FIGURE 7.20 Initial and boundary conditions for reactive flow simulations.

FIGURE 7.20 Initial and boundary conditions for reactive flow simulations.

CFD results can provide guidelines to select an appropriate simplified model. Some examples of such an approach are discussed in Chapter 9. A simple example, which illustrates the evaluation of the often-used assumption of a completely mixed reactor, is discussed here, by continuing the case of the cubical reactor considered in earlier examples.

A simple, homogeneous (slow) first-order reaction was considered. Simulations were carried out for cases with and without impeller in the same cubical reactor. Initial and boundary conditions are shown in Fig. 7.20. It can be seen that the mean residence time of the reactor is 10 s. Three cases with different first-order reaction rate constants (0.01 s-1, 0.1 s-1, 1.0 s-1) were simulated (samples of the results are listed with Fig. 7.20). Results of simulations with an impeller velocity of 5 m s-1 are discussed first. As expected, for the lowest reaction rate constant, where the characteristic reaction time scale is much higher than mean residence time, the simulated results agree quite well with the analytical solution obtained based on the assumption of a completely mixed reactor. Even for the case of characteristic reaction time scale of 10 s (which is the same as the residence time), deviation from the analytical solution (of predicted outlet concentration of reactant) is just about 1% (for the case with rate constant 0.1 s-1). As the reaction time scale becomes smaller than residence time (rate constant 1.0 s-1), deviation increases and is equal to 33%! If the reaction rate becomes even faster, one has to use special reactive mixing models discussed in Chapter 5. This simple exercise illustrates the well-known fact that the extent of deviation from ideal mixing is dependent on relative time scales of reaction and mixing. Simulations of a case with rate constant 1.0 s-1 for an impeller speed 1 m s-1 indicates an even higher deviation of 51% from the ideal mixed predictions. The case without an impeller, however, leads to 17.5% deviation. This means that the situation with impeller velocity of 1 m s-1 leads to the highest conversion of reactant. Deviation from ideal mixing is expected to lead to higher conversion of reactant than that predicted by the ideal model. The higher the impeller velocity, the closer the system becomes to the ideal system. Therefore, higher conversion is obtained with an impeller velocity of 1 m s-1 than 5 m s-1. However, when there is no impeller, the inlet fluid short circuits through the reactor. This causes a decrease in the effective volume of the reactor resulting in lower conversion, although it gives a maximum deviation from the ideally mixed situation. Additional examples of using CFD models for reactor applications are discussed in later chapters. Some issues relevant to the application of CFD methods to industrial equipment are discussed in the following section.

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