Direct Numerical Simulations of Three-Layer Viscosity-Stratified Flow
Bibliographic record
Abstract
Two-dimensional simulations of flow instability at the interface of a three-layer, density-matched, viscosity-stratified Poiseuille flow are performed using a front-tracking/finite difference method. This is an extension of the study for the stability of two-layer viscosity-stratified flow of Cao et al., Int. J. Multiphase Flow, 30, 1485-1508 (2004). We present results for large-amplitude non-linear evolution of the interface for varying viscosity ratio m, Weber number We, and phase difference between the perturbations of the two interfaces. Strong non-linear behaviour is observed for relatively large initial perturbation amplitude. The higher viscosity fluid is drawn out as a finger that penetrates into the lower viscosity layer. The finger originates at the crest of the perturbation at the interface. The simulated interface shape compares well with previously reported experiments. Increasing interfacial tension retards the growth rate of the interface as expected, whereas increasing the viscosity ratio enhances it. The sinuous instability appears to evolve faster than the varicose one. For certain flow parameters the high-viscosity finger displays a bulbous tip, which is also seen in our previously conducted experiments and two-layer results, although it is less pronounced. The low-viscosity intruding finger does not display this curious bulbous tip. Drop formation is precluded by the two-dimensional nature of the calculations. On a effectué à l'aide d'une méthode de différences finies avec capture de front des simulations bidimensionnelles de l'instabilité de l'écoulement à l'interface d'un écoulement de Poiseuille stratifié en viscosité mais de masse volumique à trois couches. Ceci fait suite à l'étude de la stabilité de l'écoulement stratifié en viscosité à deux couches de Cao et al., Int. J. Multiphase Flow, 30, 1485-1508 (2004). Nous présentons des résultats pour l'évolution non linéaire à grande amplitude de l'interface pour un rapport de viscosité m, un nombre de Weber We et une différence de phases entre les perturbations des deux interfaces. Un comportement non linéaire marqué est observé pour une amplitude de perturbation initiale relativement grande. Le fluide ayant la viscosité la plus élevée prend la forme d'un doigt pénétrant la couche de viscosité inférieure. Le doigt prend naissance à la crête de la perturbation à l'interface. La forme simulée de l'interface se compare bien aux expériences décrites antérieurement. L'augmentation de la tension interfaciale retarde la vitesse de croissance de l'interface comme prévu, tandis que l'augmentation du rapport de viscosité la renforce. Il semble que l'instabilité sinueuse évolue plus vite que la variqueuse. Pour certains paramètres d'écoulement, le doigt de plus forte viscosité montre une pointe bulbeuse, ce qu'on a également observé dans nos expériences antérieures et résultats à deux couches, bien que de façon moins prononcée. Le doigt intrusif de faible viscosité ne montre pas cette curieuse pointe bulbeuse. La formation de gouttelettes est évitée par la nature bidimensionnelle des calculs.
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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 | 0.000 | 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".