Flow patterns in stirred tanks

A qualitative picture of the flow field created by an impeller in a mixing vessel in a single-phase liquid is useful in establishing whether there are stagnant or dead regions in the vessel, and whether or not particles are likely to be suspended. In addition, the efficiency of mixing equipment, as well as product quality, are influenced by the flow patterns prevailing in the vessel. 

Basically, the propeller creates an axial flow through the impeller, which may be upwards or downwards depending upon the direction of rotation. The velocities at any 

Propeller turning counterclockwise looking down on shaft 

Streamlines in a tank with a gate agitator, drawn relative to the arm of the stirrer 

Clearly, the flow pattern established in a mixing vessel depends critically upon the vessel/impeller configuration and on the physical properties of the liquid (particularly viscosity). In selecting the appropriate combination of equipment, it must be ensured that the resulting flow pattern is suitable for the required application. 

Flow patterns produced in a mixing vessel are very much dependent upon the geometry of the impeller. It is thus convenient to classify the agitators used in non-Newtonian applications into three types  

The flow patterns for single phase Newtonian and non-Newtonian fluids in tanks agitated by class 1 impellers have been reported in the literature by, amongst others, Metzner and Taylor [1960], Norwood and Metzner [1960], Godleski and Smith [1962] and Wichterle and Wein [1981]. The experimental methods used have included the introduction of tracer liquids, neutrally buoyant particles or hydrogen bubbles and measurement of local velocities by 

The constant was found to be 0.3 for propellers, 0.6 for turbines and 0.375 (Por) / for other types where Po, is the constant value of the Power number imder fiilly turbulent conditions. The Reynolds number here is defined by assuming kg = 1, i.e. jm. 

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Desouza, A. and R. W. Pike, Fluid dynamics flow patterns in stirred tanks with a turbine impeller, Can. J. Chem. Eng., 50, 15-23 (1972). 

This chapter deals with basic fundamentals of novel reactor technology and some of green reactor design softwares and their applications. Basic understanding of flow pattern in stirred-tank reactor by computational fluid dynamics and simulation of CSTR model by using ASPEN Plus were mainly presented in this chapter. 

The flow patterns in stirred tank reactors are complicated and are mostly difficult to model in a way that is practically applicable. Consequently, the quantitative effects of the rate of macro-mixing are difficult to estimate. There is one exception the situation where the reactor contents can be considered to be completely segregated (very slow micro-mixing). This situation, that has limited practical importance, was discussed in section 7.2.1.2. 

Some approximate methods have been applied previously to deal with the inhomogeneous nature of flow patterns in stirred tanks [67, 68]. Koh [67] divided the stirred tank into three compartments, the impeller zone, the bulk zone and a dead space, and assigned different shear rates for each compartment. Furthermore, Koh et al. [69] ignored the dead space, but split the impeller zone into impeller tip zone and impeller zone. Ducoste [68] essentially followed the same approach, dividing the suspension volume into two zones, the impeller discharge zone and the bulk zone. 

The previous sections describe how mixing is accomplished in a liquid phase. However, many industrial processes carried out in stirred tank reactors involve mixing of solids, gases and other liquids in a continuous liquid phase. The presence of a second phase will affect both the power consumption and the flow pattern in the tank. In the sequel, the mixing phenomena caused by the presence of gas bubbles, liquid droplets and solid particles are discussed. 

The objeetive of the following model is to investigate the extent to whieh Computational Fluid Mixing (CFM) models ean be used as a tool in the design of industrial reaetors. The eommereially available program. Fluent , is used to ealeulate the flow pattern and the transport and reaetion of ehemieal speeies in stirred tanks. The blend time predietions are eompared with a literature eonelation for blend time. The produet distribution for a pair of eompeting ehemieal reaetions is eompared with experimental data from the literature. 

In these model equations it is assumed that turbulence is isotropic, i.e. it has no favoured direction. The k-e model frequently offers a good compromise between computational economy and accuracy of the solution. It has been used successfully to model stirred tanks under turbulent conditions (Ranade, 1997). Manninen and Syrjanen (1998) modelled turbulent flow in stirred tanks and tested and compared different turbulence models. They found that the standard k-e model predicted the experimentally measured flow pattern best. 

Stirred tank model A simple convective flow pattern in tanks, characterized by complete and instantaneous mixing in all directions. Also called the continuously stirred tank reaction or the mixing tank model. See Eqs. (3) and (4) and Figure 2. 

Flow patterns in a stirred tank (lumped parameter system) and a tubular reactor (distributed parameter system). 

At present our 6-m tank reactor gives 75% conversion for the first order reaction A R. However, since the reactor is stirred with an underpowered paddle turbine, we suspect incomplete mixing and poor flow patterns in the vessel. A pulse tracer shows that this is so and gives the flow model sketched in Fig. E12.2. What conversion can we expect if we replace the stirrer with one powerful enough to ensure mixed flow ... 

Figure 7.7b shows a two-flat blade paddle. If the flat blades are pitched, then the liquid flow pattern becomes intermediate between axial and radial flows. Many other types of impellers are used in stirred tanks, but these are not described at this point. 

Cell models. In order to predict chemical conversion in stirred tanks, Patterson and coworkers ( 3, 39 > 40) divided the tank volume into 30 mixing segments connected by specified flowrates Q-jj Nd2. The turbulence level in each segment is characterized by Ls ( dT) and e( d2) (HDM model). Mann and coworkers (148,149) also studied a model where cells (or segments) are connected according to the average flow pattern. Commutation according to a specified probability at each cell s outlet allows a stochastic path to be simulated, for instance for a flow follower. They thus obtained circulation time distributions very similar to experimental ones (135, 140, 141). 

Convective bulk transport is also an extremely important factor in the suspension of solids in a stirred tank (this is also responsible for the flow pattern at the tank bottom). P/V cannot be used as a scale-up criterion in this process either. Measurements have shown that the minimum rotational speed, ncrit, of the stirrer which is necessary for the suspension (whirling-up) of particles in the turbulent regime is given by the appropriate Froude number ... 

The first flow pattern in Fig. 7-7(a), shows the usual mixed suspension, mixed product removal (MSMPR) pattern. The most common example of this is a well-mixed continuous stirred tank reactor (CSTR). 

FIGURE 11.43 Flow patterns in a stirred tank reactor (a), radial flow, (b) axial upflow, (c) axial downflow. 

Figure 2 Flow patterns in a 100 mm stirred tank by PEPT (positron emission...

In Chapter 2, the design of the so-called ideal reactors was discussed. The reactor ideahty was based on defined hydrodynamic behavior. We had assumedtwo flow patterns plug flow (piston type) where axial dispersion is excluded and completely mixed flow achieved in ideal stirred tank reactors. These flow patterns are often used for reactor design because the mass and heat balances are relatively simple to treat. But real equipment often deviates from that of the ideal flow pattern. In tubular reactors radial velocity and concentration profiles may develop in laminar flow. In turbulent flow, velocity fluctuations can lead to an axial dispersion. In catalytic packed bed reactors, irregular flow with the formation of channels may occur while stagnant fluid zones (dead zones) may develop in other parts of the reactor. Incompletely mixed zones and thus inhomogeneity can also be observed in CSTR, especially in the cases of viscous media. 

Flow Pattern Ideality. A straightforward interpretation of the observed kinetics can only be made if the flow pattern in the reactor used corresponds to an ideal flow pattern. In particular for plug flow reactors, deviations from the ideal reactor behavior can be encountered. For perfectly mixed reactors such as a batch reactor and a continuous stirred tank reactor, the rotation speed of the stirrer is the key parameter that needs to be set sufficiently high to ensure complete mixing. Deviations from the ideal plug flow pattern can, for example, be caused by a less-dense packing of the catalyst pellets near the reactor wall, by a too high dilution of the catalyst bed with inert pellets or by the importance of effective axial diffusion compared to convection (15). 

To go from volume element models to reactor models the macro flow patterns in the reactor need to be considered. For stirred tank reactors this can be quite simple, in those cases where volume elements in the stirred tank can be described in terms of average conditions. This is not so when macro mixing or residence time distribution are scale dependent, see Chapter 7. When the reactor is tubular, with two countercurrent or parallel flows, the volume element models have to be combined with reactor flow models, including axial mixing. Also this is treated in Chapter 7, for various cases. 

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