On the critical-throat boundary condition in quasi-one-dimensional linearised-Euler equation models
Bibliographic record
Abstract
Based on the assumption of locally quasi-steady behaviour, Duran & Moreau (2013 J. Fluid Mech. 723 , 190–231), assumed that, at a critical nozzle throat, the fluctuations of the Mach number vanish for linear perturbations of a quasi-one-dimensional isentropic flow. This appears to be valid only in the quasi-steady-flow limit. Based on the analytical model of Marble & Candel (1977 J. Sound Vib. 55 , 225–243) an alternative boundary condition is obtained, which is valid for nozzle geometries with a finite limit of the second spatial derivative of the cross-section on the subsonic side of the throat. When the nozzle geometry does not satisfy this condition, the application of a quasi-one-dimensional theory becomes questionable. The consequences of this for the quasi-one-dimensional modelling of the acoustic response of choked nozzles are discussed for three specific nozzle geometries. Surprisingly, the relative error in the inlet nozzle admittance and acoustic wave transmission coefficient remains below a per cent, when the quasi-steady boundary condition is used at the throat. However, the prediction of the acoustic fluctuations assuming a quasi-steady critical-throat behaviour is incorrect, because the predicted acoustic field is singular at the throat.
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How this classification was reachedexpand
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".