Maximum intensity of rarefaction shock waves for dense gases
Bibliographic record
Abstract
Modern thermodynamic models indicate that fluids consisting of complex molecules may display non-classical gasdynamic phenomena such as rarefaction shock waves (RSWs) in the vapour phase. Since the thermodynamic region in which non-classical phenomena are physically admissible is finite in terms of pressure, density and temperature intervals, the intensity of RSWs is expected to exhibit a maximum for any given fluid. The identification of the operating conditions leading to the RSW with maximum intensity is of paramount importance for the experimental verification of the existence of non-classical phenomena in the vapour phase and for technical applications taking advantage of the peculiarities of the non-classical regime. This study investigates the conditions resulting in an RSW with maximum intensity in terms of pressure jump, wave Mach number and shock strength. The upstream state of the RSW with maximum pressure drop is found to be located along the double-sonic locus formed by the thermodynamic states associated with an RSW having both pre- and post-shock sonic conditions. Correspondingly, the maximum-Mach thermodynamic and maximum-strength loci locate the pre-shock states from which the RSW with the maximum wave Mach number and shock strength can originate. The qualitative results obtained with the simple van der Waals model are confirmed with the more complex Stryjek–Vera–Peng–Robinson, Martin–Hou and Span–Wagner equations of state for selected siloxane and perfluorocarbon fluids. Among siloxanes, which are arguably the best fluids for experiments aimed at the generation and measurement of an RSW, the state-of-the-art Span–Wagner multi-parameter equation of state predicts a maximum wave Mach number close to 1.026 for D 6 (dodecamethylcyclohexasiloxane, [O-Si-(CH 3 ) 2 ] 6 ). Such value is well within the capacity of the measurement system of a newly built experimental set-up aimed at the first-ever demonstration of the existence of RSWs in dense vapours.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".