Numerical Investigation of Hydrodynamic Instabilities in Singing Risers

Abstract : Offshore transportation of gaseous fluids frequently relies on flexible pipes. Flexible pipes are obtained from the helicoidal rolling of steel tape which induces a geometrical cavity from edge to edge. Along the pipe, the gas infinitely encounters the edge to edge cavity of the same shape at regular interval. In some service conditions, acoustic vibrations of huge amplitude can arise. Indeed, in front of each cavity, there is a shear layer where Kelvin-Helmholtz instability can occur. The flow encounters a large number of cavities on its path which gives rise to a new specific problem: is there a stabilized flow?Results of large eddy scale simulations are presented as a reference but they are very costly. This gives reason to develop a numerical solution of the Orr-Sommerfeld equation in order to analyze the temporal and spatial wave lengths generated by the shear layers in front of the cavities.First, we introduce the problem of flexible risers and the analysis of some RANS and LES modeling. Second, a bibliographical study describes the state of the art about vibrations induced by cavity. Third, we state the Orr-Sommerfeld equation and set the problem we want to solve in terms of generalized eigen values Numerical discretizations are based on finite difference approaches of fourth orders. The choice of the relevant eigen values among all those provided by the solutions of the numerical problem is the main difficulty to be tackled.
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J. Brac, L.-M. Berthe, F. Pradel. Numerical Investigation of Hydrodynamic Instabilities in Singing Risers. Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles, Institut Français du Pétrole, 2012, 67 (4), pp.671-692. ⟨10.2516/ogst/2012005⟩. ⟨hal-01936507⟩

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