Mathematical Model to Describe Double Circular Arc and Multiple Circular Arc Compressor Blading Profiles
Bibliographic record
Abstract
Abstract For the past seven decades, a compressor aerodynamicist has developed various methodologies to design, analyze, and simulate compressor stages. In compressor design, three major subsequent steps can be identified: the one-dimensional mean-line methodology, the two-dimensional through-flow analysis, and the three dimensional computational fluid dynamics. One of the interconnecting threads, between these various x-dimensional analysis, is the compressor blade profile shape. This shape, of known and controllable geometric parameters, is usually accompanied by, or related to, loss models and known flow physics, either defined by theory or through experimental test. In this paper, a novel mathematical approach is described to define axial compressor airfoil profile shapes. These shapes, developed in a Cartesian coordinate system, can be used to create Double Circular Arc, Multiple Circular Arc, and a hybrid combination of the two types. The proposed methodology, based on the mathematics of circles, can be easily applied using generalized software such as Python or MATLAB, or be embedded in specialized engineering design software. In doing so, researchers and engineers can create compressor airfoil shapes which are consistent and flexible with respect to geometric parameter manipulation. Full details of the formulas, with respect to the camber line definition and the calculation of the profile intrados and extrados, are presented. A URL link to an equivalent MATLAB code, and a specialized engineering software, has been provided for those researchers that wish to apply the formulations and review its use.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".