**4.2 Macro-instabilities**

236 Hydrodynamics – Advanced Topics

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

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

(a)

(b)

(c)

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).

linearly dependent on the impeller speed according to f' = f/N = 0.12.

regime.

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 mechanisms driving such instabilities.
