Anti-phase oscillations of an elliptical cavitation vortex in Francis turbine draft tube
Bibliographic record
Abstract
In this paper, the dynamic behavior of a precessing cavitation vortex featuring an elliptical cross section in Francis turbine draft tube is investigated. This phenomenon may occur for values of discharge coefficient within 70%–85% of the discharge coefficient at the best efficiency point, for which Francis turbines can experience the onset of the so-called upper-part load (UPL) instability. The latter is characterized by the propagation of high-amplitude synchronous pressure fluctuations through the complete hydraulic circuit. High-speed visualizations of the cavitation vortex are performed on a Francis turbine model by means of two cameras synchronized with pressure sensors arranged along the draft tube for different Thoma numbers at a given discharge coefficient. A simplified analytical model of the cavitation vortex is proposed. It enables the interpretation of the video post-processing results in the frequency domain and the estimation of both the vortex cross section dimensions and their oscillations with time. It is first demonstrated that both the vortex cross section ellipticity (given by the ratio between its semi-major and semi-minor axes) and the amplitude of its oscillations are directly correlated with the amplitude of UPL pressure fluctuations during intermittent UPL instability. Furthermore, the evolution along the draft tube of the dimensions of the elliptical vortex cross section and their oscillations during fully developed UPL instability is highlighted. The ellipticity of the vortex cross section increases as the vortex center position gets closer to the draft tube wall away from the turbine outlet. In addition, the vortex cross section dimensions oscillate with opposite phase from either side of a pressure node located along the draft tube. This results in low oscillations of the total void fraction in the draft tube, compared with results obtained locally. This effect should be considered in the one-dimensional modeling of the cavitation flow during UPL instability for further stability analysis. The new insights on UPL instability presented in this paper may potentially lead to a better theoretical understanding and modeling of this phenomenon in Francis turbines draft tube.
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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 | 0.000 | 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 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".