Flow induced by the rotation of two circular cylinders in a viscous fluid
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916116568211456 |
|---|---|
| author | Dormy, E. Moffatt, H. K. |
| author_facet | Dormy, E. Moffatt, H. K. |
| contents | The low-Reynolds-number Stokes flow driven by rotation of two parallel cylinders of equal unit radius is investigated by both analytical and numerical techniques. In Part I, the case of counter-rotating cylinders is considered. A numerical (finite-element) solution is obtained by enclosing the system in an outer cylinder of radius $R_{0}\!\gg\!1$, on which the no-slip condition is imposed. A model problem with the same symmetries is first solved exactly, and the limit of validity of the Stokes approximation is determined; this model has some relevance for ciliary propulsion. For the two-cylinder problem, attention is focused on the small-gap situation $\varepsilon \ll 1$. An exact analytic solution is obtained in the contact limit $\varepsilon=0$, and a net force $F_{c}$ acting on the pair of cylinders in this contact limit is identified; this contributes to the torque that each cylinder experiences about its axis. The far-field torque doublet (`torquelet') is also identified.
Part II treats the case of co-rotating cylinders, for which again a finite-element numerical solution is obtained for $R_{0}\!\gg \!1$. The theory of Watson (1995) is elucidated and shown to agree well with the numerical solution. In contrast to the counter-rotating case, inertia effects are negligible throughout the fluid domain, however large, provided Re $\ll 1$.
In the concluding section, the main results for both cases are summarised, and the situation when the fluid is unbounded ($R_{0}=\infty$) is discussed. (...) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_04432 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Flow induced by the rotation of two circular cylinders in a viscous fluid Dormy, E. Moffatt, H. K. Fluid Dynamics The low-Reynolds-number Stokes flow driven by rotation of two parallel cylinders of equal unit radius is investigated by both analytical and numerical techniques. In Part I, the case of counter-rotating cylinders is considered. A numerical (finite-element) solution is obtained by enclosing the system in an outer cylinder of radius $R_{0}\!\gg\!1$, on which the no-slip condition is imposed. A model problem with the same symmetries is first solved exactly, and the limit of validity of the Stokes approximation is determined; this model has some relevance for ciliary propulsion. For the two-cylinder problem, attention is focused on the small-gap situation $\varepsilon \ll 1$. An exact analytic solution is obtained in the contact limit $\varepsilon=0$, and a net force $F_{c}$ acting on the pair of cylinders in this contact limit is identified; this contributes to the torque that each cylinder experiences about its axis. The far-field torque doublet (`torquelet') is also identified. Part II treats the case of co-rotating cylinders, for which again a finite-element numerical solution is obtained for $R_{0}\!\gg \!1$. The theory of Watson (1995) is elucidated and shown to agree well with the numerical solution. In contrast to the counter-rotating case, inertia effects are negligible throughout the fluid domain, however large, provided Re $\ll 1$. In the concluding section, the main results for both cases are summarised, and the situation when the fluid is unbounded ($R_{0}=\infty$) is discussed. (...) |
| title | Flow induced by the rotation of two circular cylinders in a viscous fluid |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2008.04432 |