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  • Vortex-induced Vibration of Slender Structures in Unsteady Flow

    by

    Jung-Chi Liao

    M.S. Mechanical Engineering (1998) Massachusetts Institute of Technology

    B.S. Mechanical Engineering (1993)

    National Taiwan University

    Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the Requirements for the Degree of

    Doctor of Philosophy

    at the

    Massachusetts Institute of Technology

    February 2002

    2001 Jung-Chi Liao. All rights reserved.

    The author hereby grants to MIT permission to reproduce

    and to distribute publicly paper and electronic copies of this thesis document in whole or in part.

    Signature of Author:_______________________________________________________ Department of Mechanical Engineering

    September 28, 2001

    Certified by: _____________________________________________________________ J. Kim Vandiver

    Professor of Ocean Engineering Thesis Supervisor

    Accepted by:_____________________________________________________________ Ain A. Sonin

    Professor of Mechanical Engineering Chairman, Department Committee on Graduate Students

  • Vortex-induced Vibration of Slender Structures in Unsteady Flow

    by

    Jung-Chi Liao

    Submitted to the Department of Mechanical Engineering on September 28, 2001 in Partial Fulfillment of the

    Requirements for the Degree of Doctor of Philosophy Abstract Vortex-induced vibration (VIV) results in fatigue damage of offshore oil exploration and production structures. In recent years, the offshore industry has begun to employ curved slender structures such as steel catenary risers in deep-water offshore oil systems. The top-end vessel motion causes the slender riser to oscillate, creating an unsteady and non-uniform flow profile along the riser. The purpose of this research is to develop a VIV prediction model for slender structures under top-end periodic motions. The key approach to this problem requires identifying the dimensionless parameters important to the unsteady VIV. A set of data from a large-scale model test for highly compliant risers conducted by industry is available. The spectral analysis of the data showed a periodic pattern of the response frequencies. A constant Strouhal (St) number model was proposed such that shedding frequencies change with local inline velocities. The Keulegan-Carpenter number (KC) controls the number of vortex pairs shed per cycle. A KC threshold larger than 40 was found to have significant response for a long structure with finite length excitation region. An approximate solution to the response of an infinite beam with a finite excitation length was obtained; this solution provided an explanation for the high KC threshold. A model for an equivalent reduced damping Sg under a non-uniform, unsteady flow was proposed. This equivalent reduced damping Sg was used to establish a prediction model for the VIV under top-end periodic motions. A time domain simulation of unsteady VIV was demonstrated by using Greens functions. The turning point problem wave propagation was solved for a pipe resting on a linearly varying stiffness foundation. Simple rules were established for conservative estimation of TDP fatigue damage with soil interactions. Guidelines for model test experiment design were provided based on dimensional analysis and scaling rules. Thesis Supervisor: J. Kim Vandiver Title: Dean of Undergraduate Research Professor of Ocean Engineering

  • Acknowledgements First, I would like to take this opportunity to thank my thesis supervisor, Professor J. Kim Vandiver. It is my great pleasure to work with him. He provided me the ability of engineering thinking rather than mathematical thinking. This will be a treasure for my entire professional career. He also guided me to approach the important problem in the field. I thank him for all the effort to enhance my physical sense. Also, I would like to thank my committee members, Professor T. R. Akylas in Mechanical Engineering and Professor E. Kausel in Civil Engineering. They gave me great support and guidance in the committee meetings. Professor Akylas served as the chair of the committee and I would like to thank him for his encouragement. Professor M. S. Triantfyllou helped me in the first committee meeting and gave suggestions in the research direction. Thank Professor H. Cheng for his time in the discussion of the asymptotic method. Thank Professor A. Whittle for the discussion of soil properties. Thank Dr. R. Rao for the discussion of the signal processing in wave propagation. I would like to thank my group mates Dr. Yongming Cheng, Dr. Enrique Gonzalez, and Chadwick T. Musser. They are good friends and provided supports in the research. Thank my Taiwanese friends Prof. Yu-Hsuan Su, Dr. Juin-Yu Lai, Dr. Koling Chang, Dr. Su-Ru Lin, Dr. Ginger Wang, Dr. Chen-Pang Yeang, Chen-Hsiang Yeang, Ching-Yu Lin, Chung-Yao Kao, Yi-San Lai, Hui-Ying Hsu, Shyn-Ren Chen, Yi-Ling Chen, Dr. Steve Feng, Te-San Liao, Mrs. Su, Dr. Sean Shen, Dr. Yu-Feng Wei, Bruce Yu, Jung-Sheng Wu, Rei-Hsiang Chiang, Flora Suyn, Chun-Yi Wang, Dr. Ching-Te Lin for their supports during the time of my doctoral study. Finally, I would like to thank my fiance Kai-Hsuan Wang, for her endless love and support in this period of time. She gave me all the encouragements to accomplish this work. And I would like to thank my dear parents, for their long-distance love and support to help me facing all the difficulties. This thesis is dedicated to them, my dearest parents. This work was sponsored by the Office of Naval Research under project number N00014-95-1-0545.

  • Vortex-induced Vibration of Slender Structures in Unsteady Flow

    Table of Contents Abstract Acknowledgements Chapter 1 Introduction

    1.1 Problem Statement

    1.2 Overview of the Thesis

    Chapter 2 Background

    2.1 Dimensional Analysis

    2.2 Available Data

    2.3 Previous Research

    Chapter 3 Dispersion Relation

    3.1 Derivation of the Dispersion Relation

    3.2 Root Loci for the Dispersion Relation

    3.3 Verification of the Dispersion Relation

    Chapter 4 Wave Propagation on Material with Varying Properties

    4.1 Discontinuity and Cutoff Frequency

    4.2 Spatial Variation of Properties: the WKB Method

    4.3 Varying Foundation Stiffness: Turning Point Problem

    4.4 Data Analysis for the Effects of Boundary Conditions

    4.5 Soil Interaction Model

    Chapter 5 Unsteady VIV Model

    5.1 The Approach to the Unsteady VIV Problem

    5.2 Top-end Motion: Response Amplification

    5.3 Reduced Damping gS for Steady Flow

    5.4 Time Evolution of Excitation Frequency and St Number

    5.5 Effect of KC Number on the Frequency Content

    5.6 Spring-mounted Cylinder in Unsteady Flow

    5.7 Equivalent Reduced Damping gS for Unsteady Flow

    5.8 The gS -RMS A/D Relationship for Unsteady VIV

  • 5.9 Non-dimensional Frequency

    5.10 Fatigue Damage Rate Prediction

    Chapter 6 Summary

    6.1 New Insights Other Than Steady Flow VIV

    6.2 Guidelines for Model Test Experiment Design

    6.3 New Contributions

    6.4 Further Work

    Appendix

    1. Derivation of the Solution for the Turning Point Problem

    2. Derivation of Greens Function Solutions

    3. Time Domain Response Simulation for the Unsteady VIV

  • Chapter 1 Introduction

    1.1 Problem Statement

    Vortex-induced vibration (VIV) is an important source of fatigue damage of offshore oil

    exploration and production risers. These slender structures experience both current flow

    and top-end vessel motions, which give rise to the flow-structure relative motion and

    cause VIV. The top-end vessel motion causes the riser to oscillate and the corresponding

    flow profile appears unsteady. In recent years, the industry has begun to employ curved

    slender structures such as steel catenary risers in deep-water applications. The

    configurations of the curved structures determine the flow profiles along the structures

    and therefore affect the VIV fatigue damage rates. Also, these long slender structures

    tend to have low fundamental frequencies, so VIV of these long structures is often in

    higher modes, e.g., 30th mode or even 100th mode. At these high modes with

    hydrodynamic damping, the dynamic response is often propagating waves rather than

    standing waves.

    This thesis focuses on vortex-induced vibration problems for slender structures under

    unsteady flow situations. The unsteady flow here is confined to cases involving the top-

    end periodic motion of the structure. The purpose of understanding the VIV behavior is

    to estimate the fatigue damage rate of structures. Three typical configurations of slender

    risers used in industry are shown in Figures 1.1 to 1.3: the Combined Vertical Axis Riser,

    or CVAR (Figure 1.1), the Lazy Wave Steel Catenary Riser, or LWSCR (Figure 1.2), and

    the Steel Catenary Riser, or SCR (Figure 1.3). These three configurations were evaluated

    in a model test conducted by PMB/Bechtel in 1998. Under top-end periodic excitation of

    the CVAR model, examples of inline acceleration at one location and the spatial variation

    of the velocity along the riser are shown in Figures 1.4 and 1.5. As can be seen in these

    figures, the flow is both non-uniform and unsteady. The principal goal of this thesis is to

    develop a VIV prediction model for slender structures under top-end periodic motions

    based on available data, considering the effects of the non-uniform, unsteady flow and

    very high mode number. In order to achieve this goa

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