Study of frequency band in Von Karman excitation of Francis turbine

Abstract

The objective of this study is to reveal the frequency characteristics caused by Von Karman excitation observed at the stationary field of a Francis turbine. The multiple equidistant frequency (frequency band) of the integer multiple of rotation frequency spacing peaks occur when sound pressure caused by Von Karman excitation is measured at the stationary field. The principles of the generation of multiple equidistant frequencies observed at the stationary field caused by Von Karman excitation have not been clearly revealed. This study revealed the cause of the principles by theoretical analysis. The interesting phenomenon cannot be explained by the blade vibration frequency caused by Von Karman excitation alone, so attention was focused on periodic fluctuations in the relative position between the sound source and observer accompanied by runner rotation i.e. Doppler effect. The equation derived with the Doppler effect implies that the frequency caused by a single vibration by Von Karman excitation is observed by an observer located at the stationary field as frequency band with the span of the rotation frequency. This study yielded the following four findings. Frequency modulation of the integer multiple of rotation frequency occurs at the stationary field. Multiple blades vibrate at the same frequency. The runner is excited as a whole not as individual blade. Since the radius of the excitation location in the runner can be identified, the location to be modified to suppress Von Karman excitation can be estimated.

Keywords

• francis turbine
• rotating blade vibration
• von karman excitation
• doppler effect
• theoretical analysis