Stirred tank simulation

The grid used in these MRRF stirred tank simulations is shown in Fig 7.22. The overall flow fields in a vertical layer between two baffles and in a horizontal layer at the disc axial level are shown as vector plots in Fig 7.23 and... 

The last three entries in the table were gridded with somewhat different constraints than the usual stirred tank simulation. The work by Gosman et al. [9] is for... 

The sliding mesh model is the most rigorous and informative solution method for stirred tank simulations. Transient simulations using this model can capture low-frequency (well below the blade passing frequency) oscillations in the flow field (Bakker et ak, 2000 Roussinova et al., 2000) in addition to those that result from the periodic impeller-baffle interaction. 

It must be emphasized that even though these results seem reasonable and that extensive validation of stirred-tank simulations has been done for various continuous flow and semibatch cases, only isothermal validation has been done, and no large ratio scale-up validations have been done. The feed time of 50 s for a 3.8 m vessel is very short and exaggerates the heat effects. These aspects of the problem need to be studied before complete confidence may be placed on the CFD simulation of highly exothermic reactions. 

The grid used in these MRRF stirred tank simulations is shown in Fig. 7.22. 

Reactor types modeled A, stoichiometric conversion B, equiUbrium/free-energy minimization, continuous stirred tank, and plug flow C, reactive distillation. Some vendors have special models for special reactions also, private company simulators usually have reactors of specific interest to their company. 

Knowledge of these types of reaetors is important beeause some industrial reaetors approaeh the idealized types or may be simulated by a number of ideal reaetors. In this ehapter, we will review the above reaetors and their applieations in the ehemieal proeess industries. Additionally, multiphase reaetors sueh as the fixed and fluidized beds are reviewed. In Chapter 5, the numerieal method of analysis will be used to model the eoneentration-time profiles of various reaetions in a bateh reaetor, and provide sizing of the bateh, semi-bateh, eontinuous flow stirred tank, and plug flow reaetors for both isothermal and adiabatie eonditions. 

A model frequently employed to simulate the behavior of an aetual reaetor is a series of ideal stirred tank reaetors as shown in Figure 8-24. 

Computer program PROGS 1 determines the number of tanks, the varianee, dispersion number, and the Peelet number from Hull and von Rosenberg data. The results of the simulation suggest that about three stirred tanks in series are equivalent to the RTD response eurve. Figure 8-44 shows the shows E(6), Fe p(6), and Fjy[gjgi(6) versus 6. 

Guichardon etal. (1994) studied the energy dissipation in liquid-solid suspensions and did not observe any effect of the particles on micromixing for solids concentrations up to 5 per cent. Precipitation experiments in research are often carried out at solids concentrations in the range from 0.1 to 5 per cent. Therefore, the stirred tank can then be modelled as a single-phase isothermal system, i.e. only the hydrodynamics of the reactor are simulated. At higher slurry densities, however, the interaction of the solids with the flow must be taken into account. 

Flollander etal. (2001) report numerieal simulations of orthokinetie aggregation in a turbulent ehannel flow and in a stirred tank, respeetively. Using a... 

Nomura and Fujita (12), Dougherty (13-14), and Storti et al. (12). Space does not permit a review of each of these papers. This paper presents the development of a more extensive model in terms of particle formation mechanism, copolymer kinetic mechanism, applicability to intervals I, II and III, and the capability to simulate batch, semibatch, or continuous stirred tank reactors (CSTR). Our aim has been to combine into a single coherent model the best aspects of previous models together with the coagulative nucleation theory of Feeney et al. (8-9) in order to enhance our understanding of... 

Figure 15.5 Measured and simulated turbulent kinetic energies (normalized with the impeller tip speed) at the impeller plane in a stirred tank reactor (From [17]).

Choose the right type of reactor for testing There are quite a number of different reactors. The above-mentioned plug flow reactor and the continuously stirred tank reactor are usually preferred for research laboratory use, but other set-ups may also be of interest for simulating real industrial conditions. 

Results of simulations of batch stirred-tank reactors (BSTR) and... 

In this case, three time constants in series, X, %2 and X3, determine the form of the final outlet response C3. As the number of tanks is increased, the response curve increasingly approximates the original, step-change, input signal, as shown in Fig. 2.12. The response curves for three stirred tanks in series, combined with chemical reaction are shown in the simulation example CSTR. 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

Thus the respective rate expressions depend upon the particular concentration and temperature levels, that exist within reactor, n. The rate of production of heat by reaction, rg, was defined in Sec. 1.2.5 and includes all occurring reactions. Simulation examples pertaining to stirred tanks in series are CSTR, CASCSEQ and COOL. 

This analysis is limited, since it is based on a steady-state criterion. The linearisation approach, outlined above, also fails in that its analysis is restricted to variations, which are very close to the steady state. While this provides excellent information on the dynamic stability, it cannot predict the actual trajectory of the reaction, once this departs from the near steady state. A full dynamic analysis is, therefore, best considered in terms of the full dynamic model equations and this is easily effected, using digital simulation. The above case of the single CSTR, with a single exothermic reaction, is covered by the simulation examples, THERMPLOT and THERM. Other simulation examples, covering aspects of stirred-tank reactor stability are COOL, OSCIL, REFRIG and STABIL. 

Setting k = 0, simulate the tracer response (F-curves) for 3 perfectly-stirred tanks in series. 

Non-ideal mixing conditions in a reactor can often be modelled by combinations of tanks and tubes. Here, three, stirred tanks are used to simulate the tubular, by-passing condition. 

The Stirred Tanks in Series Model Another model that is frequently used to simulate the behavior of actual reactor networks is a cascade of ideal stirred tank reactors operating in series. The actual reactor is replaced by n identical stirred tank reactors whose total volume is the same as that of the actual reactor. 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

An inherent property of the LES approach is that the simulated flow field is no longer steady, but exhibits a transient character due to the presence and motion of large-scale eddies. The LES methodology has proven to be a powerful tool for studying and visualizing stirred tank flows (Eggels, 1996 Derksen et al. 1999 Bakker et al., 2000 Derksen, 2001 Bakker and Oshinowo, 2004), as it inherently takes the unsteady and periodic behavior of the flow (around impeller and baffles) into account. 

On the analogy of simulating the process of adding blobs of a miscible liquid, two-phase flow in stirred tanks in a RANS context may be treated in two ways Euler-Lagrange or Euler-Euler, with the second, dispersed phase treated according to a Lagrangian approach and from a Eulerian point of view, respectively. 

Large eddy simulations explicitly resolves the inherently unsteady character of the turbulent flow in a stirred tank into account, including the periodic phenomena associated with the motion of the impeller and their interaction with... 

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