Thermodynamic modeling of rolling fluid turbine

• Thesis title in Czech: Termodynamické modelování Sedláčkovy turbíny
• Thesis title in English: Thermodynamic modeling of rolling fluid turbine
• Key words: Nerovnovážná termodynamika, Sedláčkova turbína, stabilita, vířivost, simulace
• English key words: Non-equilibrium thermodynamics, Rolling fluid turbine, stability, vorticity, simulation
• Academic year of topic announcement: 2018/2019
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Mathematical Institute of Charles University (32-MUUK)
• Supervisor: doc. RNDr. Michal Pavelka, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 12.12.2018
• Date of assignment: 14.02.2019
• Confirmed by Study dept. on: 21.04.2020
• Date and time of defence: 09.07.2020 08:30
• Date of electronic submission: 22.05.2020
• Date of submission of printed version: 28.05.2020
• Date of proceeded defence: 09.07.2020
• Opponents: RNDr. Jaroslav Hron, Ph.D.
• Advisors: prof. Ing. František Maršík, DrSc.

Guidelines

The goal of the thesis is to develop a non-equilibrium-thermodynamic model of a rolling turbine according to these steps:
1) Balance equations of fluid mechanics and the evolution equation of vorticity adapted to the geometry of a particular turbine design [1, 2].
2) Linear stability analysis of the vorticity equation shows creation of vortices, and circulation is generated.
3) Numerical simulation of an simplified geometrical configuration and estimation of power generation.
4) If possible, the obtained results should be compared with experimental data.

References

[1] Landau L.D., Lifschitz E.M.: Fluid mechanics, Pergamon Press, Oxford, 1987
[2] Maršík, F., Tomek, R. and Vondruška, M., Performance and efficiency of rolling turbines and its application. Submitted (2017)

Preliminary scope of work in English

Rolling turbines are fluid motors, which are capable of utilizing very small sources with small elevation of water levels and slow horizontal flows (from 0.8 m/s). They operate on the basis of hydrodynamic stability of vortices. Solid body vortex transforms due to viscosity into a more stable potential vortex. Circulation generated in the core of the vortex is then transmitted to the rolling rotating rotor, which is axially symmetric, e.g. a sphere or truncated cone. The theoretical efficiency of such a device reaches 66% while approximately 50% efficiency is observed in practice.