Impeller outflow

Figure 15.1 Instantaneous PIV measurement of velocity and vorticity in the impeller outflow from a Rushton turbine in a 1-1 laboratory reactor.

The use of a draught tube generally leads to a reduction in both Na and ( )js when used in conjunction with either a propeller or an angle-blade turbine (see Table 16.3). However, care should be taken with the position and size of the draught tube. For instance, if the bottom of the tube restricts the impeller outflow, the local head loss can cause a marked enhancement of (i-r)]s - Ideally, the flow area in the core, in the annulus, between the bottom of the tube and the base and between the top and the liquid surface should all be equal. Finally, the use of a specially contoured base, maintaining the flow area constant Figure 16.5) leads to an even further reduction in A(is and (er)js by eliminating ail dead spots. 

The exact shape of the velocity profile in the outflow of an impeller does not depend solely on the impeller. It is also affected by such variables as the impeller Reynolds number, impeller off-bottom distance C/T, and impeller diameter D/T. If the flow is fully turbulent (i.e.. Re > Kf ), the impeller outflow profiles are typically independent of Reynolds number. If the flow is flansitional or laminar, however, care should be taken so that the velocity profiles used were either measured at a similar Reynolds number, or that the prescribed velocities are being interpolated from data sets measured over a range of Reynolds numbers. Similarly, for impeller off-bottom clearance and diameter, if data for various C/T and D/T values are available, interpolations can be used to obtain the prescribed velocities for the actual conditions. 

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 3.14 shows the simulated mean bubble size just below the impeller plane (tank diameter 1 m). A clear variation of the bubble size is found, with the Rushton turbine rotating at 285 rpm and decreasing the bubble size in its outflow by more... 

The impeller is modelecl by fixing Itie liquid velocities in te outflow zone based on measured data. 

An alternative way to bypass calculation of the startup period is to solve for a steady-state solution first using the MRF model. The MRF model (Section 5-5.2) provides a solution for the moving impeller at a fixed orientation relative to the baffles. Tools are available in commercial codes to use the solution data from the MRF simulation and apply it to the sliding mesh simulation as an initial condition. A moderately coarse time step can be nsed initially (say, corresponding to a 10° rotation, as in the example above) and rednced at a qnicker rate than would otherwise be advisable. This approach can also be nsed if inflow and outflow boundaries are present or if a multiphase calculation is to be performed. In the case of multiphase flows, however, care must be taken to wait until the periodic steady-state condition has been reached before introducing the secondary phase. 

In this expression, is the flow rate produced by the impeller. The subscript is used to ensure that the flow rate for the liquid phase alone is used in the calculation. To compute Qt for an impeller, a surface needs to be created for the discharge region. This surface would be circular for an axial flow impeller and a section of cylinder waU for a radial flow impeller. By integrating the total outflow through this surface, the flow rate, Q, and subsequently the flow number, Nq, can be obtained. 

Figure 5-22 Product distribution, Xs as a function of impeller speed (rpm) for two vessels of different size, with the second reactant being added in the outflow of the impeller. Model predictions are compared with data from Middleton et al. (1986).

Two impeller types were simulated the standard six-blade disk turbine and a 45° pitched blade turbine. The outflow from the disk turbine was simulated by fixing the tangential velocities at the blade tip locus (the FIX option in Fluent). The radial velocities and k/e ratios generated were close to the values that have been measured by Wu and Patterson (1989). The outflow velocities and turbulence energy from the pitched blade turbine were fixed at the bottom locus of the impeller blades using the data of Fort et al. (1999). The resulting flow patterns were close to the data measured. 

Periodic boundary conditions are very useftil when a system has periodic behavior. The inflow at one boundary is set as the outflow from another surface, e.g. only 1/6 of a tank reactor with six impeller blades and no baffles is calculated by using the radial outflow on one side as the inflow on the other side. 

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