Magnus force acting upon a rotating sphere passing in an incompressible viscous flow
| Thesis title in Czech: | Magnusova síla působící na rotující kouli pohybující se v nestlačitelné viskózní kapalině |
|---|---|
| Thesis title in English: | Magnus force acting upon a rotating sphere passing in an incompressible viscous flow |
| Key words: | Magnusova síla, Navierovy-Stokesovy rovnice, hydrodynamika |
| English key words: | Magnus Force, Navier-Stokes Equations, Hydrodynamics |
| Academic year of topic announcement: | 2017/2018 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Department of Geophysics (32-KG) |
| Supervisor: | prof. RNDr. Zdeněk Martinec, DrSc. |
| Author: | Mgr. Dominik Beck - assigned and confirmed by the Study Dept. |
| Date of registration: | 13.10.2017 |
| Date of assignment: | 16.10.2017 |
| Confirmed by Study dept. on: | 28.11.2017 |
| Date and time of defence: | 13.09.2018 09:00 |
| Date of electronic submission: | 19.07.2018 |
| Date of submission of printed version: | 19.07.2018 |
| Date of proceeded defence: | 13.09.2018 |
| Opponents: | prof. RNDr. Ondřej Čadek, CSc. |
| Guidelines |
| The aim of this bachelor thesis is to derive the Magnus drag force acting on a rotating sphere, which is placed in the Newtonian viscous fluid moving with a constant velocity.
Hints: 1. Formulate the problem by Navier-Stokes equations. 2. Assume that the fluid passing around a sphere is slow such that the fluid acceleration can be neglected. 3. Solve the Stokes problem for a flow passing a non-rotating sphere analytically. 4. Perturb a primary flow for the case of a rotating sphere which is moved through an incompressible viscous flow. 5. Derive the approximate relation for the Magnus force. 6. Make first the derivation analytically and then validate the analytical result by a numerical approach applied to the initial steady Navier-Stokes equations. |
| References |
| I. Rubinow , S & Keller, Joseph. (1961). The Transverse Force on Spinning
Sphere Moving in a Viscous Fluid. Journal of Fluid Mechanics. 11. 447 - 459. 10.1017/S0022112061000640. Bagchi, P & Balachandar, Sivaramakrishnan. (2002). Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Re. PHYSICS OF FLUIDS. 14. 2719-2737. 10.1063/1.1487378. |