An extended quadrature‐based mass‐velocity moment model for polydisperse bubbly flows
Bibliographic record
Abstract
Abstract Accurately predicting polydisperse bubbly flow is a nontrivial task due to the complexity of the bubble number density function (NDF) and the strong dependence of the instantaneous bubble velocity on the bubble size and shape. To describe polydisperse bubbly flow, a joint mass‐velocity NDF is adopted in this work. In the absence of mass transfer between phases and coalescence or breakage, the bubble mass is a conserved quantity from which the bubble size and shape can be found given the liquid pressure and surface tension. Quadrature‐based moment methods (QBMM) are applied to solve numerically the kinetic equation of the joint NDF using the extended quadrature method of moments (EQMOM) coupled with an open‐source incompressible Navier–Stokes solver for the liquid phase. Transport equations for the joint mass‐velocity moments are derived from a kinetic equation for the joint NDF and closure is attained using a monokinetic NDF valid in the limit of small bubble Stokes number. The integer moments with respect to mass are used to reconstruct the continuous univariate NDF with EQMOM, while the joint mass‐velocity moments are used to determine the bubble velocity as a continuous function of the bubble mass. The model is first applied to simulate a quasi‐2‐D bubble column with different aeration profiles and a narrow bubble size distribution in order to validate the approach with experimental data from the literature. Additional cases with a wide continuous bubble size distribution are used to show the ability of the modelling approach to describe polydisperse bubbly flows.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".