Kolmogorov eddy

Davies (Turbulence Phenomena, Academic, New York, 1972) presents a good discussion of the spectrum of eddy lengths for well-developed isotropic turbulence. The smallest eddies, usually called Kolmogorov eddies (Kolmogorov, Compt. Rend. Acad. Sci. URSS, 30, 301 32, 16 [1941]), have a characteristic velocity fluctuation given by... 

Most of the energy dissipation occurs on a length scale about 5 times the Kolmogorov eddy size. The characteristic fluctuating velocity for these energy-dissipating eddies is about 1.7 times the Kolmogorov velocity. 

In stirred chemical reactors, unlike in combustion and with other gas-phase reactions, these closure terms should take into account that for liquids the Schmidt number (Sc = v/D) is in the order 100-1,000, and, hence, the role of species diffusion at scales within the Kolmogorov eddies should explicitly be taken into account (Kresta and Brodkey, 2004). Essential is that diffusion of chemical species is governed by the Batchelor length scale rjB which obeys to... 

Physically, this closure attempts to model the effect of SGS fluctuations on the filtered reaction rate by assuming that the largest of the SGS are dynamically similar to the smallest of the resolved scales. The influence of the smallest eddies, in particular Kolmogorov eddies, on the filtered reaction rate is assumed negligible because the large viscosity in the flame tends to rapidly dissipate these scales [19]. Further discussion and assessment of this model with comparisons to other SGS combustion closures and DNS results can be found in [17]. 

For multiphase flow that is normally encountered in fluidized bed reactors, there are two kinds of definitions of the micro-scale first, it is the scale with respect to the smaller one between Kolmogorov eddies and particles second, it is the scale with respect to the smallest space required for two-phase continuum. If the first definition is adopted, the... 

Kolmogorov eddy length (microscale of turbulence) (L) specific growth rate (T1) maximum specific growth rate (T1) kinematic viscosity (L2 T"1)... 

Literature reports have used the following reactor parameters to correlate the effects of agitation intensity with cell injury in bioreactors agitator rpm, impeller tip speed, integrated shear factor and Kolmogorov eddy size. Additional parameters have been used for microcarrier bioreactors (discussed below). All correlations of cell injury with a bioreactor parameter should be used only qualitatively. These correlations are, at present, indicative of various trends or mechanistic hypotheses and should not be used for quantitative bioreactor scale-up. In addition, such correlations are applicable to the specific cell type, because different cell types are likely to exhibit different responses to fluid forces. 

---