Eddy size

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. 

Micro-scale variables are involved when the particles, droplets, baffles, or fluid chimps are on the order of 100 [Lm or less. In this case, the critical parameters usually are power per unit volume, distribution of power per unit volume between the impeller and the rest of the tanh, rms velocity fluctuation, energy spectra, dissipation length, the smallest micro-scale eddy size for the particular power level, and viscosity of the fluid. 

Macromixing The phenomenon whereby residence times of clumps are distributed about a mean value. Mixing on a scale greater than the minimum eddy size or minimum striation thickness, by laminar or turbulent motion. 

Micromixing Mixing among molecules of different ages (i.e., mixing between macrofluid clumps). Mixing on a scale smaller tlian tlie minimum eddy size or minimum striation diickness by molecular diffusion. 

C 6 m, 1000 °C 15 m, 1100°C and 30 m, 1200 °C [14], The explanation is provided by Koseki [15] (Figure 10.12), showing how Xr decreases for large-diameter fires as eddies of black soot can obscure the flame. The eddy size or soot path length increases as the fire diameter increases, causing the transmittance of the external eddies to decrease and block radiation from leaving the flame. From Table 10.2,... 

A turbulent eddy can be visualized as a large number of different-sized rotating spheres or ellipsoids. Each sphere has subspheres and so on until the smallest eddy size is reached. The smallest eddies are dissipated by viscosity, which explains why turbulence does not occur in narrow passages there is simply no room for eddies that will not be dissipated by viscosity. 

Eddy size decreases near boundaries to the flow field. Because the eddy size is zero at a solid boundary, and often close to zero at a fluid density interface (like an air-water interface), the turbulent eddy size has to decrease as one approaches the boundaries. In addition, because the flow cannot go through a boundary, the largest eddy size cannot be greater than the distance from the center of the eddy to the boundary. 

Turbulent diffusion occurs because turbulent eddies are transporting mass, momentum, and energy over the eddy scale at the rotational velocity. This transport rate is generally orders of magnitude greater than the transport rate due to molecular motion. Thus, when a flow is turbulent, diffusion is normally ignored because e Z). The exception is very near the flow boundaries, where the eddy size (and turbulent diffusion coefficient) decreases to zero. 

For an eddy-size greater than the particle diameter Q > dp ... 

Data from some authors (see [10]) suggest that the fraction Sh/Sc,/3 vs. Reynolds number, as defined above, correlate well (see Fig. 5.3-6). The eddy size from the isotropic turbulence theory is calculated from the following expression ... 

With the aid of the Kolmogorov micro-measures for eddy size Lt and the eddy life time t c, the following relationships, Eqs. (19) and (20) follow ... 

F or turbulent pipe flow, the friction velocity u = Vx ,/p used earlier in describing the universal turbulent velocity profile may be used as an estimate for V Together with the Blasius equation for the friction factor from which e may be obtained (Eq. 6-214), this provides an estimate for the energy-containing eddy size in turbulent pipe flow ... 

Finally, the original eddy size distribution can be obtained as... 

It is possible to apply the same consideration to the eddy size distribution in a turbulent flow because eddies in a turbulent flow are produced by the impeller, shear stress, and so on, without artificiality. There is no difficulty in considering the following relationships between the wavenumber k and the diameter of eddy l in a turbulent flow ... 

The number and volume of the respective scale of eddies can be obtained by using Eq. (5.27), and the eddy size distribution can be shown in the following equation by assuming that the energy per unit volume of the eddy is equal irrespective of the eddies ... 

The eddy size probability density distribution can be expressed by the newly defined PSD. 

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