In stirred vessels

Turbulent Flow in Stirred Vessels Turbulence parameters such as intensity and scale of turbulence, correlation coefficients, and... 

In many important cases of reactions involving gas, hquid, and solid phases, the solid phase is a porous catalyst. It may be in a fixed bed or it may be suspended in the fluid mixture. In general, the reaction occurs either in the liquid phase or at the liquid/solid interface. In fixed-bed reactors the particles have diameters of about 3 mm (0.12 in) and occupy about 50 percent of the vessel volume. Diameters of suspended particles are hmited to O.I to 0.2 mm (0.004 to 0.008 in) minimum by requirements of filterability and occupy I to 10 percent of the volume in stirred vessels. 

Collisional break-up of erystals suspended in stirred vessels may oeeur as a result of eollision between erystal-crystal, erystal-impeller or erystal-vessel, and has been deseribed by many authors e.g. Ottens and de Jong (1973), Kuboi etal. (1984), Mazzarotta (1992). 

Conti, R. and Nienow, A.W., 1980. Particle Abrasion at High Solids Concentration in Stirred Vessels - II. Chemical Engineering Science, 35, 543-547. 

Kuboi, R., Nienow, A.W. and Conti, R., 1984. Mechanical Attrition of Crystals in Stirred Vessels. In Industrial Crystallization 84. Eds. S.J. Jancic and E.J. de Jong, Amsterdam Elsevier Science Publishers B.V. 

Mersmann and Geisler, R., 1991. DeteiTnination of the local turbulent energy dissipation rates in stirred vessels and its significance for different mixing tasks. In 4th World Congress of Chemical Engineering. Karlsruhe, Germany. 

Ranade, V.V., 1997. An efficient computational model for simulating flow in stirred vessels a case of Rushton turbine. Chemical Engineering Science, 52, 4473-4484. 

In an airlift fermenter, mixing is accomplished without any mechanical agitation. An airlift fermenter is used for tissue culture, because the tissues are shear sensitive and normal mixing is not possible. With the airlift, because the shear levels are significantly lower than in stirred vessels, it is suitable for tissue culture. The gas is sparged only up to the part of the vessel cross section called the riser. Gas is held up, fluid density decreases causing liquid in the riser to move upwards and the bubble-free liquid to circulate through the down-comer. The liquid circulates in airlift reactors as a result of the density difference between riser and down-comer. 

Ng, K. and Yianneskis, M. (1999) Observations on the distribution of energy dissipation in stirred vessels. Eluid Mixing 6 Symposium, 1999, Bradford. 

Fig. 16. Comparison of floe destruction in stirred vessels with baffles, bubble columns and viscosimeters...

It could be shown (see Sect. 6) that in stirred vessels with baffles and under the condition of fully developed turbulence, particle stress can be described by Eqs. (2) and (4) alone. The turbulent eddys in the dissipation range are decisive for the model particle systems used here and many biological particle systems (see Fig. 2), so that the following equation applies to effective stress ... 

Much higher shear forces than in stirred vessels can arise if the particles move into the gas-liquid boundary layer. For the roughly estimation of stress in bubble columns the Eq. (29) with the compression power, Eq. (10), can be used. The constant G is dependent on the particle system. The comparison of results of bubble columns with those from stirred vessel leads to G = > 1.35 for the floccular particle systems (see Sect. 6.3.6, Fig. 17) and for a water/kerosene emulsion (see Yoshida and Yamada [73]) to G =2.3. The value for the floe system was found mainly for hole gas distributors with hole diameters of dL = 0.2-2 mm, opening area AJA = dJ DY = (0.9... 80) 10 and filled heights of H = 0.4-2.1 m (see Fig. 15). 

Figure 22 shows a comparison of results from model particle systems and h-terature data with biological systems in stirred vessels. The dependency of particle diameter on maximum energy dissipation dp of yeast and BHK... 

The experimental results for hybridoma and protozoa cells given as examples in Fig. 25 indicate that much higher stress (4 to 30 times) is required under laminar flow conditions of viscosimeters than in stirred vessels to achieve the same death rate k. Here the death rate k is defined as first order deactivation constant k = 1/t In (Nq/N), where N, is the initial and N the time-dependent number of living cells in special deactivation experiments under otherwise optimal living conditions. The stress in Fig. 25 was calculated with Eq. (28) for stirred vessels and with Eq. (1) for the viscosimeter. Our own results for hybri-... 

Various empirical equations are available for the circulation time constant, Xcirc> in stirred vessels, columns, etc. Usually the value of the time constant, however, will represent a mean value, owing to the stochastic nature of flow. 

Flow in stirred vessels was also investigated by Holmes et al. (H5), who simulated mass transfer in a diaphragm diffusion cell stirred by magnetic stirrer bars. This is a good example of a simple model study with a direct practical purpose. A minimum stirring speed in such cells is necessary to avoid appreciable errors in the cell constant. The experiment permits this stirring speed to be related to the solution properties. 

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

CFD might provide a way of elucidating all these spatial variations in flow conditions, in species concentrations, in bubble drop and particle sizes, and in chemical reaction rates, provided that such computational simulations are already capable of reliably reproducing the details of turbulent flows and their dynamic effects on the processes of interest. This Chapter reviews the state of the art in simulating the details of turbulent flows and turbulent mixing processes, mainly in stirred vessels. To this end, the topics of turbulence and CFD both need a separate introduction. 

This paper deals with the advanced CFD of turbulent stirred vessels. The advances attained in recent years in the field of CFD really matter for the degree of accuracy and confidence at which the performance of stirred reactors and of other operations carried out in stirred vessels can be simulated, as these processes and operations may strongly depend on the details of the physics and chemistry involved. The latter details require the more advanced CFD techniques indeed. 

First of all, the increased computer power makes it possible to switch to transient simulations and to increase spatial resolution. One no longer has to be content with steady flow simulations on relatively coarse grids comprising 104-105 nodes. Full-scale Large Eddy Simulations (LES) on fine grids of 106—107 nodes currently belong to the possibilities and deliver realistic reproductions of transient flow and transport phenomena. Comparisons with quantitative experimental data have increased the confidence in LES. The present review stresses that this does not only apply to the hydrodynamics but relates to the physical operations and chemical processes carried out in stirred vessels as well. Examples of LES-based simulations of such operations and processes are due to Flollander et al. (2001a,b, 2003), Venneker et al. (2002), Van Vliet et al. (2005, 2006), and Flartmann et al. (2006). 

An aspect of CFD in stirred vessels that needs separate discussion is the issue of the revolving impeller and the way its motion is dealt with in the simulations. 

In stirred vessels and static mixers the flow domain is bounded by complex boundaries due to the curvature of containing walls, the revolving impeller axis and/or static mixing elements. 

In simulating physical operations carried out in stirred vessels, generally one has the choice between a Lagrangian approach and a Eulerian description. While the former approach is based on tracking the paths of many individual fluid elements or dispersed-phase particles, the latter exploits the continuum concept. The two approaches offer different vistas on the operations and require different computational capabilities. Which of the two approaches is most... 

In whichever approach, the common denominator of most operations in stirred vessels is the common notion that the rate e of dissipation of turbulent kinetic energy is a reliable measure for the effect of the turbulent-flow characteristics on the operations of interest such as carrying out chemical reactions, suspending solids, or dispersing bubbles. As this e may be conceived as a concentration of a passive tracer, i.e., in terms of W/kg rather than of m2/s3, the spatial variations in e may be calculated by means of a usual transport equation. 

In addition, it is dubious whether this new correlation due to Brucato et al. (1998) should be used in any Euler-Lagrangian approach and in LES which take at least part of the effect of the turbulence on the particle motion into account in a different way. So far, the LES due to Derksen (2003, 2006a) did not need a modified particle drag coefficient to attain agreement with experimental data. Anyhow, the need of modifying particle drag coefficient in some way illustrates the shortcomings of the current RANS-based two-fluid approach of two-phase flow in stirred vessels. 

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