Publication detail
Model of Pressure Pulsations in Hydraulic Turbine Draft Tube Based on Linearized Rayleigh-Plesset Equation
RUDOLF, P. HABÁN, V. POCHYLÝ, F.
Czech title
Model tlakových pulzací v sací troubě vodní turbíny založený na linearizované Rayleigh-Plessetově rovnici
English title
Model of Pressure Pulsations in Hydraulic Turbine Draft Tube Based on Linearized Rayleigh-Plesset Equation
Type
conference paper
Language
en
Original abstract
Vortex rope appears in hydraulic turbine draft tube for partial load operation. This rope can, for certain sigma values, cavitate and contain saturated water vapour. Cavitating vortex rope is cause of pressure pulsations and effects dynamics of the whole turbine unit. Time behaviour of the spherical cavitating bubble is described by well-known Rayleigh-Plesset equation. This contribution presents derivation of the Rayleigh-Plesset equation for infinitely long cylindrical cavity imitating vortex rope. Linearized form of this equation accompanied by continuity equation and force equillibrium equation create basis for transfer matrix of the draft tube with cavitating vortex rope. Paper discusses ideas, steps of the derivation, but also necessary assumptions and simplifications leading to this new model. The final transfer matrix includes effect of the vortex rope volume change and can be included into the system of transfer matrices describing behaviour of the turbine unit with penstock.
Czech abstract
Pro určité hodnoty čísla sigma se vsací troubě vodní turbíny objevuje kavitující vírový cop, který způsobuje tlakové pulzace a ovlivňuje dynmiku stroje. V příspěvku je odvozena Rayleigh-Plessetova rovnice pro kavitjící válcový cop. Následně je linerizována a je vytvořena přenosová matice sací trouby s kavitujícím vírovým copem. Ta může být začleněna do systému přenosových matic celeého soustrojí.
English abstract
Vortex rope appears in hydraulic turbine draft tube for partial load operation. This rope can, for certain sigma values, cavitate and contain saturated water vapour. Cavitating vortex rope is cause of pressure pulsations and effects dynamics of the whole turbine unit. Time behaviour of the spherical cavitating bubble is described by well-known Rayleigh-Plesset equation. This contribution presents derivation of the Rayleigh-Plesset equation for infinitely long cylindrical cavity imitating vortex rope. Linearized form of this equation accompanied by continuity equation and force equillibrium equation create basis for transfer matrix of the draft tube with cavitating vortex rope. Paper discusses ideas, steps of the derivation, but also necessary assumptions and simplifications leading to this new model. The final transfer matrix includes effect of the vortex rope volume change and can be included into the system of transfer matrices describing behaviour of the turbine unit with penstock.
Keywords in Czech
sací trouba, kavitace, Rayleigh-Plessetova rovnice, přenosová matice
Keywords in English
draft tube, cavitation, Rayleigh-Plesset equation, transfer matrix
RIV year
2006
Released
28.06.2006
Location
Barcelona (Spain)
Book
Proceedings of abstracts "International Meeting of the Work Group Cavitation and Dynamic Problems in Hydraulic Machienry and Systems
Pages count
1
BIBTEX
@inproceedings{BUT24570,
author="Pavel {Rudolf} and Vladimír {Habán} and František {Pochylý},
title="Model of Pressure Pulsations in Hydraulic Turbine Draft Tube Based on Linearized Rayleigh-Plesset Equation",
booktitle="Proceedings of abstracts "International Meeting of the Work Group Cavitation and Dynamic Problems in Hydraulic Machienry and Systems",
year="2006",
month="June",
address="Barcelona (Spain)"
}