Dynamic Divergence Mechanism in Shells With Internal Axial Flow
Bibliographic record
Abstract
Recent experimental studies have shown that supported tubes with internal fluid flow lose stability by dynamic divergence which is well modelled by the sloshing mechanism described in the work by Heil & Boyle and Heil & Hazel. In this study thin tubes supported at both ends subjected to axial internal fluid flow are investigated experimentally and numerically. Experiments for different L/R ratios were conducted for elastomer thin tubes clamped at both ends and subjected to internal air-flow. The numerical analysis is based on geometrically nonlinear structural equations coupled with potential flow theory to describe the fluid-structure interaction. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations is integrated numerically using pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. The current study investigates experimentally the dynamics of tubes with L/R∼1, L/R∼2 and L/R∼3 in axial internal flow. The experimental results indicated that the tubes lost stability by dynamic divergence resembling the Heil & Boyle Type B oscillatory scenario discussed in Païdoussis (2014). For the L/R∼2 case the amplitude of the maximum shell deformation observed in the experiments was extracted using digitized images from the experiments. The numerical results were analyzed using bifurcation theory predicting that the tubes lose stability by static divergence exhibiting large hysteresis. The numerical results produced for all cases presented in this paper do not predict tube oscillatory solutions for the range of flow velocities considered in this analysis. For the L/R∼2 case, which was also modeled in this paper, the numerical results are in good agreement with experiments for the maximum tube amplitude.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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 teacher head, 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".