Dimensional scaling of flame propagation in discrete particulate clouds
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Bibliographic record
Abstract
The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate sources are not resolved and the heat release is assumed spatially uniform, is solved via conventional finite difference techniques. Second, a discrete source model, wherein the heat diffusion from individual sources is modeled via superposition of the Green's function of each source, is employed to examine the influence of the random, discrete nature of the media. Heat transfer to cold, isothermal walls and to a layer of inert gas surrounding the reactive medium are considered as the loss mechanisms. Both cylindrical and rectangular (slab) geometries of the reactive medium are considered, and the flame speed is measured as a function of the diameter and thickness of the domains, respectively. In the continuum model with inert gas confinement, a universal scaling of critical diameter to critical thickness near 2:1 is found. In the discrete source model, as the time scale of heat release of the sources is made small compared to the interparticle diffusion time, the geometric scaling between cylinders and slabs exhibits values greater than 2:1. The ability of the flame in the discrete regime to propagate in thinner slabs than predicted by continuum scaling is attributed to the flame being able to exploit local fluctuations in concentration across the slab to sustain propagation. As the heat release time of the sources is increased, the discrete source model reverts back to results consistent with the continuum model. Implications of these results for experiments are discussed.
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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 it