Theoretical Solutions for Unsteady Flows Past Oscillating Flexible Airfoils Using Velocity Singularities
Bibliographic record
Abstract
A new method of solution is presented for the analysis of unsteady e ows past oscillating airfoils. This method is based on the derivation of the singular contributions of the leading edge and ridges (points where the airfoil boundary conditions change ) in the solutions of the e uid velocity and pressure coefe cient. The method has been validated by comparison with the results obtained by Theodorsen and by Postel and Leppert for rigid airfoil and aileron oscillations in translation and rotation. An excellent agreement was found between the present solutions and these previous results. This method has then been used to obtain solutions for the e exural oscillations of the e exible airfoils, e tted or not with oscillating e exible ailerons, which are of interest for the aeroelastic studies. The aerodynamic stiffness, damping, and virtual (or added) mass contributions in the solutions of the unsteady pressure distribution, lift coefe cient, and moment coefe cient are specie cally determined. An analysis of the relative magnitude of the quasi-steady and vortex shedding contributions in the aerodynamic coefe cients is also presented. In all cases studied, this method led to very efe cient and simple analytical solutions in closed form.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".