An empirical expression for on the axis of a slightly heated turbulent round jet
Bibliographic record
Abstract
Self-preservation analyses of the equations for the mean temperature and the second-order temperature structure function on the axis of a slightly heated turbulent round jet are exploited in an attempt to develop an analytical expression for $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$ , the mean dissipation rate of $\overline{\unicode[STIX]{x1D703}^{2}}/2$ , where $\overline{\unicode[STIX]{x1D703}^{2}}$ is the temperature variance. The analytical approach follows that of Thiessetet al.(J. Fluid Mech., vol. 748, 2014, R2) who developed an expression for $\unicode[STIX]{x1D716}_{k}$ , the mean turbulent kinetic energy dissipation rate, using the transport equation for $\overline{(\unicode[STIX]{x1D6FF}u)^{2}}$ , the second-order velocity structure function. Experimental data show that complete self-preservation for all scales of motion is very well satisfied along the jet axis for streamwise distances larger than approximately 30 times the nozzle diameter. This validation of the analytical results is of particular interest as it provides justification and confidence in the analytical derivation of power laws representing the streamwise evolution of different physical quantities along the axis, such as: $\unicode[STIX]{x1D702}$ , $\unicode[STIX]{x1D706}$ , $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$ , $R_{U}$ , $R_{\unicode[STIX]{x1D6E9}}$ (all representing characteristic length scales), the mean temperature excess $\unicode[STIX]{x1D6E9}_{0}$ , the mixed velocity–temperature moments $\overline{u\unicode[STIX]{x1D703}^{2}}$ , $\overline{v\unicode[STIX]{x1D703}^{2}}$ and $\overline{\unicode[STIX]{x1D703}^{2}}$ and $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$ . Simple models are proposed for $\overline{u\unicode[STIX]{x1D703}^{2}}$ and $\overline{v\unicode[STIX]{x1D703}^{2}}$ in order to derive an analytical expression for $A_{\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}}$ , the prefactor of the power law describing the streamwise evolution of $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$ . Further, expressions are also derived for the turbulent Péclet number and the thermal-to-mechanical time scale ratio. These expressions involve global parameters that are most likely to be influenced by the initial and/or boundary conditions and are therefore expected to be flow dependent.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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".