By using the Reynolds-averaged Navier-Stokes (RANS) equations, the complex unsteady vortical flow in the entire draft tube of a Francis turbine under a part-load condition, with severe low-frequency pressure fluctuation, is investigated numerically to gain an in-depth understanding of the physical characters of the flow including its stability and robustness, and thereby to seek effective control means to alleviate or even eliminate the strong pressure fluctuation. Our main findings are as follows: In the cone segment of the draft tube, the vortex rope is due to the global instability of the flow caused crucially by the reversed axial flow at the inlet. In the elbow segment of the draft tube, the reversed flow coexists side by side with a fluid channel that carries the mass flux downstream due to favorable axial pressure gradient. In the outlet segment of the draft tube, the mass-flux channel always goes through a fixed outlet, leaving the other two with nearly zero flux. The entire draft-tube flow, although undesired under part-load condition, forms a globally robust system. The principles for effectively controlling this complex flow are proposed. A simple water jet injection at the inlet is numerically proven successful.

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