Rms velocity fluctuations

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. 

The transition from laminar to turbulent flow in micro-channels with diameters ranging from 50 to 247 pm was studied by Sharp and Adrian (2004). The transition to turbulent flow was studied for liquids of different polarities in glass micro-tubes having diameters between 50 and 247 pm. The onset of transition occurred at the Reynolds number of about 1,800-2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. 

Longitudinal component of velocity rms velocity fluctuation Slip velocity Friction velocity... 

RMS velocity fluctuations normal to the wall are larger than those parallel to the wall. 

Numerous experiments show that power per unit volume in the zone of the impeller (which is about 5% of the total tank volume) is about 100 times higher than the power per unit volume in the rest of the vessel. Making some reasonable assumptions about the fluid mechanics parameters, the root-mean-square (rms) velocity fluctuation in the zone of the impeller appears to be approximately 5-10 times higher than in the rest of the vessel. This conclusion has been verified by experimental measurements. 

The ratio of the rms velocity fluctuation to the average velocity in the impeller zone is about 50% with many open impellers. If the rms velocity fluctuation is divided by the average velocity in the rest of the vessel, however, the ratio is on the order of 5-10%. This is also the level of rms velocity fluctuation to the mean velocity in pipeline flow. There are phenomena in microscale mixing that can occur in mixing tanks that do not occur in pipeline reactors. Whether this is good or bad depends upon the process requirements. 

Recently, one of the most practical results of these studies has been the ability to design pilot plant experiments (and, in many cases, plant-scale experiments) that can establish the sensitivity of process to macroscale mixing variables (as a function of power, pumping capacity, impeller diameter, impeller tip speeds, and macroscale shear rates) in contrast to microscale mixing variables (which are relative to power per unit volume, rms velocity fluctuations, and some estimation of the size of the microscale eddies). 

Other background on turbulent velocity parameters is given by Cutter (3) who calculated several parameters from photographs of flow patterns in a mixing vessel. He found that the RMS velocity fluctuation was primarily related to energy dissipation. His measurement scale In making these photographic studies could be quite different from the scale velocities from the hot wire velocity meter reported here, so that a direct comparison of these results with those of Cutter has not been made in this paper. 

It since appears that the frequency and size of the turbulent velocity fluctuations are more compatible with phenomena on a molecular micron size scale In a mixing vessel. For example, in a publication Paul Treybal (4) shows the yield of a given reaction which had several alternate paths was determined by the RMS velocity fluctuations at the feed point. Paul used data from Schwartzberg Treybal (5) and Cutter to calculate RMS velocity at the feed point. 

Figure 6. The ratio of RMS velocity fluctuations to average velocity at different distances above and below the impeller centerline...

Figure 7. Effect of distance from impeller shaft on the ratio of RMS velocity fluctuation to the average velocity at a point...

What about the micro-scale phenomena These are dependent primarily on the energy dissipation per nnit volnme, althongh one must also be concerned about the energy spectra. In general, the energy dissipation per unit volume around the impeller is approximately 100 times higher than in the rest of the tank. This results in an rms velocity fluctuation ratio to the average velocity on the order of 10 1 between the impeller zone and the rest of the tank. 

Turbulence in Microchannels, Fig. 1 (a) Rms velocity fluctuations and (b) Reynolds shear stress as measured by microPIV for turbulent flow in a 536 )im diameter glass microtube... 

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