Mode split prediction for rotating disks with flexible stator coupling
Bibliographic record
Abstract
High-head turbine runners are subject to multiple sources of excitation. Coupled with the added mass of water, rotation induces a mode split in the natural frequencies of runners, where co-rotating and counter-rotating waves travel through the runner at different relative speeds. Disks, by displaying a similar behavior, can be used as a geometrically simpler model. Mode split is characterized for a rotating disk in dense fluid but, in high-head turbines, the runner and the compliant confinement are coupled through the axial gap fluid. In this article, we develop an analytical model of coupled stationary and rotating disks to analyze the effect of their interaction on the mode split phenomenon. First, we apply the potential flow theory, considering the fluid as irrotational, inviscid and incompressible. We assume that the modeshapes of the disk in a dense fluid are similar to their shapes in vacuum. We then derive the potential flows that respect the no-penetration boundary conditions. One after the other, each disk is considered flexible while the other one is rigid. By applying the superposition principle, we then couple the two obtained fluid flows through the structural equations of motion. A finite-element vibro-acoustic modal analysis was developed to verify the analytical model and propose a fast numerical tool for hydraulic turbine design. Analytical results show that rotation induces a split of the coupled rotor–stator frequencies as for a lone rotor, while the ratio of their amplitudes varies slightly. A change in the relative thickness of the rotor and stator affects their individual frequencies in vacuum, and in turn their coupling by the fluid, with a potential shift in dominance. • Analytical and numerical models of rotor rotating in water with stator. • Confined rotating disk with a radial gap and a coupled stationary disk. • Rotation causes a split of the ratio of the rotor and stator amplitudes. • Rotor–stator coupling is affected by a change in thickness of both components.
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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 | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| 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".