Effect of Tube-to-Pellet Diameter Ratio on Turbulent Hydrodynamics in Packed Beds: A Magnetic Resonance Velocity Imaging Study
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Bibliographic record
Abstract
Abstract The 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, $$N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> , for $$N=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 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, $$R{e}_{\mathrm{p}}=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>e</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 2500, at a spatial resolution of 0.70 mm ( $$\tt x$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>x</mml:mi> </mml:math> ) $$\times$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>×</mml:mo> </mml:math> 0.70 mm ( $$\tt y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>y</mml:mi> </mml:math> ) $$\times$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>×</mml:mo> </mml:math> 1.0 mm ( $$\tt z$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>z</mml:mi> </mml:math> ). The resulting flow images give insight into the bed and pellet scale hydrodynamics, which were systematically compared as a function of $$N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> . Some changes in hydrodynamics with $$N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> were observed. Namely, the near-wall hydrodynamics changed with $$N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> , with the $$N=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 4.8 bed showing higher velocity at the wall compared to the $$N=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 2.3 and $$N=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 3.7 beds. Further, in the $$N=$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> </mml:mrow> </mml:math> 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 $$N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> . 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 $$N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> on the hydrodynamics.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it