Kolmogorov scale of turbulence

FIGURE 10.5. Parameter plane of nondimensional intensity and nondimensional Kolmogorov scale of turbulence for premixed turbulent combustion, showing regimes of combustion and lines for constant values of turbulence Reynolds numbers, nondimensional integral scale, and a Damkohler number. 

X Kolmogorov s micro-scale of turbulence (Section 10.1) dynamic viscosity... 

Instead, the Kolmogorov micro-scales (1.328) to (1.330) characterize the dissipation scales of turbulence and might indicate the effectiveness of micromixing in the flow provided that the turbulent energy dissipation rate and the kinematic viscosity of the fluid is known. If the Kolmogorov micro length scale is much larger than the molecular scales, the molecules are not efficiently mixed by turbulent diffusion. 

Where e is the rate of kinetic energy dissipation per unit mass and Cx is of order 1. Equation (36) is valid for drops whose diameter falls within the inertial subrange of turbulence, < d < L, where L is the integral scale of turbulence and q = is the Kolmogorov microscale of turbulence. 

The method proposed by Kolmogorov (53) and Hinze (54) was extended by Ba+dyga and Podgorska (56) and Ba+dyga and Bourne (57) to the case of more realistic intermittent turbulence, which was described by means of multifractal formalism. In this model drop size in the inertial subrange also depends on the integral scale of turbulence, which is related to the scale of the system. This new formalism predicts... 

Second, some of the issues pertaining to the small (Kolmogorov) scales of the flow can be addressed. The PIV measurements are spatially filtered, and a correct estimate of the Kolmogorov scale cannot be obtained directly from the experimental setup. Direct numerical simulation does not have such a restriction since for an accurate simulation of turbulent flows the smallest scales have to be resolved, i.e., the grid has to be fine enough to capture the smallest scales. The knowledge of the behavior of the small scales is of interest since dissipation processes that directly affect the chemistry take place at these scales. 

The process of deformation and breakage of a drop is caused by small-scale pulsations 2 (see Section 11.3) since large-scale pulsations vary little over distances of the order of the diameter of a drop. The velocity Ux of such pulsations depends on X being greater or smaller than the internal scale of turbulence, 2q (Kolmogorov scale) ... 

For turbulent flow, because the ratio between the integral and the Kolmogorov scales of length and time are given, respectively, by... 

So what is the characteristic length scale of turbulence This question is analogous to asking, What is the diameter of an elephant We might say that the Kolmogorov scale is analogous to the diameter of the elephant s tail. Many... 

The apparent success of P/pV as a correlating parameter for ( ) and kLa in the turbulent regime implies that it is strongly linked to bubble size as well as to liquid circulation. Indeed, P/pV can be eqnated to the vessel-average value of 8, the turbulent energy dissipation rate at the smallest scales of turbulence, if it is assumed (classically) that all the power eventually dissipates at these scales. Several workers have postulated that bubble breakup occurs (finally) by impact of turbulent eddies at this smallest (Kolmogorov) scale, presumably via pressure fluctuations distorting the bubble sufficiently to disrupt it. Hinze (1979)... 

---