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.

The Kristin platform is a catenary moored semi-submersible production vessel (SSPV) intended for production of gas at the Kristin field at Haltenbanken. Kristin has 24 riser guide tubes for tie in of flexible risers, umbilicals and electric cables to the riser balcony. The riser guide tubes (RGT) provide the necessary guiding, support and protection for risers and cables. The guide tubes run vertically from the deck and through the extended east pontoon. The guide tubes are welded to the pontoon and horizontally supported at the underside of the balcony deck. During model tests of the Kristin platform performed in the Ocean Basin laboratory at Marintek, high frequency in-line vibrations of the RGTs were observed during passage of steep waves. The resonance period for the individual RGTs is 0.3 sec. To mitigate the vibration problem, a vibration suppression arrangement of stiff rods was introduced between the guide tubes. Model tests were performed with respect to extreme- and fatigue loads in regular and irregular waves, with and without the suppression arrangement. The model included the floating framework representing the hull and the 24 RGTs with correct diameter and resonance period. The model was suspended in a horizontal mooring system, giving resonance periods in surge and sway close to the prototype platform. A load-response model for the interaction between large steep waves and vertical flexible cylinders has been developed. A slender body load model derived from Morison’s equation is shown to be able to excite the resonant vibrations. The dominant part of the loading comes from the rapid change of added mass momentum, giving rise to an additional slamming term in the load formulation. The structural response is calculated from a recognized non-linear slender body response program. Numerical simulations have been carried out and compared with model tests for both regular and irregular waves. The numerical predictions confirm the effect observed in the model tests; i.e. connecting the tubes generally leads to a reduction of the high frequency response amplitudes.