An Iterative Inverse Design Method Based on Aerodynamic Streamline Equations
Bibliographic record
Abstract
Aerodynamic characteristics are very sensitive to airfoil leading-edge geometry, and its accurate treatment is a limitation of many existing design methods. The objective of the present research is to develop an interactive inverse design method that is not only efficient but can also treat the leading-edge region accurately. In the formulation of the method, a small-perturbation geometric equation is deduced from the streamline momentum equations, the continuity equation, and the isentropic relations with the geometry similarity assumption of near streamlines to the airfoil surface. Moreover, the transonic correction is considered in the aforementioned equation with the assumption for the effects of waves reflected from the free surface (sonic line) because the method based on the surface flow values cannot take into account the transonic characteristics such as wave interference. The geometric perturbation normal to the airfoil surface is then calculated by solving this second-order initial value ordinary differential equation iteratively to obtain an airfoil design. Techniques such as airfoil smoothing, nonuniform relaxation, and the strained coordinate transfer are employed to accelerate convergence. The airfoil design cases demonstrate the remarkable efficiency and accuracy of the method not only for compressible flows but also for low-speed flows. Moreover, the method allows the leading-edge shape to be determined accurately and, thus, to overcome the deficiency of many of the related methods.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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)
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".