Effect of Tube-to-Pellet Diameter Ratio on Turbulent Hydrodynamics in Packed Beds: A Magnetic Resonance Velocity Imaging Study
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jats:titleAbstract</jats:title>jats:pThe hydrodynamics in packed reactors strongly influences reactor performance. However, limited experimental techniques are capable of non-invasively measuring the velocity field in optically opaque packed beds at the turbulent flow conditions of commercial relevance. Here, compressed sensing magnetic resonance velocity imaging has been applied to investigate the hydrodynamics of turbulent flow through narrow packed beds of hollow cylindrical catalyst support pellets as a function of the tube-to-pellet diameter ratio, jats:inline-formulajats:alternativesjats:tex-math$$N$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>, for jats:inline-formulajats:alternativesjats:tex-math$$N=$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miN</mml:mi> mml:mo=</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> 2.3, 3.7, and 4.8. 3D images of time-averaged velocity for the gas flow through the beds were acquired at constant Reynolds number, jats:inline-formulajats:alternativesjats:tex-math$$R{e}_{\mathrm{p}}=$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miR</mml:mi> mml:msub mml:mie</mml:mi> mml:mip</mml:mi> </mml:msub> mml:mo=</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> 2500, at a spatial resolution of 0.70 mm (jats:inline-formulajats:alternativesjats:tex-math$$\tt x$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mix</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>) jats:inline-formulajats:alternativesjats:tex-math$$\times$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mo×</mml:mo> </mml:math></jats:alternatives></jats:inline-formula> 0.70 mm (jats:inline-formulajats:alternativesjats:tex-math$$\tt y$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miy</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>) jats:inline-formulajats:alternativesjats:tex-math$$\times$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mo×</mml:mo> </mml:math></jats:alternatives></jats:inline-formula> 1.0 mm (jats:inline-formulajats:alternativesjats:tex-math$$\tt z$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miz</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>). The resulting flow images give insight into the bed and pellet scale hydrodynamics, which were systematically compared as a function of jats:inline-formulajats:alternativesjats:tex-math$$N$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>. Some changes in hydrodynamics with jats:inline-formulajats:alternativesjats:tex-math$$N$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> were observed. Namely, the near-wall hydrodynamics changed with jats:inline-formulajats:alternativesjats:tex-math$$N$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>, with the jats:inline-formulajats:alternativesjats:tex-math$$N=$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miN</mml:mi> mml:mo=</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> 4.8 bed showing higher velocity at the wall compared to the jats:inline-formulajats:alternativesjats:tex-math$$N=$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miN</mml:mi> mml:mo=</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> 2.3 and jats:inline-formulajats:alternativesjats:tex-math$$N=$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miN</mml:mi> mml:mo=</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> 3.7 beds. Further, in the jats:inline-formulajats:alternativesjats:tex-math$$N=$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miN</mml:mi> mml:mo=</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> 3.7 bed, channels of high velocity, termed flow lanes, were found 1.3 particle diameters from the wall, possibly due to the bed structure in this particular bed. At the pellet scale, the hydrodynamics were found to be independent of jats:inline-formulajats:alternativesjats:tex-math$$N$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>. The results reported here demonstrate the capability of magnetic resonance velocity imaging for studying turbulent flows in packed beds, and they provide fundamental insight into the effect of jats:inline-formulajats:alternativesjats:tex-math$$N$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:miN</mml:mi> </mml:math></jats:alternatives></jats:inline-formula> on the hydrodynamics.</jats:p>
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Acknowledgements: The authors thank Shell Global Solutions International B.V. for funding this work, provision of the catalyst pellets used in this study, and providing water absorption measurements for determining pellet material density. SVE further thanks the Sir Winston Churchill Society of Edmonton and the Natural Sciences and Engineering Research Council of Canada (NSERC) for additional funding. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission.
Funder: Sir Winston Churchill Society of Edmonton
Funder: Shell Global Solutions International; doi: http://dx.doi.org/10.13039/100016773
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1613-7507