Kolmogorov dissipative scale

Rate of turbulence production (m s ) Velocity of a turbulent eddy of size X Rate of turbulence dissipation (m s ) Kolmogorov length scale (m)... 

By definition, the dissipation range is dominated by viscous dissipation of Kolmogorov-scale vortices. The characteristic time scale rst in (2.74) can thus be taken as proportional to the Kolmogorov time scale rn, and taken out of the integral. This leads to the final form for (2.70),... 

Deduced in 1941 by A. N. Kolmogorov, it is generally referred to the Kolmogorov length or dissipation scale (9). 

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. 

In turbulent flow the same mechanism takes place inside the smallest eddies, on the Kolmogorov micro scale. It can be shown that the average shear rate within these eddies is proportional to the root of the specific energy dissipation ... 

Where does this leave us We have three ways to estimate the dissipation and the Kolmogorov length scale The first requires experimental information for Cu. Cl, and A the second uses the power number and the impeller swept volume to get an estimate of the maximum local dissipation the third uses the total volume of the tank to get an estimate of the gross average dissipation and introduces a factor of (D/T) into the equation. More recent detailed studies on the Rushton turbine in particular (Michelet, 1998 Escudier, 2001) have shown that these estimates are reasonably accurate over some portion of the impeller discharge stream. All three methods will allow us to assess trends on scale-up, where physical properties often remain constant, but dimensions and rotational speeds change. The power per impeller swept volume is recommended as the best practice estimate. 

Batchelor (1959) developed an expression for the smallest concentration (or temperature) striation based on the argument that for diffusion time scales longer than the Kolmogorov scale, turbulence would continue to deform and stretch the blobs to smaller and smaller lamellae. Only once the lamellae could diffuse at the same rate as the viscous dissipation scale would the concentration striations disappear. The Batchelor length scale is the size of the smallest blob that can diffuse by molecular diffusion in one Kolmogorov time scale. Using the lamellar diffusion time from eq. (13-6) gives... 

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. 

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