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On Vortex Shedding and Prediction of Vortex-Induced Vibrations of Circular Cylinders

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On Vortex Shedding and Prediction of Vortex-Induced Vibrations of Circular Cylinders INEI-NO NTNU Trondheim Norges teknisk-naturvitenskapelige universitet — , Doktor ingenieravhandling 1997:44 1049 Institutt for marine konstraksjoner MTA-rapport 1997:117 cylinders On Vortex Shedding and Prediction of Vortex-Induced Vibrations of Circular Cylinders A thesis submitted in partial fulfillment of the requirements for the degree of doktor ingenipr by Karl H. Halse Trondheim, February 1997 Department of Marine Structures Faculty of Marine Technology Norwegian University of Science and Technology DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. Abstract This work addresses the vortex shedding phenomenon and the problem of predicting vortex- induced vibrations of slender marine structures. This high-frequency response form may con ­ tribute significantly to the fatigue damage of a structure. As the development of hydrocarbons moves to deeper waters, the importance of accurately predicting the vortex-induced response has increased. Thus the need for proper response prediction methods is large. The problem of vortex-induced vibrations is a classical example of a fluid-structure interaction problem, which involves both fluid dynamics and structural mechanics. In this work an extensive review of existing research publications about vortex shedding from circular cylinders and the vortex-induced vibrations of cylinders is presented. Furthermore an overview of the different numerical approaches to modelling the fluid flow is given. A comparison study of existing response prediction methods revealed very large deviations be ­ tween the response predicted by the different methods. Differences were observed both in re­ sponse shapes and in vibration amplitudes. Most of the existing prediction methods are based upon simple force expressions, where the flow velocity is the only parameter representing the flow. Today, workstations and supercomputers have increased the value of flow simulations signifi ­ cantly. This has initiated the possibility of using computational fluid dynamics as a means in the response prediciton of vortex-induced vibrations. One such alternative prediction method is presented in this work; a fully three-dimensional structural finite element model is integrated with a laminar two-dimensional Navier-Stokes solution modelling the fluid flow. The two-dimensional Navier-Stokes solution has been used to study the flow both around a fixed cylinder and in a flexibly mounted one-degree-of-freedom system. The results have been compared with existing experimental and numerical results. The conclusion is that the vortex shedding process (in the low Reynolds number regime) is well described by the computer pro­ gram, and that the vortex-induced vibration of the flexibly mounted section do reflect the typical dynamic characteristics of lock-in oscillations. However, the exact behaviour of the experimental results found in the literature were not reproduced. The three-dimensional structural model is excited by two-dimensional hydrodynamic sections applied at sections along the span. This model is used to find the response of a simply supported beam, and in a more realistic case in which a free-spanning pipeline is modelled and analysed. The response of the three-dimensional structural model is found to be larger than the expected 1 11 ABSTRACT difference between a mode shape and a flexibly mounted section. The explanation is found in using independent hydrodynamic sections along the cylinder. In this way, the sections towards the ends acts to excite the cylinder even after the expected maximum amplitude is reached at the mid span. However, the predicted response is not unrealistic, and considering the completeness of the in ­ formation provided by the hydroelastic response prediction, the method is considered a powerful tool. An improvement of the fluid modelling to handle full scale conditions and three-dimensional flow, will increase its applicability. Acknowledgements This work was carried out at the Department of Marine Structures at the Norwegian University of Science and Technology (NTNU), under the supervision of Professor Carl M. Larsen. I wish to thank him for inspiring and encouraging my work. His guidance and valuable comments on the manuscript are gratefully acknowledged. Thanks to Dr. Kjell Herfjord for providing the FEM code used to solve the fluid problem, discussions with him have been enlightening. Thanks also to Dr. Yves-Marie Scolan for providing the computer code applying the VIC approach. Thanks to fellow students and staff at the Departments of Marine Structures and Marine Hy­ drodynamics and to colleagues at the Department of Structural Engineering at SINTEF Civil and Environmental Engineering. They have all contributed to make the process of this work enjoyable both socially and scientifically. This study was made possible by a research grant from the Norwegian Research Council (NFR). I am grateful to the Faculty of Marine Technology and to the Department of Structural Engineering at SINTEF Civil and Environmental Engineering for support in the final stages of this work. I am also greatful to my new employer Statoil for a flexible attitude in the completion of this work. Lastly, I want to thank my wife Barbro for her patient support during the course of this work, and our daughter Vilde for her omnipresent enthusiasm. m Contents Abstract i Acknowledgements in Contents v Nomenclature ix 1 Introduction 1 1.1 Background and motivation ...................................................................................... 1 1.2 Vortex-induced vibrations ......................................................................................... 3 1.3 Dimensionless parameters in fluid-structure interaction problems ........................ 4 1.3.1 Flow parameters ............................................................................................ 5 1.3.2 Structural parameters ................................................................................... 6 1.3.3 Interaction parameters ................................................................................... 7 2 Vortex shedding on circular cylinders 13 2.1 Vortex shedding — What is it and why does it occur? .......................................... 13 2.1.1 Historic introduction on vorticity and vortex motion ................................. 13 2.1.2 Early research on vortex shedding and vortex-induced vibrations ............ 15 2.1.3 Towards an understanding — Flow separation and vortex formation ... 16 2.2 Steady flow around a fixed cylinder.......................................................................... 21 2.2.1 Classification of different flow regimes......................................................... 21 2.2.2 Vortex formation ............................................................................................ 24 2.2.3 Hydrodynamic instabilities .......................................................................... 27 2.2.4 Vortex-induced forces. Magnitude and frequency ....................................... 31 2.2.5 Influence from other parameters on flow-induced forces.............................. 36 2.3 Steady flow around a vibrating cylinder .................................................................. 37 2.3.1 Free vibrations of an elastically mounted cylinder ....................................... 39 2.3.2 Forced-displacement method ....................................................................... 41 2.3.3 Force excitation method ................................................................................ 49 2.3.4 Additional parameters in use for oscillating cylinders ................................. 51 2.4 Oscillating flow around a fixed cylinder .................................................................. 52 2.5 Oscillating flow around a vibrating cylinder ............................................................ 56 2.6 Suppression devices or flow control .......................................................................... 61 2.7 Summary of Chapter 2............................................................................................... 64 v VI CONTENTS 3 Vortex-induced vibrations of slender marine structures 65 3.1 Introduction ................................................................................................................. 65 3.2 Response behaviour — short or long cylinder? ......................................................... 66 3.3 Uniform, steady flow .................................................................................................. 68 3.4 Sheared, steady flow .................................................................................................. 71 3.5 Oscillating flow........................................................................................................... 76 3.6 VIV on marine pipelines ............................................................................................. 77 3.6.1 Stationary cylinder......................................... 78 3.6.2 Vibrating cylinder ......................................................................................... 81 3.6.3 Effect of uneven seabed ................................................................................. 83 4 Numerical methods for flow simulation 87 4.1 General background to numerical methods ............................................................... 88 4.1.1 Differential formulation ...................
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