagation of the flame) 4) B. Karlovitz, JChemPhys 19, 541-46(1951) Sc CA 45, 9341 (1951)(Theory of turbulent flames) 5) G. Klein, Phil-TransRoySocLondon 249, 389—415 (1957)... 

Two other points about the present state of experimental work should be mentioned. One is that measurements of turbulence scale and intensity are necessarily made in the cold flow the flame may upset the flow field, even generating added turbulence as suggested by Karlovitz (42). The second point is that the flame can never be thought of as burning in a region with constant scale and intensity throughout, not only because of the ordinary decay of turbulent fluctuations, but also because there may be (as in Bunsen... 

Karlovitz B., et al. (1953). A. Flame propagation across velocity gradients. B. Turbulence measurement in flames. Fourth Symposium (International) on Combustion, Williams and Wilkins, Baltimore, p. 613. 

B. Karlovitz, "Combustion Waves in Turbulent Gases, in Combustion Processes, vol. II of High Speed Aerodynamics and Jet Propulsion, B. Lewis, R. N. Pease, and H. S. Taylor, eds., Princeton Princeton University Press, 1956, 312-364. 

Another turbulence producing mechanism may occur due to strong velocity gradients parallel to the curved reaction zone which impose shear forces on the interface. This can lead to a roll up of the flame front and, hence, to a larger reaction surface and a higher burning velocity. This kind of flame generated turbulence was found to be important by Karlovitz et al. ° and Scurlock et al. ... 

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. 

It was revealed in [11] that when the pulsating speed exceeds the laminar flame velocity, the pulsating speed dependence of becomes linear. Therefore, the coordinates were chosen which allowed the use of this empirical dependence and to verify the possibility of a generic expression for the turbulent flame velocity that takes the Karlovitz correction into account ... 

The circle locations around the plotted line in Fig. 3.9 support the Karlovitz hypothesis of additional turbulence generated by the flame and allows the estimation of the turbulent flame velocity in lean mixtures (13.7% H2-27% H2) at atmospheric pressure. 

Fig. 3.9 The linear dependence supporting the Karlovitz hypothesis of flame generated turbulence...

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