Impeller swept

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... 

In spite of all the simplifications Bakker and Van den Akker applied and given the black box approach for the impeller swept domain, their simulations resulted in values for the bubble size just below the liquid surface, overall holdup, and average kfl values which are in good agreement with their experimental data (see Table II). The major step forward they made was the acquisition of the different spatial distributions of average bubble size (see Fig. 13), bubble holdup and kfl as effected by three common impeller types. As a matter of fact, their approach may be restricted to low values of the gas hold-up. 

Flow in baffled stirred reactors has been modeled by employing several different approaches which can be classified into four types, and are shown schematically in Fig. 10.3. Most flow simulations of stirred vessels published before 1995 were based on steady-state analyses (reviewed by Ranade, 1995) using the black box approach. This approach requires boundary conditions (mean velocity and turbulence characteristics) on the impeller swept surface, which need to be determined experimentally. Although this approach is reasonably successful in predicting the flow characteristics in the bulk of the vessel, its usefulness is inherently limited by the availability of data. Extension of such an approach to multiphase flows and to industrial-scale reactors is not feasible because it is virtually impossible to obtain (from experiments) accurate... 

Specify boundary conditions on impeller swept surface... 

Fig. 7.16. Simulating the effect of a Rushton turbine on the flow one practice is to impose empirical profiles for the physical quantities like Vr, vg, k and e on the vertical control surface bounding the impeller-swept region in a stirred vessel [10].

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... 

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