Current Developments in Mathematical Sciences

Current Developments in Mathematical Sciences

Volume: 2

Liutex-based and Other Mathematical, Computational and Experimental Methods for Turbulence Structure

The knowledge of quantitative turbulence mechanics relies heavily upon the definition of the concept of a vortex in mathematical terms. This reference work introduces the reader to Liutex, which is ...
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*(Excluding Mailing and Handling)

Vortex and Flow Structure inside Hydroturbines

Pp. 232-242 (11)

Yuning Zhang and Yuning Zhang


In this chapter, various kinds of vortex in the hydroturbines are briefly introduced with a focus on the swirling vortex rope in Francis turbine and the vortex in the vaneless space of the reversible pump turbine. The vortex induced pressure fluctuation and vibrations are initially demonstrated based on the on-site measurement in the prototype power stations. Then, influences of the vortex in the upstream on the flow status in the downstream are discussed. Finally, detailed characteristics of the swirling vortex in the draft tube section of the hydroturbines are demonstrated based on the plenty of examples together with the aid of a quantitative swirl number analysis.


Hydroturbines, Pressure fluctuations, Vibrations, Vortex, Vortex rope.


Key Laboratory of Power Station Energy Transfer Conversion and System (Ministry of Education), School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing, China