Airfoil Vortex Induced Vibration Suppression Devices
by
Evan J. Lee
B.S. Naval Architecture and Marine Engineering, Webb Institute, 2005
Submitted in partial fulfillment of the requirements for the degree of
Master of Science in Naval Architecture and Marine Engineering
and
Master of Science in Ocean Systems Management
at the
Massachusetts Institute of Technology
May 2007 Th author ereby grnts to MTf permlaen to reprodusm
and to
distribute publicly paper and electronic copies of this thesis documel
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in whole or in part in any nmedim 1ow Mnown or hereter r.rezatad.
Signature of Author: ..................................... ........
........ .
.........
Department of Mechanical Engineering
fl17 8
Certified by: ...............
May 17, 2007
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.. .. .,.................................................
W/-
.Michael
Triantafyllou
Director, Center for Ocean Engineering
In
Certifiedby:
...........................
Certified by: .............................
r.
./
Thesis Supervisor
-
/V .............................................
X
..
J...
Henry Marcus
Professor of Marine Systems
Thesis Supervisor
Accepted by: ....................... ...
...........
............
Lallit Anand, Professor of Mechanical Engineering
Chairman, Graduate Committee
MASSACHUSETTS INSTITUTE'
OF TECHNOLOG3Y
JUL 18 2007
LIBRARIES
r
ARCHIVES
Airfoil Vortex Induced Vibration Suppression Devices
By
Evan J. Lee
Submitted to the Department Of Engineering
on May 17, 2007 in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
Naval Architecture and Marine Engineering and
Master of Science in Ocean Systems Management
Abstract
Vortex Induced Vibrations (VIV) is a major concern of the offshore oil industry. This
problem leads to fatigue failure in the marine risers and causes costly replacement of the
risers. Appendages such as helical strakes have proven that VIV can be eliminated but at
the cost of increased drag. Increased drag reduces the time that the riser can operate.
This thesis looks at adding airfoils to cylinders to both eliminate VIV as well as reducing
drag. Two sets of tests were performed at the MIT Towing Tank to determine the
effectiveness of these airfoils. The first tests utilized a flexible to model a riser. The
second set of tests used a rigid cylinder to better understand the dynamics of the system.
The airfoils were able to achieve both goals when the airfoils are aligned with the flow.
Future work needs to be completed to study the airfoils when they are not aligned with
the flow.
Thesis Supervisor: Michael Triantafyllou
Title: Director, Center for Ocean Engineering and Professor of Mechanical and Ocean
Engineering
Thesis Supervisor: Henry Marcus
Title: Professor of Marine Systems
Contents
1
Introduction ..................................................................................................................
4
1.1
V ortex Induced V ibrations...................................................... ................
4
1.3
M arine Risers ..................................................
6
1.4
Cost Benefits of Reducing D rag ........................................ ........................... 8
1.5
Previous Work ............................................................................................
9
1.6
Scope................................................................................................................. 13
1.7
Tow Tank .................................................. .................................................. 14
1.8
Force Sensor............................................... ................................................. 15
2 Experim ents ............................................................................................................... 16
2.1
Flexible Cylinder Test.............................................................................. 16
2.1.1
Cylinder Construction ..................................... ..................... 16
2.1.2
Flexible Cylinder Rig ......................................................................
17
2.1.3
Testing Evolution........................................................ ........................... 18
2.1.4
A irfoils .................................................................... ............................ 19
2.1.5
Results .......................................................................................................
21
2.2
Large A irfoils.............................................. ................................................ 28
2.2.1
Spring Cylinder Rig ..................................................... 28
2.2.2
Linear Motor System ....................................................
33
2.2.3
Sensors .................................................................... ............................ 34
2.2.4
Large A irfoils.......................................................35
2.2.5
Testing Procedure ..................................................................................... 38
2.2.6
Results .................................................................... ............................. 41
3 Concluding Rem arks............................................................................................
48
3.1
Conclusions....................................................................................................... 48
3.2
Recommendations for Future Work.......................................................
49
Bibliography ..................................................................................................................... 51
Appendix A..................................................
52
Flexible Cylinder .................................................. .................................................. 52
Arrangem ent A ................................................. ................................................... 52
Arrangem ent B ..........................................................................................................
53
A rrangem ent C ................................................ .................................................... 54
Arrangem ent D and E ............................................................... .......................... 55
Rigid Cylinder............................................................................................................... 56
Arrangem ent A ................................................. ................................................... 56
Arrangem ent C ................................................ .................................................... 58
Arrangement A3 Fixed and D3 Fixed.............................................
60
Appendix B ..................................................
61
Appendix C ..................................................
84
Chapter 1
Introduction
1.1 Vortex Induced Vibrations
Vortex induced vibrations (VIV) is a phenomenon that is exhibited by many bluff bodies.
A simple example of VIV is when pulling one's hand and arm through the water. It is
very difficult to prevent one's arm from vibrating back and forth. To understand VIV
one must first understand the flow around an object. When an object is placed in a flow,
the fluid will bend around the object. As the flow bends around the object, it will no
longer travel smoothly, but become turbulent. This is due to the boundary condition on
the surface of the object. At the surface, the velocity of the fluid is the velocity of the
surface.
If the object is shaped such that there is a positive pressure gradient moving in the
direction of the flow, separation can occur. Separation is the transition from smooth flow
to chaotic flow or from laminar to turbulent flow (Figure 1.).
'• ~'3,UIOC.LJ
UUIK F
Figure 1. Separation(Hoerner 1965)
The turbulent zone between the separation on the top and bottom of the body is called the
wake. The wake is of much lower pressure than the high pressure region on the front of
the body. Thus there is a net force in the direction of flow called form drag. As Figure 2.
shows, the flow around the object depends heavily on the shape of the object.
(A) FIOWPATTERION CIRCULLR
OLINDER IIN0'VTISCOUS
(B) CYLINDERAt
REYOLDS
(C) CTLINDERBETWN R
IWIMBRSIN TH ORDEROF 40;
=
FLOW;
10 DRAG.
CD.-
1.2.
104 and 105 VORTE•
,
STRUT WITH CD.. 1.2.
(D) PLATE WITH "SPLITTER" DEVICE IN WAM; CD.
(9) CYLINDERABOVE CRITICAL REYNOLDSUMBnRWITH
1.6.
CD. - 0.5.
(1) STREAMLINE
SZOCTIOWITHCD. IN TRB ORDERO0 0.06.
Figure 2. Flow Around Bodies (Hoerner 1965)
The smaller the wake is behind an object, the lower the form drag the body has (Figure
2f.). On bluff bodies, such as cylinders (Figure 2c.), vortices are alternately shed in the
wake. A vortex is fluid rotating in a clockwise or counter clockwise direction. This
alternating vortex pattern is called the Von Kairman Vortex Street. These vortices have
low pressure causing a force towards the side that the vortex was shed. The vortex
shedding is dependant on the Reynolds Number.
Re =
UD
(1)
Re=Reynolds Number
U=Velocity of fluid
D=Diameter of object
v=Kinematic Viscosity
The tests were performed at Reynolds Numbers between 20,000 and 80,000. This places
the tests within the range for vortex shedding. When the frequency of vortex shedding is
the same as the natural frequency of the cylinder, the alternating force of each vortex
being shed would cause the cylinder to VIV.
1.3 Marine Risers
Marine risers are a key component of extracting oil from the undersea ocean
deposits. The riser connects the drilling site to the oil platform. It provides a passage
way for the drill to reach the drilling site and also is the pipe that the oil is pumped out of.
One would think that being made of steel, the risers would not be able to flex. At the
great depths that the oil companies are drilling at these days, the marine riser is not rigid,
but acts like a tensioned string. The natural frequency of a string is dictated by the
following equation (Blevins 1977).
ffn=Natural frequency
(2)
E=Modulus of elasticity
I=Moment of inertia
M=Mass per unit length
L=Length
As the length of the marine riser increases, the frequency goes down the most because it
is raised to the fourth power. Increasing the mass also decreases the natural frequency.
Increasing the modulus of elasticity and the moment of inertia increases the natural
frequency. At the Reynolds Number that the marine risers operate at, the Strouhal
Number is about 0.2
S= fD
U
(3)
fn=Natural frequency
D=Diameter of Cylinder
U=Inflow Velocity
The marine riser has natural frequency that is near the shedding frequency of the
cylinder. Thus bare marine risers VIV when currents flow over them. This vibration
causes fatigue stress on the riser that leads to failure. Fatigue failure is best exhibited
when one bends a paper clip back and forth and after many repetitions, it snaps. Another
concern with the marine riser is the drag that imparted on the cylinder. Once again since
the marine riser is very long and acts like a string, so as the drag is imparted on the
cylinder, it bows in the middle. This bowing causes an angle at both the top and the
bottom of the marine riser. The drill is limited to a certain range of angles in which it can
operate. If the currents are too strong, the marine riser will bend excessively and the drill
cannot be used. This lost drilling time costs the oil company. Over the Reynolds
Numbers that were tested, the drag coefficient is about 1.2. When the cylinder is
vibrating, the wake becomes larger as the vortices are shed at the peak of the motion.
Therefore the drag increases for vibrating cylinders. So oil companies are looking to
eliminate vibrations to eliminate fatigue failure and reduce drag to allow for more drilling
time.
1.4 Cost Benefits of Reducing Drag
The cost of oil production has been ever increasing. With the high prices of oil,
drilling rigs have been ever increasing in prices. The largest offshore drilling rigs are
being chartered at $400,000 a day (Sanders). Every day that the rig is not drilling is lost
revenue and hurt profits. Therefore reducing the drag imparted on the marine riser to
reduce the bowing and increase the days of production is imperative. The P-36
semisubmersible oil rig has a maximum production of about 180,000 barrels per day
(Offshore-Technology). James Mulva of ConocoPhillips stated that of every gallon of oil
sold, the oil companies earn about 10 cents of profits (PBS). A sensitivity analysis was
performed to determine the number of extra days that the modified marine riser would
have to operate to pay back the extra cost of the modifications to the marine riser. The
number of barrels that is produced by the oil rig as well as the cost difference between the
two risers was analyzed. The data can be seen in Appendix C. As seen in Figure 3., at
lower production levels, the number of days to break even increases dramatically. This
would mean that the cost benefit of the reducing the drag of the marine riser would not be
great. On the other hand, as the number of barrels produced per day increases, the
incremental reduction of number of days to break even is reduced. Thus it is important to
use a lower drag marine riser on large oil platforms, but the benefit pushing production
higher is not that great. The differential cost per day also has a large impact on the
number of days to break even. The number of days to break even is directly proportional
to the differential cost per day. This analysis does not take into account the effects of
VIV. The cost of the bare marine riser would increase due to maintenance replacement
from fatigue failure and possibly failure.
Days to Break Even vs. Barrels per day
70.00
~j
*~i" -'R?-~
60.00
50.00
---- $5,000
-U-$10,000
$20,000
-- $30,000
-I-$40,000
-0-$50,000
-4--$60,000
$70,000
-$80,000
U 40.00
a
m
* 30.00
0
20.00
10.00
AnM
v.
20,000
40,000
60,000
80,000
100,000 120,000
Barrels Per Day
140,000
160,000
180,000
200,000
Figure3. Days to Break Even
1.5 Previous Work
M.M. Zdravkovich, in his paper, Review and Classificationof Various
Aerodynamic and HydrodynamicMeans for Suppressing Vortex Shedding, compiled VIV
suppression devices that were tested at the time (Figure 4.). There are four major groups
of suppression devices. The first is omni-directional devices, Group i(a). The flow
direction does not change the effectiveness of an omni-directional device. The second
group, Group i(a), are uni-directional devices. These devices have an optimal direction in
which they are most effective. Group ii, are shrouds, which completely go over the
cylinder. Group iii are miscellaneous suppression devices.
I(1o))
e
hi]
0
~Iij
0
1(17)
2(16)
3(16)
4(25)
5 (19)
0
6 (20)
TT
SI
II
eNil EI I
it
0
8 (26)
7(21)
F1 0
SI
II
'
a'
9 (27)
10(22)
11(23)
*1
0
12 (24)
SIEI
ElD:~
(21)
C
14(28)
15(29)
16 (29)
17(34)
01
.-o-
C=
22(34)
224)
.,-
20(33)
15 (31)
eI
2JIl
..
19(32)
I.
21(34)
23(35)
24(36)
Figure 4. VIV Suppression Devices
Each arrangement is shown in both the cross-sectional view and the longitudinal view.
The plus sign next to the arrangement indicates that it was successful in eliminating
vibrations and drag coefficient is noted if known. The helical strake (Figure 4(1).) is a
design that is successful in eliminating VIV but at the expense of increased drag. A
rectangular or pyramid shape protrusion is added to the surface of the cylinder and
wrapped along the length of the cylinder like a helix. A cylinder usually has three or four
of these protrusions per cylinder. Research has shown that this arrangement is able to
disrupt the Von Ka"rman Vortex Street. The increased cross-sectional area of the helical
strake arrangement increases the drag on the cylinder. A benefit of helical strakes is that
it is omni-directional. No matter which direction the flow is coming into the cylinder, the
helical strakes eliminate VIV. The purpose of the research is to eliminate VIV while also
decreasing drag. One possible solution to this problem that has been tested before, but
not studied extensively is the use of airfoils (Figure 4(21 and 22)). If airfoils are placed
on either side of a cylinder, they can redirect the flow. By redirecting the flow, the goal
is to disrupt the Von Kdrmin Vortex Street and eliminate VIV. Also by redirecting the
flow, the width of the wake can be reduced and as a result have a lower drag.
G. Grimminger in his paper Effect of Rigid Guide Vanes on the Vibration and
Drag of a Towed CircularCylinderfirst looked at applying guide vanes to redirect the
flow around a cylinder. 15/16" brass cylinders were cantilevered from the ship model
carriage and towed at David Taylor Model Basin. A brass plate was placed 3" below the
water surface to eliminate surface effects. A dynamometer was used to measure the drag
of the cylinder. The guide vanes were made of 1/64" (1/60D) thick pieces of copper and
offset by a 1/10" (8/75D) washer. Figure 5. shows the arrangements of the guide vanes.
Guide Vane 1 had the longest overall length at 2" and also extended 0.2" forward of the
vertical point. Guide Vane 2 is shorter in length and only extends 0.125" forward of the
vertical point. Guide Vane 3 has the same length aft of the vertical point but arcs around
to 450 forward of the vertical point. Guide Vane 4 only utilizes flat pieces of copper. For
Guide Vanes 1, 2, and 3, the gap at the trailing edge of the two Guide Vanes was varied.
The results showed that none of the arrangements exhibited vibration. Figure 6. shows
that as the gap between the foils was increased, the drag was reduced. The width could
be increased to about the size of the cylinder and still be effective. Guide Vane 3 was the
most effective of the arrangements that were tested.
25"
0
0.2"
Guide Vanes
Guide Vones
I
2
Oirection of Motion
--
0.125"
0
).92"I
Guide Vanes
Guide Vanes
3
Figure 5. Guide Vanes
4
55
50
45
40
35
C
S30
o
25
20
15
10
P
1
2
3
4
5
6
Speed in knots
7
8
Figure 6. Guide Vane I with variation in gap opening
1.6 Scope
9
The scope of research covers two different experiments with airfoils. The first
experiment exclusively looked at the foils fixed to the flow. The airfoils were mounted
on a flexible cylinder that closely modeled a marine riser. The second experiment
studied both fixed and freely rotating foils. These airfoils were mounted on a rigid
cylinder that was allowed to move transverse to the flow.
1.7 Tow Tank
The MIT Towing Tank is 100ft long, 8ft wide, and 4ft deep. The carriage is
supported by an overhead rail and a rail on the side of the tank. The carriage carries the
testing equipment and provides a point where the test specimens can be mounted. The
carriage is pulled by metal belt that is powered by servo motor. The MIT Towing Tank
last year was upgraded last year and a new motion controller and motor with installed.
The data acquisition now could operate both the carriage and record data. At the
beginning of testing, three different computers had to be used. The first was the data
acquisition computer. Second was the computer to run the motion controller. The third
was to reset the Kistler force sensors. This created a lot of work for each run and the
system was streamlined. Using a system that was developed for remote operation of the
MIT Towing Tank, operating the carriage, recording data, and resetting the force sensors
were all combined into one program. The additional benefit of this program is that the
complete set of tests for an arrangement could be queued up and the carriage would reset
the force sensors, start the carriage, record the data, back the carriage to its original
position, wait for the tank to calm down, and repeat the test.
1.8 Force Sensor
The force sensor used was common to both sets of tests. The sensor is a Kistler
piezoelectric three-axis sensor. The sensors look like small rings with a hole in the
middle. These sensors work under compression and measure the shear forces imparted
on the sensor. The sensors are placed on a bolt and clamped tight to create the
compression that is needed. The sensors are mounted on the bottom on each spar and the
cylinder is mounted onto the bolt on each end. These sensors output charge and are
converted by amplifiers on the carriage to an output voltage that could be read by the data
acquisition system. The sensors have drift and will create an error over time. Therefore
the amplifiers need to be reset to zero before each run. This can be done remotely or at
the amplifier itself.
Chapter 2
Experiments
2.1 Flexible Cylinder Test
2.1.1 Cylinder Construction
The first set of tests that were performed on airfoils at the MIT Towing Tank was
the flexible cylinder experiment. To better simulate a marine riser, a flexible rather than
a rigid cylinder was used. This test allowed for three dimensional motions. The cylinder
was made from a flexible rubber and was supported by Kevlar strings in the middle of the
cylinder. The Kevlar allowed the cylinder to be tensioned and provided the restoring
force to generate the desired natural frequency. A mold was made by slicing a 1.5 inch
PVC pipe down the middle. Two end caps were used to plug each end of the pipe. There
were holes for the Kevlar to be placed in the cylinder. There was also a hole to pour the
flexible rubber. To build a cylinder, the Kevlar was fed through the end caps and down
the length of the pipe. Next, the two halves of the pipe were joined and sealed using a
glue gun. Then the end caps were placed on the pipe. Then the Kevlar was hot glued to
one end cap. Tension was placed on the Kevlar strands and the other end was glued to
the other end cap. Then the two part rubber was mixed and poured into the mold. When
measuring the motions using the accelerometer, two Kevlar strands were used instead of
one. This allowed the accelerometers to be placed in the center. Plugs were made and
hot glued into the mold. Then the Kevlar was hot glued around the plugs. This made the
building of the mold more difficult. Having two strands of Kevlar in the cylinder rather
than one strand helped reduce the rotation of the cylinder.
2.1.2 Flexible Cylinder Rig
The tests were performed on a new rig developed specifically for the experiments.
The Flexible Cylinder Rig (FCR) recorded drag and displacement of a flexible vibrating
cylinder. The FCR is a completely rigid structure that contained two spars and its support
structure. As seen in Figure 7., the cylinder above the water was used to connect the two
spars together and provided a point where the FCR could be mounted to the carriage.
The FCR is mounted using the same mounting block as the Virtual Cable Towing
Apparatus (VCTA). The mounting block of the VCTA is allowed to move but for the
FCR, it is fixed in place. On one spar, the force sensor is mounted. The other spar holds
the tensioning system. The tensioning system consists of three components, a spring, a
screw rod, and nut. The screw rod is a rod that has threading on one end and the
clamping device on the other. The cylinder is then mounted in between the two spars.
To mount the cylinder, the cylinder is attached to the force sensor. Then the cylinder is
attached to the screw rod. The screw rod is then fed through a hole in the other airfoil.
The spring is then placed over the screw rod and the nut is used to tension the cylinder.
As the nut is tightened, the Kevlar is tightened and the spring is compressed. This system
allows for tension in the cylinder and the ability for it to lengthen when it vibrates.
Originally the force sensor mount and the screw rod were slotted so that the Kevlar exited
the piece on centerline and had a hole in the slot. To tie the Kevlar to the mounts, the
Kevlar would be placed in the slot and then fed down the hole and then tied off in a knot.
The Kevlar had too much give and as the cylinder was tightened, the knot would get
smaller and eventually slip through the hole. The next evolution was to tie a knot around
the washer to make the knot bulkier and not slip through the hole. This prevented the
knot from slipping through the hole, but the sharp edges of the washer were now slicing
the Kevlar when the cylinder was tightened. New mounts were designed where the
Kevlar was clamped between a plate and the mount. This allowed for the Kevlar to be
clamped without any sharp turns.
Force
Sensor
Threaded
Rod
Figure 7. FCR Drawing
2.1.3 Testing Evolution
There had been a long evolution of the method that displacement was determined
on the FCR. The first method that was used was to take a video of each run and while
playing the video, estimate the displacement of the cylinder. The results were crude
estimates of the amplitude and also made the recording and analysis of the data
cumbersome. An accelerometer was the first sensor that was tried. This was a three axis
accelerometer from Kistler. These accelerometers use the same amplifiers that the
Kistler force sensors use. The voltage output by the sensor is then amplified and output
to the data acquisition system. The data was read in Matlab and the acceleration was
integrated twice to determine the position. These sensors were placed at the mid span
and the quarter span of the cylinder. The first problem with this sensor is that the
cylinder is vibrating freely and the sensor axes in relation to the cylinder are consistently
changing. The sensor and its cabling are separate and have to be attached to run. This
attachment was submerged and was prone to leakage. To eliminate the leakage silicone,
epoxy, and scotchkote were tested to seal the attachment point. None of these methods
worked and water was able to leak into the sensor and cause it to malfunction. The main
reason for the failure of the sealants was the extreme shaking of the accelerometer when
the cylinder was vibrating. This caused the wire to whip violently and break the seal.
The final method for measuring the displacement was to use a position linear string
potentiometer. A string potentiometer has a string that is connected rotary sensor. The
sensor takes voltage in and outputs a differential voltage based on the length the string is
extended. The string potentiometer is mounted on the support cylinder directly above the
flexible cylinder. The string is attached to the flexible cylinder at the mid span. Since
the inline motion is small compared to the transverse motion, the three dimensionality of
the motion is neglected and the transverse position is recorded.
2.1.4 Airfoils
The airfoils used for these tests were not curved, but rather bent plates of
aluminum. This was due to the simple construction using a sheet metal bender. Each
airfoil was 2.75 inches in span and supported in the center. The short span and the single
mounting point allowed for the airfoils not to interfere with the flexing cylinder. The
center support did allow for some rotation of the airfoils. Spacers to control the distance
the airfoils were from the cylinder were squares cut from birch plywood. The spacers
were drilled in the middle and the airfoils were drilled in the center of the span and 3/16
inches from the leading edge. Wood screws were used to screw the airfoil and spacer
directly to the cylinder.
For these sets of tests, four different airfoils were tested. The first airfoil was a
flat piece ¾" in chord length. Since the cylinder is 1.36", all the dimensions were nondimensionalized to the diameter of the cylinder. The first set had a nominal length of
.5D. The other three airfoils were bent at 3/8" from the leading edge. The difference
between the airfoils is their chord length. The second set had a chord length of ¾"
(Nominally .5D). The third had a chord length of 1.5" (Nominally 1D) and the last had a
chord length of 1.125" (Nominally .75D). The airfoils were spaced off the cylinder at
two different heights. The first height was 3/32" with a nominal distance of .138R. The
second height was 3/16" corresponding to a nominal distance of .276R. Lastly, there was
the continuous and staggered case. The continuous case had airfoils on both sides of the
cylinder for the entire span of the cylinder. The staggered case had airfoils alternating on
the top and the bottom along the length of the cylinder. The foils were oriented at three
different angles; 450, 60 ° , 75 ° . Each arrangement was tested 0" and 200 with respect to
the flow. The flexible cylinder was tested at Vrn 3, 5, 6, 7, and 9. The resolution is
higher around Vrn 6 where vibration is expected and the higher Vrn is used to check for
galloping.
2.1.5 Results
The Al arrangement was using the short IR flat foils. The spacing was .138R
and the orientation was 45". The airfoils were continuous. The drag is about average for
the A arrangements. The vibrations were also average for the arrangements. No second
mode vibrations were present. The 200 orientation had slightly higher drag than the 00
orientation. The vibrations were about the same as the 00 orientation. This arrangement
did not have any second mode vibrations.
The Alb arrangement was using the short IR flat foils. The spacing was .138R
and the orientation was 45". The airfoils were staggered. At the 0" orientation, the drag
was the highest for the 00 orientation. The vibrations were normal for the A
arrangements. There were no second mode vibrations. At the 200 orientation, the drag
was higher and the highest of the A arrangements. The vibrations were slightly higher
for the 200 orientation compared to the 0" orientation. No second mode vibrations were
observed.
The A2 arrangement was using the short 1R flat foils. The spacing was .138R
and the orientation was 60'. The airfoils were continuous. The 00 orientation exhibits
lower vibrations than most of the A arrangements. The vibrations were about average.
There were second mode vibrations at Vrn 9. The 200 orientation has higher drag than
the 0" orientation. On the other hand, the vibrations were lower for the 200 orientations.
At both Vrn 7 and Vrn 9, there were second order vibrations.
The A2b arrangement was using the short 1R flat foils. The spacing was .138R
and the orientation was 600. The airfoils were staggered. This arrangement exhibited the
lowest drag of all the A arrangements. The vibrations were average for all the
arrangements that were tested. From Vrn 6-9, there were second mode vibrations. The
drag was higher for the 200 orientation compared to the 0' orientation. The vibrations
were about the same as the 00 orientation. There were second mode vibrations at Vrn 9.
The A3 arrangement was using the short 1R flat foils. The spacing was .138R
and the orientation was 750. The airfoils were continuous. The O0orientation had drag
that was about average. The vibrations were also about average. There were second
mode vibrations at Vrn 9. The 20' orientation had drag that was lower than the 00
orientation and one of the lowest for all the arrangements. The vibrations were also
lower than the 00 orientation and one of the two lowest arrangements. At both Vrn 7 and
Vrn 9 there were second mode vibrations.
The A3b arrangement was using the short I R flat foils. The spacing was .138R
and the orientation was 750. The airfoils were staggered. In the 00 orientation, the drag is
higher than the average. This arrangement has one of the higher vibrations compared to
the other arrangements. There were second mode vibrations at Vrn 9. In the 200
orientation, the drag is slightly higher. The vibrations are about the same as the 00
orientation. There were second mode vibrations at both Vrn 7 and Vrn 9.
The B I arrangement was using the short IR bent foils. The spacing was .138R
and the orientation was 450. The airfoils were continuous. This arrangement had the
lowest drag coefficient of all the tests that were performed at the 00 case. The cylinder
did not vibrate at Vrn 3. The vibration in the middle reduced velocities is lower than
most of the other arrangements. At Vrn 9, the vibration was in the second mode where
there was a nodal point at the mid span of the cylinder. The 200 case also has lower drag
coefficient than most of the other cases. The amplitude of vibration is about average for
all the runs.
The Bib arrangement was using the short 1R bent foils. The spacing was .138R
and the orientation was 450 . The airfoils were staggered. When at 00, Bib has higher
drag than most of the other arrangements. There was no vibration at the lowest reduced
velocity. The amplitude was the greatest with about 1 A/D. There was no second mode
vibration. The drag for the 200 orientation was about average for all the arrangements.
The maximum vibration was at a little lower reduced velocity and higher when compared
toe the 00 orientation. Again there was no second mode vibration.
The B2 arrangement was using the short 1R bent foils. The spacing was .138R
and the orientation was 600. The airfoils were continuous. At the 00 orientation, the drag
is about average about average. The vibration is also about average for the arrangements.
No second order vibration was exhibited. Surprisingly, the 200 orientation had lower
drag as well as lower vibration than the 0' orientation.
The B2b arrangement was using the short 1R bent foils. The spacing was .138R
and the orientation was 600. The airfoils were staggered. The drag coefficient for the 00
orientation was slightly lower than the Bib but slightly higher than the B2 arrangement.
The vibration was one of the highest of all arrangements. There was a second mode of
vibration at Vrn 6. At the 200 orientation, the drag was lower but the vibration was
higher at Vrn 5. There was no second mode vibration.
The B3 arrangement was using the short 1R bent foils. The spacing was .138R
and the orientation was 750 . The airfoils were continuous. At the 0' orientation, the drag
was lower than most of the other arrangements. The amplitude was also lower than most.
There was a second mode of vibration at the highest reduced velocity. The drag was also
one of the lower arrangements. At the 200 orientation, the drag was higher than the 0'
orientation. The vibration was lower for this arrangement and there was no second mode
of vibration.
The B3b arrangement was using the short IR bent foils. The spacing was .138R
and the orientation was 750 . The airfoils were staggered. At the 00 orientation, the drag
was one of highest exhibited by the foils. The vibrations were also one of the largest out
of all the arrangements. The second mode of vibration at the highest velocity is almost as
high as the first mode vibration of other arrangements. At the 200 orientation, the drag
was even higher than the 00 orientation. On the other hand, the vibration was lower than
the 0" orientation.
The Cl arrangement was using the short 1R bent foils. The spacing was .276R
and the orientation was 45". The airfoils were continuous. The drag for this arrangement
at the 0" orientation was moderate. The vibrations had lower amplitude than most of the
other arrangements. There was a second mode vibration at the highest reduced velocity.
The 200 orientation has about the same drag as the 0' orientation. The vibrations for the
200 orientation is about the same as for the 00 orientation. There were second mode
vibrations at the highest reduced velocity.
The Clb arrangement was using the short IR bent foils. The spacing was .276R
and the orientation was 450. The airfoils were staggered. At the 00 orientation, the Clb
arrangement had similar drag and vibrations to the Blb arrangement. It did not exhibit
any second mode vibration. The drag was higher than most of the other arrangements.
The vibrations were moderate when compared to the rest of the tests. At the 200
orientation, the drag was about the same as the 0' orientation. The vibrations were higher
than most of the other arrangements. No second order vibrations were exhibited at this
orientation.
The C(2 arrangement was using the short 1R bent foils. The spacing was .276R
and the orientation was 600. The airfoils were continuous. The drag at the 00 orientation
was lower than the average of all the arrangements. The vibrations were also low
compared to the other arrangements. There was no second order vibrations exhibited.
The 200 orientation had one of the highest drags. On the other hand it had one of the
lowest vibrations. There were no second order vibrations in this orientation as well.
The C2b arrangement was using the short 1R bent foils. The spacing was .276R
and the orientation was 600. The airfoils were staggered. The drag at the 0' orientation
was about the same as the C b arrangement and higher than the C2 arrangement. The
vibrations were higher than the C2 arrangement and about the same as the Clb
arrangement. There were second order vibrations at the highest reduced velocity. The
200 orientation has about the same drag as the 00 orientation. The vibrations are a little
larger than the 00 orientation. There were no second mode vibrations.
The C3 arrangement was using the short 1R bent foils. The spacing was .276R
and the orientation was 750. The airfoils were continuous. In the 00 orientation, had
higher drag than the other continuous B and C arrangements. The vibrations were
moderately high. There were second order vibrations at the highest reduced velocity.
The 200 orientation had higher drag than the 0' orientation. On the other hand, the
vibrations were less than the 00 orientation. There were no second mode vibrations
exhibited.
The C3b arrangement was using the short 1R bent foils. The spacing was .276R
and the orientation was 750 . The airfoils were staggered. The drag in the 0O orientation
was high compared to the other orientations. The vibrations were relatively high
compared to the other arrangements. There were no second order vibrations. At the 200
orientation had similarly high drag as the 0' orientation. The vibrations were similar in
amplitude to the 00 orientation.
The D1 arrangement was using the long 2R bent foils. The spacing was .138R
and the orientation was 750. The airfoils were continuous. This was by far the best
arrangement of all those that were tested. When the tests were run it was shocking to see
the cylinder not vibrating. At all speeds that were tested, there were no vibrations. The
drag was also one of the lowest of all the arrangements. At the 200 orientation the drag
was higher than the 0' orientation. There was also vibration exhibited at this orientation.
The vibrations were no where as high as the B and C arrangements.
The Dib arrangement was using the long 2R bent foils. The spacing was .138R
and the orientation was 750 . The airfoils were staggered. At the 0' orientation, the drag
was lower than the D arrangement. There were small vibrations exhibited. These
vibrations were no where as big as the B and C arrangements. At the 20' orientation, the
drag was higher than the 0O orientation. Also the vibrations were higher than that of the
00 orientation. The vibrations were similar to the D at the 200 orientation.
The D2 arrangement was using the long 2R bent foils. The spacing was .138R
and the orientation was 1000. The airfoils were continuous. This arrangement exhibited
vibrations that were slightly lower than the B and C arrangements. The drag was high
compared to the other arrangements. There were no second mode vibrations. In the 200
orientation, the drag was slightly lower than the 00 orientation. The vibrations were also
less for this arrangement compared to the 0O orientation.
The D2b arrangement was using the long 2R bent foils. The spacing was .138R
and the orientation was 1000. The airfoils were staggered. The drag was about the same
compared to the D2 arrangement. It was higher compared to the D1b arrangement. The
vibrations were about the same compared to the D2 arrangement and more than the Dib
arrangement. At the 200 orientation, the drag was high compared to other arrangements.
The vibrations were about the same as the B and C arrangements with the lowest
vibrations.
The El arrangement was using the medium 1.5R bent foils. The spacing was
.138R and the orientation was 750 . The airfoils were continuous. The 00 orientation had
drag that was lower than the Dl orientation. There were also no vibrations exhibited by
this arrangement. The 200 exhibited high drag when compared to the other runs. The
vibrations were also high when compared to the D1 arrangement.
The EBlb arrangement was using the medium 1.5R bent foils. The spacing was
.138R and the orientation was 750 . The airfoils were staggered. The 0Oorientation had
drag that was slightly higher than El and lower between Dlb and D2b. This arrangement
vibrated and was about equal in amplitude compared to the D2b. The 200 orientation had
higher vibratiions when compared to the D and E configurations and was about average
for the B and C arrangements.
2.2 Large Airfoils
2.2.1 Spring Cylinder Rig
The large airfoil tests are being performed at the MIT Towing Tank. The tests are
being performed using the Spring Cylinder Rig (SCR). The SCR is a two degree of
freedom free response system. The cylinder used is .035 inches in wall thickness to help
reduce the mass ratio of the system. The cylinder is 3 inches in diameter. This diameter
is the same as the original tests performed on the SCR. A second set of tests using the
SCR was performed using a smaller diameter of 2 inches, but the forces and
displacements were much smaller. Also since the cylinder was not as buoyant, more
springs were needed to support the smaller cylinder. Therefore the larger cylinder of 3
inches was used. The cylinder is mounted between two spars that pierce the surface of
the water and hold the cylinder under water. To attach the cylinder, end caps are made
and used to plug each end of the cylinder and mount the cylinder. The original end caps
had a cone indentation and a rubber stopper was mounted on the spars. The cone
indentation would fit over the rubber stopper when the cylinder was installed. This
arrangement allowed for rotation of the cylinder. For plain cylinder tests, this rotation
was acceptable. For these tests, the airfoils are appended to the cylinder and rotation of
the cylinder during the run would change the position of the airfoils relative to the flow.
As a result, a new attachment system was developed (Figure 8.). This system involved
the mounting bolt and a cross bolt. The end caps were now slotted at the specific angles
that the cylinder was to be mounted at. The two spars are welded to a cylinder to
provide structure and form the free component of the apparatus. The fixed structure is
attached to the carriage. The main part of the fixed structure spans the width of the tank
and supports the free component of the SCR (Figure 9. and 10.). Figure 11. is a CAD
model of the SCR without the arms and the spring bank. There are two arms that extend
fore and aft from the main part. There is also an arm that extends vertically from the
main part. These three arms represent the anchor points on the structure for the springs.
The free component is attached to the main part on either end. At the attachment point,
there are bearings that allow the cylinder to move in the inline and transverse directions.
Attached to the free component is the spring bank. This provides the anchor point for the
springs on the free component. To allow the cylinder to have free vibrations, springs are
used. The springs in the transverse direction are attached from the spring bank to the
vertical arm to raise the cylinder and provide most of the spring force on the cylinder.
The limit of the upward spring force in the vertical direction is pulling the cylinder until it
is in the middle of the bearing travel range. If a higher spring force is desired, springs are
attached from the spring bank to the lower region of the main part as well as to the
vertical arm. These lower springs pull the cylinder down towards the center of the
bearing travel range. The spring force in the inline direction is generated by attaching
springs from the spring bank to the horizontal arms. Springs are added on both sides to
keep the cylinder centered on the bearings.
Figure 8. End Cap
Figure 9. SCR Front
Figure 10. SCR Angled
Free Colllpon~t
Figure 11. SCR CAD
2.2.2 Linear Motor System
The bearings are linear roller bearings and there is some friction remaining in the
system due to misalignment of the SCR. Thus linear motors are used to try to counter act
the friction. There is a string velocity potentiometer attached to the carriage in both the
transverse and inline directions. The velocity is then read by a computer on the carriage
and transforms it into a force that is exerted by the linear motor on the free component.
The function is F(V)=kl+k2*VApl. The values of kl, k2 and pl can changed so that the
damping ratio can be maintained as the friction in the SCR is variable. Due to the steep
of the function through zero velocity, the force can jump to large positive and negative
forces. Due to the slight inaccuracies in the potentiometer, this leads to chatter in the
system. To eliminate the chatter, there is a velocity threshold built into the program. If
the velocity from the potentiometer is less than the velocity threshold, there is no force
exerted by the linear motors. This eliminates the chatter at the expense of lower damping
ratios at lower amplitudes of motion. Therefore the velocity threshold is set as low as
possible while still eliminating chatter.
The SCR allows the transverse and the inline directions to be tuned to two
different natural frequencies. One issue with the arrangement is that the cross coupling
of the springs. Since they are not independent in both directions, if there are springs in
one direction, they will apply a force in both directions. For example, we can not have
any springs in the transverse direction, but there would still be a spring force in the
transverse direction due to the springs in the inline direction. Because of the coupling of
motion, the linear motors were not working perfectly and thus increased the damping on
the system. Since the tests on the airfoils are a comparison of different arrangements, the
SCR was locked in the inline direction and allowed to vibrate only in the transverse
direction. The two dimensional system allows a more realistic representation of a riser,
but the added damping makes the tests more difficult.
2.2.3 Sensors
The SCR can measure forces and displacements in the inline and transverse
directions. The displacements are measured using linear potentiometers attached to the
main part of the carriage. There is a slider that is attached to the free component of the
SCR and slidles over the potentiometer. The slider attracts a magnet that is within the
potentiometer and the magnet moves with the slider as the free component moves. There
is a voltage supplied to the sensor and a differential voltage is outputted by the sensor
based on the position of the magnet. This voltage is read directly into the data acquisition
system. The forces are measured by the Kistler three axis piezoelectric force sensors.
2.2.4 Large Airfoils
Two (different airfoils were used. The first (Figure 12.) is a standard NACA
section profil[e and camber line. The profile is a 63A010 and an a=.2 camber line.
Figure 12. Flat Airfoil
Profile: 63A010 Camber line: a=.2
The second (Figure 13.) airfoil is more cambered. The meanline follows the radius of the
circle around the cylinder. The profile is still the 63A010.
Figure 13. Curved Airfoil
An aluminum mold was made of each section 36 inches long. The airfoils are made by
mixing epoxy with milled fiberglass. This method of airfoil construction worked well
and only one foil broke. This method provided sufficient strength so that only twos
supports were needed per pair of foils. The only drawback of this type of airfoil is that it
is heaver than water so the foils generally hung below the cylinder. Pipes are sized so
that the inner diameter is standard. Therefore the 3 inch pipe fit over the 3 inch cylinder.
The 3 inch pipe was cut into 3/8" rings and drilled with screw holes. The foils were
drilled and a screw was inserted through the foil and attached to the rings (Figure 8.).
Small aluminum airfoil extrusions were inserted between the airfoil and the rings to
further offset the airfoils from the cylinder and also reduce the drag from the screws. The
first set of rings had setscrews so that they could be clamped to the cylinder. When the
airfoils were allowed to freely rotate, a new set of rings were fabricated. The rings were
over bored on a lathe so that they were loosely fitting over the cylinder.
Figure 14. Arrangement
The parameters that were varied were the orientation about the cylinder, the
distance of the airfoil off the cylinder and whether the foils were staggered, single, or
continuous. The orientation of the cylinder is defined by the angle the screw makes with
the aft centerline. This variable is called phi (cp). The airfoils were tested at three angles;
900,750, and 600. The distance of the airfoil off the cylinder (d) was either .333R or
.666R. Also the two airfoils had two different chord lengths (c). Figure 9. shows the D3
arrangement with the dimensions defined.
Figure 15. Rigid Airfoil C3 Arrangement Dimensions
Continuous means that there were four foils and the whole cylinder was covered with
foils. A pair of foils is both a foil on the top and bottom, and in this arrangement, each
pair is mounted on two rings (Figure 16.).
Figure 16. Continuous Arrangement
The staggered arrangement means that the one foils is on the bottom for half the span of
the cylinder and the other half of the span has an airfoil on the top. Three rings were used
so that the two foils are connected together (Figure 17.).
Figure 17. Staggered Arrangement
The single arrangement is where one foil covers each half of the span. Unlike the
staggered arrangement, the single arrangement are not connected together (Figure 18.).
Figure 18. Single Arrangement
Each arrangement is tested at Vrn 4, 5, 6, 7, 8, 10, 12, and 14. This allows for a good
resolution around the expected reduced velocities of vibration and checks the higher
reduced velocities for any galloping phenomenon.
2.2.5 Testing Procedure
Every time the cylinder is reattached to the SCR, a pluck test and a calibration
have to be performed. The pluck test is used to determine the natural frequency of the
system as well as the damping ratio. The test is performed by pushing the free
component of the SCR to the bottom of the rails in the transverse direction and releasing.
The cylinder is allowed to oscillate until it stops moving. The data from the transverse
linear potentiometer is recorded. Using a Matlab program, the range of data is selected
and it is analyzed to determine the mean natural frequency and the mean damping ratio.
Plots of the time trace for the pluck test as well as a plot of damping ratio vs. A/D. The
second plot is very useful in tuning the linear motor system. The constants of the
transformation function can be modified to try to achieve the same damping ratio at all
A/D. Calibration tests are performed in both the transverse and inline directions. The
original calibration system for the inline direction utilized pulleys. A string was attached
to the cylinder and then run through a series of pulleys so that a weight could be hung.
There was friction in the pulleys so that there would be residual tension in the string
when a weight was hung and then removed. This gave inaccurate results for the
calibrations. A new system was developed to calibrate in the inline direction. A rod was
hung from the rail parallel to the water across the width of the tank. Then a long piece of
two by four is suspended from the rod into the water. An arm a third of the way down
the wood created a platform where the calibration weights were placed. The weight that
was placed is converted into a horizontal force at the bottom of the two by four. A string
connected the two by four to the cylinder. This allowed for a frictionless system to
calibrate the inline direction. The transverse direction is calibrated by suspending a
weight from the cylinder. Originally, the directions were calibrated independently. Then
it was found that there is cross coupling between the two directions and instead of using a
single factor for each direction, a calibration matrix is used. Matlab is used to determine
the matrix. During the calibration, both directions are recorded. First the drift of the
force sensor is eliminated. The voltages output in each direction for the calibration for
each direction are found and placed into a matrix. The forces that were applied during
the calibration are placed into a second matrix. The calibration matrix is found by
multiplying the force matrix by the inverse of the voltage matrix. From the test a
calibration matrix is created for each of the force sensors. The calibration for the linear
potentiometers is performed less frequently because unlike the force sensors, they are
extremely stable. A ruler is placed next to the potentiometer and the free component is
moved a specific distance. Using Matlab, the voltage is found for each distance and the
calibration is found.
Matlab is used to analyze the data. The program that was developed asks for the
number of runs that want to be analyzed. Then it asks for the speeds corresponding to
the runs that are being tested. Next, each run is processed. A dialog box appears where
the run is selected. The drift is eliminated and the calibrations are applied to the voltages.
Then a plot of the drag force is plotted and the range of data to be analyzed is then
selected. The drag coefficient and the Amplitude over Diameter ratio for the run are
calculated. This is repeated for each of the runs that were specified to be analyzed. The
results from the batch of runs are output as a matrix and then are placed in the
spreadsheet.
The tests were originally supposed to be with the arrangements fixed to the
cylinder. Each of the arrangements was supposed to be rotated 00, 300, and 600 with
respect to the flow. The first case that was tested was A3. The cylinder did not vibrate
and had reduced drag. So then the project moved to a more realistic case with the airfoils
allowed to freely rotate around the cylinder. To determine the position of the freely
rotating airfoil, a video was taken starting with the C arrangements. A picture was
captured from the video and using a CAD program, the angle of the foil was determined.
The angle of the airfoil is measuring the lower airfoil and from the aft centerline similar
to the position for the arrangement. Due to the weight of the airfoils, starting with the
C_A arrangements, a screw was mounted to the front of the rings and used to
counterbalance the weight of the airfoils.
2.2.6 Results
The A3 arrangement was using the flat airfoils. The spacing was .333R and the
orientation was 900. The airfoils were continuous. A3 was the first test that was
performed for the rigid foils in the large tank. The foils were held fixed to the cylinder.
No tests were performed at other angles of attack. There was a peak in drag at Vrn 7.
The A3 arrangement with the foils fixed to the cylinder was repeated. This test was
performed to see if there was still an increase in drag coefficient at Vrn 7. This is the
case. With the promising results of the fixed airfoil arrangement, the next step was to test
a more realistic scenario. In the ocean, the flow would not always be coming in the ideal
direction. Therefore a unidirectional arrangement such as the airfoils needs to be able to
freely rotate around the cylinder. The next set of tests was then performed with the
airfoils freely rotating around the cylinder. The hope was that the airfoils would be able
to self-align themselves with the flow. The first test of A3 that was performed where the
foils were allowed to rotate had a damping about 1%with the fully foiled cylinder. There
was sustained vibration from Vrn 6 to Vrn 10 when the cylinder was perturbed. The drag
was slightly higher at the lower reduced velocities due to the foils being on the bottom of
the cylinder. When in sustained motion, the foils would align themselves with the flow.
The gains for the linear motor were reduced because when the damping was check with
the bare cylinder, the motors were adding too much energy to the system. The A3
arrangement free to rotate was retested. This test was with the lower gain settings. There
was sustained motion only at Vrn 6.
The Al arrangement was using the flat airfoils. The spacing was .333R and the
orientation was 60'. The airfoils were continuous. The foils did not rotate so that they
were symmetrical with the centerline of the cylinder. Instead, the lower foil rotated to
align itself to the flow. The upper foil was in the back of the cylinder. The drag at the
lower reduced velocities is higher because the foils are hanging down. The drag was
about average when compared the other arrangements. There were no vibrations for this
arrangement.
The A2 arrangement was using the flat airfoils. The spacing was .333R and the
orientation was 750 . The airfoils were continuous. At Vrn 6 there was sustained motion
when perturbed. The foils were aligning itself with the water inflow. When there was no
vibration, the lower foil aligned itself with and the upper foil was behind the cylinder.
Once again the lower velocities had higher drag coefficient because the foils were
hanging down below and did not align. The drag was high when compared to the other
arrangements but not as high as Cl. The vibrations were also high but no the highest
overall.
A4 was an arrangement that I thought was interesting to test. The A4
arrangement was using the flat airfoils. The spacing was .333R. This utilized only one
foil and it was set to be the lower foil. The foil would sit near the bottom and move a
little to align itself with the flow. The drag at the lower velocities is lower than the twin
foil tests because the foil is not perpendicular to the flow, but more aligned. There was
no motion in this arrangement. The drag was one of the lowest for all of the
arrangements.
The A5 arrangement was using the flat airfoils. The spacing was .333R. A5 is
another arrangement that utilizes a single foil. In this case, the foil remaining is the upper
foil. When the foil was perturbed, the foil would flip onto the top side of the cylinder and
stay in a "sweet spot" at the top. When the cylinder was not perturbed, the foil would be
behind the cylinder. There were sustained vibrations when the cylinder was perturbed at
Vrn 6. Vrn 12 did not get the foil to flip to the top side. The drag was slightly below
average for the arrangements. The vibrations were lower than most of the arrangements
that had sustained vibrations.
The A1A arrangement was using the flat airfoils. The spacing was .333R and the
orientation was 600. The airfoils were staggered. This was a test of A1A allowing it to
freely rotate. As with the continuous case, the foil was not symmetrical about the
centerline but the lower foil was aligned with the flow. This arrangement had sustained
vibration over the largest range of speeds. This is similar to what was observed on the
flexible cylinder. The vibrations were higher than the average for all the arrangements.
The drag was also higher than most of the arrangements.
The A2A arrangement was using the flat airfoils. The spacing was .333R and the
orientation was 75' . The airfoils were staggered. A2A was tested with the ability to
freely rotate. There was sustained motion at Vrn 6 and 7. Similar to A2, the foils did not
become aligned symmetrically about the inflow direction. This arrangement had one the
highest vibrations. The drag was also above average.
The A3A arrangement was using the flat airfoils. The spacing was .333R and the
orientation was 90'. The airfoils were staggered. A3A was allowed to freely rotate about
the cylinder. Only at a reduced velocity of 6 was there sustained motion. The drag was
also lower than A2A and A1A. These results are similar to those that were found on the
flexible cylinder.
The C3 arrangement was using the curved airfoils. The spacing was .333R and
the orientation was 900. The airfoils were continuous. This was the case of C3 allowed to
freely rotate. The cylinder vibrated at Vrn 5 to 8 when the cylinder was perturbed and
Vrn 6 and 7 when it was not. The overall drag on the cylinder is higher than that of A3.
One the other hand, the vibrations was less than the C3 arrangement. Also there was no
self tailing capability exhibited. The foils generally hung towards the bottom of the
cylinder. This is shown by the high angles, far from the ideal.
The C2 arrangement was using the curved airfoils. The spacing was .333R and
the orientation was 75' . The airfoils were continuous. This test was of the C2
arrangement allowed to freely rotate. The cylinder vibrated at Vmrn5 and Vrn 6. The drag
was higher at the lower reduced velocities due to the foils not aligning with the flow. The
foils did not have the self aligning characteristics as the less cambered foils. This can be
seen in the high lift coefficients as the foils hung at the bottom. The foils were also far
forward in relation to the ideal. This can also be confirmed by the videos. The drag was
about average for most of the arrangements. It was much lower than the Cl or C3
arrangement. The vibrations were also about average.
The Cl arrangement was using the curved airfoils. The spacing was .333R and
the orientation was 600. The airfoils were continuous. This is the Cl arrangement
allowed to freely rotate. The drag is higher due to the foils not rotating into the flow.
The lift is also high because of the same reason. The cylinder vibrated at Vrn 5 and 6.
The foils were unable to self align themselves with the flow. The foils were quite far
forward. The drag was the highest of all the continuous foil arrangements and the second
highest of all the arrangements. This arrangement had the highest vibrations out of all the
arrangements tested.
The CIA arrangement was using the curved airfoils. The spacing was .333R and
the orientation was 60. The airfoils were staggered. This is the C A arrangement free to
rotate and counter balanced. The counter balancing seemed to help a little with the
orientation problem. It also helped make the foils align better to reduce the drag
coefficient. Vrn 5-8 had sustained motion Vrn 8 did not need to be perturbed to have the
sustained motion. This arrangement is about average when compared to the other
arrangements in both drag and vibrations.
The C2A arrangement was using the curved airfoils. The spacing was .333R and
the orientation was 75' . The airfoils were staggered. This is a test of the C2A
arrangement free to rotate and with the counterbalance system. The foils are further back
when compared to C2 at the lower speeds, but were further forward at the higher speeds.
Vrn 5 had small motions when perturbed. Vrn 6 and Vrn 8 had sustained motions when
not perturbedl. On the other hand Vrn 7 did not have sustained motion when not
perturbed. I think that this arrangement is extremely sensitive to motion. The drag is
about average when compared to the other staggered arrangements. The vibrations were
also about average for the arrangements tested.
The C3A arrangement was using the curved airfoils. The spacing was .333R and
the orientation was 900. The airfoils were staggered. This is the C3A arrangement free to
rotate and with the counter weight system. The foils were further back on the cylinder
compared with C3. Also the drag was reduced across the entire speed range. There was
sustained motion at Vrn 5-8 when perturbed. The vibrations were about average when
compared to the other arrangements. The drag was also about average compared to the
other arrangements.
The C4 arrangement was using the curved airfoils. The spacing was .333R. This
was the C4 arrangement allowed to freely rotate. The drag coefficient is high because
the foils did not align themselves with the flow. At Vrn5-8 there was vibration. The lift
coefficient is also high due to the asymmetry of the arrangement. The foils aligned
themselves far forward on the cylinder. The drag for the arrangement was higher than
most of the other arrangements. The vibrations were slightly higher than average for the
arrangements.
The C5 arrangement was using the curved airfoils. The spacing was .333R. This
is the C5 arrangement. The foil angles were a little further forward than perpendicular.
The drag was much higher than the A case. The foils also had high lift due to the
asymmetry. The cylinder vibrated at Vrn 5-7 when perturbed and Vrn7 when it was not
perturbed. This arrangement showed the highest vibrations of all the single foil
arrangements and had highest drag compared to the other arrangements.
The C6 arrangement was using the curved airfoils. The spacing was .333R. One
foil is oriented as the lower foil and the other foil is oriented as the upper foil. This is the
C6 arrangement allowed to freely rotate. The drag was higher than the A configuration.
The foils were a little farther forward than perpendicular. Vibration occurred at Vrn 5-8
when it was perturbed and Vrn 6 when it was not perturbed. The vibrations were
comparable to the other C single foil arrangements. The drag was about the same as the
C4 arrangement and slightly less than the C5 arrangement.
The D3 arrangement was using the curved airfoils. The spacing was .666R and
the orientation was 900. The airfoils were continuous. This arrangement was tested both
fixed as well as free with the counter weight system. In the fixed case, the drag was
higher than the A3 fixed case. Both arrangements exhibited no vibrations. This
arrangement was tested twice in the free arrangement. Both set of tests were perturbed.
In the first set of tests, the airfoils were allowed to move to whatever position they
wanted to. After each run in the second set of tests, the airfoils were readjusted so that
they were about aligned with the flow. In the first set of tests of free vibration, there were
vibrations at Vrn 6 and 7. At Vrn 5 and 8, there were vibrations at the beginning of the
run, but the airfoils would align themselves with the flow and eliminate the vibration.
Since the counter weight is slightly heavy, the airfoils would be sitting towards the top
when the cylinder is initially perturbed. As the run progressed, the airfoils would align
themselves to the flow. Since the foils were allowed to rotate to any position they want,
the drag was slightly higher over the entire speed range. When the airfoils were aligned
after each run, the airfoils would shift to the top of the cylinder when perturbed and then
they would fall back down as they align themselves with the flow. The same
characteristics were observed from the first set of tests at Vrn 5 and 8. So at Vrn 5-9, the
vibrations would occur when the cylinder was initially perturbed and then the airfoils
would align themselves and then the vibrations would stop.
Chapter 3
Concluding Remarks
3.1 Conclusions
In the flexible cylinder experiments, the Dl arrangement was clearly the best
performer. This arrangement was one of only two that eliminated vibrations in the series
of tests. Vane 2 in Figure 1. and Dl in Appendix A look quite similar and the results are
similar as there were no vibrations exhibited. When the DI arrangement is not aligned
with the flow, there are small vibrations but not as large as the other cases. Removing
some of the airfoils was not effective as the cylinder began to vibrate. Using airfoils with
shorter spans (E configuration) were beneficial as the drag was reduced. This is to be
expected as there is less airfoil extending into the wake behind the cylinder. When the
airfoils were not aligned, they were not as effective as the longer airfoils. This is possibly
due to the longer airfoils ability to redirect the flow more.
The rigid cylinder experiments do not have an overall hand down winner as not
all the tests were tested under the same condition. The Al and A4 arrangements did not
exhibit any vibrations when allowed to freely rotate. These two arrangements probably
should be studied further. The fixed cases show that the airfoils are successful at
eliminating vibrations as well as reducing drag. When testing in the free case, the
counter weight system has shown that it allows the airfoils to be more aligned with the
flow for the continuous cases. The true way to model a marine riser would be to have
foils that are neutrally buoyant. The flat airfoils were able to rotate around the cylinder
quite easily. When the cylinder was vibrating, the airfoils would align themselves to the
instantaneous inflow direction. When the cylinder was not vibrating, gravity played an
important role in the position of the airfoils. At the lower reduced velocities, the airfoils
hung with the trailing edge pointing down. At the higher reduced velocities, the lower
airfoil would align itself to the flow and the upper foil would be somewhere behind the
cylinder. The airfoils would never align to the position that was designed. The lower
airfoil would position itself in a similar position every run. This position could be
considered the ideal foil position for the airfoil at .333R from the cylinder and 0' angle of
attack. On the other hand the curved foils did not self orient themselves. The curved
foils would orient themselves in various positions. Due to gravity, most of these
positions would be close to the bottom. The counter weight system helped them move
into the aligned position, but was not perfect. The difference of the self aligning
capabilities could be attributed to that the flat foils protruded further into the flow and
could provide more of a moment to rotate around the cylinder. The curved foils were
closer to the cylinder so they could not provide the moment to rotate around the cylinder.
The drag was slightly higher for the curved airfoils compared to the flat airfoils. This is to
be expected as the curved foils have more area projected to the flow.
3.2 Recommendations for Future Work
The results of the tests that were performed are extremely promising and further
work should be performed on airfoils. The interesting case is when these unidirectional
suppression devices are allowed to freely rotate around the cylinder. Further tests should
be performed with the current airfoils on the SCR to understand how different parameters
affect the drag and vibrations. First the airfoils should be rebuilt so that they are neutrally
buoyant. There are neutrally buoyant two part plastics, but the plastics are much weaker
in bending than the fiberglass/epoxy foils that were built. This would eliminate the need
for the counter weight system and also gravity should not be such a big factor. This
would allow the airfoils to align themselves more realistically to the flow. Only the
orientation of the airfoil around the cylinder and the height of the airfoil off the cylinder
were varied during the set of tests. Another parameter that could be varied would be the
angle of attack the airfoils have in relation to the flow. A further area of study could go
into the reason why the flat airfoils were able to rotate around the cylinder so easily while
the curved airfoils would not rotate that much. Another future area of study would be
returning to a flexible cylinder test. The flexible cylinder is a much more realistic
representation of the marine riser. There are some inherent problems working with the
rubber cylinder on the FCR. First is that the mounts for the airfoils must be modified.
Since the airfoils were just screwed into the rubber, the screw holes would become lose
and the airfoils would become lose and swivel. The mounts would have to be further
modified to allow for free rotation around the cylinder. The cylinder that was used in the
FCR was small and so it was difficult to make airfoils with thickness. One possible
solution is to increase the diameter of the cylinder or to use a hot wire foam cutter to cut
the airfoil sections.
Bibliography
Blevins, R.D. (1977), Flow-Induced Vibrations, Nostrand Reinhold Co., New York.
Grimminger, G. (1945). Effect of Rigid Guide Vanes on the Vibration and Drag of a
Towed CircularCylinder,David Taylor Model Basin Report 504.
Hoerner, I. S. F. (1965), Fluid-Dynamic Drag, Hoerner Fluid Dynamics, Bakersfield
PBS. (3 May 2006) ConocoPhillips CEO Defends Oil Company Profits [Video]. Online
NewsHourhttp:llwww.pbs.org/newshour/bb/business/jan-juneO6/mulva_0503.html. (14 May 2007)
Offshore Technology (2007) Roncador, Campos Basin, Brazil. http://www.offshore-
technology.com/projects/roncador/
Sanders, L. (2006), Oil DrillersHit a Profit Gusher,
http://www.businessweek.com/investor/content/apr2006/pi20060421
378143.htm
(14 May 2007)
Zdravkovich, M.M. (1980). Review and Classificationof Various Aerodynamic and
HydrodynamicMeansfor Suppressing Vortex Shedding. Journal of Wind
Engineering and Industrial Aerodynamics, 7 (1981) 145-189.
Appendix A
Flexible Cylinder
Arrangement A
Arrangement C
1R
1R
1R
1R
1R
1R
1R
1R
1R
1R
1R
1R
A10
A120
Al bO
Al b20
A20
A220
A2b0
A2b20
A30
A320
A3b0
A3b20
D
d
T
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
0.138R
0.138R
0.138R
0.138R
0.138R
0. 138R
0.138R
0.138R
0.138R
0.138R
0.138R
0. 138R
450
450
450
450
750
750
750
750
900
900
900
900
Al
Arrangement
Vrn
3
5
6
7
9
A10
Cd
0.83
1.41
1.44
1.48
1.40
A120
Cd
1.03
1.56
1.56
1.48
1.48
0O
200
0'
200
0O
200
00
200
00
200
00
200
Continuous
Continuous
Staggered
Staggered
Continuous
Continuous
Staggered
Staggered
Continuous
Continuous
Staggered
Staggered
A3
A2
Al bO
Cd
1.03
1.81
1.76
1.77
1.30
A120 Al bO
Arrangement A10
-A/D
-AND
-A/D
Vrn
0.00
0.00
3
0.10
0.50
0.50
5
0.50
0.50
0.60
6
0.60
0.40
0.50
0.50
7
0.30
0.50
9
0.30
Al b20
Cd
A20
Cd
A220
Cd
A2b0
Cd
A2b20 A30
Cd
Cd
1.30
1.78
1.45
1.39
1.38
1.48
1.34
1.38
1.43
1.31
A220 A2b0 A2b20
Al b20 A20
-A~D
-A~D
-A/D -A~D
-A/D
0.10
0.20
0.50
0.50
0.00
0.60
0.50
0.40
0.70
0.50
0.60
0.60
0.30
0.70
0.60
0.40
0.50
0.30
0.50
0.50
0.30
0.50
0.40
0.30
0.30
A30
-A~D
0.50
0.70
0.70
0.50
0.30
1.14
1.63
1.84
1.86
1.75
1.47
1.43
1.37
1.33
1.27
1.66
1.71
1.62
1.65
1.74
1.31
1.17
1.23
1.23
1.32
A320
Cd
A3b0
Cd
A3b20
Cd
1.27
1.73
1.66
1.58
1.42
1.84
1.78
1.64
1.43
1.38
A320 A3b0
-A~D -AND
0.30
0.10
0.70
0.30
0.70
0.50
0.20
0.50
0.30
0.20
A3b20
-A/D
0.70
0.70
0.60
0.50
0.60
1.22
1.24
1.26
1.31
1.34
Arrangement B
Arrangement C
1R
1R
1R
1R
1R
1R
1R
1R
1R
1R
1R
1R
B10
B120
BlbO
Blb20
B20
B220
B2b0
B2b20
B30
B320
B3b0
B3b20
D
d
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
450
450
450
450
750
750
750
750
900
900
900
90*
B2
00
200
00
200
00
200
00
200
00
200
00
200
Continuous
Continuous
Staggered
Staggered
Continuous
Continuous
Staggered
Staggered
Continuous
Continuous
Staggered
Staggered
B3
Arrangement B10
Cd
Vrn
3
0.84
5
1.25
6
1.28
7
1.30
9
1.00
B120
Cd
0.68
1.46
1.35
1.39
1.07
BlbO
Cd
2.55
1.91
2.28
2.21
2.25
Blb20
Cd
1.08
1.93
1.89
1.86
1.57
B20
Cd
1.14
2.12
1.94
1.39
1.07
B220
Cd
2.01
1.44
1.57
1.57
1.52
B2b0
Cd
1.07
2.15
2.15
2.09
1.77
B2b20 B30
B320
Cd
Cd
Cd
2.73
1.00
3.91
1.84
1.88
2.23
1.80
1.91
2.32
1.81
1.55
2.25
1.77
1.46
2.10
B3b0 B3b20
Cd
Cd
1.28
2.02
2.30
2.51
2.39
2.75
2.39
2.50
1.76
2.38
Arrangement
Vrn
3
5
6
7
9
B120
BlbO
-AD
0.04
0.84
1.00
0.88
0.81
Blb20
B20
B220
-~ND -A/D
0.04
0.11
0.91
0.61
0.95
0.78
0.97
0.83
0.92
0.82
B2b0
-A/D
0.04
1.08
1.03
1.02
0.78
B2b20 B30
B320
-ND
-A/D -A/D
0.13
0.07
0.44
1.13
0.87
0.54
0.89
0.88
0.62
0.93
0.75
0.56
0.85
0.21
0.65
B3b0 B3b20
-A/D -A/D
0.19
0.57
0.91
0.77
1.07
0.89
1.16
0.86
0.64
0.90
B10
-~ND -ND
0.04
0.71
0.64
0.67
0.18
0.13
1.02
1.14
0.97
0.44
-ND
0.09
1.15
0.94
0.90
0.83
Arrangement C
Arrangement C 7D d
1R
1R
1R
1R
1R
1R
1R
1R
1R
1R
1R
1R
C10
C120
ClbO
Clb20
C20
C220
C2b0
C2b20
C30
C320
C3b0
C3b20
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
4
0.276R
0.276R
0.276R
0.276R
0.276R
0.276R
0.276R
0.276R
0.276R
0.276R
0.276R
0.276R
450
450
450
450
750
750
750
750
900
900
900
90°
C3
ClbO Clb20
Cd
Cd
1.26
1.18
C320
Cd
3.19
C3b0
Cd
1.49
C3b20
Cd
1.81
1.95
2.04
2.21
2.29
2.64
2.16
2.14
1.97
1.92
1.85
1.48
2.29
2.28
2.21
2.48
2.21
1.90
2.56
2.57
2.35
C2b20
-A/D
0.18
C30
-A/D
0.05
C320
-A/D
0.09
C3b0
-A/D
0.24
C3b20
-A/D
0.53
1.06
1.07
0.88
0.62
0.96
0.98
0.97
0.96
0.67
1.20
0.95
0.92
0.86
0.87
0.46
0.75
0.79
0.89
1.07
0.99
0.75
0.97
1.02
0.93
C10
Cd
1.12
C120
Cd
1.06
5
1.74
1.71
2.09
1.94
1.57
2.49
2.31
6
7
9
1.74
1.69
1.52
1.81
1.52
1.45
2.20
2.10
1.90
2.18
1.68
1.59
1.48
1.42
1.30
2.55
2.45
2.19
2.15
2.06
1.85
Arrangement C10
-A/D
Vrn
3
0.07
C120
-A/D
0.07
ClbO
-A/D
0.05
Clb20
-A/D
0.13
C20
-A/D
0.07
C220
-A/D
0.30
C2b0
-A/D
0.04
0.62
0.85
1.10
0.75
0.53
6
7
9
0.67
0.65
0.17
0.69
0.45
0.12
0.97
0.83
0.74
1.25
0.88
0.77
C20
C220
Cd
Cd
1.06
4.26
C2b0 C2b20 C30
Cd
Cd
Cd
1.12
1.37
2.33
Arrangement
Vrn
3
0.67
Continuous
Continuous
Staggered
Staggered
Continuous
Continuous
Staggered
Staggered
Continuous
Continuous
Staggered
Staggered
C2
C1l
5
0'
200
0*
200
0O
200
00
200
00
200
00
200
0.69
0.65
0.52
0.59
0.61
0.56
Arrangement D and E
ArrangementC
D d
D10
D120
DlbO
Dlb20
D20
D220
D2b0
D2b20
E10
E120
ElbO
n
2R
2R
2R
2R
2R
2R
2R
2R
1.5R
1.5R
1.5R
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
1.36"
4 cm
4 f3&1 I f%4
D1
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
0.138R
D2
D20
D220
750
75*
750
750
1000
100*
1000
1000
750
750
750
I 7ro
0*
200
00
200
00
200
00
200
00
200
00
Continuous
Continuous
Staggered
Staggered
Continuous
Continuous
Staggered
Staggered
Continuous
Continuous
Staggered
I
_.1
Arrangement
D10
D120
Vrn
Cd
1.43
1.38
1.38
1.37
1.40
Cd
Cd
Cd
Cd
Cd
Cd
Cd
1.16
1.22
1.44
1.16
3.97
1.05
1.50
1.93
1.33
1.86
2.27
2.18
1.77
2.45
2.01
1.21
1.82
2.43
1.84
1.65
2.27
2.03
1.15
1.71
2.39
1.62
1.65
1.93
1.92
1.08
1.60
2.14
2.34
1.52
1.92
3
5
6
7
9
Arrangement
Vrn
3
5
6
7
9
DlbO
Dlb20
D10
D120 DIbO Dlb20 D20
D220
-~ND -~ND -~ND -ND
-ND
~ND
0.04
0.04
0.04
0.10
0.04
0.04
0.04
0.48
0.21
0.46
0.44
0.42
0.05
0.50
0.18
0.45
0.50
0.18
0.05
0.51
0.13
0.46
0.52
0.05
0.05
0.49
0.08
0.44
0.54
0.47
D2b0
D2b20 E10
D2b0 D2b20
-ND
-A/D
0.05
0.04
0.51
0.89
0.45
0.79
0.41
0.45
0.46
0.33
Cd
1.15
1.29
1.23
1.24
1.18
E120
ElbO
Cd
Cd
2.05
1.14
2.35
1.55
2.33
1.42
2.32
1.31
2.23
1.48
E10
E120 ElbO
-~ND -~ND -ND
0.06
0.46
0.06
0.07
0.67
0.51
0.08
0.72
0.44
0.08
0.70
0.39
0.06
0.75
0.18
Elb20
Cd
Elb20
-A/ND
0.65
0.81
0.89
0.81
0.67
Rigid Cylinder
Arrangement A
Arrangement
Al
Al A
c
D Id
Type
Arran
1.67R
1.67R
3" 0.333R 600
3" 0.333R 600
Flat
Flat
Continuous
Staggered
Free
Free
no
no
no
no
A2
A2A
1.67R
1.67R
3"
3"
0.333R
0.333R
750
750
Flat
Flat
Continuous
Staggered
Free
Free
no
no
no
no
A3
1.67R
3"
0.333R
900
Flat
Continuous
Free
no
no
A3A
A4
A5
1.67R
1.67R
1.67R
3" 0.333R
3" 0.333R
3" 0.333R
900 Flat
Flat
Flat
Staggered
Continuous
Staggered
Free
Free
Free
no
no
no
no
no
no
Video Counterbalance
tFixity
Fixed and
Arrangement
Vrn
4
5
6
7
8
10
12
14
Al
A2
A4
A5
Al
A/D
0.0043
0.0054
0.0053
0.0039
0.0023
0.0025
0.0028
0.0028
A1A
A/D
0.0029
0.0031
0.7161
0.9701
0.7696
0.3461
0.0027
0.0026
A2A
A2
A/D
A/D
0.0008
0.0049
0.0047
0.004
1.1456
1.1099
0.3127
1.2136
0.001
0.0112
0.0033
0.0074
0.0011
0.0034
0.0616
0.0168
A3
A3
A/D
0.0005
0.0023
0.6042
0.0037
0.0023
0.002
0.0036
0.0064
A3A
A/D
0.002
0.0043
0.702
0.0045
0.0043
0.0042
0.0025
0.0014
A4
A/D
0.0007
0.0016
0.0056
0.0015
0.0029
0.0006
0.0011
0.0036
A5
A/D
0.0039
0.0033
0.7618
0.0045
0.003
0.0009
0.0012
0.0048
D3
A/D
0.0015
0.0031
0.0042
0.0036
0.0032
0.004
0.0054
0.0041
Arrangement
Vrn
4
5
6
7
8
10
12
14
Al
Arrangement
Vrn
4
5
6
7
8
10
12
14
Al
Cd
1.5865
1.6945
1.4644
1.182
1.063
1.0586
1.0269
0.9397
CI
0.3583
0.0778
0.0288
-0.1078
-0.6632
-0.4379
-0.561
-0.5897
A1A
Cd
0.9234
1.2992
2.04
2.1106
1.6909
1.1186
1.0222
0.9599
A2
AlA
CI
0.0068
-0.2111
-0.438
-0.3296
-0.2484
-0.4596
-0.0003
0.0192
A2
A2A
Cd
Cd
1.1992
0.978
2.1486
1.2608
3.1142
2.525
1.6195
2.6705
0.9957
0.9077
1.046
1.1351
1.1157
0.9509
0.8862
1.0632
Cl
0.9861
0.5128
0.178
0.4246
0.4701
0.2931
0.4126
-0.1171
A2A
Cl
1.1465
0.2381
0.9959
-0.1782
0.0437
-0.353
-0.2481
-0.0957
A3
A4
Cd
0.6048
1.4311
1.8851
0.9929
0.649
0.6367
0.6857
0.6525
A3A
Cd
0.6837
0.9567
1.3464
1.05
1.009
0.9946
0.9217
1.0235
A3A
Cl
0.4246
0.0855
0.8073
0.0423
-0.0785
-0.0306
0.0748
-0.0958
A4
CI
0.8286
-0.3102
-0.1394
0.0106
0.3962
-0.1518
-0.0493
-0.1418
A3
Cd
0.5664
0.9647
1.0478
1.0422
0.9756
0.9817
0.9082
0.7088
CI
0.8286
-0.3102
-0.1394
0.0106
0.3962
-0.1518
-0.0493
-0.1418
A5
Cd
1.0657
1.3638
2.7595
1.1018
1.0032
1.0789
0.9196
1.0108
A5
CI
-0.4264
-0.7792
0.4577
0.7539
0.9273
1.0049
-0.4044
0.9262
Arrangement C
Arrangement
C1
C1A
c
1.5R
1.5R
D
3"
3"
d
0.333R
0.333R
60*
600
C2
C2A
C3
1.5R
1.5R
1.5R
3"
3"
3"
0.333R
0.333R
0.333R
C3A
C4
C5
1.5R
1.5R
1.5R
3" 0.333R
3" 0.333R
3" 0.333R
IC6
Curved
Curved
Arrangement
Staggered
Continuous
Fixi
Free
Free
Video
yes
yes
Counterbalance
no
no
750
750
900
Curved
Curved
Curved
Staggered
Continuous
Staggered
Free
Free
Free
yes
yes
yes
no
no
no
900
Curved
Curved
Curved
Continuous
Stagered
Continuous
Free
Free
Free
yes
es
yes
no
yes
yes
1L
C1
Arrangement
Vrn
C1
A/D
CIA
A/D
C2
A/D
lr
•
_1
C2
C3
C5
C6
C2A
A/D
C3
A/D
C3A
A/D
•
I
C4
AND
I
C5
A/D
C6
A/D
4
0.0041
0.0041
0.0036
0.0032
0.0058
0.0048
0.0038
0.004
5
6
7
8
10
12
14
0.0038
0.3822
0.2426
0.0057
0.0016
0.0094
0.0373
0.2855
0.4951
0.6338
0.688
0.0031
0.0782
0.0032
0.6523
0.2675
0.0022
0.0043
0.0048
0.0042
0.0839
0.1984
0.5772
0.7436
0.7632
0.005
0.002
0.0045
0.766
1.1695
1.2069
0.8297
0.0048
0.001
0.0032
0.4464
0.308
0.4907
0.6097
0.0464
0.0286
0.0661
0.6776
0.9191
0.982
0.9421
0.0019
0.0041
0.0056
0.8672
1.169
0.8131
0.0054
0.0051
0.0039
0.0026
0.6569
0.9805
1.0036
0.8356
0.006
0.0044
0.0037
C1
C1A
Cd
1.0617
1.5065
1.7282
1.8936
1.7012
1.1642
1.1247
1.0515
C5
Cd
1.7959
3.4853
4.6999
3.6776
1.7818
1.8169
1.8683
1.7617
C6
Cd
Arrangement
Vrn
4
5
6
7
8
10
12
14
Cd
1.6959
1.8836
3.0734
2.7904
1.8153
1.8356
1.8035
1.7709
C2
Cd
1.2414
2.1241
1.1482
0.9902
0.9791
0.9653
0.8256
0.8969
C2A
Cd
1.0491
1.4687
1.8244
2.0411
1.8784
0.9874
0.9471
0.9397
C3
Cd
2.1548
2.1513
4.2722
3.9605
2.2271
1.1512
1.1502
1.1253
C3A
Cd
1.1387
1.6702
1.3936
1.6884
1.7686
1.2776
0.9879
1.009
C4
Cd
1.7008
2.89
3.2497
3.8068
3.1495
1.5736
1.6126
1.6552
3.1158
3.9501
3.6089
2.9237
1.4744
1.423
1.7302
Arrangement
Vrn
4
5
6
7
8
10
12
14
Arrangement
C1
ClA
C2
CI
-1.5727
-1.8064
-3.0981
-2.7842
-1.98
-2.04
-1.9883
-1.9502
CI
0.0095
0.2972
-0.0782
0.0501
0.2038
-0.0203
0.0267
-0.0081
CI
-1.3255
-2.4004
-1.4155
-1.2644
-1.2231
-1.4378
-1.3461
-1.5214
C1
ClA
C2
Vrn
Angle
4
137
103
5
6
7
8
10
12
14
115
113
130
1:32
1:30
132
1:31
108
87
78
91
105
86
120
C2A
CI
0.2035
-0.0801
-0.2177
-0.2512
-0.1153
-0.3049
-0.2774
-0.3414
C2A
C3
CI
-1.0964
0.473
-0.3817
-0.507
-0.6744
-0.077
-0.0162
-0.0447
C3A
C4
C5
CI
0.0525
0.0868
0.2962
0.3551
0.3808
0.2798
0.4435
0.4927
Cl
-1.5706
-2.9796
-3.2042
-3.1929
-3.0895
-1.8328
-1.8316
-1.8731
CI
-1.5777
-3.0049
-4.4666
-2.862
-1.6696
-1.9756
-1.8825
-2.0139
-3.0911
-2.8489
-2.5223
-3.3944
-1.8458
-2.0878
-1.9062
C3A
C3
C4
C6
CI
C5
C6
Angle
Angle
Angle
Angle
Angle
Angle
131
53
147
54
112
105
120
113
102
110
107
95
97
37
102
120
118
110
111
110
124
107
140
137
126
122
123
40
119
110
116
117
117
116
137
120
120
108
121
119
106
110
95
90
105
108
107
106
AngleAngle
108
107
100
90
110
109
108
Arrangement A3 Fixed and D3 Fixed
Arrangement
c
Dd
A3
1.67R 3" 0.333R
D3
1.5R
Type
900 Flat
Arrangement
Fixity
Fixed and
Video
Counterbalance
Continuous
Free
no
no
yes
yes
Fixed and
3" 0.666R 900
A3
Arrangement
Vrn
4
5
6
7
8
10
12
14
A3
Fixed
A/D
0.0056
0.0043
0.0043
0.0071
0.005
0.0049
0.0091
0.0051
Staggered
Curved
Free
D3
D3
Fixed
AID
0.0037
0.0037
0.0051
0.0041
0.0037
0.0038
0.0069
0.0038
Arrangement
Vrn
4
5
6
7
8
10
12
14
A3
Fixed
Cd
0.7545
0.7407
0.8365
1.0884
0.8724
0.8447
0.8568
0.8981
D3
Fixed
Cd
1.1968
1.189
1.2048
1.1574
1.1406
1.0949
1.0841
1.1006
Arrangement
Vrn
4
5
6
7
8
10
12
14
A3 Fixed
CI
0.1232
0.1366
0.1012
-0.1697
0.0371
0.1391
0.1008
0.0968
D3 Fixed
Cl
0.022
0.0567
0.0512
-0.027
-0.0585
-0.2053
-0.1827
-0.1766
Appendix B
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Appendix C
NUMBER OF DAYS TO BREAK EVEN (Less Than 60 Days)
Additional Cost per day For VIV Suppression Device
.
100,000
110,000
5,000
29.44
19.62
14.72
11.77
9.81
8.41
7.36
6.54
5.89
5.35
m"
120,000
4.91
9.81
19.62
29.44
39.25
58.87
53.52
49.06
130,000
140,000
150,000
160,000
170,000
4.53
4.21
3.92
3.68
3.46
9.06
8.41
7.85
7.36
6.93
18.11
16.82
15.70
14.72
13.85
27.17
25.23
23.55
22.08
20.78
36.23
33.64
31.40
29.44
27.70
45.29
42.05
39.25
36.79
34.63
54.34
50.46
47.10
44.15
41.56
58.87
54.95
51.51
48.48
58.87
55.41
180,000
3.27
6.54
13.08
19.62
26.16
32.71
39.25
45.79
52.33
20,000
30,000
40,000
50,000
60,000
70,000
80,000
ca
S90,000
10,000
58.87
39.25
29.44
23.55
19.62
16.82
14.72
13.08
11.77
10.70
20,000
30,000
40,000
58.87
47.10
39.25
33.64
29.44
26.16
23.55
21.41
58.87
50.46
44.15
39.25
35.32
32.11
58.87
52.33
47.10
42.82
50,000
60,000
58.87
70,000
80,000