Numerical estimation of the leakage flow force coefficients of a Francisturbine runner for shaft-line dynamics
Bibliographic record
Abstract
Leakage flow present in the radial clearance of a Francis turbine runner gives rise to restoring and damping forces on the runner. These forces can be modelled with dynamic force coefficients on the shaft-line dynamics and are important for predicting whirling vibrations. However, the hydrodynamic characteristics of this leakage flow around a Francis turbine runner are not well known and not included in the traditional shaft line rotor dynamic calculation. This study aims to determine the rotor dynamic coefficients to improve the accuracy of shaft line analyses. Firstly, the fluid radial and tangential forces acting on the runner are described as polynomial functions of the whirling frequency, of which the coefficients correspond to the rotor dynamic coefficients. These forces are calculated for different values of the whirling frequency with a computational fluid dynamics (CFD) model by ANSYS CFX. An interpolation of the forces against the whirling frequencies hence yields the dynamic coefficients. Secondly, a vibroacoustic model in ANSYS Mechanical APDL is set up to calculate the same dynamic coefficients. In this second model, a mean flow is applied, modal analyses are performed, and normalisation by the expected eccentricity yields the fluid structural forces corresponding to the correct whirling vibration. These two models are firstly validated against literature using a simple conical disc geometry. Then, they are applied to a real Francis turbine radial seal geometry. Comparisons of the coefficients from both models are accomplished. Moreover, variations of the dynamic coefficients against different key parameters, such as mean radial clearance, eccentricity, whirling frequency, rotor frequency input and flow rate, are studied. The resultant rotor dynamic coefficients help to improve the shaft line analysis, as more physical phenomena are considered on a real case geometry.
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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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 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".