Effects of Shear Flow on Vortex-Shedding-Induced Vibration of Marine Risers

ABSTRACT Lateral vibrations of marine risers due to vortex shedding in a vertically sheared cross flow are analyzed. In contrast to the uniform cross flow case, shear flow can excite more than one modal frequency at a time. Thus, the net response of the riser is a superposition of several vibration modes. The amplitude of each mode is determined by a balance between energy fed into the structure over a "locked-on" region of the riser and energy dissipated by fluid damping over the remainder of the riser. A solution method based on random vibration analysis is developed that uses an empirically derived lift coefficient and correlation length. The technique is capable of handling both uniform and sheared (depth-varying) current profiles. Comparisons are made between theory and data derived from laboratory and field tests for the cases of uniform and shear flows. Results obtained by the present technique agree well with the test data for the case of uniform flow. Good qualitative agreement is also found between the present method and the very limited field data available for shear flows, although it is concluded that the shear conditions in the tests were not sufficiently strong to validate the theory conclusively. The results also show how the use of uniform flow approximations to treat shear flow cases can significantly over-predict vibration amplitudes due to vortex shedding. INTRODUCTION Vortex-shedding-induced oscillation of marine structures, such as risers. OTEC cold water pipes, and ocean-mining lift pipes. is an important fluid structure interaction phenomenon since it can lead to reduced fatigue life and increased hydrodynamic loads. Structural damage and even destructive failures can sometimes result. While a great deal of attention has been focused on this problem. most of the previous work has been devoted. by expediency. to structures in uniform cross flows. The subject has been reviewed recently in King [1]. Sarpkaya [2]. and Griffin [3,4]. When the approaching free stream is not uniform. one is tempted to use a uniform-flow approximation based, say on the maximum or average cross-flow velocity. This approximation is only valid when the flow variation over the length of the structure is small and when the frequency of any unsteady flow component is small in comparison with the vortex shedding frequency and the modal frequencies of the structure. In general, neither of these conditions is satisfied for very long risers operating in a typical ocean environment where wind and geostrophic currents cause the cross flow to be both oscillatory and sheared. Fundamental questions concerning the effects of unsteadiness and nonuniformity in the approaching free stream on the formation and shedding of vortices remain unanswered. The purpose of the present work is to investigate the effects of shear in the oncoming flow. Specifically, the cross-flow velocity is assumed to be time-invariant and unidirectional with a magnitude that decreases monotonically with distance below the ocean free surface (see Fig. 1). A solution technique is developed that is based on the random vibration analysis of Blevins and Burton [5J (also see Blevins [6J). who investigated flow-induced oscillations in uniform flow. Their method is extended to handle sheared flows as well. The empirically-derived dependence of lift coefficient and correlation length on cylinder amplitude that is part of their analysis is retained. In addition. the present method makes use of the laboratory observations of vortex shedding in shear flows by Hair and Stansby [7] and Stansby [8}. These tests indicate that. despite the continuous spanwise variatio