Optimized Laminar Axisymmetrical Nozzle Design Using a Numerically Validated Thwaites Method
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Bibliographic record
Abstract
This paper presents the Thwaites method as an accurate and efficient design tool for laminar, axisymmetrical nozzles. Based on historical developments, it is improved to describe internal flows with highly favorable pressure gradients in cylindrical coordinates. The calculation of the core flow velocity distribution based on the continuity equation is proposed as a replacement to other sophisticated numerical methods. A remarkably good agreement is obtained when comparing the results of the current Thwaites method against those of computational fluid dynamics (CFD) simulations, for which the integral boundary layer thicknesses are calculated with equations developed from first principles in the course of the work. This consistency among the results and the low time and resource costs of the Thwaites method confirm its applicability and usefulness as an engineering design and optimization tool.
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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 it