On a uniformly valid analytical rectilinear cascade response function
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Bibliographic record
Abstract
This paper extends an existing analytical model of the aeroacoustic response of a rectilinear cascade of flat-plate blades to three-dimensional incident vortical gusts, by providing closed-form expressions for the acoustic field inside the inter-blade channels, as well as for the pressure jump over the blades in subsonic flows. The extended formulation is dedicated to future implementation in a fan-broadband-noise-prediction tool. The intended applications include the modern turbofan engines, for which analytical modelling is believed to be a good alternative to more expensive numerical techniques. The initial model taken as a reference is based on the Wiener–Hopf technique. An analytical solution valid over the whole space is first derived by making an extensive use of the residue theorem. The accuracy of the model is shown by comparing with numerical predictions of benchmark configurations available in the literature. This full exact solution could be used as a reference for future assessment of numerical solvers, of linearized Euler equations for instance, in rectilinear or narrow-annulus configurations. In addition, the pressure jump is a key piece of information because it can be used as a source term in an acoustic analogy when the rectilinear-cascade model is applied to three-dimensional blade rows by resorting to a strip-theory approach. When used as such in a true rectilinear-cascade configuration, it reproduces the exact radiated field that can be derived directly. The solution is also compared to a classical single-airfoil formulation to highlight the cascade effect. This effect is found important when the blades of the cascade overlap significantly, but the cascade solution tends to the single-airfoil one as the overlap goes to zero. This suggests that both models can be used as the continuation of each other if needed.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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