Rudi Walujo Prastianto

称号及び氏名博士（工学）

学位授与の日付

平成 21 年 3 月 31 日

論An Experimental Study on Flow-induced Vibration Characteristicsof Flexible Cylinders

文

論文審査委員

名主査

大塚耕司

副査

池田良穂

副査

馬場信弘

副査

宇都正太郎

Summary
Flow-induced vibration of structures, in general, is of practical interest to many fields ofengineering such as a riser system of offshore structures, heat exchangers, clusters ofbuildings and stacks, etc. In offshore structures applications, one important aspect ismulti-mode vortex-induced vibration (VIV) of flexible slender structures in fluid flowsuch as a petroleum risers system, especially for deep water application. From structural
point of view, one important implication of such multi-mode VIV is the existence of higher
harmonic frequencies in the response. Recent researches found a significant contributionof the higher harmonic frequencies to the total fatigue life of the risers.
Another important aspect related to the structure-fluid interaction of flexible structures
is the dynamics of free-hanging type of riser, such as the riser system of ocean thermalenergy conversion (OTEC) or CO2 sequestration floating platforms. The riser’s dynamic
behavior due to the current, obviously, would be different from typicalat-sea-floor-terminated riser type of oil or gas platforms, because of, e.g., the free-end
condition of the risers.
So far, general characteristics of such phenomena, multi-mode VIV of long and dynamics
of the free-hanging flexible cylinders subjected to water flow are not well understood in
various parameters. Dynamic response characteristics of such interactive systems arevery complex. Several factors influencing on such complexity can be the range of
Reynolds number, characteristics of water flow, variability of pretension in the cylinders,
aspect ratio, strong interaction between transverse and inline motion, bottom-end
condition of the cylinders, etc.
Despite large number of studies dedicated to those problems, there have been no studies

on the VIV and wake-induced vibration (WIV) of free-hanging flexible cantilever
cylinders in which the cylinders are allowed to freely oscillate in two-degrees-of-freedom,
inline and transverse to the flow with free-end condition taken into account. Therefore,
for the design purpose, a better understanding on such dynamics phenomena is definitelyrequired, particularly due to additional specific parameters of the free bottom-endcondition (creates three-dimensional effect on the flow around the bottom-end of thecylinder) and bidirectional motion aspects of the cylinders.
The present study is addressed to improve our understanding to such phenomena
through simplified experimental models in a laboratory. The interaction between a long
flexible riser and sea current is treated as an interaction between a small-long flexible
horizontal cylinder and uniform water crossflows as a multi-mode VIV problem.
Meanwhile, the VIV and interaction problem of the free-hanging risers with sea current
are simplified into an interaction between a single and group of free-hanging flexible
cantilevers and uniform water crossflows as VIV and WIV problems, respectively.

Chapter 1 deals with an introduction including the background, objectives, methodologyof the study, and brief reviews of some existing related experimental works.
In Chapter 2, highly flexible silicon tubes are used as a small-long flexible cylinder whichfreely vibrates in inline and transverse directions subjected to uniform flows. Generally,by using image processing techniques, the experiment has succeeded to simulate amulti-mode vibration behavior due to VIV, until about 9th mode, even though only with asmall-scale model. The same behaviors found in either the large-scale experiments orfield measurements, such as lock-in response in transverse direction and inline response
frequency of twice the transverse (Strouhal frequency) one can be identified. A new
phenomenon of high frequencies response in inline direction is observed for the inclined(by 5o) cylinder case even at a low flow velocity. It can be expected that these highfrequencies of 2.5 times the Strouhal frequency, may have a significant contribution to
the fatigue life as well as the 3rd higher harmonic frequency in transverse response as
mentioned by other researchers.

Chapter 3 describes low-mode dynamics of a free-hanging flexible cylindrical cantilever
due to VIV, including the induced hydrodynamic forces and the motion of the cylinder. Inorder to model the free-hanging riser of an OTEC or CO2 sequestration platform, a
polyvinyl chlorite (PVC) pipe with an aspect ratio (length-to-diameter ratio) of 34.4 isused. New findings are found in hydrodynamic forces acting on and motion of the cylinder.
An extreme reduction occurs on the mean drag coefficient in the present case. At thesame Reynolds number of about 10,600, the coefficient is very small; approximately 10times smaller than that of the static cylinder case with similar bottom-end conditions. Inaddition, at high flow velocities, the 3rd higher harmonic frequencies of the transverse
response become predominant that produce quite different motion trajectories of thecylinder compared to the other existing comparable works with two-dimensionalbottom-end condition, even same in bidirectional motion aspect. These phenomena are
due to the combination effect between the aspect ratio and factor of self-excitedbidirectional motion of the cylinder.

Chapter 4 presents wake interference effects on the time-dependent forces and motion of

a two-cantilever system in tandem configurations. The same pipe used in single cylindercase (Chapter 3) and another similar PVC pipe are used as test cylinders. As found in thesingle case, the drag-lift ratios for both the upstream and downstream cylinders areapproximately constant at 2 within high reduced velocities. Characteristics of the forces
acting on the downstream cylinder in the tandem configurations are completely different
from that of the single cylinder case. Contrary to the single case, at high reduced velocity,Ur, (Ur > 4.0), the transverse amplitudes of the downstream cylinder in tandem cases arelarger than the inline amplitudes for all gap, LUD, values. Remarkable reduction of theresponse amplitude of the downstream cylinder in inline, Ax, and transverse, Ay,directions are identified if compared to the single cylinder case. As an illustration, for LUD= 12D at Ur = 6.79, the Ax and Ay drastically decrease from the single case values byapproximately 93 % and 75 %, respectively. The response trajectory patterns of thedownstream cylinder in the tandem configurations clearly change with the parameters
Ur and LUD. The predominant frequencies in transverse direction as large as theircorresponding Strouhal frequencies are responsible to the figure-of-eight responsepatterns. It is interesting to note that the decrease in transverse amplitude of thedownstream cylinder controverts another existing interference experiment carried out
with a stationary upstream cylinder. The oscillating upstream cylinder in the present
test creates larger wake area that significantly suppresses the motion of the downstream
one. Additionally, the oscillation upstream cylinder causes the characteristics of thedownstream cylinder are never approaching to that for the single cylinder one; although
the gap LUD > 10D.

Chapter 5 discusses the results of another two-cantilever system of staggeredconfigurations. For the upstream cylinder, there is similarity on each curve pattern of thetotal drag and lift coefficients as a function of the Ur at different transverse gap between
the cylinders, LT, even different in magnitude. There is an opposite characteristics
between these two coefficients as a function of the Ur at Ur ≥ 5.5. The LT = 2.5D becomes“a critical value” at which the forces coefficients starting to jump into the higher values
as the LT increases (LT > 2.5D). More complicated characteristics on the forces
coefficients occur on the downstream cylinder. Due to the stronger wake interference atsmall gaps (LT = 1D, 1.5D, and 2.0D), the total drag and lift coefficients characteristics inthe domain Ur are definitely different than at larger gaps (LT = 2.5D, 3.5D, and 4.5D) andthe single cylinder case. Frequency of the drag force is found approximately twice thecorresponding lift force frequency at the related Ur for all cases and linearly increases asa function of the Ur. It has been proven that the forces frequencies ratios are constant ata value of 2 and independent of the Ur and LT parameters within the range used. The
response amplitude at bottom-end of the downstream cylinder in inline, Ax, andtransverse, Ay, directions linearly increase with the Ur and LT. Again it can be seen thatthe influence of the wake interference on the amplitude of Ax and Ay are gradually getting
weaker as the LT increases. Beyond a stagger angle of 41.2o (LT ≥ 3.5D), more than twice
the angle in the case with a stationary upstream cylinder, the downstream cylinder
similarly behaves as the single cantilever case. The trajectory of the response
displacements are strongly dictated by the parameters Ur and LT. In the present
staggered configurations test, as the LT increases (at the LT ≥ 4.5D), the trajectory
patterns for all Ur step by step approach the characters of the single cantilever case.

Chapter 6 describes the WIV effects on time-dependent forces and motion for more
complex three-cantilever systems of two different triangular configurations. The
characteristics of the total drag and lift coefficients are strongly influenced by the Ur,
with unique characters at three distinct regimes within the Ur. For small LUD, at themoderate Ur, the configuration with dual downstream cylinders (called as Case B)
produces higher total drag and lift coefficients on the downstream cylinders than theopposite configuration of only one downstream cylinder (called as Case A). The existenceof such two downstream cylinders cause stronger wake interference between each otherand in turn slightly reduce the total drag and lift coefficients of the upstream cylinder.
The mean drag coefficients, CD.mean, of the upstream cylinders almost linearly increase
with the Ur and the oscillating drag coefficients are fluctuated as nonlinear functions
within the Ur for both Case A and Case B. Meanwhile, for the downstream cylinders, thevariation on the coefficients much more complicated which is characterized for instance,by a nonlinear relationship between the CD.mean and the Ur for small LUD values. From theanalysis of the total, mean, and oscillating drag and lift forces, it is found that theinfluence of the LUD variation on the upstream cylinders is weak, but in contrast strongon the downstream cylinders for both Case A and Case B. For all LUD, at higher Ur (Ur ≥3.0), the drag-lift frequency ratios are constantly at 2; thus independent of theparameters of Ur and LUD within the range used in the experiment. An exception, at low
Ur (Ur < 3.0), the ratios are larger than factor of 2. Generally, the change on theamplitude of inline motion, Ax, as a function of the Ur and LUD is more complicated thanthat of the Case B. At the Ur ≥ 4.0, as the LUD increases, the Ax drops and approaching
the values of the amplitude of transverse motion, Ay. For the Case A, at LUD = 10D, the Ax
becomes smaller than that of the Ay values. The Case A produces larger reduction on themotion amplitudes of the downstream cylinder in both inline and transverse directions
than the Case B, if compared to the single cylinder case. As an illustration, for LUD = 10D
at Ur = 6.79, the Ax and Ay drastically decrease from the single case values byapproximately 73 % and 51 %, respectively. Meanwhile, for the Case B, the reductions areonly 42 % and 25 %, respectively. For both Case A and Case B, because at large LUD andhigh Ur the predominant frequencies in transverse direction are the Strouhalfrequencies, so that the amplitudes and trajectories of the motion become smaller andsimpler, respectively; no longer approaching the characters found in either the single
cylinder or the tandem cases.
Finally, Chapter 7 presents a conclusion of the study in which the general discussion of
all results and some new findings are drawn. Important results that relevant for thedesign process are underlined. Some suggestions for further relevant works to this field
are described in the last subsection of this chapter.

審査結果の要旨
本論文は、海底石油／天然ガス開発・海底鉱物資源開発・海洋温度差発電等で用いられるライザー管や、二酸化炭素海洋隔離で用いられる液体 CO2 注入管等、柔軟な円柱形状をした構造物の流れならびに渦による励振特性を、流体力と運動の両面から実験的に研究したものであり、以下のような成果が得られている。
(1)小径のシリコン・チューブを用いて、大水深柔軟ライザー管を模擬した高次モードの励振特性に関する模型実験を行い、流速と渦放出周波数ならびに振動モードの関係について明らかにするとともに、振動周波数が渦放出周波数に同調する”lock-in”現象が生じる条件、さらに振動周波数が渦放出周波数の 3 倍になる”higher harmonic”現象が生じる条件を示した。
(2)下端がフリーな単独の塩化ビニルパイプを用いて、深層水取水管や液体 CO2 注入管を模擬した基本的な励振特性に関する模型実験を行い、下端がフリーな場合には、円柱全体に働く流体力が両端固定の場合に比べて大幅に減少すること、流速が速い場合には自由下端が 8 の字運動するモードが支配的となることを示した。
(3)下端がフリーな 2 本の塩化ビニルパイプを用いて、上流側パイプの流れのかく乱による下流側パイプの励振特性に与える影響に関する模型実験を行い、下流側パイプに働く流体力が単独パイプの場合に比べて大幅に減少すること、下流側のパイプの振動周波数が、上流側の渦放出周波数に支配されることを示した。また、上流側パイプに対して流れに直角方向に下流側パイプを離した場合には、その間隔がパイプ直径の 2.5 倍より大きくなると上流側パイプの影響が急激に減少することを示した。
(4)下端がフリーな 3 本の塩化ビニルパイプを用いて、2 本の上流側パイプの流れのかく乱による 1 本の下流側パイプの励振特性に与える影響、ならびに 1 本の上流側パイプのかく乱による 2 本の下流側パイプの励振特性に与える影響に関する模型実験を行い、前者の場合による流れの遮蔽効果は後者の場合に比べて非常に大きく、下流側パイプの流体力が単独パイプに比べて大きく減少すること、下流側パイプの自由下端が 8 の字運動しにくくなることを示した。
以上の研究成果は、長大で柔軟なパイプの設計にとって非常に重要である励振特性について多くの有用な情報を提供したものであり、今後ますます重要となる海洋資源開発・二酸化炭素海洋隔離等の技術の発展に寄与するところ大である。また、申請者が自立して研究活動を行うに必要な能力と学識を有することを証したものである。