Mathematical modelling of gas and gas-liquid jets injected into a fluidized bed
Bibliographic record
Abstract
This thesis presents the development of novel mathematical models of jet injection into fluidized beds. Two types of injections are considered: the first is gas-assisted liquid atomization including flow through a variable cross-section nozzle, followed by spray dispersion and interaction with fluidized bed particles (jet-bed interaction), and the second is a high speed injection of a gas jet with a purpose to break down solid particles (particle attrition). Both models are based on a multi-fluid Eulerian-Eulerian treatment and include the system of the ensemble-averaged Navier-Stokes equations together with the particle number density equation for each phase written independently of the local nature of the continuous phase. The models rely on a number of sub-models that form constitutive equations. Some of the sub-models, such as ones used for atomization, moisture and heat transport in a bed due to particle collisions, heat conduction through the particle core, multiphase wall functions, and breakage frequency, are developed during the course of this project. The jet-bed interaction model includes break-up and coalescence of bubbles and droplets due to interfacial (mean and turbulent) shear and collisions in order to account for spatial variations of the average diameters. Atomization is considered as a catastrophic phase inversion triggered by a critical local volume fraction. The jet-bed interaction model is applied to gas-liquid flow through a nozzle, spray dispersion in open air, and spray injection into the bed. Modelling results are compared with experimental data for pressure variation along the nozzle wall, radial profiles of the liquid flow rate and average droplet diameter, and cumulative liquid distribution in a fluidized bed. It is demonstrated that there is an overall satisfactory agreement. The particle attrition model connects the solid phase properties and the granular temperature with the breakage rate. Modelling results allow calculation of the grinding efficiency – a quantitative measure of the attrition performance. For validation purposes, the model is applied to a number of cases that have been previously investigated experimentally with a good agreement. Both models are also applied to cases of practical interest, and a detailed flow analysis is conducted.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".