This example is taken from the M.Sc. Thesis of Sandro Goisis and Alessandra Osio (Chapter 5). For further details and comments, we suggest to download the Thesis here!
The annular reactor studied in the previous example was modelled using a 2D domain, due to the axysymmetry of the sytem. Anyway, an eccentricity of the annulus is possible when dealing with systems of such small dimensions (i.e. short contact time reactors). Usually the eccentricity is not a desired property of the system and it is a result of manufacturing tolerances or of deformation in service. For the experimental apparatus considered, the eccentricity parameter can rise up to 50% (Beretta A., personal communication). In the rest of this discussion the following definition of eccentricity will be adopted:
where Δx is the distance between the centers of the circles and r0 and ri are respectively the outer and the inner radius.
The system studied in the following is the same studied in the previous example, but it presents an eccentricity of 50%. The operating conditions are listed in the following Table. The simulations are performed in isothermal and isobaric conditions.
|Inner radius||2.35 mm|
|Outer radius||4.50 mm|
|Reactor length||15 mm|
|O2 mole fraction||0.04|
|H2 mole fraction||0.01|
|N2 mole fraction||0.95|
The study of eccentric annular ducts is only made possible by adopting a three dimensional model. The system considered is symmetric and thus the final computational mesh represents only one half of the reactor. This results in a great saving of computational effort. The grid employed is composed by 10 cells in the radial direction, 100 cells in the axial coordinate and 20 cells in the azimuthal direction and it is reported in Figure 1.
According to (Shah and London 1978), the effect of eccentricity is to lower the asymptotic value of the Sherwood number. Specifically, for the eccentricity of 50% and with a ratio between the radius of 0.5 the Sherwood number is expected to fall from 5.76, in case of perfect concentric annulus, to 2.18. For this reason, we expect to observe a reduced conversion of O2 in the eccentric reactor. The O2 mole fraction profiles at the reactor outlet are shown in Figure 2 for the two different configurations.
It is possible to see that the O2 is mostly consumed on the catalytic layer and specifically in the reduced part of the section.The axial O2 profiles in the 3D mesh are represented in Figure 3.
The profiles of conversion of O2 at different temperatures are depicted in Figure 4. It is possible to notice that with an eccentricity of 50% the O2 conversion is inferior to that obtained with the concentric configuration. For this reason the predicted results obtained with catalyticFOAM are coherent with the expected behaviour of the system.