On the Phase Relation in Aeroacoustic Feedback Loops
Bibliographic record
Abstract
Aeroacoustic feedback loops can occur in a variety of flows: high speed jets interacting with a plate or a corner, supersonic non-ideally expanded free jets, grazing flow over a cavity, flow around an airfoil, flow passing two diaphragms in tandem, and flow passing through compressor blade rows, among many others. These feedback loops can induce acoustic tones. The typical model used to predict the corresponding tone frequencies dates back from the 50’s [1], and is still used to this day, with some minor modifications. This model consists of two steps. First, in a shear layer or a boundary layer, an aerodynamic disturbance is convected downstream and amplified through the Kelvin-Helmholtz instability from the starting point to the ending point of the feedback loop. It interacts with a singularity at the ending point, and then generates an acoustic wave propagating upstream. This wave excites the shear layer (or the boundary layer), leading to the formation of a new aerodynamic disturbance, thus generating a new cycle. To apply correctly the original model of Powell consisting of the addition of two propagating times, one needs to know the convection velocity, the speed of sound, the positions of the starting and ending points of the feedback loop, and the phase relations between the hydrodynamic and the acoustic pressure fluctuations on both endings. First, we propose to revisit phase relation in aeroacoustics feedback loop. Then, those phase relations are studied for supersonic impinging jets, and for flow around a airfoil. For the latter case, the phase relation is still an open question in the literature and it is shown that, for the present SD7003 airfoil, a phase shift of 180° is found both at the starting point of the feedback loop, taken here as the separation point, and at the ending point of the feedback loop, that is the trailing edge. This is not in agreement with standard model used in the literature. A 2D toy model is finally derived to mimic the feedback loop arising in airfoil tonal noise. This toy model permits to recover the phase shifts found before for the airfoil tonal noise.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".