**1. Introduction**

226 Hydrodynamics – Advanced Topics

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A detailed knowledge of the hydrodynamics of stirred vessels may help improving the design of these devices, which is particularly important because stirred vessels are among the most widely used equipment in the process industry.

In the last two decades there was a change of perspective concerning stirred vessels. Previous studies were focused on the derivation of correlations able to provide global performance indicators (e.g. impeller flow number, power number and mixing time) depending on geometric and operational parameters. But recently the attention has been focused on the detailed characterization of the flow field and turbulence inside stirred vessels (Galletti et al., 2004a), as only such knowledge is thought to improve strongly the optimization of stirred vessel design.

The hydrodynamics of stirred vessels has resulted to be strongly three dimensional, and characterised by different temporal and spatial scales which are important for the mixing at different levels, i.e. micro-mixing and macro-mixing.

According to Tatterson (1991) the hydrodynamics of a mechanically agitated vessel can be divided at least into three flow systems:


Trailing vortices originating behind the impeller blades have been extensively studied for a large variety of impellers. For instance for a Rushton turbine (RT) they appear as a pair, behind the lower and the upper sides of the impeller blade, and provide a source of turbulence that can improve mixing. Assirelli et al. (2005) have shown how micro-mixing efficiency can be enhanced when a feeding pipe stationary with the impeller is used to release the fed reactant in the region of maximum dissipation rate behind the trailing vortices. Such trailing vortices may also play a crucial role in determining gas accumulation behind impeller blades in gas-liquid applications, thus affecting pumping and power dissipation capacity of the impeller.

But in the last decade lots of investigations have pointed out that there are other important vortices affecting the hydrodynamics of stirred vessels. In particular it was found that the flow inside stirred vessels is not steady but characterised by different flow instabilities,

Flow Instabilities in Mechanically Agitated Stirred Vessels 229

the fluid velocity. It is based on the Doppler shift of the light scattered from a 'seeding' particle, which is chosen to be nearly neutrally buoyant and to efficiently scatter light. LDA does not need any calibration and resolves unambiguously the direction of the velocity. Moreover it provides high spatial and temporal resolutions. These are very important for flow instability detection. In addition, more than one laser Doppler anemometer can be combined to perform multi-component measurements. The application of LDA to cylindrical stirred vessels requires some arrangement in order to minimize refraction effects

Particle Image Velocimetry (PIV) is also an optical technique which allows the velocity of a fluid to be simultaneously measured throughout a region illuminated by a two-dimensional light sheet, thus enabling the instantaneous measurements of two velocity components. However recently the use of a stereoscopic approach allows all three velocity components to be recorded. So far the temporal resolution of PIV measurements has been limited because the update rate of velocity measurements, governed by the camera frame rate and the laser pulse rate, was too low. Thus PIV was not suited for the investigation of flow instabilities. However recently, high-frame rate PIV systems have been developed allowing flow measurements with very high update rates (more than 10 kHz); thus its use for the analysis of flow instabilities in stirred vessels has been explored by some investigators. Similarly to LDA, also PIV requires the fluid and vessel walls to be transparent as well as actions to

Different flow visualization techniques have also been used to help clarifying the mechanism of flow instabilities. Such flow visualization techniques may simply consist of tracing the fluid with particles and recording with a camera a region of the flow illuminated by a laser sheet. More sophisticated techniques are able of providing also concentration distribution: for example Laser Induced Fluorescence, LIF, uses a fluorescent marker and a camera (equipped with a filter corresponding to the wave of fluorescence) which detects the

In addition to such optical instruments, different mechanical devices have been used in literature for the detection of flow instabilities. Such devices are based on the measurements of the effect of flow instabilities on some variables. Bruha et al. (1995) employed a "tornadometer", that is a device which allows measuring the temporal variation of the force acting on a small target placed into the flow where instabilities are thought to occur. Paglianti et al. (2006) proved that flow instabilities in stirred vessels could be detected by pressure transducers positioned at the tank walls. The pressure transducers provided time series of pressure with a temporal resolution suited for the flow instability detection. Such a technique is particularly interesting as it is well suited for industrial applications. Haam et al. (1992) identified flow instabilities from the measurement of heat flux and temperature at the walls through heat flux sensors and thermocouples. Hasal et al. (2004) measured the tangential force acting on the baffles as a function of time by means of mechanical devices. Also power number measurements (as for instance through strain gauge techniques) have been found to give an indication of flow instabilities related to change in the circulation loop

Numerical models have also been used for the investigation of flow instabilities in stirred vessels, especially because of the increasing role of Computational Fluid Dynamics (CFD). Logically, since the not steady nature of such instabilities, transient calculation techniques

at the tank walls, so often the cylindrical vessel is placed inside a square trough.

minimize refraction effects at the tank curvature.

fluorescence levels in the liquid.

(Distelhoff et al., 1995).

**2.2 Numerical techniques** 

which can influence the flow motion in different manners. Their knowledge and comprehension is still far from complete, however the mixing optimisation and safe operation of the stirred vessel should take into account such flow variations.

The present chapter aims at summarizing and discussing flow instabilities in mechanically agitated stirred vessels trying to highlight findings from our research as well as from other relevant works in literature. The topic is extremely wide as flow instabilities have been detected with different investigation techniques (both experimental and numerical) and analysis tools, in different stirred vessel/impeller configurations.

Thus investigation techniques and related analysis for the flow instability detection will be firstly overviewed. Then a possible classification of flow instabilities will be proposed and relevant studies in literature will be discussed. Finally, examples of findings on different flow instabilities and their effects on the mixing process will be shown.
