**4.2.1 Precessional macro-instabilities (P-MIs)**

The first subgroup comprehends flow instabilities which seem to be associated with a vortex moving about the shaft. The first evidence of this vortex was provided by Yianneskis et al. (1987) who noticed that the vortex motion produced large temporal and spatial fluctuations superimposed on the mean flow pattern. A similar vortex was also observed by Haam et al. (1992) cited earlier.

Precessional MIs were investigated by Nikiforaki et al. (2003), who used two different impellers (RT and PBT) having the same diameter D = T/3 for Re > 20,000. The frequency of the macro-instabilities was found to be linearly related to the impeller speed with f' = f/N = 0.015-0.020, independently on impeller clearance and design. In a more recent work Nikiforaki et al. (2004) studied the effect of operating parameters on macro-instabilities. In particular they observed the presence of other frequencies varying from f'= 0.04-0.15 , as the Reynolds number was reduced.

Hartmann et al. (2004) performed a LES simulation of the turbulent flow (Re = 20,000 and 30,000) in a vessel agitated with a D = T/3 RT set at C = T/2. The geometries of the vessel and impeller were identical to those used for the experiments of Nikiforaki et al. (2003). The simulation indicated the presence of a vortical structure moving round the vessel centreline in the same direction as the impeller. Such structure was observed both below and above the impeller (axial locations of z/T = 0.12 and z/T = 0.88 were monitored), however the two vortices were moving with a mutual phase difference. The frequency associated with the vortices was calculated to be f' = 0.0255, therefore slightly higher than the 0.015-0.02 reported by Nikiforaki et al. (2003). The authors concluded that this may encourage an improvement of the sub-scale grid and/or the numerical settings.

Importantly, the presence of a phase shift between the precessing vortices below and above the impeller was confirmed by the LDA experiments of Micheletti & Yianneskis (2004).

Flow Instabilities in Mechanically Agitated Stirred Vessels 239

 *<sup>D</sup> <sup>f</sup> a b T*

A deep clarification of precessional MIs triggering mechanism in both laminar and turbulent regimes was provided by Ducci & Yianneskis (2007) for a D = T/3 RT placed at C = T/2. The authors used 2-point LDA and a 2-D PIV with a 13kHz camera. Through a vortex identification and tracking technique, the authors showed that P-MIs stem from a precessional vortex moving around the vessel axis with f' = 0.0174 for the turbulent regime. In laminar regime the frequency corresponding to a precession period was higher, of about f' = 0.13. The slight differences on the frequencies with the work of Galletti et al. (2004b) may be imputed to the different spectral analysis. For instance in the vortex tracking method the frequency was evaluated from the time needed to a vortex to complete 360°, whereas the FFT analysis of Galletti et al. (2004b) covered several MI cycles. But importantly Ducci & Yianneskis (2007) showed that in the laminar regime the vortex precessional motion was much closer to the axis than in turbulent regime (for which the vortex tends to stay rather far from the axis). In addition to that the authors showed a change in the flow pattern between the laminar and turbulent conditions, which

In a later work Ducci et al. (2008) investigated also the transitional regime showing the interaction between the two frequency instabilities (f' = 0.1 and f' = 0.02 of the laminar and turbulent regime, respectively). They found that the two simultaneous instabilities are associated to two different types of perturbation of the main mean flow: an off-centering instability that results in a precession of the vortex core centre with a f' = 0.02 and a stretching instability that induces an elongation of the vortex core along a direction that is rotating with f' = 0.1 around the vessel axis. For higher Re, the authors identified an interaction between the perturbations of the mean vortex core associated to f' = 0.02 off-

A deep investigation of precessional MIs was also carried out by the same group (Doulgerakis et al., 2011) for an axial impeller (PBT) with D = T/2 placed at C = T/2 with Re = 28,000. The MI frequency distribution across the vessel indicated the presence of many frequencies reported before in literature. However the two dominant frequencies were f' = 0.1 and f' = 0.2. The POD analysis showed that the first mode can be seen as a radial offcenter perturbation of the mean flow that results in a precession of the vortex core around the impeller axis with f' = 0.1. The second mode is an instability which stretches/squeezes the vortex core in a direction that is rotating with f' = 0.1. Importantly also for the PBT, the higher frequency was exactly double than the lower one as for the RT case. This would be also in agreement with many spectral analysis reported in Galletti (2005) which showed the

presence of an additional peak frequency about the double of the P-MI frequency.

Kilander et al. (2006) identified through LSP analysis of LDA data frequencies with f' = 0.025 for the turbulent regime (thus in fully agreement with the work by Hartmaan et al., 2006) in

Lately, many other computational methods confirmed also the presence of precessional MIs. Nurtono et al. (2009) obtained from LES simulations a frequency f' = 0.0125 for a D=T/3 RT

The DNS simulations of Lavezzo et al. (2009) for an unbaffled vessel equipped with a 8 blade paddle impeller indicated the presence of a spiralling vortex with f' = 0.162 for Re = 1686. The application of Eq. [1] developed by Galletti et al. (2004b) to the above case would

centering structures and a f' = 0.04 stretching/squeezing instability.

=⋅ + (1)

'

affects the precessional MI frequency.

a vessel agitated by a D = T/3 RT.

placed at C = T/2 for Re = 40,000.

These authors used a cross-correlation method between data taken in the upper and lower parts of the vessel, and estimated a phase difference between the vortices in the two locations of approximately 180°.

The presence of the precessing vortex was assessed also in a solid-liquid system by the LES simulation of Derksen (2003).

Hasal et al. (2004) investigated flow instabilities with a Rushton turbine and a pitched blade turbine, both of D = T/3 with the proper orthogonal decomposition analysis. They confirmed the presence of the precessing vortex, however they found different f' values depending on the Re. In particular f' values akin to those of Nikiforaki et al. (2003) were observed for high Re, whereas higher values, i.e. f' = 0.06-0.09 were found for low Re.

Galletti et al. (2004b) investigated macro-instabilities stemming from the precessional motion of a vortex about the shaft for different impellers, geometries and flow regimes. The authors confirmed that the P-MI frequency is linearly dependent on the impeller rotational speed, however they indicated that different values of the proportionality constant between MI frequency and impeller rotational speed were found for the laminar and turbulent flow regimes, indicating different behaviour of MIs depending on the flow Re (see Fig. 5a). For intermediate (transitional) regions two characteristic frequencies were observed, confirming the presence of two phenomena. In particular in the laminar flow region P-MIs occurred with a non-dimensional frequency f' about 7-8 times greater than that observed for the turbulent region. This was proved for two RTs (D/T = 0.33 and 0.41 RT) as well as for a D/T = 0.46 PBT. Thus the impeller design does not affect P-MIs for both laminar and turbulent regions. The impeller off-bottom clearance does not affect significantly the P-MI frequency for the Rushton turbine and the pitched blade turbine (see for instance Fig. 5b). However differences in the regions where P-MIs are stronger may be found, as for instance lower impeller clearances originated weaker P-MIs near the liquid surface.

Fig. 5. (a) Non-dimensional macro-instability frequency as a function of the impeller Reynolds number. RT, D/T = 0.41, C/T = 0.5. (b) Macro-instability frequency as a function of the impeller rotational speed for different clearances. RT, D/T = 0.41. Galletti (2005).

Importantly, Galletti et al. (2004b) found that the MI frequency is affected by the impeller diameter. For the laminar regime a linear dependence of the non-dimensional macroinstability frequency on the impeller to tank diameter ratio was established:

These authors used a cross-correlation method between data taken in the upper and lower parts of the vessel, and estimated a phase difference between the vortices in the two

The presence of the precessing vortex was assessed also in a solid-liquid system by the LES

Hasal et al. (2004) investigated flow instabilities with a Rushton turbine and a pitched blade turbine, both of D = T/3 with the proper orthogonal decomposition analysis. They confirmed the presence of the precessing vortex, however they found different f' values depending on the Re. In particular f' values akin to those of Nikiforaki et al. (2003) were observed for high Re, whereas higher values, i.e. f' = 0.06-0.09 were found for low Re. Galletti et al. (2004b) investigated macro-instabilities stemming from the precessional motion of a vortex about the shaft for different impellers, geometries and flow regimes. The authors confirmed that the P-MI frequency is linearly dependent on the impeller rotational speed, however they indicated that different values of the proportionality constant between MI frequency and impeller rotational speed were found for the laminar and turbulent flow regimes, indicating different behaviour of MIs depending on the flow Re (see Fig. 5a). For intermediate (transitional) regions two characteristic frequencies were observed, confirming the presence of two phenomena. In particular in the laminar flow region P-MIs occurred with a non-dimensional frequency f' about 7-8 times greater than that observed for the turbulent region. This was proved for two RTs (D/T = 0.33 and 0.41 RT) as well as for a D/T = 0.46 PBT. Thus the impeller design does not affect P-MIs for both laminar and turbulent regions. The impeller off-bottom clearance does not affect significantly the P-MI frequency for the Rushton turbine and the pitched blade turbine (see for instance Fig. 5b). However differences in the regions where P-MIs are stronger may be found, as for instance lower

Importantly, Galletti et al. (2004b) found that the MI frequency is affected by the impeller diameter. For the laminar regime a linear dependence of the non-dimensional macro-

impeller clearances originated weaker P-MIs near the liquid surface.

(a) (b)

instability frequency on the impeller to tank diameter ratio was established:

Fig. 5. (a) Non-dimensional macro-instability frequency as a function of the impeller Reynolds number. RT, D/T = 0.41, C/T = 0.5. (b) Macro-instability frequency as a function of the impeller rotational speed for different clearances. RT, D/T = 0.41. Galletti (2005).

locations of approximately 180°.

simulation of Derksen (2003).

$$f' = a \cdot \left(\frac{D}{T}\right) + b \tag{1}$$

A deep clarification of precessional MIs triggering mechanism in both laminar and turbulent regimes was provided by Ducci & Yianneskis (2007) for a D = T/3 RT placed at C = T/2. The authors used 2-point LDA and a 2-D PIV with a 13kHz camera. Through a vortex identification and tracking technique, the authors showed that P-MIs stem from a precessional vortex moving around the vessel axis with f' = 0.0174 for the turbulent regime. In laminar regime the frequency corresponding to a precession period was higher, of about f' = 0.13. The slight differences on the frequencies with the work of Galletti et al. (2004b) may be imputed to the different spectral analysis. For instance in the vortex tracking method the frequency was evaluated from the time needed to a vortex to complete 360°, whereas the FFT analysis of Galletti et al. (2004b) covered several MI cycles. But importantly Ducci & Yianneskis (2007) showed that in the laminar regime the vortex precessional motion was much closer to the axis than in turbulent regime (for which the vortex tends to stay rather far from the axis). In addition to that the authors showed a change in the flow pattern between the laminar and turbulent conditions, which affects the precessional MI frequency.

In a later work Ducci et al. (2008) investigated also the transitional regime showing the interaction between the two frequency instabilities (f' = 0.1 and f' = 0.02 of the laminar and turbulent regime, respectively). They found that the two simultaneous instabilities are associated to two different types of perturbation of the main mean flow: an off-centering instability that results in a precession of the vortex core centre with a f' = 0.02 and a stretching instability that induces an elongation of the vortex core along a direction that is rotating with f' = 0.1 around the vessel axis. For higher Re, the authors identified an interaction between the perturbations of the mean vortex core associated to f' = 0.02 offcentering structures and a f' = 0.04 stretching/squeezing instability.

A deep investigation of precessional MIs was also carried out by the same group (Doulgerakis et al., 2011) for an axial impeller (PBT) with D = T/2 placed at C = T/2 with Re = 28,000. The MI frequency distribution across the vessel indicated the presence of many frequencies reported before in literature. However the two dominant frequencies were f' = 0.1 and f' = 0.2. The POD analysis showed that the first mode can be seen as a radial offcenter perturbation of the mean flow that results in a precession of the vortex core around the impeller axis with f' = 0.1. The second mode is an instability which stretches/squeezes the vortex core in a direction that is rotating with f' = 0.1. Importantly also for the PBT, the higher frequency was exactly double than the lower one as for the RT case. This would be also in agreement with many spectral analysis reported in Galletti (2005) which showed the presence of an additional peak frequency about the double of the P-MI frequency.

Kilander et al. (2006) identified through LSP analysis of LDA data frequencies with f' = 0.025 for the turbulent regime (thus in fully agreement with the work by Hartmaan et al., 2006) in a vessel agitated by a D = T/3 RT.

Lately, many other computational methods confirmed also the presence of precessional MIs. Nurtono et al. (2009) obtained from LES simulations a frequency f' = 0.0125 for a D=T/3 RT placed at C = T/2 for Re = 40,000.

The DNS simulations of Lavezzo et al. (2009) for an unbaffled vessel equipped with a 8 blade paddle impeller indicated the presence of a spiralling vortex with f' = 0.162 for Re = 1686. The application of Eq. [1] developed by Galletti et al. (2004b) to the above case would

Flow Instabilities in Mechanically Agitated Stirred Vessels 241

impeller stream on either the vessel walls or bottom, converging radial flow at the vessel bottom from the baffles and shedding of trailing vortices from the impeller blades. For the resonant geometry, the first mechanism coincided with the impingement of the discharge stream on the vessel corner, generating pressure waves reflected back towards the impeller. The impingement jet frequency was approached with a dimensional analysis based on the Strouhal number. We well denote such flow instabilities as jet impingement instabilities (J-MIs). In a later investigation Roussinova et al. (2004) extended the analysis to different axial

Paglianti et al. (2006) analysed literature data on MIs as well as comprehensive data obtained from measurements of wall pressure time series, and develop a simple model (based on a flow number) for predicting the MI frequency due to impinging jets (J-MI). Also Galletti et al. (2005b) investigated flow instability for a PBT and detected a f' = 0.187 (thus akin the Roussinova et al., 2003). Such instabilities were found to prevail in the region

Nurtono et al. (2009) found a similar frequency f' = 0.185 from LES modelling of a D=T/3

The LES results on different impellers (DT, PBTD60, PBTD45, PBTD30 and HF) from Murthy & Joshi (2008) showed the presence of J-MIs with f' = 0.13-0.2. Moreover they observed a frequency f' = 0.04–0.07, which lies in between the precessional and the jet instability; such frequency was attributed to the interaction of precessing vortex instability

Roy et al. (2010) investigated through both experimental (PIV) and numerical (LES) techniques, the flow induced by a PBT impeller at different Reynolds numbers (Re = 44,000, 88,000 and 132,000). They found low frequency flow instabilities with frequencies of about f' = 0.2. They could not resolve lower frequencies because of the short observation (due to computational cost of LES models) of their simulations. The authors showed changes in the three-dimensional flow pattern during different phases of the macro-instability cycle. They concluded that one mechanism driving flow instabilities was the interaction of the impeller jet stream with the tank baffles. The flow-instabilities were also observed to affect the

More recently Galletti & Brunazzi (2008) investigated through LDA and flow visualisation the flow features of an unbaffled vessel stirred by an eccentrically positioned Rushton turbine. The flow field evidenced two main vortices: one departing from above the impeller towards the top of the vessel and one originating from the impeller blades towards the vessel bottom. The former vortex was observed to dominate all vessel motion, leading to a

The frequency analysis of LDA data indicated the presence of well defined peaks in the frequency spectra of velocity recordings. In particular three characteristic frequencies were observed in different locations across the vessel: f' = 0.105, 0.155 and 0.94. Specifically, the f' = 0.155 and 0.105 frequencies were related to the periodic movements of the upper and lower vortices' axis, respectively, which are also well visible from flow visualization experiments (see Fig. 6a and Fig. 6b, respectively). The f' = 0.94 frequency was explained by considering the vortical structure – shaft interaction, which occurs in eccentric configuration and leads to vortex shedding phenomena. The authors provided an interpretation based on

In a later work (Galletti et al., 2009) the effect of blade thickness tb was investigated, finding that for a thicker impeller (tb/D = 0.05) the frequency of the upper vortex movement was

impellers. In such work the authors used the LSP method for the spectral analysis.

close to the impeller (just above it and below it in the discharged direction).

PBT placed at C = T/2 at Re = 40,000.

dynamics of trailing edge vortices.

strong circumferential flow around it.

the Strouhal number.

with either the mean flow or jet/circulation instabilities.

give a higher frequency f' = 0.24, however it should be pointed out that the equation was developed for baffled configurations.

#### **4.2.2 Jet impingement macro-instabilities (J-MIs)**

Other evidence of large temporal and spatial variations of the flow macro-instabilities have been reported in the last decade and they not always seem to be related to a precessional vortex.

Bruha et al. (1995) used a device called "tornadometer" to estimate the flow instabilities induced by a 6-bladed 45° PBT of D = 0.3T set at C = 0.35T. The target was axially located above the impeller at z/C = 1.2 and 1.4 and at radial distance equal to the impeller radius. The aforementioned authors found a linear relation between the instability frequency f and the impeller rotational speed N, according to f = -0.040 N +0.50. In a later work (Bruha et al., 1996) the same authors reported a linear dependence of the MI frequency on N (f' = 0.043- 0.0048) for Re values above 5,000. No flow-instabilities were noted for Re < 200 and an increase in f' was observed for 200 < Re < 5,000.

Montes et al. (1997) studied with LDA the flow instabilities in the vicinity of the impeller. induced by a 6-bladed 45° PBT of D = 0.33T set at C = 0.35T and observed different values for f' depending on the Reynolds number: f' = 0.09 for Re = 1140 and f' = 0.0575 for Re = 75,000. They suggested that macro-instabilities appear as the switching between one loop and two or many loops, taking place between the impeller and the free surface and they are able to alter this surface. This leads to different flow patterns in front of the baffles or between two adjacent baffles. The mechanism is complex and three-dimensional but the large vortices clearly appear in a regular way, with a well defined frequency. Hasal et al. (2000) used the proper orthogonal decomposition to analyse LDA data observed for a PBT and found a f' = 0.087 for Re = 750 and Re = 1,200, and a value of 0.057 for Re = 75,000. In addition they noticed that the fraction of the total kinetic energy carried by the flow instabilities (relative magnitude) varied with the location inside the stirred vessel, they being stronger in the central and wall regions below the impeller but weaker in the discharge flow from the impeller.

Myers et al. (1997) used digital PIV to investigate flow instabilities in a stirred tank equipped with two different impellers: a 4-bladed 45° PBT of D = 0.35T and a Chemineer HE-3 of D = 0.39T. The PBT was set at C = 0.46T and 0.33T, whereas the Chemineer HE-3 was set at C = 0.33T. The Reynolds number was ranging between 6,190 and 13,100. For the higher clearance, i.e. C = 0.46T, the PBT showed flow fluctuations of about 40 s for an impeller rotational speed N = 60 rpm, therefore f' = 0.025. The same impeller set at the lower clearance, C = 0.33T, showed more stable flow fields, with not very clear peaks in the low frequency region of the spectra, at around f' = 0.07-0.011. The Chemineer HE-3 impeller showed fluctuations of much longer periods than those of the PBT.

Roussinova et al. (2000, 2001) performed LDA measurements in two tank sizes (T = 0.24 and 1.22 m), using various impeller types, impeller sizes, clearances, number of baffles (2 and 4) and working fluids in fully turbulent regime. For a 45° PBT of D = T/2 they observed a macro-instability non-dimensional frequency of f' = 0.186. Such frequency was coherent as the PBT was set at C = 0.25T, and such a configuration was called "resonant" geometry, whereas a broad low frequency band was observed for different clearances. The same authors performed also a LES of the vessel stirred by a PBT and confirmed the above non dimensional frequency value. In a later work Roussinova et al. (2003) identified three possible mechanisms triggering the above flow instabilities: the impingement of the jet-like

give a higher frequency f' = 0.24, however it should be pointed out that the equation was

Other evidence of large temporal and spatial variations of the flow macro-instabilities have been reported in the last decade and they not always seem to be related to a precessional

Bruha et al. (1995) used a device called "tornadometer" to estimate the flow instabilities induced by a 6-bladed 45° PBT of D = 0.3T set at C = 0.35T. The target was axially located above the impeller at z/C = 1.2 and 1.4 and at radial distance equal to the impeller radius. The aforementioned authors found a linear relation between the instability frequency f and the impeller rotational speed N, according to f = -0.040 N +0.50. In a later work (Bruha et al., 1996) the same authors reported a linear dependence of the MI frequency on N (f' = 0.043- 0.0048) for Re values above 5,000. No flow-instabilities were noted for Re < 200 and an

Montes et al. (1997) studied with LDA the flow instabilities in the vicinity of the impeller. induced by a 6-bladed 45° PBT of D = 0.33T set at C = 0.35T and observed different values for f' depending on the Reynolds number: f' = 0.09 for Re = 1140 and f' = 0.0575 for Re = 75,000. They suggested that macro-instabilities appear as the switching between one loop and two or many loops, taking place between the impeller and the free surface and they are able to alter this surface. This leads to different flow patterns in front of the baffles or between two adjacent baffles. The mechanism is complex and three-dimensional but the large vortices clearly appear in a regular way, with a well defined frequency. Hasal et al. (2000) used the proper orthogonal decomposition to analyse LDA data observed for a PBT and found a f' = 0.087 for Re = 750 and Re = 1,200, and a value of 0.057 for Re = 75,000. In addition they noticed that the fraction of the total kinetic energy carried by the flow instabilities (relative magnitude) varied with the location inside the stirred vessel, they being stronger in the central and wall regions below the impeller but weaker in the

Myers et al. (1997) used digital PIV to investigate flow instabilities in a stirred tank equipped with two different impellers: a 4-bladed 45° PBT of D = 0.35T and a Chemineer HE-3 of D = 0.39T. The PBT was set at C = 0.46T and 0.33T, whereas the Chemineer HE-3 was set at C = 0.33T. The Reynolds number was ranging between 6,190 and 13,100. For the higher clearance, i.e. C = 0.46T, the PBT showed flow fluctuations of about 40 s for an impeller rotational speed N = 60 rpm, therefore f' = 0.025. The same impeller set at the lower clearance, C = 0.33T, showed more stable flow fields, with not very clear peaks in the low frequency region of the spectra, at around f' = 0.07-0.011. The Chemineer HE-3 impeller

Roussinova et al. (2000, 2001) performed LDA measurements in two tank sizes (T = 0.24 and 1.22 m), using various impeller types, impeller sizes, clearances, number of baffles (2 and 4) and working fluids in fully turbulent regime. For a 45° PBT of D = T/2 they observed a macro-instability non-dimensional frequency of f' = 0.186. Such frequency was coherent as the PBT was set at C = 0.25T, and such a configuration was called "resonant" geometry, whereas a broad low frequency band was observed for different clearances. The same authors performed also a LES of the vessel stirred by a PBT and confirmed the above non dimensional frequency value. In a later work Roussinova et al. (2003) identified three possible mechanisms triggering the above flow instabilities: the impingement of the jet-like

showed fluctuations of much longer periods than those of the PBT.

developed for baffled configurations.

vortex.

**4.2.2 Jet impingement macro-instabilities (J-MIs)** 

increase in f' was observed for 200 < Re < 5,000.

discharge flow from the impeller.

impeller stream on either the vessel walls or bottom, converging radial flow at the vessel bottom from the baffles and shedding of trailing vortices from the impeller blades. For the resonant geometry, the first mechanism coincided with the impingement of the discharge stream on the vessel corner, generating pressure waves reflected back towards the impeller. The impingement jet frequency was approached with a dimensional analysis based on the Strouhal number. We well denote such flow instabilities as jet impingement instabilities (J-MIs). In a later investigation Roussinova et al. (2004) extended the analysis to different axial impellers. In such work the authors used the LSP method for the spectral analysis.

Paglianti et al. (2006) analysed literature data on MIs as well as comprehensive data obtained from measurements of wall pressure time series, and develop a simple model (based on a flow number) for predicting the MI frequency due to impinging jets (J-MI).

Also Galletti et al. (2005b) investigated flow instability for a PBT and detected a f' = 0.187 (thus akin the Roussinova et al., 2003). Such instabilities were found to prevail in the region close to the impeller (just above it and below it in the discharged direction).

Nurtono et al. (2009) found a similar frequency f' = 0.185 from LES modelling of a D=T/3 PBT placed at C = T/2 at Re = 40,000.

The LES results on different impellers (DT, PBTD60, PBTD45, PBTD30 and HF) from Murthy & Joshi (2008) showed the presence of J-MIs with f' = 0.13-0.2. Moreover they observed a frequency f' = 0.04–0.07, which lies in between the precessional and the jet instability; such frequency was attributed to the interaction of precessing vortex instability with either the mean flow or jet/circulation instabilities.

Roy et al. (2010) investigated through both experimental (PIV) and numerical (LES) techniques, the flow induced by a PBT impeller at different Reynolds numbers (Re = 44,000, 88,000 and 132,000). They found low frequency flow instabilities with frequencies of about f' = 0.2. They could not resolve lower frequencies because of the short observation (due to computational cost of LES models) of their simulations. The authors showed changes in the three-dimensional flow pattern during different phases of the macro-instability cycle. They concluded that one mechanism driving flow instabilities was the interaction of the impeller jet stream with the tank baffles. The flow-instabilities were also observed to affect the dynamics of trailing edge vortices.

More recently Galletti & Brunazzi (2008) investigated through LDA and flow visualisation the flow features of an unbaffled vessel stirred by an eccentrically positioned Rushton turbine. The flow field evidenced two main vortices: one departing from above the impeller towards the top of the vessel and one originating from the impeller blades towards the vessel bottom. The former vortex was observed to dominate all vessel motion, leading to a strong circumferential flow around it.

The frequency analysis of LDA data indicated the presence of well defined peaks in the frequency spectra of velocity recordings. In particular three characteristic frequencies were observed in different locations across the vessel: f' = 0.105, 0.155 and 0.94. Specifically, the f' = 0.155 and 0.105 frequencies were related to the periodic movements of the upper and lower vortices' axis, respectively, which are also well visible from flow visualization experiments (see Fig. 6a and Fig. 6b, respectively). The f' = 0.94 frequency was explained by considering the vortical structure – shaft interaction, which occurs in eccentric configuration and leads to vortex shedding phenomena. The authors provided an interpretation based on the Strouhal number.

In a later work (Galletti et al., 2009) the effect of blade thickness tb was investigated, finding that for a thicker impeller (tb/D = 0.05) the frequency of the upper vortex movement was

Flow Instabilities in Mechanically Agitated Stirred Vessels 243

However except for such drawbacks, MIs may be beneficially utilized to improve mixing,

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

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

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

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

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-

provided that their phenomenology is well understood.

correspondence of the vortices shown in Fig. 6.

enhancing the mass transfer.

mixing times as the additional raising or lowering of the impeller.

MIs can broaden real turbulence levels up to 25% for a PBT.

68% near the surface.

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

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