Physics-informed scaling laws for the performance of pitching foils in schooling configurations
Bibliographic record
Abstract
This study introduces novel physics-based scaling laws to estimate the propulsive performance of synchronously pitching foils in various schooling configurations. These relations are derived from quasi-steady lift-based and added mass forces. Hydrodynamic interactions among the schooling foils are considered through vortex-induced velocities imposed on them, constituting the ground effect. Generalized scaling equations are formulated for cycle-averaged coefficients of thrust and power. These equations encompass both the pure-pitching and induced velocity terms, capturing their combined effects. The equations are compared to computational results obtained from two-foil systems, exhibiting foil arrangements over a wide range of parameter space, including Strouhal number (0.15 ≤ St ≤ 0.4), pitching amplitude ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo>≤</mml:mo> <mml:msub> <mml:mi>θ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>≤</mml:mo> <mml:msup> <mml:mn>14</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> ) and phase difference ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>0</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo>≤</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>≤</mml:mo> <mml:msup> <mml:mn>180</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> ) at Re = 1000−10 000. The individual contributions of pure-pitching and induced velocity terms to propulsive performance elucidate that solely relying on the pure-pitching terms leads to inadequate estimation, emphasizing the significance of the induced velocity terms. The validity of the approach is further assessed by testing it with three-foil and five-foil configurations, which displays a collapse of estimated and measured results. This indicates that the scaling laws are applicable to multi-foil arrangements.
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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) | 0.000 | 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".