Impeller swept volume

In the early days, see, e.g., Bakker and Van den Akker (1994a), a black box representing the impeller swept volume was often used in RANS simulations, with boundary conditions in the outflow of the impeller which were derived from experimental data. The idea behind this approach was that such nearimpeller data are hardly affected by the rest of the vessel and therefore could be used throughout. Generally, this is not the case of course. Furthermore, this approach necessitates the availability of accurate experimental data, not only... 

Figure 2-15 Scaling of maximum local dissipation with the power per impeller swept volume across a range of geometries. Use of the power per tank volume with exact geometric similarity will give a similar result however, when the geometry is varied, values of the local dissipation can vary dramatically from one tank to anotha-, even at the same power per tank volume. (Modified from Zhou and Kresta, 1996b.)...

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. 

Applying the same scaling arguments in a stirred tank, Lg is equal to some fraction of D and s is estimated using the power per impeller swept volume. This gives... 

Where the objective is to uncover the governing physics in the problem, the effects of the local dissipation must be separated from the effects of other variables. To accomplish this, geometric similarity will often not be maintained, and the best available scaling for the local dissipation is NpN D, or the power input per unit of impeller swept volume. 

A simple concept is to use the impeller swept volume as the dissipation volume to correlate data for different geometries in the absence of data for 8max. The idea is to assume that aU power is dissipated uniformly in the volume swept out by the impeller rather than throughout the tank volume. Then, according to eq. (12-21), drop size for different geometry should scale approximately with McManamey (1979) correlated many systems with other types of... 

Relative swept volume, that is, the volume swept by the impeller (and chopper) per unit time, divided by the mixer volume, has been suggested as a scale-up factor. This parameter is related to work done on the material and was studied extensively at various blade angles. Higher swept volume leads to higher temperature and denser granules. However, it was shown by Horsthuis et that the same relative... 

Impeller shaft power intensity (kW/kg) has been used both as a rheological tool to characterize formulation deformability and as a control technique to judge granulation endpoint, primarily due to its relationship to granule deformation [see Kristensen et al., Acta. Pharm. Sci., 25, 187 (1988), and Holm et al.. Powder Technol., 43, 225 (1985)]. Swept volume ratio is a preliminary estimate of ejq)ected... 

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