Torsional galloping is a large amplitude oscillation phenomenon that can occur when cylinders with non circular cross sections are placed in cross-flow. Riser bundles are such kind of structures that may experience torsional galloping. To determine loads to apply when considering such slender structures, the question of spanwise force correlation arises. This paper is a contribution to the determination of spanwise force correlations. More precisely, the focus is on how a three-dimensional flow can affect hydrodynamic. The influence of the Reynolds number and the correlation of hydrodynamic forces along the cylinder are investigated. In addition to static forces, coupled fluid-structure simulations are performed on a square cylinder in order to delve in the three-dimensional aspects of torsional galloping.


Galloping of bluff bodies is a flow-induced oscillation phenomenon that can reach large amplitudes. It is usually characterized by a low frequency response of rigid bodies. This Fluid-Structure Interaction (FSI) phenomenon is prominent for high values of the reduced velocities (equation) where (equation) is the natural frequency of the body, L its reference length while U is the reference flow velocity. In fact the higher the reduced velocity, the larger the amplitude of oscillation. The observed vibrational frequency is close to the natural frequency of the cylinder even when the fluid non-linear effects are accounted for. Parkinson (1971) classified galloping in four categories: transverse (or translational) galloping, torsional (or rotational) galloping, quartering wind and stall flutter. The present paper focuses on torsional galloping for which there are only a few studies in the literature (see e.g. Van Oudheusden, 1996, Corbeil- Létourneau, 2014, Zabarjad-Shiraz, 2014, Battaglia, 2015).

The range of parameter values for which galloping occurs is usually predicted using the quasi-steady theory which involves polars of loads resulting from static tests or simulations. Following Den Hartog's work (Den Hartog, 1956), the hydrodynamic force acting on the body is linearized and a galloping criterion is derived (Blevins, 1990). This theory leads to different criterions that state that galloping could occur if (equation) for translational galloping (Den Hartog's criterion) and (equation) for rotational galloping (Blevins criterion) where α is the steady angle of attack, CD and CL the drag and lift coefficients and Mα the moment exerted by the flow. Compared to its transverse counterpart, "rotational galloping is much more difficult to analyze" (Païdoussis, 2011, Robertson, 2003).

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