Kolmogorov microscale turbulence

Typical quoted values for the Kolmogorov microscale of turbulence for agitated vessels are normally in the range 25 —50 pm. 

Thus, the criterion to be satisfied if a laminar flame is to exist in a turbulent flow is that the laminar flame thickness <5L be less than the Kolmogorov microscale 4 of the turbulence. 

The smallest size for turbulent eddies is given by the Kolmogorov microscale A. Energy loss below this size only occurs via viscous dissipation. Here also, several scales have been introduced in the framework of turbulence theory, depending whether velocity or concentration fluctuations are considered, namely Ak> Ag, and Ac (see Table I). In liquids, Ak is typically between 10 and 100 ym. The Kolmogorov microscale Ak is frequently used in the in-... 

Earlier it was stated that the structure of a turbulent velocity field may be presented in terms of two parameters—the scale and the intensity of turbulence. The intensity was defined as the square root of the turbulent kinetic energy, which essentially gives a root-mean-square velocity fluctuation U. Three length scales were defined the integral scale /q, which characterizes the large eddies the Taylor microscale X, which is obtained from the rate of strain and the Kolmogorov microscale 1, which typifies the smallest dissipative eddies. These length scales and the intensity can be combined to form not one, but three turbulent Reynolds numbers Ri = U lo/v, Rx. = U X/v, and / k = U ly/v. From the relationship between Iq, X, and /k previously derived it is found that / ... 

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. 

Saffinan and Turner (43) considered collisions between droplets due to turbulence in rain clouds. Under turbulent conditions, droplet collision is governed by two different mechanisms isotropic turbulent shear and turbulent inertia. The choice of regime applicable to a droplet is determined by its size in relation to the Kolmogorov microscale denned earlier. Droplets of diameter d > t are subjected to die former of these processes (small-scale motion). Spatial variations in the flow give neighboring droplets different velocities and fliis result in collisions. Droplets of diameter d > T] are subjected to turbulent inertia. In this case, collisions result from the relative movement of droplets in the surrounding fluid. Droplets of different diameter will have different inertias and this results in collisions. Droplets of equal diameter, however, will not collide under this mechanism as fliey have the same inertia. 

The effects of secondary flow on droplet collision and coalescence mechanisms have not been considered in the literature currently reviewed. The scale of secondary flow is much larger than the Kolmogorov microscale q and it will, therefore, only affect droplets of diameter d > q (those subject to turbulent inertia). Secondary flow will be most prevalent following changes in duct geometry, particularly where there is some form of duct divergence. 

When the porosity would not change with the aggregate size, d would be 3. In many aggregation processes d turns out to be a constant, often between 2 and 2.5. It has been shown by calculations that the growth rate for lower values of d increases more progressively with time (Kusters 1991, Kusters et al., 1994). However, this applies only for aggregates that are smaller than the Kolmogorov microscale of turbulence. 

Although vortices of small scale, such as Kolmogorov scale or Taylor microscale, are significant in modeling turbulent combustion [4,6-9], vortices of large scale, in fhe order of millimeters, have been used in various experiments to determine the flame speed along a vorfex axis. 

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

The energy dissipation number is derived from the Kolmogorov theory [289, 290]. This theory is based on the concept, that in the turbulent flow range the kinetic energy is transferred by inertial forces from large to ever smaller eddies, until it is finally dissipated through viscosity forces. The eddies produced by the stirrer have the size of the stirrer head and are responsible for the macroscopic turbulence, the smallest eddies on the other hand are directionless. On the microscale so-called isotropic turbulence exists, see Section 1.4.2. 

Kolmogorov (29) is believed to have been one of the first workers to investigate droplet break-up in dispersed systems. For turbulent flow, Kolmogorov determined the microscale eddy length to be ... 

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