Stability of a rotating cylindrical shell containing axial viscous flow
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The present thesis studies the stability of a rotating cylindrical shell containing a co-rotating axial viscous flow. The system can be thought of as a long thin-walled pipe carrying an internal axial flow while the whole is in a frame of reference rotating at a prescribed rate. The equations of the previously solved inviscid model are rederived and the problem is studied further. The results obtained for purely axial flow are reproduced, but as expected from literature, it is impossible to obtain satisfactory results for the system subjected to rotation due to the presence of singularities in the flow pressure solution. A hypothetical physical explanation for these singularities is put forward and has similarities with the phenomenon of atmospheric flow blocking. Considering the unsuccessful results obtained with the inviscid theory, it is believed that the added realism brought in by the introduction of viscosity in the theory can lead to a successful model. Assuming a travelling-wave perturbation scheme, the linear Donnell-Mushtari thin shell equations are coupled with the fluid stresses obtained by solving numerically the incompressible Navier-Stokes equation for a laminar or turbulent flow. A novel triple-perturbation approach is established to consider the interaction between the fluid and the structure. This triple-perturbation approach is in essence a superposition of three fluid fields caused by the three components of the shell deformation for a given oscillation mode. It is found that the usual technique for linear aeroelasticity studies consisting of applying the fluid boundary conditions at the undeformed position of the wall instead of the instantaneous deformed position greatly alters the stability of the system. To remedy to this problem, three different corrections are applied and tested on the carefully derived model. The dynamics of the system subjected to purely axial flow with no rotation is successfully studied with the viscous model for both laminar and turbulent flow conditions. Because no experimental or previous theoretical data is available, it is impossible to validate the results obtained in the laminar regime. For the turbulent regime, as the Reynolds number is increased, the results tend more and more towards those obtained with the inviscid theory. The results obtained for small rates of rotation show that both in the laminar and in the turbulent regime, the system tends to be stabilised when subjected to a small rate of rotation. On the other hand, this tendency should be reversed for higher rates of rotation, but it is impossible to show this due to the limitations of the root-finding method employed.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.008 | 0.002 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 it