Abstract: This paper develops a three-dimensional numerical simulation method for the entire flow passage of a huge Francis turbine using the SST k-ω turbulence model. The formation mechanism of vortex ropes and the variations in pressure fluctuations in the draft tube of the Francis turbine have been explored under different load conditions at the low water head. The results showed that under low-load conditions, the mainstream at the draft tube inlet tended to form an eccentric spiral vortex rope with the action of a positive velocity circulation at the runner outlet, which would rotate in the same direction of the runner, with the detection of low-frequency pressure pulsation of dominant frequency 0.17 times the runner rotation frequency (1.85 Hz) inside the draft tube. However, as the flow rate of the unit increased, a vortex zone rotating opposite to the runner emerged in the straight cone section of the draft tube, accompanied by high-frequency pressure pulsation dominated by the frequency of 2.16 times the runner rotational frequency. By comparison of predicted results among various discharge cones, we found out that the extension of discharge cone structure could suppress the generation of spiral vortices under certain working conditions, so as to cut down the amplitude of the dominant frequency of pressure pulsation in the draft tube by nearly 45.9%.

Key words: numerical simulation, Francis turbine, draft tube, vortex rope, pressure fluctuation