Aerodynamic Shape Optimization for Natural Laminar Flow Using a Discrete-Adjoint Approach
Bibliographic record
Abstract
A framework for the design of natural-laminar-flow airfoils is developed based on multipoint aerodynamic shape optimization capable of efficiently incorporating and exploiting laminar–turbulent transition. A two-dimensional Reynolds–averaged Navier–Stokes flow solver making use of the Spalart–Allmaras turbulence model is extended to incorporate an iterative laminar–turbulent transition prediction methodology. The natural transition locations due to Tollmien–Schlichting instabilities are predicted using a simplified method or the compressible form of the Arnal–Habiballah–Delcourt criterion. The Reynolds–averaged Navier–Stokes solver is subsequently used in a gradient-based sequential quadratic programming shape optimization framework. The transition criteria are tightly coupled into the objective and gradient evaluations. The gradients are obtained using an augmented discrete-adjoint formulation for nonlocal transition criteria. Robust design over a range of cruise flight conditions is demonstrated through multipoint optimization. Finally, a technique is proposed and demonstrated to enable the design of natural-laminar-flow airfoils with robust performance over a range of critical factors: the optimizer is seen to produce transition ramps similar to those used by experienced designers.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".