**5. Effect of flow instabilities**

Flow instabilities may affect mixing operations in mechanically agitated vessels in different manners.

Since the energetic content of J-MIs may be significant, they can exert strong forces on the solid surfaces immersed in the stirred tank, i.e. the shaft, baffles, heating and cooling coils, etc. (Hasal et al., 2004). These forces may cause mechanical failure of the equipment and therefore they should be taken into account in the design of industrial-scale stirred vessels.

(a) (b)

decreasing the blade thickness (Rutherford et al., 1996b).

D/T = 0.33, tb/D = 0.01.

**5. Effect of flow instabilities** 

manners.

vessels.

Fig. 6. Frames taken from flow visualisation experiments with sketches at N = 400 rpm (from Galletti & Brunazzi, 2008). Unbaffled vessel, RT, eccentricity E/T =0.21, C/T= 0.33, ,

lower, i.e. f' = 0.143 than for the thinner one (f' = 0.155 for tb/D = 0.01). The origin of the above instabilities in not fully clarified. The frequencies are one order of magnitude higher than the P-MIs frequencies. The values of f' found are more similar to frequencies typical of J-MIs. Actually the eccentric position of the shaft and the consequently reduced distance between the impeller blade tip and the vessel boundaries, is likely to enhance the strength of the impeller discharged stream – wall interaction. In such a case, resulting flow instabilities will show a frequency which is expected to increase with increasing the velocity of the impeller discharged stream (see the flow-instability analysis in terms of pumping number by Paglianti et al., 2006, and/or peak velocity by Roussinova et al., 2003), thus with

Flow instabilities may affect mixing operations in mechanically agitated vessels in different

Since the energetic content of J-MIs may be significant, they can exert strong forces on the solid surfaces immersed in the stirred tank, i.e. the shaft, baffles, heating and cooling coils, etc. (Hasal et al., 2004). These forces may cause mechanical failure of the equipment and therefore they should be taken into account in the design of industrial-scale stirred However except for such drawbacks, MIs may be beneficially utilized to improve mixing, provided that their phenomenology is well understood.

It has been proved than flow instabilities in stirred vessels can have a direct effect on overall parameters, which are fundamental for the design practice. The different studies on the change of circulation pattern (mentioned in section 4.1) have evidenced that such change is accompanied by a change of power number. In case of solid suspension, changes in the Njs is observed. Thus the knowledge of parameters affecting the circulation change may help optimising solid-liquid operations. Moreover, the heat flux studies of Haam et al. (1992) showed that precessional MIs may induce a variation of the heat transfer coefficient up to 68% near the surface.

Macro-instabilities may have beneficial implications for mixing process operation and efficiency as such flow motions can enhance mixing through mean-flow variations. For example, the associated low-frequency, high-amplitude oscillatory motions in regions of low turbulence in a vessel, have the capability of transporting substances fed to a mixing process over relatively long distances, as demonstrated by Larsson et al. (1996). These authors measured glucose concentration in a cultivation of Saccharomyces Cerevisiae and observed fluctuations of glucose concentration which were more pronounced as the feed was located in a stagnant area rather than in the well-mixed impeller area. Therefore flow instabilities may help destroying segregated zones inside the tank. Ducci & Yianneskis (2007) showed that the mixing time could be reduced even by 30% if the tracer is inserted at or near the MI vortex core. Houcine et al. (1999) reported with LIF a feedstream jet intermittency in a continuous stirred tank reactor due to MIs. Recently also Galletti et al. (2009) observed from decolourisation experiments in an eccentrically agitated unbaffled vessel that the flow instability oscillations help the transport of reactants far away if these are fed in correspondence of the vortices shown in Fig. 6.

Subsequently MIs have similar effects to those reported for laminar mixing in stirred tanks by Murakami et al. (1980), who observed that additional raising and lowering of a rotating impeller produced unsteady mean flow motions that either destroyed segregated regions or prevented them from forming, and could produce desired mixing times with energy savings of up to 90% in comparison to normal impeller operation. Later Nomura et al. (1997) observed that the reversal of the rotational direction of an impeller could also decrease mixing times as the additional raising or lowering of the impeller.

For a solid-liquid system (solid volume fractions up to 3.6%) agitated by a D = T/3 RT in turbulent regime (Re = 100,000 and 150,000) Derksen (2003) showed that the precessing vortex may help the resuspension of particles lying on the bottom of the tank, thus enhancing the mass transfer.

Guillard et al. (2000a) carried out LIF experiments on a stirred tank equipped with two RT observing large time scale oscillations of the concentration, induced by an interaction between the flows from the impeller and a baffle. They argued that circulation times can be altered when the flow direction changes, the turbulence levels measured with stationary probes can be significantly broadened and thus can provide an erroneous interpretation of the true levels of turbulence in a tank, and mixing in otherwise quiescent regions can be significantly enhanced due to the presence of flow variations (Guillard et al., 2000b). Knoweledge of true levels of turbulence is needed for the optimum design of micro-mixing operations (as in cases of chemical reactions). Also Nikiforaki et al. (2003) observed that P-MIs can broaden real turbulence levels up to 25% for a PBT.

Flow Instabilities in Mechanically Agitated Stirred Vessels 245

A similar analysis was carried out for a PBT: in this case the P-MIs and J-MIs were studied (see Table 3). The authors found the presence of both instabilities, indicating that the occurrence and magnitude, i.e. energetic content, of MIs and JIs vary substantially from one region of a vessel to another. P-MIs affect strongly the region of the vessel near the surface and around the shaft, whereas the bulk of the vessel is dominated more by J-MIs generated from the interaction of the impeller discharged stream and the vessel boundaries. J-MIs are also stronger upstream of the baffles and near the walls, which may confirm their origin. Table 4 reports the energetic contribution of the different macro-instabilities at different

Pitched Blade Turbine Flow instability J-MIs P-MIs

> large temporal and spatial fluctuation superimposed on the mean flow pattern

(*C*/*T* = 0.25 with *D*/*T* = 0.5)

Temporal appearance continuously present continuously present

interaction between impeller discharged stream and vessel base/walls

Table 3. Characteristics of JIs and MIs investigated with the pitched blade turbine. Galletti

Average *EMI*/*ETUR*

*z*/*T* = 0.05 1.9% 5.7% 2.7% 6.3% *z*/*T* = 0.6 6.2% 12% 10.1% 20% *z*/*T* = 0.93 14.6% 39.8% 1.7% 7% Table 4. Average and maximum relative energy of MIs and JIs with respect to the turbulent

For the eccentric agitation in an unbaffled vessel, Galletti & Brunazzi (2008) showed that the flow instability related to the movement of the two vortices described in section 4.2.2. was very strong, as its energetic contribution was evaluated to be as high as 52% of the turbulent kinetic energy. Also the shedding vortices from flow-shaft interaction considerably affected the turbulence levels (energetic contribution of 82%), hence they should be considered in

P-MIs J-MIs

Max *EJI*/*ETUR*

Non-dimensional frequency *f'* = 0.186 *f'* = 0.015

large temporal and spatial fluctuation superimposed on the mean flow pattern

several configurations (different impeller types *D*/*T*, *C*/*T*)

precessional motion of a vortex about the shaft

> Average *EJI*/*ETUR*

axial location in the vessel.

How they manifest

Possible origin

Location of the horizontal plane

(2005).

Impeller/vessel configuration specific configuration

Max *EMI*/*ETUR*

energy, for different horizontal planes. Galletti (2005).

evaluating the micro-mixing scales.

Actually the problem is rather complex as Galletti et al. (2005b) as well other investigators (e.g. Ducci & Yianneskis, 2007, Roussinova et al., 2004) showed that different kinds of macro-instabilities may be present simultaneously in stirred vessels. For instance Galletti et al. (2005b) studied simultaneously with 2-point LDA the combined effect of precessional MIs and flow instabilities stemming from impeller clearance variations (CIs) in different regions of a vessel stirred with a RT. Table 1 summarizes the flow instability characteristics. The authors removed from the total energetic content of a LDA signal, the contribution of blade passage, P-MIs and CIs, evaluating the real turbulent energy. They found that the occurrence and energetic content of P-MIs and CIs depend on both measurement location and flow regime. In particular, near the vessel surface P-MIs are stronger, with energetic contents that reach 50% of the turbulent energy, meaning that they can broaden turbulence levels up to 22%. In the vicinity of the impeller the energetic content of the P-MIs is smaller, whereas CIs contribute strongly to the fluid motion with average energetic contents of about 21% of the turbulent energy for the transitional regime. Results are summarised in Table 2.




Table 2. Relative energy of MIs and CIs with respect to the turbulent energy for the double-, single- and transitional patterns. Galletti (2005).

Actually the problem is rather complex as Galletti et al. (2005b) as well other investigators (e.g. Ducci & Yianneskis, 2007, Roussinova et al., 2004) showed that different kinds of macro-instabilities may be present simultaneously in stirred vessels. For instance Galletti et al. (2005b) studied simultaneously with 2-point LDA the combined effect of precessional MIs and flow instabilities stemming from impeller clearance variations (CIs) in different regions of a vessel stirred with a RT. Table 1 summarizes the flow instability characteristics. The authors removed from the total energetic content of a LDA signal, the contribution of blade passage, P-MIs and CIs, evaluating the real turbulent energy. They found that the occurrence and energetic content of P-MIs and CIs depend on both measurement location and flow regime. In particular, near the vessel surface P-MIs are stronger, with energetic contents that reach 50% of the turbulent energy, meaning that they can broaden turbulence levels up to 22%. In the vicinity of the impeller the energetic content of the P-MIs is smaller, whereas CIs contribute strongly to the fluid motion with average energetic contents of about 21% of the turbulent energy for the transitional

Rushton turbine Flow instability CIs P-MIs

> specific configuration (*C*/*T* = 0.17-0.2 with *D*/*T* = 0.33)

Temporal appearance intermittently present continuously present

interaction between impeller discharged stream and vessel base/walls

Near the surface Impeller region *EMI*/*ETUR* ECI/ETUR *EMI*/*ETUR ECI*/*ETUR*

Non-dimensional frequency *f'* = 0.13 *f'* = 0.015

Table 1. Characteristics of CIs and MIs investigated with the Rushton turbine. Galletti

double-loop up to 50% ~4% ~5% ~3% transitional state up to 25% up to 25% negligible ~ 21%

single-loop ~ 12 % ~ 3% negligible negligible

Table 2. Relative energy of MIs and CIs with respect to the turbulent energy for the double-,

large temporal and spatial fluctuation superimposed on the mean flow pattern

several configurations (different impeller types *D*/*T*, *C*/*T*)

precessional motion of a vortex about the shaft

regime. Results are summarised in Table 2.

Impeller/vessel configuration

Possible origin

single- and transitional patterns. Galletti (2005).

(2005).

How they manifest change in circulation

A similar analysis was carried out for a PBT: in this case the P-MIs and J-MIs were studied (see Table 3). The authors found the presence of both instabilities, indicating that the occurrence and magnitude, i.e. energetic content, of MIs and JIs vary substantially from one region of a vessel to another. P-MIs affect strongly the region of the vessel near the surface and around the shaft, whereas the bulk of the vessel is dominated more by J-MIs generated from the interaction of the impeller discharged stream and the vessel boundaries. J-MIs are also stronger upstream of the baffles and near the walls, which may confirm their origin. Table 4 reports the energetic contribution of the different macro-instabilities at different axial location in the vessel.


Table 3. Characteristics of JIs and MIs investigated with the pitched blade turbine. Galletti (2005).


Table 4. Average and maximum relative energy of MIs and JIs with respect to the turbulent energy, for different horizontal planes. Galletti (2005).

For the eccentric agitation in an unbaffled vessel, Galletti & Brunazzi (2008) showed that the flow instability related to the movement of the two vortices described in section 4.2.2. was very strong, as its energetic contribution was evaluated to be as high as 52% of the turbulent kinetic energy. Also the shedding vortices from flow-shaft interaction considerably affected the turbulence levels (energetic contribution of 82%), hence they should be considered in evaluating the micro-mixing scales.

Flow Instabilities in Mechanically Agitated Stirred Vessels 247

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