**4.1.1 Clearance instabilities (CIs)**

Galletti et al. (2003, 2005a, 2005b) studied the flow pattern transition for a D = T/3 RT and identified a kind of flow instabilities, which will be denoted as CIs (clearance instability). The authors found that the flow pattern transition (single- to double-loop pattern) occurred for C/T = 0.17-0.2, thus within an interval of clearances of about 0.03T. Such C interval was dependent on the fluid properties, lower clearances being observed for more viscous fluids. At clearances of flow pattern transition the velocity time series indicated flow pattern instabilities as periods of double-loop regime, single-loop regime and "transitional" state that followed each other. When the flow underwent a change from one type of circulation to another, the transitional state was always present and separated in time the single- from the double-loop flow regime. Nevertheless, a flow pattern could change firstly into the transitional state and afterwards revert to the original flow regime, without changing the type of circulation. The occurrence of the three flow regimes was shown to be random, and

Flow Instabilities in Mechanically Agitated Stirred Vessels 237

Therefore the flow pattern transition which occurs for a RT when changing the impeller position is governed by two types of instability. The first one manifests as a random succession of double-loop regime, single-loop regime and transitional state over large time intervals. The second one is the instability encountered during the transitional state,

The exact nature of the clearance-related instabilities is not fully understood, but it is not likely to be related to the turbulence content of the flows, as the phenomenon is characterised by a single frequency even for the lowest Re range studied with the most viscous fluid, for which Re is around 5,200 and the corresponding flows should be mostly laminar. Some evidences as the increase of f' with lowering C/T (or increasing the impeller stream mean velocity by reducing the impeller blade thickness to diameter ratio tb/D) may confirm that it is the interaction between the impeller discharge stream and the vessel

Another kind of instability (see the right-hand side of the diagram of Fig. 3) manifests itself as large temporal and spatial variations of the flow superimposed to the mean flow patterns, thus such flow instabilities are called "macro-instabilities". On the basis of results achieved during our work and from other works in literature it was chosen to divide this kind of flow instability into two subgroups, because we think that there were two different underlying

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.

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

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

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).

improvement of the sub-scale grid and/or the numerical settings.

characterised by a well-defined periodicity of the order of few seconds.

base/walls to play a major role in the formation of such instability.

**4.2 Macro-instabilities** 

(1992) cited earlier.

Reynolds number was reduced.

mechanisms driving such instabilities.

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

their lifetimes could be significant, often of the order of few minutes. The time duration of the three flow regimes depended on the impeller clearance, higher clearances promoting the double-loop regime. Moreover the time duration of the three flow regimes depended on the impeller rotational speed, higher impeller rotational speeds promoting the double-loop regime.

An example of flow pattern transition is shown in the LDA time series of Fig. 4a which indicated different regimes, that can be attributed to the double-loop, transitional and single-loop patterns. The most surprising finding was that within the transitional state an instability was manifested as a periodic fluctuation of the flow between the double and the single-loop regimes, characterised by a well-defined frequency f. Such frequency was linearly dependent on the impeller speed according to f' = f/N = 0.12.

Fig. 4. Wavelet power analysis of axial velocity data: (a) time series; (b) Wavelet power spectrum; (c) dependence of frequency on impeller clearance (B is the highest, F the lowest clearance). Taken from Galletti et al. (2003).

Therefore the flow pattern transition which occurs for a RT when changing the impeller position is governed by two types of instability. The first one manifests as a random succession of double-loop regime, single-loop regime and transitional state over large time intervals. The second one is the instability encountered during the transitional state, characterised by a well-defined periodicity of the order of few seconds.

The exact nature of the clearance-related instabilities is not fully understood, but it is not likely to be related to the turbulence content of the flows, as the phenomenon is characterised by a single frequency even for the lowest Re range studied with the most viscous fluid, for which Re is around 5,200 and the corresponding flows should be mostly laminar. Some evidences as the increase of f' with lowering C/T (or increasing the impeller stream mean velocity by reducing the impeller blade thickness to diameter ratio tb/D) may confirm that it is the interaction between the impeller discharge stream and the vessel base/walls to play a major role in the formation of such instability.
