Resonant geometries for circulation pattern macroinstabilities in a stirred tank
Bibliographic record
Abstract
Abstract Circulation pattern macroinstabilities and precessing vortices are known to exist in stirred tanks, but until recently they have eluded a full quantitative analysis. In this article, frequency analysis of the axial velocity reveals a resonant frequency and geometry for the 45° pitched‐blade turbine (PBT) in a flat‐bottom cylindrical tank. Unlike other axial impellers, such as the hydrofoils A310 and HE3, the PBT produces a large‐scale circulation macroinstability at the scale of the vessel diameter. The macroinstability is superimposed on the turbulent random fluctuations with a timescale that is very long compared to the blade passage frequency and the inertial convective range of the turbulent cascade. In this article it is shown that the circulation pattern macroinstabilities generated by the 45° PBT are coherent and propagate throughout the tank only under very specific conditions (D = T/2 and C/D = 0.50). The normalized frequency of the coherent macroinstability, or Strouhal number, is fMI/N = 0.186. This corresponds to a period of roughly five rotations of the impeller, or 20 individual blade passages. The laser Doppler velocimeter data used in this work are unevenly spaced because they are collected in burst detection mode. This severely complicates spectral or frequency analysis. Standard algorithms such as the fast Fourier transform, autocorrelation methods, and wavelet analysis all require evenly spaced data. The Lomb periodogram was successfully used to extract the low‐frequency content of the unevenly spaced data with a higher accuracy than is possible with other methods. The Lomb method also eliminates a short time‐averaging step that was required in earlier work. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2986–3005, 2004
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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) | 0.001 | 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".