Stirred vessels impellers

Reynolds number for stirred vessel (impeller), p D /]I Reynolds number for spherical particle, PfVood/p,f Schmidt number, p,f/ppDab Suratman number for stirred vessel, PcaD/ Xj viscosity group for stirred vessel, (Pc/Pd) ttdND/0 for static mixer, (Pc/Pd) P-dV /0 Weber number for stirred vessel, PcN D /0 for static mixer, PcVg Dp/o... 

Impeller Reynolds Number The presence or absence of turbulence in an impeller-stirred vessel can be correlated with an impeller Reynolds number defined... 

Suspensions of fine sohds may have pseudoplastic or plastic-flow properties. When they are in laminar flow in a stirred vessel, motion in remote parts of the vessel where shear rates are low may become negligible or cease completely. To compensate for this behavior of slurries, large-diameter impellers or paddles are used, with (D /Df) > 0.6, where Df is the tank diameter. In some cases, for example, with some anchors, > 0.95 Df. Two or more paddles may be used in deep tanks to avoid stagnant regions in slurries. 

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). 

Considering a stirred vessel in which a Newtonian liquid of viscosity p, and density p is agitated by an impeller of diameter D rotating at a speed N the tank diameter is DT, and the other dimensions are as shown in Figure 7.5, then, the functional dependence of the power input to the liquid P on the independent variables (fx, p, N, D, DT, g, other geometric dimensions) may be expressed as ... 

Baldi, S. and Yianneskis, M. (2004) On the quantification of energy dissipation in the impeller stream of a stirred vessel from fluctuating velocity gradient measurements. Chem. Eng. Sci., 59 (13), 2659-2671. 

Fig. 10. Comparison of stirred vessels with and without baffles Reference floe diameter dpv in dependency on specific impeller power P/V H/D = 1 D = 0.4 m...

In the case of stirred vessels the values A/riL can be calculated by the following equation using the geometry parameter d/D, H/D, the Newton number Ne, the Reynolds number Re = nd /v, the energy dissipation ratio e/e and the related macro scale A/d. For standard turbines e.g. Mockel [24] found the value A/d = 0.08 close to the impeller. Corresponding to this the maximum of the dissipation ratio ,/ has to be used which can be estimated by Eq. (20). 

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. 

This review paper is restricted to stirred vessels operated in the turbulent-flow regime and exploited for various physical operations and chemical processes. The developments in the field of computational simulations of stirred vessels, however, are not separated from similar developments in the fields of, e.g., turbulent combustion, flames, jets and sprays, tubular reactors, and multiphase reactors and separators. Fortunately, there is a strong degree of synergy and mutual cross-fertilization between these various fields. This review paper focuses on aspects specific to stirred vessels (such as the revolving impeller, the resulting strong spatial variations in turbulence properties, and the macroinstabilities) and on the processes carried out in them. 

In the case of droplets and bubbles, particle size and number density may respond to variations in shear or energy dissipation rate. Such variations are abundantly present in turbulent-stirred vessels. In fact, the explicit role of the revolving impeller is to produce small bubbles or drops, while in substantial parts of the vessel bubble or drop size may increase again due to locally lower turbulence levels. Particle size distributions and their spatial variations are therefore commonplace and unavoidable in industrial mixing equipment. This seriously limits the applicability of common Euler-Euler models exploiting just a single value for particle size. A way out is to adopt a multifluid or multiphase approach in which various particle size classes are distinguished, with mutual transition paths due to particle break-up and coalescence. Such models will be discussed further on. 

Implementing complex boundaries in LB simulations is relatively easy compared to doing so for FV techniques (Chen and Doolen, 1998). In view of the usually complex boundaries of process equipment, particularly in the case of stirred vessels with a revolving impeller, this is a distinctive advantage. 

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. 

An example rather than linking average bubble size to just or essentially the (overall) power input of a particular vessel-impeller combination, dedicated CFD (preferably DNS and LES) allows for studying ( tracking ) the response of bubble size to local and spatial variations in the turbulence levels in a stirred vessel. In this way, the validity of certain modeling assumptions may be affirmed or disproved. Particularly, effects of spatial variations in e which... 

Montante, G., Micale, G., Brucato, A., and Magelli, F., CFD Simulation of Particle Distribution in a Multiple-Impeller High-Aspect-Ratio Stirred Vessel . Proceedings of the 10th European Conference on Mixing, Delft, Netherlands, 125-132 (2000). 

A deep stirred vessel is provided with two impellers on a single shaft. Feed is between the impellers. A plausible model for such a vessel is two CSTR s partly in parallel and partly in series, followed by a PER, as indicated on the sketch. Let a be the fraction of the total feed that goes to the first CSTR, and let 0 and j be the fractions of the volume occupied by each of the CSTRs. Find the transfer function of the whole vessel and the response to impulse input. 

Fig. 4.9. Multiple-impeller stirred vessel (a) and tall bubble column (b) showing similarity of liquid circulation patterns...

A further unfortunate characteristic of the stirred vessel is that its mixing capability is also a strong function of its size. Scale-up usually proceeds on the basis of a constant impeller tip speed, and since the mean circulation speed in the vortices is broadly proportional to the tip speed chosen, the circulation time is proportional to the vessel diameter. Thus the turnover time of the vessel contents increases at the larger scale and the macro mixing performance deteriorates. 

Challenge 2.2. Relationship between mixing capacity and impeller rotational speed and set of positions of the inlet and outlet in a flow-stirred vessel... 

Although flow-stirred vessels have been used widely, the issue of the best position for the inlet and outlet in order to establish effective mixing is still unsolved. Additionally, the effect of impeller rotational speed on the mixing... 

Stirred vessel Figure 2.5(a) (Cylindrical flat bottom vessel, four baffles). Impeller six-flat blade turbine type. 

Figure 2.5 (a) Stirred vessel of a flow system, (b) Four sets of positions of inlet and outlet of a flow system, (c) Mixing capacity change with impeller rotational speed for four sets of positions of inlet and outlet of a flow system. 

There are various purposes of using a stirred vessel, and the required mixing effect depends on the purpose. For any mixing purpose, rapid and homogeneous dispersion is required. In a stirred vessel, forced convection by the rotation of an impeller occurs, that is, each element of the fluid has an individual velocity finally, turbulent flow based on the shear stress accelerates the mixing. Therefore, the shape of the impeller has a very important effect on the mixing state. However, there are various types of impeller shapes, and traditional impellers are classified into three types ... 

Figure 2.7 (a) Stirred vessel of a batch system and imaginary partition of vessel, (b) Three types of impeller, (c) Relationship between mixedness and real time of FBDT impeller in a stirred vessel, (d) Relationship between mixedness and dimensionless time of FBDT in a stirred vessel, (e) Relationship between mixedness and dimensionless time of FBT and 45° PBT in a stirred vessel. 

Challenge 2.4. Relationship between mixedness and impeller rotational speed in an aerated stirred vessel... 

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