Stirred tank laminar mixing

In laminar flow stirred tanks, the packet diffusion model is replaced by a slab-diffusion model. The diffusion and reaction calculations are similar to those for the turbulent flow case. Again, the conclusion is that perfect mixing is almost always a good approximation. 

RTD in Two Systems in a Series The accompanying figure shows two combinations of a tubular vessel and a well-mixed stirred tank, (a) Assuming plug flow in the tube, prove that the RTDs in both combinations are identical, (b) Repeat (a), assuming laminar flow in the tube. 

Mixing times are normally short. If the Reynolds number lies between 10 and conditions are referred to as transitional. Mixing times will be longer than at turbulent conditions, but short compared with laminar flow conditions. At a Reynolds number of <10, conditions are laminar. While stirred tanks using proprietary devices can be used at these conditions, one ought to consider using a motionless mixer. 

The use of the tanks-in-series model for packed beds can be more strongly justified. The fluid can be visualized as moving from one void space to another through the restrictions between particles. If the fluid in each void space were perfectly mixed, the mixing could be represented by a series of stirred tanks each with a size the order of magnitude of the particle. This has been discussed in detail by Aris and Amundson (A14). The fluid in the void spaces is not perfectly mixed, and so an efficiency of mixing in the void spaces has to be introduced (C6). This means that the analogy is somewhat spoiled and the model loses some of its attractiveness. In laminar flow the tanks-in-series model may be still less applicable. 

There is one further point of comparison. Interpretation of results from a stirred-tank reactor depends on the assumption that the contents of the tank are well mixed. Interpretation of results from a tubular reactor rests on the assumption of plug flow unless the flow is laminar and is treated as such. Which of these two assumptions can be met most satisfactorily in practical experiments Unless the viscosity of the reaction mixture is high or the reaction extremely fast, a high speed stirrer is very effective in maintaining the contents of a stirred tank uniform. On the other hand, a tubular reactor may have to be very carefully designed if back-mixing is to be completely eliminated, and in most practical situations there is an element of uncertainty about whether the plug flow assumption is valid. 

It is usual in laminar mixing simulations to represent the flow using tracer trajectories. The computation of such flow trajectories in a coaxial mixer is more complex than in traditional stirred tank modelling due to the intrinsic unsteady nature of the problem (evolving topology, flow field known at a discrete number of time steps in a Lagrangian frame of reference). Since the flow solution is periodic, a node-by-node interpolation using a fast Fourier transform of the velocity field has been used, which allowed a time continuous representation of the flow to be obtained. In other words, the velocity at node i was approximated... 

In the transition range, spreading with the stirrer speed appears, and indeed all the more strongly, the higher the rotation speed. There is a satisfactory explanation for this circumstance, after Rautenbach and BoUenrath [451] calculated the temperature profile for a stirred tank with a low wall clearance for the laminar flow range according to their modified penetration theory. This theory assumes, that a parallel layered flow exists between the tank wall and the stirrer (similar to Couette flow), but that the liquid occluded by the stirrer is ideally mixed. For the temperature profile this means, that the layer near to the wall is at rest, but the layer near the stirrer at every stirrer blade pass is included and is mixed with the liquid bulk and acquires its temperature. After a certain number of stirrer blade passes a steady-state temperature profile is realized. 

Harvey III A.D., West D.H., Tufiliaro N.B., Evaluation of laminar mixing in stirred tanks using a discrete-... 

For reactors with known mixing characteristics the response curve and the RTD can be predicted no experiments are necessary. As an illustration let us deyelop the RTD for the plug-flow reactor, a single ideal stirred-tank reactor, and a tubular reactor with laminar flow. 

In un-baffled stirred tanks, a vortex formation occurs at Reynolds larger than 300. This phenomenon should be avoided by working in laminar regime, or by using baffles in turbulent mixing (Re > lO" ). Because Np = Kp the following relation is obtained ... 

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. 

Laminar Mixing in Stirred-Tank Reactor Numerical Study... 

Dielot J.Y., Delaplace G, Guerin R, Briarme J.P, LeuUet G. Laminar mixing performances of a stirred tank equipped with helical ribbon agitator subjected to steady and unsteady rotational speed. Chem. Eng.Res. Design, 2008 80(4) 335-344. 

Mario A.M., Paulo A.E., Fernando M.J. Laminar mixing in eccentric stirred tank systems. Can.. Chem. Eng., 2002 80(4) 546-557. 

Yakoob Z., Kamruddin S.K., Hasran U.A. Experimental and numerical studies of laminar mixing in stirred tanks. CIMMA CS 08 Proceedings of the 7th WSEAS International Conference on Computational Intelligence, Man-Machine Systems and Cybernetics, 2008 978(474) 149-151. 

Chapter 5 gives an overview of novel green reactors and the application of the CFD technique in modelling of green reactors. This chapter presents detailed discussions on a number of novel reactors, namely, the microreactor, microwave reactor and spinning disc reactor. A brief introduction on CFD and the application of CFD in modelling laminar mixing in a stirred tank reactor is presented. 

The study of mixing is therefore primarily a study of hydrodynamics. First we have to make a distinction between laminar and turbulent flow conditions. In most practical situations where well stirred tanks are used, turbulent flow conditions prevail. However, when handling highly viscous materials, such as polymer solutions or concentrated emulsions, laminar flow conditions are often unavoidable. 

Conclusions and recommendations for laminar mixing The equations presented in sections 4.2.3.1 and 4.23.2 give only a rough indication of the flow and mixing phenomena in laminar flow in stirred tanks (of Newtonian liquids). There are as yet no theories that are generally applicable to this type of mixing problems. There are several reasons for this ... 

Situation I was discussed in Chapter 3. Situations II and m will be discussed in the next sections. Note that both situations can occur in laminar and in turbulent flow conditions. In the following we shall concentrate primarily on the meso-mixing in continuous stirred tank reactors (CSTR), since the mixing effects in these reactors are relatively simple to visualize. The effect of meso-mixing on reactions in semi-batch reactors will be discussed thereafter. 

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