Heat Transfer Correlations for Smooth and Rough Airfoils
Bibliographic record
Abstract
Low-fidelity methods such as the Blade Element Momentum Theory frequently provide rotor aerodynamic performances. However, these methods must be coupled to databases or correlations to compute heat transfer. The literature lacks correlations to compute the average heat transfer around airfoil. The present study develops correlations for an average heat transfer over smooth and rough airfoil. The correlation coefficients were obtained from a CFD database using RANS equations and the Spalart–Allmaras turbulent model. This work studies the NACA 0009, NACA 0012, and NACA 0015 with and without the leading roughness representative of a small ice accretion. The numerical results are validated against lift and drag coefficients from the literature. The heat transfer at the stagnation point compares well with the experimental results. The database indicates a negligible dependency on airfoil thickness. The work presents two correlations from the database analysis: one for the smooth airfoils and one for the rough airfoils. For the zero lift coefficient, the average Nusselt number is maximum. This increases with Re0.636 for the smooth surface and with Re0.85 for the rough surface. As the lift increases, the average Nusselt is reduced by values proportional to the square of the lift coefficient for the smooth surface, while it is reduced by values proportional to Re and the square of the lift coefficient for the rough surface.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".