A Scatter Diagram Approach to the Selection of Design Currents for
Prediction of Marine Riser Vortex-Induced Vibration
by
Jessica Mary Donnelly
B.S., Ocean Engineering
Massachusetts Institute of Technology, 2002
SUBMITTED TO THE DEPARTMENT OF OCEAN ENGINEERING IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN OCEAN ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
MASSACHUSETTS INSTITLUTE1
FEBRUARY 2004
OF TECHNOLOGY
SEP 0 1 2005
2004 Massachusetts Institute of Technology
All rights reserved
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January
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2004
Certified By
J. Kim Vandiver
Professor of Ocean Engineering
Thesis Supervisor
Accepted By
Michael Triantafyllou
Professor of Ocean Engineering
Chair, Departmental Committee on Graduate Studies
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A Scatter Diagram Approach to the Selection of Design Currents for
Prediction of Marine Riser Vortex-Induced Vibration
by
Jessica Mary Donnelly
B.S., Ocean Engineering
Massachusetts Institute of Technology, 2002
Submitted to the Department of Ocean Engineering
on January 16 th, 2004 in Partial Fulfillment of the Requirements
for the Degree of Master of Science in Ocean Engineering
ABSTRACT
This paper describes a scatter diagram approach for the classification of large numbers of
current profiles for use in the prediction of riser fatigue damage due to vortex-induced
vibration. Scatter diagrams have long been used to characterize the probability of various
combinations of wave height and period, which are then used to assess wave forces. To
predict VIV fatigue damage the designer needs to know which current profiles have the
combined property of long regions of relatively constant velocity and relatively high
speed. A sorting algorithm is proposed which searches every current profile for long
regions of relatively constant flow speed. The probability of each length and speed
combination is assessed and the data is used to populate the bins of the scatter diagram.
The designer need only select relatively few representative profiles for detailed VIV
analysis from those bins that would account for the most damage. The method is tested
by making comparison to a brute force approach in which each of many thousands of
profiles is evaluated for fatigue damage by running it in the SHEAR7 VIV response
prediction program.
This scatter diagram method could reduce the cost of risers by reducing the overconservatism that is introduced by the common practice of using an envelope design
current profile. It also reduces the analysis time required for the brute force approach by
allowing the designer to focus on only the most relevant profiles.
Thesis Supervisor:
Title:
J. Kim Vandiver
Professor of Ocean Engineering
2
Biographical Note
Jessica Mary Donnelly received her B.S. from the MIT Department of Ocean
Engineering in 2002. She is the recipient of undergraduate scholarship awards from
Niagara Mohawk Power Corporation and the Society of Naval and Marine Engineers,
and the winner of the 2002 Course 13 Student Engineering Association (13SEAs) Spirit
of Ocean Engineering Undergraduate Award. She was named an MIT Presidential
Fellow in 2003. Her first publication, "The Use of Velocity Profile Scatter Diagrams in
the Prediction of Vortex-Induced Vibration," co-authored by J. Kim Vandiver, was
included in the Proceedings of the 2003 Offshore Technology Conference, Houston, TX.
3
Acknowledgements
First, I would like to thank my advisor, J. Kim Vandiver, whose wonderful teaching in
the Ocean Engineering undergraduate program inspired me to study dynamics and
vibration. I am grateful for his support and guidance, and for the opportunity to be the
first person to develop an idea.
I would like to thank the Trinidad and Tobago Ministry of Energy and Energy Industries,
ExxonMobil, BP and Shell for providing the data used in this report.
I also like to thank Alex Vandiver for the use of his Shear7-related perl scripts.
I am indebted to the MIT Presidential Fellowship program, whose financial support
allowed me to focus on my research during the first year of my graduate studies.
I would like to thank the faculty and staff of the MIT Department of Ocean Engineering
for a fine and personal education.
I owe much of my success to the Bennett Park Montessori Center and the Buffalo
Seminary of Buffalo, NY. The nurturing, freedom and opportunities they gave me
allowed my education to be a wild adventure.
I am grateful to Jonathan Reed for his support and patience during the most stressful
times.
I would like to thank my father and stepmother, Michael and Charmaine Donnelly, for
their love and pride.
Above all, I am indebted to my mother, Christina Donnelly who encouraged without
pushing, helped me find the Divine Order in any situation, and always believed that I
could achieve the impossible.
4
Table of Contents
ABSTRACT ................................................................................................................................................... 2
BIOGRAPH ICAL NO TE ............................................................................................................................. 3
ACKNO W LEDGEM ENTS .......................................................................................................................... 4
TABLE OF CONTEN TS .............................................................................................................................. 5
NOM ENCLATURE ...................................................................................................................................... 7
1 INTRODUCTIO N ...................................................................................................................................... 8
M OT IV A TIO N ............................................................................................................................................... 8
PROPOSED SOLUTION ................................................................................................................................... 9
S c atte r p lo t ............................................................................................................................................. 9
Pa ram e ters............................................................................................................................................. 9
U T ILIT Y ..................................................................................................................................................... 10
11THEO RY ................................................................................................................................................. 11
OVERVIEW OF VIV THEORY AND TERMINOLOGY ...................................................................................... I I
Strouhal Relationship .......................................................................................................................... I I
Lo c k -in ................................................................................................................................................. 1 2
Lock-in criterion: reduced velocity bandwidth.................................................................................... 12
IDENTIFYING THE POWER-IN REGION ......................................................................................................... 13
111PRO CEDURE ........................................................................................................................................ 16
A L G O R IT H M ..............................................................................................................................................
V A L IDA TIO N ..............................................................................................................................................
P roced ure ............................................................................................................................................
R iser Mo d el..........................................................................................................................................
Da ta S e t ...............................................................................................................................................
16
18
18
19
19
IV RESULTS AND ANALYSIS ................................................................................................................ 20
VALIDATION RESULTS ..............................................................................................................................
L en gth R a tio ........................................................................................................................................
F re quency ............................................................................................................................................
DAMAGE RATE DISTRIBUTION ...................................................................................................................
CONSERVATISM .........................................................................................................................................
SCATTER DIAGRAM USE IN DESIGN ............................................................................................................
20
20
21
22
22
23
V RECO M M ENDATIO NS ........................................................................................................................ 23
EXPLORE BIN SIZING ..................................................................................................................................
Absolute vs. scaleable bin boundaries.................................................................................................
Nu m b e r of b in s .....................................................................................................................................
OUTLIER PATTERNS ...................................................................................................................................
M ULTI-MODE SITUATIONS .........................................................................................................................
23
23
23
24
24
REFERENCES ............................................................................................................................................ 25
APPENDICES ............................................................................................................................................. 26
APPENDix A: USER GUIDE ....................................................................................................................... 26
Installing the sifterfiles ....................................................................................................................... 26
Preparinginput matrices ..................................................................................................................... 26
Running the program........................................................................................................................... 28
APPENDix B: SOURCE CODE ..................................................................................................................... 32
N ew runp r( fi les .................................................................................................................................... 3 2
N ew idw in n e r ........................................................................................................................................ 3 3
T rimran ge 6 .......................................................................................................................................... 3 5
Trimin ..................................................................................................................................................
Trimlo w 2 ..............................................................................................................................................
Trimh ig h 2 ............................................................................................................................................
S trca lc ..................................................................................................................................................
36
37
39
41
Idw ino u ts ............................................................................................................................................. 4 2
S ca tterprep2 ......................................................................................................................................... 4 3
Co lo rc o de 3 .......................................................................................................................................... 4 6
Nomenclature
AID = amplitude to diameter ratio [-I
CL= Lift Coefficient [-]
CRH= high reduced velocity damping coefficient [-I
CRL= low reduced velocity damping coefficient [-1
D = hydrodynamic diameter [in]
dVR = reduced velocity bandwidth [-I
naturalfrequency [Hz]
fN=
fs= vortex sheddingfrequency [Hz]
fv= vibrationfrequency [Hz]
HighVR= the region in which the reduced velocity is higher than the greatestfound in the
power-in region
LowVR= the region in which the reduced velocity is lower than the lowest found in the
power-in region
<Pi>= the average mechanical power dissipated over a vibration cycle [ft-lb/si
QN= the modal force estimate [lb/mi
RHigI= high reduced velocity dampingforce per unit length per unit speed [lb s/im2
RLoW= low reduced velocity dampingforce per unit length per unit speed [lb -s/im2
RN= the modal damping estimate [lb s/m2
Rsw= still water damping force per unit length per unit speed [lb s/im 2
St = Strouhal number [-]
V(x)= local flow velocity [ft/s]
Vc= the center velocity of a power-in region[ft/s]
VIV = Vortex-Induced Vibration
VMAX= the greatestflow speed included in a power-in region [ft/si
VMJN
the lowest flow speed included in a power-in region [ft/si
VR,center= the reduced velocity associated with the center velocity of a power-in region [-i
VR= reduced velocity [-]
=
x=relative position of measurementpoint on the riser[-]
$(x) = local mode shape [-]
w= angularfrequency of vibration[radians/s]
p- fluid density [slugs/ft3 ]
v= fluid kinematic viscosity [ft2/sec]
7
I Introduction
Motivation
Before a riser can be designed for deployment in a new location, information on the
local currents must be obtained. Because this data often consists of tens of thousands of
measured current profiles, it is difficult to know which ones are important for riser
design. To overcome this difficulty, common industry practice is to prescribe a
conservative design profile based on the data set. One type of design profile is the
envelope of maximum values. This profile is found by plotting the maximum velocity
found in the data set at each measured depth, and incorporating these points into a single
"envelope profile". Therefore, at any point along the riser, the greatest velocity to be
found at that depth in the entire data set will be used. Sometimes a "slab" of constant
velocity is drawn in the region of the peak of the envelope profile, the area of highest
velocities. An example of each method is shown in Figure 1. In this case, the slab's
magnitude is equal to the highest velocity found in the data set. These conservative,
artificial design profiles don't occur in nature, and usually result in much higher damage
rates due to vortex-induced vibration (VIV) than any of the measured profiles. The slab
profile is particularly inaccurate, as demonstrated by the damage rate comparisons shown
in Figure 5. Any riser designed to this specification will be built far more conservatively
and, therefore, more expensively than the actual currents in the region require.
Slab
Envelope
Velocity
Figure 1: envelope and slab design profiles
8
Another option is the
"brute
force"
approach,
which requires computing
the riser response to each
profile using a numerical
analysis tool. However, this
takes too long due to the
large effort required to
prepare and process the tens
of thousands of individual
program runs. This study
alternative
an
presents
method, which sorts the
entire set of profiles in order
to identify those that are
likely to cause significant
fatigue damage.
This
information can be used to
create
more
meaningful
design criteria.
Proposed solution
Scatter plot
The solution proposed here is to sort all the profiles into a scatter diagram, which
identifies those profiles likely to cause the greatest fatigue damage. The scatter diagram
is based on two parameters known to be indicators of significant VIV response: the
length of the VIV power-in region and its velocity. The scatter diagram has rows and
columns representing ranges of the two parameters. In each bin space is recorded the
number of profiles in the data set with that particular combination of length and velocity.
A sample scatter diagram, including a color-coded overlay of fatigue life data found by
SHEAR7, can be found in Figure 2. Once the profiles have been sorted into bins, the
designer can select those bins most likely to be associated with significant damage rates
due to VIV and use only their profiles to perform a more detailed analysis.
Length Ratio
0.010.08
0.54- 0.91
0.92- 1.28
Center
Velocity
2.04- 2.41
2.42- 2.79
(ftlsec)
2.80-3 .16
0.090.16
173
27
0.170.24
634
10
604
8
0.250.32
0.330.40
594
42
0.410.49
574
26
0.500.58
443
97
641
0.580.65
0.660.73
20g.
36
61
2
13
0
0
0
0
0
0
3
______0
4.30-4467230
4.68-5.04
5.05-5 .42
5.43-5.91
0.740.82
__
_
11
0
0
*0
0
0
0
0
0
0
0
0
0 10-100
0 100-1000
0 1000+
Figure 2: Scatter diagram for 15,000+ data set
Color-coded using Shear7 fatigue life predictions
Parameters
Successful VIV prediction depends on identifying the power-in region of the dominant
mode. A power-in region includes those portions of the riser in which the vortex
shedding excites a particular mode at its resonant frequency. For this study, the two
parameters chosen to characterize this region were the length of the power-in region
deemed most likely to drive VIV and the flow speed that excites the dominant mode in
that region. The length is expressed in terms of the non-dimensional length ratio, LR,
which is the percentage of the riser length occupied by the power-in region. The flow
velocity that excites the dominant mode is commonly called the center velocity, Vc.
These parameters are shown in Figure 3 and defined in more detail in section II.
9
L
Power-in Region
Vc
Figure 3: Length ratio and center velocity. Power-in region indicated by the
heavier line
Utility
The scatter diagram is a familiar concept to ocean engineers because it has been used to
present the probability of occurrence of wave height and period combinations, which are
then used in wave force computations. Similarly, center velocity and length ratio can be
used to define a two-parameter scatter diagram. If the current profile measurements are
equally spaced in time, the scatter diagram presents the probability of occurrence of
profiles that cause significant fatigue damage due to VIV. Furthermore, a relative
damage rate ranking of the current profiles can be inferred from the scatter diagram
without doing any further calculations, because profiles with larger center velocity and
length ratio values tend to cause the greatest damage rates, when applied to a riser.
10
11 Theory
Overview of VIV theory and terminology
Strouhal Relationship
Vortex-induced vibration is vibration of a body caused by the shedding of vortices by a
passing fluid flow. When the body is cylindrical, as in the case of a typical oil riser, the
Strouhal number relates the flow velocity and the vortex-shedding frequency, sometimes
called the Strouhal frequency:
=
StV(x)
D
.'.'.'..'.''.'''.''....'.''.'..(1
)
fS (X)
Where x is the location of a measurement point on the riser, V(x) is the local flow
velocity, D is the riser's hydrodynamic diameter, fs(x) is the local shedding frequency,
and St is the Strouhal number, which is a function of the Reynolds number. This
relationship is also shown in Figure 4.
Strouhal Frequency
V
fs
PP_
Figure 4: Strouhal relationship
The Strouhal number is approximately 0.2 for most riser-scale Reynolds numbers.
11
Lock-in
When a riser is in a sheared (non-uniform) flow, V varies continuously along its length,
and so the riser could be excited at an infinite number of frequencies. In random
vibration at a large number of frequencies, the motions due to different modes tend to
cancel each other out. However, risers in vortex-induced vibration often do not vibrate
randomly.
When the vortex shedding frequency coincides with one of the riser's natural
frequencies, the resulting resonant motion may cause the vortex shedding in a section of
the wake to synchronize; the shedding in that region will no longer occur with random
phase. Portions of the riser with similar (but not identical) flow velocities may be
"locked in" to this shedding regime. They will be forced to shed vortices at this
dominant frequency, rather than at the Strouhal frequency that corresponds to their local
flow velocity, and they do so in phase with the rest of the synchronized wake. This
synchronized shedding causes the lift forces to act in concert, encouraging the riser to
vibrate at resonance, which, in turn, keeps the wake locked in to its shedding regime.
The shedding and vibration form a self-exciting system, and the sustained resonant
response can produce a large accumulation of fatigue damage.
This wake synchronization, or "lock-in" may only occur over a region in which the
flow velocity varies slightly about the velocity whose Strouhal frequency corresponds to
the excited natural frequency. This "ideal" velocity shall be called the center velocity,
Vc. The center velocity is shown in Figure 3. The wake synchronization region is
defined as the "power-in region" in this paper, because only in this region is the flow
velocity sufficiently close to the center velocity that the vortex shedding acts as excitation
to the mode.
Lock-in criterion: the reduced velocity bandwidth
A velocity may contribute to the power-in region if its corresponding reduced velocity,
falls within an acceptable tolerance. The reduced velocity can be calculated using
equation 2:
VR,
R(X)V (x)
VR (x = f D
................................ (2)
Here, fv is the vibration frequency, not the shedding frequency. However, in this
analysis, it is assumed that they are the same, and both will be referred to as f. The
greatest response will occur when the shedding and vibration frequencies are identical,
and so this assumption builds conservatism into the scatter diagram method.
12
The allowable tolerance is often expressed in terms of a user-defined reduced velocity
bandwidth, dVR, given by Equations 3 and 4:
dV- AVR
VRcenter
VR~etr.........
St
R,center
(3)
AU
C
..................... (4)
dVR is a double-sided bandwidth, so a value of 0.4 means that a velocity can contribute
to the power-in region if its reduced velocity is within +/- 20% of the center velocity's.
The power-in region does not need to be a continuous segment of the riser length; it can
include several separate regions. The percentage of the riser's length occupied by all
segments of the power-in region is known as the length ratio, LR. It is shown in Figure 3.
The center velocity and length ratio were chosen as the scatter diagram parameters
because they are correlated to the damage rate, as demonstrated in Figure 5. The center
velocity's correlation is particularly strong.
The damage rate's correlation to the damage rate is less strong than the center
velocity's for length ratios less than 0.3, but it is still good. The correlation between
damage rate and length ratio is very weak for length ratios greater 0.3. This is because of
the distribution of damage rate and length ratio in the data set: most of the cases with
long length ratios in this data set had slow center velocities. This can be confirmed by
examining the scatter diagram in Figure 2. There are very few high-velocity cases in the
right-hand side of the scatter diagram, which corresponds to long length ratios. Slow
currents excite lower modes with less curvature in their mode shapes and less frequent
loading cycles, and so it makes sense that these cases should have lower damage rates.
Identifying the power-in region
The center velocity and length ratio parameters allow us to describe a given power-in
region. However, the sifter method requires describing the dominant power-in region of
each current profile. Identifying this is a complicated task; there are several different
selection criteria in use. In this paper, it is assumed that the dominant power-in region
will be the one with that dissipates the most mechanical power (averaged over a full
cycle). The algorithm used for estimating this quantity is presented in section III. Criteria
related to the maximum available lift force and maximum amplitude were also explored.
However, the power criterion showed the best agreement with Shear7's length ratio and
center velocity predictions, and so it was chosen to predict the dominant power-in region.
13
-
I..
I
I I
I
I
-
-~
correlation between damage rate and length ratio
*
U
9
15,000+ data set
slab profile
8
7
6
5
E
4
3
2 -0
1
0
0
0
0.1
0
6
0.7
0.8
0.9
length ratio
correlation between damage rate and center velocity
U
9
*
N
8
15,000+ data set
slab profile
7
6
E
10
5
4
0
*
,ur.
3
0-
ok
-
-
0.0
2-
Vb
*
-.
4
I-
.0.
S0
L
0
6
7
center velocity (ft/sec)
Figure 5: Correlation between sifter parameters and damage rate. 15,000+ real
profiles and artificial slab design profile shown.
14
FOR EACH POINT IN PROFILE:
Calculate
VmAx,
VMIN values for the active
point's Vc
Find all points with velocities between
VmAx and VMIN, inclusive.
(Points in the power-in region)
Add up the incremental lengths associated
with each point in the power-in region.
Calculate the contribution of each point in
the power-in region to the modal force
estimate, and their sum, QNCompute vibration frequency from St , D,
and V,
Find all points in the profile less than VMIN
(low-VR power-out region)
Find the incremental contribution of each
point in the low-VR region to the damping
coefficient, dRNLOW. Sum to find RNLOW
Find all points in the profile > VmAx
(high-VR power-out region)
Find maximum and minimum Vc and
Length Ratio values in the entire data set.
Divide evenly into bin boundaries.
Find the incremental contribution of each
point in the high-VR region to the damping
coefficient, dRNHIGH. Sum to find RNHIGH-
-A
Calculate QN, RN and <Pi> for this center
velocity
FOR EACH BIN:
Find all profiles whose parameter values
fall within this bin. Count them. Record
the count in the corresponding element in
scatter diagram matrix.
OUPUT:
POPULATED SCATTER
DIAGRAM
Figure 6: Sifter algorithm conceptual flowchart
15
III Procedure
A Matlab routine was developed to "sift" the velocity profiles into their respective bins in
the scatter diagram. The general algorithm is described below and shown in the flow
chart in Figure 6. The complete Matlab routines are included in Appendix B. The sifter
algorithm's results were compared to those of the VIV prediction program Shear7 in
order to validate the method.
Algorithm
The sifter attempts to identify the dominant power-in region of each velocity profile.
It is assumed that the mode that dissipates the most mechanical power (averaged over a
full cycle) will dominate. The sifter then finds the center velocity and length ratio for
that power-in region and assigns the profile to a bin. Finally, the total number of profiles
that fall within each bin is counted, populating the scatter diagram. In order to do this,
each profile is subjected to the following procedure.
In each profile, the sifter temporarily treats the velocity at each depth point as if it
were the center velocity that corresponds to the dominant mode. Then it uses the reduced
velocity bandwidth, dVR, specified by the user to find the bounding velocity values of the
power-in region, VMAx and VMIN, given by equations 5 and 6:
=V (1 - dVR)
...........................
(5)
VMa, =VC(1+ dVR)
..........................
(6)
V
i
The sifter then identifies all points in the velocity profile whose velocities are greater
than VMIN and less than VMAx. The length ratio is found by calculating the percentage of
the riser length occupied by these points. It is important that the velocity measurement
points be relatively evenly spaced, because sparsely spaced sections may occupy too
large a portion of the riser, and so may bias the length ratio calculation. To prevent this,
the sifter interpolates the velocity profiles into closely spaced points.
In order to identify the region most likely to excite the dominant mode, the average
dissipated power, <Pi>,must be calculated for each center velocity and associated points
in the power-in region. This is done using equation 7, and requires estimating the
equivalent modal force and modal damping associated with the power in region.
2
< Pi >=
N
(7)
2RN
Where QN is the modal force estimate and RN is the modal damping estimate. These
are given by equations 8 and 9, respectively:
QN
f pCLDV 2 (X)(X)dX ........ (8)
Lin2
16
Where Li, is the power-in region, p is the fluid density, CL is the average lift
coefficient over the power-in region, and # is the local mode shape. The average lift
coefficient, the diameter and the density of water are all assumed to be constant for the
purpose of comparing potential power-in regions, and are moved outside of the integral.
The QN integral is then evaluated numerically by adding up the incremental contributions
from each point in the power-in region. Turning next to the estimation of modal
damping:
J&
RN =
(x)dx+
Rg(x)dA
....
(9)
HighVr
LowVr
LowVR is the portion of the power-out region over which the reduced velocity is lower
than the minimum power-in reduced velocity, and HighVR is the portion of the power-out
region in which the reduced velocity is higher than the maximum power-in reduced
velocity. RLOw and RHIGH are the damping coefficients for the LowVR and HighVR
regions, respectively. They are given by equations 10 and 11, respectively, [2,3]:
RL. =r , + CRLpDU(x)
CRHpU 2(X).
=igh
R
................ (10)
...............
0)
Where CRL and CRH are the low and high reduced velocity damping coefficients, and are
assumed to be 0.18 and 0.2, respectively [2,3]. o is the vibration frequency in radians per
second. Because it is assumed that the vibration and vortex-shedding frequencies are
identical, o is a function of the center velocity, as given in equation 12:
_ 2RStVc
D
Where r,
S
(12)
is the stillwater damping coefficient, and is given by equation 13 [2,3]:
opTD 2
r =K
+0.2 0
..............................
2
2)A2
.(13)
Dlo)
D
Where v is the kinematic viscosity of the fluid.
Because no information about actual riser modes is known, a rigid cylinder mode
shape is assumed for the power dissipation calculations. Therefore # is assumed to be 1.0
17
at all points on the riser. AID is the ratio of the vibration amplitude to the diameter, and
is assumed to be 0.5 in all cases.
The RN integrals are evaluated numerically by adding up the incremental modal
damping contributions of each point in the high and low reduced velocity regions.
Once QN and RN are known for each potential center velocity, the average dissipated
power, <Pi>is calculated, using equation 7.
The velocity producing the largest <Pi> value in each profile is assumed to drive the
dominant power-in region, and is dubbed the center velocity, Vc, for that profile. It is
assumed that if a real riser with many modes were exposed to the same velocity profile,
the dominant VIV mode would correspond to approximately this center velocity.
Once the "winning" power-in region has been identified for each profile, the profiles
are sorted into bins according to their center velocities and length ratios. The bins are
divided into ranges of each parameter. These ranges are divided evenly among a userspecified number of bins, with boundaries ranging between the minimum and maximum
parameter values found in the data set. For each bin, the number of profiles that fall into
that combination of parameter ranges is found, and that number is put into the scatter
diagram.
For each bin the number of occurrences divided by the total number of
velocity profiles is the probability of occurrence of profiles that belong in that bin.
Validation
Procedure
An objective of this paper is to show that a simple sifting algorithm requiring only the
information contained in a current profile is able to identify that portion of the profile
most likely to incur fatigue damage when applied to a real riser of a given diameter. To
test the validity of this assertion, the response of a riser model to a large set of current
profiles was computed using the VIV response prediction program SHEAR7, which was
written at MIT [1]. The SHEAR7 program uses a more complex set of criteria and
algorithms to find the mode with the greatest response to VIV and its corresponding
power-in region. For every profile, SHEAR7 version 4.2d was used to determine the
length ratio, center velocity and damage rate for the dominant mode. In all cases, Shear7
was forced to assume single-mode behavior, and was run using a double-sided reduced
velocity bandwidth of 0.4.
18
Shear7's Vc and LR predictions were compared to the sifter's prediction in order to
establish their validity. SHEAR7 does not directly report center velocity, but it does
report a closely related quantity, the natural frequency of the dominant mode. Knowing
the Strouhal number and the natural frequency, the center velocity corresponding to the
center of the power-in region may be found by rearranging equation 1 as follows:
V= Df .
St
.................. (14)
SHEAR7 does report the length ratio for each power-in region. Also, Shear7's
damage rate predictions were overlaid onto a populated scatter diagram in order to
demonstrate that it truly sifts the most damaging profiles into the lower-right-hand corner
of the diagram.
Riser Model
To run SHEAR7 requires that a real riser model be specified. For the purposes of this
comparison, it was desirable to select a small-diameter riser. Such a riser would have
closely-spaced natural frequencies and, therefore, a large number of modes that could be
excited by the velocities found in typical current data. With a large number of potentially
excited modes, the center velocity found by the sifter would be more likely to correspond
to a natural frequency found by SHEAR7.
A slender pinned-pinned riser model was used to meet these criteria. The riser had an
outer diameter of 13.375 inches and inner diameter of 12.375 inches. It had a length of
3350 feet and a bottom tension of 300,000 lb.-f.
Data Set
This model was subjected to a set of current profiles associated with the Northern Brazil
current rings. Over 15,000 Acoustic Doppler Current Profiles were obtained at one site
over a period of more than one year. The site was near Trinidad. A consortium made up
of Shell, ExxonMobil, and BP funded the measurement program, which is referred to by
the acronym TACOS. The data included the passage of current rings on several
occasions. More information on the rings of the North Brazil Current may be found on
the web site of The Atlantic Oceanographic and Meteorological Laboratory (AOML) at
http://www.aoml.noaa.gov/phod/nbc/index.html.
Each profile consisted of measurements at 41 different depths up to 3350 feet. The
current data were sparsely spaced near the bottom and more regularly spaced in the upper
part of the profile. An acoustic Doppler Current Profiler was used to gather the data in
the upper part of the water column. Moored current meters were used near the bottom.
The profile was interpolated in regions with spatially sparse current measurements, in
order to avoid bias in the sifter's length ratio predictions.
19
III
-~-~-i--r~~----
-
--
IV Results and Analysis
Validation Results
Length Ratio
Figure 7 shows a comparison between the SHEAR7 and sifter length ratio predictions.
Each point corresponds to one of the 15,000+ current profiles. The value of the length
ratio as obtained by the sifter program is plotted against SHEAR7's length ratio
prediction. Perfect agreement would cause all points to fall on a 45-degree line. The
right-hand graph shows only those cases with fatigue lives under 100 years, and are
grouped by symbols, which indicate the order of magnitude of the fatigue life, as
predicted by SHEAR7. From these graphs, it is clear that while there are many cases that
show large scatter, most of these correspond to profiles with very long predicted fatigue
lives. Most of the points with very long fatigue lives correspond to current profiles with
very low maximum velocities, which do not produce significant responses or fatigue
damage, and so are not important in establishing design profiles for VIV.
It is important to note that when the sifter program disagrees with Shear7's length ratio
predictions in high-damage cases, it tends to over-estimate the length ratio compared to
SHEAR7. This indicates that when the sifter program predicts a different power-in
region, its prediction is more conservative than SHEAR7's. The predictions for profiles
whose fatigue lives are short enough to be of concern agree very well.
Length Ratio Comparision
Length Ratio Comparison:
Significant Damage Rate Cases Only
0.9SFull
0.8
--
0.9
Set
deal0.8
0.7C
0 00
00
0.7
00
00~o
.0.
0
0.1
0 ,
,
0.2
0.3
0.2
,
,
0.4
0.5
,
0
,0
0
0.6
0.7
0.8
O
0*0
+ 1-10 yr
~~~0.3
eu o1y
0.2
-
04
0.9
0
0.1
0.2
0.3
ideal
g-
0.4
0.
0.6
0.7
0.8
Sifter
Sifter Prediction
Figure 7: Length ratio prediction comparison. The left graph shows
all cases, while the right shows cases with fatigue lives under 100 years.
20
-
~0.1-
0.3
0.9
-
I.
Frequency
Figure 8 shows a comparison between the dominant response frequency predictions. As
in the length ratio comparison chart, each of the individual points corresponds to one of
the 15,000+ profiles. The right-hand graph shows only cases with fatigue lives greater
than 100 years, grouped by the order of magnitude of the predicted fatigue life according
to SHEAR7. Again, the greatest scatter occurs in those cases with extremely long fatigue
lives.
A bias is apparent; the sifter seems to be consistently choosing higher frequencies than
SHEAR7. This is acceptable because higher frequencies tend to produce higher damage
rates, due to their mode shapes' greater curvature and their more frequent cycles. This
bias ensures that any error in the sifter's prediction makes the prediction more
conservative, which is desirable. Innocuous profiles are more likely to be sorted into a
bin for which we predict higher damage rates, rather than dangerous profiles mistakenly
being classified as harmless. For cases with very short fatigue lives, there is very good
agreement.
Frequency Comparision
1.2
0
N1
Frequency Comparison:
Significant Damage Rate Cases Only
-.
1.21
o 10-100yr
Full Set
* 1-10 yr
1
Ideal
* up to 1 yr
ZCO
I
.
-
-
1.4
--
0,
Ideal
-I
0.8
0
0.8
Mia
U
0.6
-
t. 0.6
0.4
0.4
03ED
C3
Y.2
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Sifter Prediction (Hz)
Q Q
0
0.2
0.4
0.6
0.8
sifter (Hz)
1
1.2
Figure 8: Frequency Prediction comparison. The left graph shows all
cases, while the right shows cases with fatigue lives under 100 years.
21
1.4
Damage rate distribution
As expected, the highest damage rate cases fall in the high velocity, higher length ratio
portions of the scatter diagram, as shown in Figure 2. Sample velocity profiles are shown
from one of the higher damage rate bins in Figure 9. The dominant power-in region of
one profile is indicated by the heavy line, showing that higher damage rates do
correspond to high center velocities. The profiles in this bin are examples of TACOS
profiles that would contribute to high fatigue damage rate predictions. However, the
profiles shown are not the worst profiles to be found in the data set. These profiles are
only examples and should not be assumed to be valid as conservative design profiles for
Northern Brazil current rings.
0.010.090.170.08
0.16
0.24
0.16-0.53 . . ...
0.54-0.91
...
0.92- 1.28
1309
9
1.29- 1.66
1094
102!1.67- 2.03
2.04- 2.41
64
2.42-2.79
3
3
2.80 3.6
4
12
Velocity profile with power-in region
.
0.9r
08L
Profile 1
Profile 2
Profile 2's Power-In Region
0
Profile 3
'
Center
Velocity
(ftlsec)
0r6
Z
0.5
034
Power-in Region Zoom
0.2
0
.
0
0
0
12
3
4
5
Velocity (ft/sec)
.
31.65- 3.921
3.93- 4.29
4.30- 4.67
4.68-5.04
5.06- 5.42
5.43- 6.91
Figure 9: Three profiles that fall within a high damage-rate bin.
These profiles have high center velocities.
Conservatism
As mentioned earlier, the scatter diagram method incorporates conservatism in several
ways. When it disagrees with Shear7, it tends to select higher winning frequencies and
longer length ratios. This implies that the sifter errs in such a way that the profiles are
put into bins that will produce higher damage rates than would be found by running the
profile in a response prediction program. The method also assumes that the riser will
always have a mode that could be excited by the center velocity found by the sifter
program. This may not always be the case, and so, in reality, most profiles would result
in lower fatigue damage. Making this assumption ensures that the profiles are classified
by the worst damage rate they could inflict on a riser of a given diameter.
22
Scatter diagram use in design
It is up to the designer to determine how to incorporate the scatter diagram into the design
process. One method would be to use it to identify potentially dangerous profiles to be
analyzed with a numerical analysis program such as Shear7. Based on the sample data
set, the profiles that would result in the shortest fatigue lives are expected to have high
center velocities and larger length ratios. These bins fall in the lower region of the scatter
diagram (the high-velocity bins), especially those that fall on the right-hand side of that
region (the longer length-ratio bins). Therefore, the designer could analyze these profiles
first, and then move to bins with lower length ratios and center velocities until the
damage rates found by running the profiles in the response prediction programs are
acceptable. In the particular example shown in Figure 2, it would only be necessary to
analyze at one quarter of the data set in order to capture all cases with fatigue lives of less
than 10 years. The remaining profiles contribute a negligible amount to the total fatigue
damage. For larger-diameter risers, which are far more common, the damage rates
predicted for the same current profiles would be lower, due to their lower frequencies,
and so even fewer bins and fewer cases would need to be examined in order to reach an
acceptable damage rate.
V Recommendations
Several avenues remain open for further exploration. The choice of bin sizing, the
pattern of the frequency outliers, and the behavior of the riser in multi-mode situations
would all benefit from further inquiry.
Explore bin sizing
There are many options for bin sizing. For this study, evenly spaced bins were chosen,
with scalable bounds ranging from the lowest parameter value found in the data set to the
highest. This method was chosen purely for simplicity; other schemes may give more
meaningful results.
Absolute vs. scaleable bin boundaries
In this study, scalable bounds were used when creating the scatter plot. However, if this
method is to be used widely, it may be desirable to establish industry- or organizationstandard, absolute bin sizes. This would facilitate communication between different
groups.
Number of bins
In this study, ten length ratio and fifteen center velocity bin divisions were used. This
was selected for simplicity, but in the Matlab routine, the user specifies the number of
bins. This leaves open the question of how many bins are needed to provide the most
meaningful information in the scatter plot.
When fewer bins are used, less resolution is provided, and more profiles will fall within a
particular bin. Similarly, when more bins are used, there is greater resolution, causing
fewer profiles to fall within a given bin. However, the natural frequencies of the riser
place an absolute limit on the meaningfulness of the Vc parameter. A false precision
23
would be produced if center velocities that fall within the double-sided reduced velocity
bandwidth were allowed to straddle more than one Vc bin. Also, including more bins is
more time-consuming; it may require analyzing more profiles. Therefore, it is worth
investigating alternate bin distributions, particularly when the riser's natural frequencies
are known and can be used to specify the resolution of the center velocity bins.
Outlier patterns
In section IV, it was pointed out that for several profiles, Shear7 and the sifter chose
different winning center velocities (corresponding to different modes). This does not
create vulnerability in the method, because the sifter tends to give the more conservative
results. However, because the sifter tends to choose a higher mode than Shear7, it is
clear that this is not a random variation, and the source of the discrepancy should be
explored in greater detail. It would be useful, for example, to find common properties of
velocity profiles that are classified differently by Shear7 and the sifter. Some potential
indicators in each profile include the Reynolds number, maximum profile velocity, center
velocity, slope, length ratio, and competition between potential power-in regions.
Once suitable indicators were determined, a check could be incorporated into the sifter
routine, warning the user when a profile is likely to be classified differently. The
designer could then choose to examine the profile in greater detail by running it through
Shear7, or to simply accept the conservative results given by the sifter.
Multi-mode situations
This study was limited to single-mode response, assuming in each case that only one
mode was excited, or that the response due to the other modes was negligible. It would
be wise to explore the accuracy of this method in cases where there are two are more
competing modes. If it proves insufficient and cannot be adapted to a multi-mode
situation, a method should be developed for identifying profiles that are likely to have a
multi-mode response, and warn the user, so that those cases can be examined more
closely.
24
References
1. Vandiver, J.K., Lee, L., "Shear7 User Guide: 2002", MIT Department of Ocean Engineering,
Cambridge. MA.
2. Venugopal, M.: "Damping and Response of a Flexible Cylinder in a Current", Ph.D. thesis,
Dept. of Ocean Eng., MIT, USA, 1996.
3. Vikestad, K., Larsen, C.M., Vandiver, J.K., "Norwegian Deepwater Riser and Mooring:
Damping of Vortex-Induced Vibrations", Proceedings of the 2000 Offshore Technology
Conference, Paper No. 11998, Houston, TX, May 1-4, 2000.
25
Appendices
Appendix A: User Guide
Installing the sifter files
The sifter algorithm is executed by a series of Matlab functions, stored as m-files. The
following m-files are needed:
*
*
*
*
*
*
*
*
*
*
*
colorcode3.m
idwinouts.m
newidwinner.m
newrunprofiles.m
plotprofiles.m
scatterprep2.m
strcalc.m
trimhigh2.m
trimin.m
trimlow2.m
trimrange6.m
These files are included in Appendix B, and may also be requested in m-file form from
the author by sending email to imdonnelly@mit.edu.
In order for these functions to be accessible to Matlab, their location must be added to
Matlab's list of search paths. In Matlab Release 13, this can be accomplished using the
following command:
>>addpath path
Where path is the path to the directory that contains the sifter's m-files. For example, in
Windows, this may look like:
>>addpath D:\matlab_sv13\toobox\viv
The command may differ for other versions and platforms. For further assistance, see the
Mathworks' web site at:
http://www.mathworks.com/
Preparing input matrices
The sifter algorithm takes as its inputs two scalar values, the riser diameter, D, and the
double-sided reduced velocity bandwidth, dVr, and one matrix containing the current
profile data, profilesall. The riser diameter should be given in inches.
26
The first column of the current profile matrix should contain the non-dimensional
location (x/L) of the current measurements. Its values should vary from zero (the bottom
of the riser) to 1 (the top of the riser). Each subsequent column should contain a current
profile, giving the velocity in ft/second at each measurement point. So a matrix
representing 100 profiles measured at 40 locations would contain 40 rows and 101
columns. An example for three profiles is shown below:
x/L
0
0.25
0.5
0.75
1
Profile 1
Profile 2
Profile 3
(ft/sec)
(ft/sec)
(ft/sec)
0
0.25
0.75
1
1
0
0.3
1
1.75
1.5
0
0.1
0.5
0.75
1.5
(This table contains dummy data created to show the form of the input matrix. It does not
correspond to any real profiles.)
The optional fatigue-life color-coding function, colorcode3.m, requires a two-column
input matrix. The first column should contain the profile number, and the second should
contain that profile's damage rate (expressed in failures per year), as predicted by Shear7
or another VIV prediction program. An example for three profiles is shown below:
Profile
Damage Rate
(failures/yr.)
1
2
3
1.5e-05
9.0e-01
1.5e+00
(This table contains dummy data created to show the form of the input matrix. It does not
correspond to any real values.)
27
Running the program
Producing a populated scatter diagram requires entering two of the sifter algorithm's
Matlab commands, newrunprofiles, and scatterprep2. If a damage rate prediction is
available for each profile, an optional color-coded fatigue life overlay may be applied
using the function colorcode3.
>> done = newrunprofiles(profilesall, D, dVr)
>> [ScatMat, VcBounds, LrBounds, wheresit, check] = scatterprep2(numVcBins, numLrBins)
>> [colors, rangedivs]= colorcode3(wheresit, damage, numrows, numcols)
STEP 1 - IDENTIFY THE POWER-IN REGION:
>> done = newrunprofiles(profilesall, D, dVr)
Which identifies the dominant power-in region in each current profile given in the matrix
profilesall, given a riser diameter, D, and double-sided reduced velocity bandwidth, dVr.
The following data for each profile is appended to a tab-delimited text file called
winnersinfo.txt:
*
*
The profile number
The first location (given non-dimensionally as x/L) at which the center velocity is
found
The center velocity in ft/sec
The length ratio of the dominant power-in region
The <Pi> value
The Strouhal frequency (given in Hz) associated with the center velocity.
*
*
*
*
Sample contents of winnersinfo.txt for a three-profile case are found below:
Profile
Location
Vc
LR
<Pi>
fs
1
2
3
0.922145
0.872564
0.95
1.532
1.957
1.625
0.2
0.18
0.09
0.023673
0.065874
0.015478
1.5
2.3
1.7
(This table contains dummy data created to show the form of the winnersinfo.txt file. It
does not correspond to any real results.)
The variable done will be assigned the value 1 if the sifter worked properly.
28
STEP 2 - POPULATE THE SCATTER DIAGRAM:
>> [ScatMat, VcBounds, LrBounds, wheresit, check] = scatterprep2(numVcBins, numLrBins)
This command requires the user to input the number of center velocity bins, numVcBins,
and the number of length ratio bins, numLrBins.
The scatter diagram bin values are given in the matrix ScatMat, and also output to the
tab-delimited text file scatterinfo.txt. The contents of ScatMat for a scatter diagram with
three rows and two columns would look like:
1
1
1
1
2
3
(This table contains dummy data created to show the form of the scatterinfo.txt file. It
does not correspond to any real results.)
The boundary values of the center velocity and length ratio bins are given in the vectors
VcBounds and LrBounds, respectively. This data is also output to the tab-delimited text
files VcBounds.txt and LrBounds.txt, respectively.
The wheresit matrix contains the bin locations of each profile. Its first column is a vector
containing the numbers of the profiles that were sifted into that bin. The vector is padded
with zeros to ensure that each vector is of the same length. The contents of each bin in
the first row are given, followed by the contents of each bin in the second row, and so on.
The wheresit matrix produced for the same scatter diagram with three rows and two
columns would be made up of the following columns:
Bin
1,1
Bin
1,2
Bin
2,1
Bin
2,2
29
Bin
3,1
Bin
3,2
And it could look like:
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
7
8
9
0
0
0
0
0
0
(This table contains dummy data created to show the form of the wheresit matrix. It does
not correspond to any real results.)
So Bin 1,1 would contain profile #3, and Bin 3,2 would contain profiles #7, 8 and 9.
This data is also output to a tab-delimited text file, wheresit.txt.
Check is a scalar variable. Its value should equal the number of current profiles, if the
sifting was performed successfully.
STEP 3- ADDING OPTIONAL COLOR-CODED FATIGUE LIFE OVERLAY
Adding a color-coded fatigue life overlay requires the use of the following command:
>> [colors, rangedivs]= colorcode3(wheresit, damage, numrows, numcols)
Where wheresit is the matrix output by scatterprep2,damage is the damage rate matrix,
and numrows and numcols are the number of rows and columns in the scatter diagram,
respectively.
The outputs of colorcode3 are the colors matrix (also output as a tab-delimited text file,
colorcodes.txt), and the rangedivs vector. Rangedivs gives the boundary values for each
color code. Colorcode3 is set to give the following 5 ranges:
Fatigue Life Range
Less than 1 yr.
1-10 yrs
10-100 yrs
100-1000 yrs
More than 1000 yrs
Color Code
1
2
3
4
5
(The number of ranges and their boundary values can be changed by editing the file
colorcode3.m.)
30
Corresponding to rangedivs values of:
0
1
10
100
1000
10A256
10A256 is chosen as an upper bound, rather than infinity for practical programming
purposes.
Colors is a matrix of the same dimensions as ScatMat, and contains the color code
assigned to each bin. The contents of Colors for a scatter diagram with three rows and
two columns would look like:
1
3
2
4
3
5
(This table contains dummy data created to show the form of the colorcodes.txt file. It
does not correspond to any real results.)
31
Appendix B: Source Code
Newrunprofiles
function [done] = newrunprofiles(profilesall, D, dVr)
%NEWRUNPROFILES takes a user-inputed velocity matrix, and runs each profile
%through idwinner.
% inputs are:
% user-inputed velocity matrix, profilesall,
% with 1st column x/L of each node, and one column for each profile velocity.
% Profiles must have top line (probability info for S7) removed when
% input into matlab.
% D should be the diameter in inches.
% dVr is the double-sided reduced
% velocity bandwidth
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 11/18/02
% set "did I work?" value
done=0;
% set density and kinematic viscosity for seawater at 50 degrees
rho= 1.9924;
%lbsecA2/ftA4
nu=1.4572* 10A(-5);
% set index vector
Index = profilesall(:,1);
ProfileNum = 1;
for n=2:(size(profilesall, 2))
P(:, 1)=Index;
P(:,2)=profilesall(:,n);
%find winner, selecting for dissipated power
newidwinner(P, ProfileNum, D, dVr, rho, nu);
ProfileNum = ProfileNum + 1;
end
done=1;
32
Newidwinner
function [Voutmat, WinnerInfo, Powerin] = newidwinner(Vall, ProfileNum, D, dVr, rho, nu)
%NEWIDWINNER identifies the center velocity candidate with
% the greatest <Pi> value (dissipated power)
% It estimates the length ratio of this region and its center velocity
% Plots full velocity profile in *s, highlighting the power-in region in red
% Also estimates the vortex-shedding frequency that corresponds to Vcwinner,
% so that it can be compared to the output of Shear7
% D should be in inches
% Includes the option to interpolate linearly, so that regions where
% data-collection is sparse don't falsely dominate
% outputs WinnerInfo to tab-delimited file 'winnersinfo.txt'
% Vall should be a matrix with 1st column = position along riser
% and 2nd column = velocity profile
% Motivation: to estimate the power-in region of a riser experiencing
% vortex-induced vibration.
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 11/18/02
% updated 11/25/02
% Set plotting mode flag
plotflag = 0;
% 0=plot nothing
% 1=plot profile with power-in region highlighted,
% 2=plot profile w/ power-in region, without asking for profile name
% Set interpolation flag
intflag = 1;
% 0=no interpolation 1=linear interpolation
interpinterv = 0.05;
% set interval for interpolation in terms of x/L
% Interpolate profile
if intflag==l
Dpth=Vall(:, 1);
Vlcty=Vall(:,2);
% Create fake velocity profile that won't need interpolation
FalseVlcty=ones(length(Vlcty), 1);
% Interpolate Depth using fake velocity profile
[DpthInterp, Vinterp] = interpm(Dpth, FalseVIcty, interpinterv);
% Interpolate for Velocity corresponding to interpolated depth
Vlctylnt=interp 1 (Dpth,Vlcty,Dpthlnterp);
Vprofile = VlctyInt;
indx = DpthInterp;
33
else
Vprofile = Vall(:,2);
indx = Vall(:,1);
end
Vnew(:, 1)=indx;
Vnew(:,2)=Vprofile;
% Create a new matrix by tacking the the velocity vector to the index vector.
Voutmat(:,1) = indx;
% col. 1= position along riser
Voutmat(:,2) = Vprofile;
% col. 2= velocities
% Find power-in region, Qn, Rnh & Rnl
[Lin, Qn, Rnh, Rnl] = trimrange6(Vnew, D, dVr, rho, nu);
% find total Rn
Rn=Rnl+Rnh;
% if Rn=O, then Vc must be zero, and so this profile can't be the winner.
%(since Vc=O means no excitation).
% BUT, if Rn=O, then QnA2/2Rn gives div by zero error.
%To keep the algorithm for selecting these cases,
% let's make Rn incredibly large.
for n=1:length(Rn)
if Rn(n)==O
Rn(n)= 10A256;
end
end
% Find <pi>
PiDisp = (Qn.^2)./(2.*Rn);
Voutmat(:,3) = Lin';
Voutmat(:,4) = PiDisp';
% col. 3= length ratio
% col. 4= dissipated power
% Find the greatest dissipated power (the "winner")
[PiWinner, indxWinner] = max(abs(PiDisp));
LocationWinner = Voutmat(indxWinner, 1);
VcWinner = Voutmat(indxWinner, 2);
LratioWinner = Voutmat(indxWinner, 3);
% Plot the full profile, highlighting the power-in region
if ((plotflag==1)I(plotflag==2))
34
[done] = plotprofiles(Vall, VcWinner, dVr, Vprofile, Vnew, Powerin, plotflag);
end
% Calculate the strouhal number and frequency associated with each profile's VcWinner
Str = strcalc(VcWinner, D, nu);
ODft=D/12;
WinFreq = Str.*VcWinner/ODft;
WinnerInfo = [ProfileNum, LocationWinner, VcWinner, LratioWinner, PiWinner, WinFreq];
% Output WinnerInfo to file
filename = 'winnersinfo.txt';
filename = idwinouts(Winnerlnfo,filename);
Trimrange6
function [Lin, Qn, Rnh, Rnl] = trimrange6(V, D, dVr, rho, nu)
%TRIMRANGE6 trims a velocity matrix V = [position, velocity] to only those vectors
% within +/- dVr of Vci (each point along the vector).
% Calculates length ratio within the trimmed region, and the Qn, Rnh & Rnl values
% associated with each Vci.
% No reordering of the velocity vector is necessary.
% Motivation: to estimate the power-in region of a riser experiencing
% vortex-induced vibration.
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 11/18/2002
% Split position and velocity from the V matrix
position = V(:,I);
velocity = V(:,2);
% Establish boundary values (vector values- same length as Viordered)
Vmin = velocity.*(1-(dVr/2));
Vmax = velocity.*(1+(dVr/2));
% Calculate Qn and dLength for power-in region
[Lin, Qn] = trimin(velocity, position, Vmin, Vmax, D, dVr, rho);
% Get strouhal number for each potential center velocity
35
Str = strcalc(velocity, D, nu);
% Find the length and Rnl of the low-Vr region
[lowregion, Rnl] = trimlow2(velocity, position, Vmin, D, dVr, rho, nu, Str);
% Find the length and Rnh of the high-Vr region
[highregion, Rnh] = trimhigh2(velocity, position, Vmax, D, dVr, rho, nu, Str);
Trimin
function [Lin, Qn] = trimin(velocity, position, Vmin, Vmax, D, dVr, rho)
%TRIMIN finds the length and location of the portion of the power-in region.
%It also calculates Qn for this region
% Motivation: to estimate the power-in region of a riser experiencing
% vortex-induced vibration.
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 11/18/02
ODft=D/12;
% Select all values >= Vmin and <= Vmax and calculate the length ratio
for i= 1:length(velocity)
% Find the points in the profile withing +/- dVr/2 of Vci
[index, onesies]=find((velocity>=Vmin(i))&(velocity<=Vmax(i)));
% Starting the j loop (within the INDEX vector)
%runningtotal(i) = 0;
dX(1)=0;
% Find the length before the first point in the INDEX vector, if it isn't the
% first point in the velocity profile
if (index(1) -= 1)
dX(1) = (position(index(1))-position(index(1)-i))/2;
end
for j=2:length(index)
dX(j)=0;
% check for continuity between current point and previous point
if (index(j-1)==(index(j)-1))
% Add the length between the current point and the previous point
dX(j) = dX(j) + (position(index(j))-position(index(j-1)));
% if not continuous
else
36
% Add half length after previous point
dX(j) = dX(j) + (position(index(j-1)) - position(index(j-1)+1))/2;
% Add half length before current point
dX(j) = dX(j) + (position(index(j)) - position(index(j)-1))/2;
% end if statement
end
% end j loop (j = location in index loop)
end
-
% Add length after last point in the INDEX vector, if it isn't the last point
% in the velocity vector
if (index(length(index)) ~= length(position))
dX(length(index)) = dX(length(index)) + (position(index(length(index))+1)
position(index(length(index))))/2;
end
%Note the power-in length for each i (location in velocity profile)
Lin(i)=sum(dX);
% calculate dQn for each pt. in power-in region
for k =1:length(index)
dQn(k)=O.5*rho*ODft*velocity(index(k)).^2*dX(k);
end
Qn(i)=sum(dQn);
% end i loop (i = location in velocity profile)
end
Trimlow2
function [lowregion, Rnl] = trimlow2(velocity, position, Vmin, D, dVr, rho, nu, Str)
%TRIMLOW2 finds the length and location of the portion of the power-out region
% in which the reduced velocity is lower than in the power-in region. It also
% calculates Rn for this region (Rnl)
% Motivation: to estimate the power-in region of a riser experiencing
% vortex-induced vibration.
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 11/18/02
ODft=D/12;
w=2*pi*Str.*velocity./ODft;
%velocity(i) = present Vc candidate
% Calculate w, Rcm
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Rcm=w*ODftA2/nu;
% Select all values less than Vmin and calculate the length ratio
for i= 1: length(velocity)
% Find the points in the profile less than -dVr/2 of Vci
[index, onesies]=find(velocity<Vmin(i));
if isempty(index)
Rnl(i)=O;
dLength(i)=O;
else
% Starting the j loop (within the INDEX vector)
%runningtotal(i) = 0;
dX(1)=O;
% Find the length before the first point in the INDEX vector, if it isn't the
% first point in the velocity profile
if (index(1) ~ 1)
dX(1) = (position(index(1))-position(index(1)-i))/2;
end
for j=2:length(index)
dX(j)=0;
% check for continuity between current point and previous point
if (index(j-1)==(index(j)-1))
% Add the length between the current point and the previous point
dX(j) = dX(j) + (position(index(j))-position(index(j-1)));
% if not continuous
else
% Add half length after previous point
dX(j) = dX(j) + (position(index(j-1)) - position(index(j-1)+1))/2;
% Add half length before current point
dX(j) = dX(j) + (position(index(j)) - position(index(j)-1))/2;
end % end if statement
end
% end j loop (j = location in index loop)
-
% Add length after last point in the INDEX vector, if it isn't the last point
% in the velocity vector
if (index(length(index)) -= length(position))
dX(length(index)) = dX(length(index)) + (position(index(length(index))+1)
position(index(length(index))))/2;
end
% end if statement
%Note the length of the region for each i (location in velocity profile)
dLength(i)=sum(dX);
if w(i)==0
Rn(i)=0;
38
else
% calculate dRnl for each pt. in low-Vr region
for k = 1:length(index)
dRnl(k)= (0.18*rho*ODft*velocity(index(k)) + 0.5*rho*pi*ODftA2*(2*sqrt(2)/sqrt(Rcm(i)) + 0.1)).*dX(k);
end
Rnl(i)=sum(dRnl);
end %end if w(i) statement
end
%end if isempty(index) statement
% end i loop (i = location in velocity profile)
end
lowregion = (abs(dLength))';
%changed here
Trimhigh2
function [highregion, Rnh] = trimhigh2(velocity, position, Vmax, D, dVr, rho, nu, Str)
%TRIMHIGH2 finds the length and location of the portion of the power-out region
% in which the reduced velocity is higher than in the power-in region. It also
% calculates Rn for this region (Rnh)
% Motivation: to estimate the power-in region of a riser experiencing
% vortex-induced vibration.
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 11/18/02
ODft=D/12;
w=2*pi*Str.*velocity./ODft;
%velocity(i) = present Vc candidate
% Select all values greater than Vmax and calculate the length ratio
for i= 1:length(velocity)
% Find the points in the profile withing +/- dVr/2 of Vci
[index, onesies]=find(velocity>Vmax(i));
if isempty(index)
Rnh(i)=0;
dLength(i)=0;
else
% Starting the j loop (within the INDEX vector)
%runningtotal(i) = 0;
39
dX(1)=0;
% Find the length before the first point in the INDEX vector, if it isn't the
% first point in the velocity profile
if (index(1) ~ 1)
dX(1) = (position(index(1))-position(index(1)-i))/2;
end
for j=2:length(index)
dX(j)=0;
% check for continuity between current point and previous point
if (index(j-1)==(index(j)-1))
% Add the length between the current point and the previous point
dX(j) = dX(j) + (position(index(j))-position(index(j- 1)));
% if not continuous
else
% Add half length after previous point
dX(j) = dX(j) + (position(index(j-1)) - position(index(j-1)+1))/2;
% Add half length before current point
dX(j) = dX(j) + (position(index(j)) - position(index(j)-1))/2;
end % end if statement
end
% end j loop (j = location in index loop)
% Add length after last point in the INDEX vector, if it isn't the last point
% in the velocity vector
if (index(length(index)) -= length(position))
dX(length(index)) = dX(length(index)) + (position(index(length(index))+1)
- position(index(length(index))))/2;
end
% end if statement
%Note the length of the region for each i (location in velocity profile)
dLength(i)=sum(dX);
if w(i)==0
Rnh(i)=0;
else
% calculate dRnl for each pt. in high-vr region
for k =1:length(index)
dRnh(k)= (0.2 *rho*(velocity(index(k)))A2/w(i)).*dX(k);
end
Rnh(i)=sum(dRnh);
end % end if w(i) statement
end
%end if isempty(index) statement
% end i loop (i = location in velocity profile)
end
highregion = (abs(dLength))';
%changed here
40
Plotprofiles
function [done] = plotprofiles(Vall, VcWinner, dVr, Vprofile, Vnew, Powerin, plotflag)
%PLOTPROFILES plots velocity profiles with their power-in regions
% highlighted.
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 11/18/02
% plot full profile
plot (Vall(:,2),Vall(:,1),'k')
% if linearly interp., will be same as plotting Vnew
hold on
plot (Vnew(:,2),Vnew(:,1),'k*')
% find points on power-in region (again)
% Find the points in the profile withing +/- dVr/2 of VcWinner
Vcmin = VcWinner*(1-dVr/2);
Vcmax = VcWinner*(1+dVr/2);
[index, onesies]=find((Vprofile>=Vcmin)&(Vprofile<=Vcmax));
% Plot points of power-in region on profile plot
Powerin=[Vnew(index, 1) Vnew(index,2)];
plot (Powerin(:,2),Powerin(:,1),'r*')
% add title and labels
if plotflag==1
% prompt user for profile name
profilename = input('What is the name of this velocity profile? \n(Please put it in ...
single quotes)\n');
titlewords = strcat(Velocity profile :', profilename,' with power-in region');
title(titlewords);
else
title('Velocity profile with power-in region');
end
xlabel('Velocity (ft/sec)')
ylabel('Relative position along riser')
Strcalc
function [St] = strcalc(Vcs, D, nu)
%STRCALC estimates the Strouhal numbers that correspond to
% Vcs, using the Str vs. Re table that corresponds to Shear7 Str code
% 200.
% Vcwinner must be entered in ft/sec
% D should be entered in inches
41
% Motivation: to estimate the power-in region of a riser experiencing
% vortex-induced vibration.
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 10/29/02
% set outer diameter of the cylinder
ODin=D;
% Change this line
ODft=D/12;
% Str curve 200 from S7- corresponds to rough cylinder
Curve200=[0 0.17; 20000 0.17; 30000 0.18; 40000 0.19; 50000 0.2;...
60000 0.21; 70000 0.22; 80000 0.23; 90000 0.24; 100000 0.24;...
110000 0.24; 120000 0.24; 130000 0.24; 140000 0.24;...
150000 0.24; 160000 0.24; 170000 0.24; 180000 0.24;...
190000 0.24; 200000 0.24; 210000 0.24; 220000 0.24;...
230000 0.24; 240000 0.24; 300000 0.24; 400000 0.24;...
500000 0.24; 600000 0.24; 800000 0.24; 1000000 0.24;...
2000000 0.24; 3000000 0.24; 4000000 0.24];
% Find Re for each Vc
Re=(Vcs*ODft)./nu;
% Find strouhal number for each Vcwinner by interpolation
St=interp1(Curve200(:, 1), Curve200(:,2), Re);
Idwinouts
function [FileName] = idwinouts(WinnerInfo, FileName)
%IDWINOUTS appends the contents of the WinnerInfo to a text file,
% resulting in a tab-delimited file. This can then be exported to
% Excel, making it easy to compare the results of idwinner to Shear7
% Motivation: to estimate the power-in region of a riser experiencing
% vortex-induced vibration.
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 4/6/2002
FID=fopen(FileName,'a');
% opens file in "append" mode
fprintf(FID,'%f\t',WinnerInfo);
fprintf(FID,'\n');
% saves contents of WinnerInfo with
% tabs between entries
% adds carriage return
fclose(FID);
% releases file
42
Scatterprep2
function [ScatMat, VcBounds, LrBounds, wheresit, check] = scatterprep2(numVcBins,
numLrBins)
%SCATTERPREP2 loads the output file from idwinner8noplot, and counts the
% number of profiles (rows) that fit into numVcBins bins in center
% velocity and numLrBins in length ratio.
% Outputs the probability matrix (in # of profiles), the matrix of Vc bin
% boundaries, and the matrix of Lratio bin boundaries.
% Also outputs a matrix with the indices of the profiles included in each bin
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% Undergraduate, class of 2002
% 4/20/2002
% load the winnersinfo matrix from the output file
load winnersinfo.txt;
% trim it to just the profile number, Vc, and Lratio
CountMat(:,1) = winnersinfo(:,1);
% profile number
% Vc winner
CountMat(:,2) = winnersinfo(:,3);
CountMat(:,3) = winnersinfo(:,4);
% Length Ratio
numprofiles = length(winnersinfo(:,3));
% Establish upper & lower bounds
VcMax=max(winnersinfo(:,3));
VcMin=min(winnersinfo(:,3));
LrMax = max(winnersinfo(:,4));
LrMin=min(winnersinfo(:,4));
% Establish bin intervals
VcInt = (VcMax-VcMin)/numprofiles;
LrInt = (LrMax-LrMin)/numprofiles;
% Make bin boundary matrices
VcBounds = linspace(VcMin, VcMax,(numVcBins+1))';
LrBounds = linspace(LrMin, LrMax,(numLrBins+ 1))';
% Create empty ScatMat matrix
ScatMat = zeros(numVcBins, numLrBins);
% Start search loop
43
% set ColCount, the variable that keeps track of which column we're in
% in the wheresit matrix, which tells us which bin we're refering to
ColCount = 1;
% initialize the wheresit matrix
wheresit = zeros(numprofiles, (numVcBins*numLrBins));
% i loop - one i is one Vc row
i= 1;
% set the (1,1) bin
number = find( (CountMat(:,2)>=VcBounds(1))&(CountMat(:,2)<=VcBounds(2))
(CountMat(:,3)>=LrBounds(1))&(CountMat(:,3)<=LrBounds(2)));
&
j=1;
if (isempty(number))
padded=zeros(numprofiles, 1);
else
padded = wextend('c', 'zpd', number, (numprofiles-length(number)), '');
end
wheresit(:,ColCount) = padded;
% set the rest of the (1,j) row - each j refers to an Lratio column
for j=2:(numLrBins)
ColCount = ColCount+ 1;
number = find( (CountMat(:,2)>=VcBounds(1))&(CountMat(:,2)<=VcBounds(2))
(CountMat(:,3)>LrBounds(j))&(CountMat(:,3)<=LrBounds(j+ 1)));
&
ScatMat(1,1)= ScatMat(1,1) + length(number);
if (isempty(number))
padded=zeros(numprofiles, 1);
else
padded = wextend(c', 'zpd', number, (numprofiles-length(number)), '');
end
wheresit(:,ColCount) = padded;
ScatMat(1,j)= ScatMat(1,j) + length(number);
end
% set the rest of the rows
for i=2:(numVcBins)
j=1;
&
ColCount = ColCount+ 1;
number = find( (CountMat(:,2)>VcBounds(i))&(CountMat(:,2)<=VcBounds(i+ 1))
(CountMat(:,3)>=LrBounds(j))&(CountMat(:,3)<=LrBounds(j+ 1)));
if (isempty(number))
padded=zeros(numprofiles, 1);
44
else
padded = wextend(c', 'zpd', number, (numprofiles-length(number)), 'r');
end
wheresit(:,ColCount) = padded;
for j=2:(numLrBins)
ColCount = ColCount+1;
number = find( (CountMat(:,2)>VcBounds(i))&(CountMat(:,2)<=VcBounds(i+1))
(CountMat(:,3)>LrBounds(j))&(CountMat(:,3)<=LrBounds(j+1)));
if (isempty(number))
padded=zeros(numprofiles, 1);
else
padded = wextend('c', 'zpd', number, (numprofiles-length(number)), 'r');
end
wheresit(:,ColCount) = padded;
ScatMat(i,j)= ScatMat(ij) + length(number);
end
end
check = sum(sum(ScatMat));
% Output ScatMat to file
FID=fopen('scatterinfo.txt','a');
% opens file in "append" mode
for counter = 1:size(ScatMat,1)
fprintf(FID,'%f\t',ScatMat(counter,:));
fprintf(FID,'\n');
end
fclose(FID);
% saves contents of ScatMat with
% tabs between entries
% adds carriage return
% releases file
% Output whereis to file
FID=fopen('wheresit.txt','a');
% opens file in "append" mode
for counter2 = 1:size(wheresit,1)
fprintf(FID,'%f\t',wheresit(counter2,:));
fprintf(FID,'\n');
end
% saves contents of wheresit with
% tabs between entries
% adds carriage return
45
&
ScatMat(i,j)= ScatMat(ij) + length(number);
% releases file
fclose(FID);
% Output VcBounds to file
FID=fopen('VcBounds.txt','a');
% opens file in "append" mode
for counter3 = 1:length(VcBounds)
fprintf(FID,'%f\t',VcBounds(counter3,:));
fprintf(FID,'\n');
end
fclose(FID);
% saves contents of VcBounds with
% tabs between entries
% adds carriage return
% releases file
% Output LrBounds to file
FID=fopen('LrBounds.txt','a');
% opens file in "append" mode
for counter4 = 1:length(LrBounds)
fprintf(FID,'%f\t',LrBounds(counter4,:));
% saves contents of LrBounds with
% tabs between entries
% adds carriage return
fprintf(FID,'\n');
end
% releases file
fclose(FID);
Colorcode3
function [colors, rangedivs] = colorcode3(wheresit, damage, numrows, numcols)
%COLORCODE3 takes the wheresit matrix (one column for each bin, containing
% the index numbers of the profiles that fall within that bin), and a two% column matrix containing the profile index (1st column) and the damage rate
% associated with that profile found by shear7. It calculates the average and
% maximum damage rates belonging to each bin, and then sorts each bin into a
% particular damage range, assigning it a color code number according to its
% damage rate.
% A damage flag is set, allowing the user to choose whether to color code by the
% average damage rate value or the maximum damage rate value. In the interests
% of conservatism, this value is pre-set ot use the maximum value.
% An output flag is set, allowing the user to specify whether to output the
% color codes for "colors" as a matrix, or to also output it to a file. It is set
% to output the color codes to a file by default.
% The bins are calculated: creating 5 bins between the max and min damage rates.
46
% Look into absolute bin boundaries for the future (standardization).
% The outputs are a numrows by numcols matrix, containing the color code for each bin,
% (i.e., formatted to be the same shape as the scatterplot matrix and a horizontal vector,
% rangedivs, containing the boundaries of each damage rate range.
% Jessica Mary Donnelly
% MIT Department of Ocean Engineering
% 4/29/2002
% Flag average damage rate vs. max damage rate for color coding
damageflag=2; % 1=use average value 2=use maximum value
% Flag the ouput type
outputflag=3; % 1=output color codes only 2=not used in this version
% 3=output color codes only, to file
% Set number of color codes. I use 5.
numcodes = 5;
% Start the damage rate-finding procedure
% initialize dmgvals matrix
dmgvals = zeros((size(wheresit, 1)),2);
% Start j loop (j= each bin)
for j=1:(size(wheresit,2)) % changed from 1
% strip out column w/ indices of profiles in bin
tempcolumn=wheresit(:,j);
tempdmg=zeros(length(tempcolumn), 1); %make empty column to hold damage values
% Start i loop (i= each element in vector)
for i=1:(length(tempcolumn))
if tempcolumn(i)-=0
tempdmg(i)=damage(tempcolumn(i),2);
else
tempdmg(i)=0;
end % end if loop
% end i loop
end
tempdmg;
% put bin's mean & max damage rate in dmgvals matrix
dmgvals(j,1) = mean(tempdmg);
dmgvals(j,2) = max(tempdmg);
end
% endj loop
% Calculate the damage range dividers
47
% Establish bounding method
% bounding = 1; % sets even bins in damage rate
bounding =0; % uses order of magnitude in fatigue life
if bounding ==1
% Establish upper & lower bounds
dmgMax=max(dmgvals(:,damageflag));
dmgMin=min(dmgvals(:,damageflag));
% Make bin boundary matrices
rangedivs = linspace(dmgMin, dmgMax,(numcodes+1))';
elseif bounding ==0
dmgvals = 1 ./dmgvals;
% coverts damage rate to fatigue life
rangedivs = [0 1 10 100 1000 10A256]';
%assumes 5 bins
end
% start color-coding process
% start k loop (k= each bin in damage matrix)
%for k= 1: (size(dmgvals, 1))
for k=1:(numrows*numcols)
if ( (dmgvals(k,damageflag)>= rangedivs(1)) & (dmgvals(k,damageflag) < rangedivs(2)))
colors(k)= 1;
elseif ( (dmgvals(k,damageflag)>= rangedivs(2)) & (dmgvals(k,damageflag) < rangedivs(3)))
colors(k)=2;
elseif ( (dmgvals(k,damageflag)>= rangedivs(3)) & (dmgvals(k,damageflag) < rangedivs(4)))
colors(k)=3;
elseif ( (dmgvals(k,damageflag)>= rangedivs(4)) & (dmgvals(k,damageflag) < rangedivs(5)))
colors(k)=4;
elseif ( (dmgvals(k,damageflag)>= rangedivs(5)) & (dmgvals(k,damageflag) <= rangedivs(6)))
colors(k)=5;
else
colors(k)=0;
end
% endif loop
end
% end k loop
colors %debug
% reformat colors to numrows by numcols matrix
colors = reshape(colors,numcols,numrows)';
% output color codes to file, if desired
if (outputflag==3)
48
size(colors, 1)
FID=fopen('colorcodesformatted.txt','a');
% opens file in "append" mode
for counter = 1: size(colors, 1)
fprintf(FID,'%f\t',colors(counter,:)); % saves contents of wheresit with
% tabs between entries
fprintf(FID,'\n');
end
% end for loop
% adds carriage return
fclose(FID);
% releases file
end
% end if loop
49