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International Journal of Rotating Machinery
Volume 2009 (2009), Article ID 349397, 7 pages
Research Article

Numerical Estimation of Torsional Dynamic Coefficients of a Hydraulic Turbine

1Lloyd's Register ODS, 10074 Stockholm, Sweden
2Department of Fluid Dynamics, Chalmers University of Technology, 41296 Göteborg, Sweden
3Division of Solid Mechanics, Department of Mechanical Engineering, Luleå University of Technology, 97187 Luleå, Sweden

Received 2 November 2008; Revised 4 March 2009; Accepted 2 April 2009

Academic Editor: Seung Jin Song

Copyright © 2009 Martin Karlsson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The rotordynamic behavior of a hydraulic turbine is influenced by fluid-rotor interactions at the turbine runner. In this paper computational fluid dynamics (CFDs) are used to numerically predict the torsional dynamic coefficients due to added polar inertia, damping, and stiffness of a Kaplan turbine runner. The simulations are carried out for three operating conditions, one at about 35% load, one at about 60% load (near best efficiency), and one at about 70% load. The runner rotational speed is perturbed with a sinusoidal function with different frequencies in order to estimate the coefficients of added polar inertia and damping. It is shown that the added coefficients are dependent of the load and the oscillation frequency of the runner. This affect the system's eigenfrequencies and damping. The eigenfrequency is reduced with up to 65% compared to the eigenfrequency of the mechanical system without the fluid interaction. The contribution to the damping ratio varies between 30–80% depending on the load. Hence, it is important to consider these added coefficients while carrying out dynamic analysis of the mechanical system.