Orthotropic hydraulic permeability of arrays of parallel cylinders
Bibliographic record
Abstract
Approximate analytical methods are presented to calculate the overall orthotropic hydraulic permeability of a flow with low Reynolds number, passing through a bundle of parallel circular cylinders. Two particular distributions are considered: (i) arrays with ordered rectangular lattices and (ii) irregular nonrandom distributions for which the unit cell cross sections are elliptical. The standard unit cell models, originally developed by Happel and Kuwabara for a random distribution of cylinders, are adapted to the case of nonrandom distributions. The drag force on a representative cylinder in a direction perpendicular to its axis is obtained based on the standard unit cell model: the actual unit cell of rectangular or elliptical cross section is replaced with an "equivalent" cylindrical unit cell of diameter equal to the maximum width of the actual unit cell. Using the obtained drag forces and referring back to the original geometry of the unit cell, closed-form approximate expressions for the overall permeabilities in the perpendicular directions are obtained. Numerical comparisons with more sophisticated approaches confirm the good efficiency of the presented approach, especially in the range of low solid volume fraction, i.e., of high porosity. Previous studies have revealed that, for the parallel fluid flow, the variation of permeability with aspect ratio (or in general the lateral arrangement) of parallel cylinders is generally weak. These observations suggest that Happel's model for parallel permeability in a random distribution of cylinders could be a good approximation for parallel permeabilities in nonrandom distributions with the same volume fraction.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".