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Transient pressure measurements at part load operating condition of a high head model Francis turbine


Hydraulic turbines are operating at part load conditions depending on availability of hydraulic energy or to meet the grid requirements. The turbine experiences more fatigue during the part load operating conditions due to flow phenomena such as vortex breakdown in the draft tube and flow instability in the runner. The present paper focuses on the investigation of a high head model Francis turbine operating at 50% load. Pressure measurements have been carried out experimentally on a model Francis turbine. Total six pressure sensors were mounted inside the turbine and other two pressure sensors were mounted at the turbine inlet pipe. It is observed that the turbine experiences significant pressure fluctuations at the vaneless space and the runner. Moreover, a standing wave is observed between the pressure tank outlet and the turbine inlet. Analysis of the data acquired by the pressure sensors mounted in the draft tube showed the presence of vortex breakdown co-rotating with the runner. The detailed analysis showed the rotating and plunging components of the vortex breakdown. The influence of the rotating component was observed in the entire hydraulic circuit including distributor and turbine inlet but not the plunging one.

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Correspondence to B K Gandhi.



best efficiency point


rotor stator interactions


rotating vortex rope


fast Fourier transform


pressure difference across the turbine (Pa)

\( {\tilde{\text{p}}} \)

acquired pressure signal (kPa)

\( {\bar{\text{p}}} \)

mean pressure (kPa)

\( {\text{p}}_{{}}^{ *} \)

fluctuating pressure (kPa)


time (s)


observed frequency (Hz)


runner rotational frequency (Hz)


normalized frequency (–)


upper cut-off frequency


lower cut-off frequency


low-pass filter


bandpass filter


9.821465 (m s−2), as tested and measured at NTNU


\( {\text{speed factor }}\left[ - \right] , {\text{ n}}_{\text{ED}} = \frac{\text{nD}}{{\sqrt {{\text{gH}}_{\text{M}} } }} \)


\( {\text{specific speed }}\left[ - \right],{\text{n}}_{s} = \frac{{\left( {{\text{n}}_{P} \cdot \frac{\pi }{180}} \right)\sqrt {{\text{Q}}_{P} } }}{{\left( {2 \cdot {\text{g}} \cdot {\text{H}}_{P} } \right)^{{\frac{3}{4}}} }} \)


pressure (kPa); harmonic order (1,2,….)


flow rate (m3 s−1)


\( {\text{discharge factor }}\left[ - \right],{\text{q}}_{\text{ED}} { = }\frac{\text{Q}}{{{\text{D}}^{2} \sqrt {{\text{gH}}_{\text{M}} } }} \)


discrete quantity

\( \overline{\text{X}} \)

average value


sampling length


wavelength (m)


angular vane/blade position (°)


uncertainty (%)

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Goyal, R., Trivedi, C., Gandhi, B.K. et al. Transient pressure measurements at part load operating condition of a high head model Francis turbine. Sādhanā 41, 1311–1320 (2016).

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