Modeling the presumed joint probability density function of conditioning variables in stratified turbulent flames
Bibliographic record
Abstract
Experimental data from the Cambridge-Sandia burner are used to calculate the conditional average of temperature and the mass fractions of H 2 O, CO, and CO 2 in the context of the Uniform Conditional State (UCS) model. The performance of various presumed joint PDF models are examined for this burner working with different swirl and stratification levels. All of the presented PDF models are based on a few statistical moments of the conditioning variables which are extracted from the data at each measuring point. Primarily, only mixture fraction and reaction progress variable are employed as the conditioning variables. The β function is employed for modeling the marginal PDF of mixture fraction in all cases. For the progress variable, the β function and Modified Laminar Flamelet (MLF)-PDF are tested for modeling the marginal PDF . It is shown that even though the MLF-PDF results in more accurate predictions overall for most of the cases, its superiority with respect to the β -PDF is relatively small in the stratified flames. The performance of the product, Plackett, and Gaussian copulas are also investigated for employing the cross-correlation of mixture fraction and progress variable in building their joint PDF . It is found that the Gaussian copula shows a superior performance over the other two. Next, normalized total enthalpy is employed as a third conditioning variable, and different PDF models are examined for the three-condition version of UCS. It is found that even though adding the third conditioning variable can improve the predictions by considering the effect of heat transfer on the chemistry manifold, such improvements depend on having a proper 3D PDF model for the conditioning variables. In the vicinity of the flame brush , the models employed for the 3D PDFs represent an inferior performance compared to the two-condition version with the use of a Gaussian copula due to complications in the marginal PDF of normalized total enthalpy in these regions. To benefit from considering the impact of heat transfer on chemistry while also avoiding complexities in modeling the 3D joint PDF near the reaction zone, a switch between the two- and three-conditional models which is triggered by the variance of progress variable is proposed. It is shown that the predictions obtained by the use of this switch are almost always superior to all other PDF models investigated in this study.
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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".