Userguide Shear7v46 for Website

User Guide for SHEAR7

Version 4.6 For Vortex-Induced Vibration Response Prediction of

Beams or Cables with Slowly Varying Tension in Sheared or Uniform Flow

Copyright by the Massachusetts Institute of Technology

February, 2011

Prof. J. Kim Vandiver, Christopher J. Wajnikonis P.E., Themistocles Resvanis and Dr. Hayden Marcollo

With contributions from:

Dr. Li Lee, Dr. Steve J. Leverette, Tae-Young Chung, J. P. Vogiatzis,

Madan Venugopal, Dick Turpin and Chenyang Fei

Distribution of this program is restricted.

Inquiries should be directed to:

Prof. J. Kim Vandiver M.I.T. Room 5-222

Cambridge, Massachusetts 02139 Telephone: +1 617 253 4366

Email: [email protected]

Licenses for commercial use may be obtained

through:

AMOG Consulting Inc. 770 South Post Oak Lane, Suite 505

Houston, TX 77056. USA. Tel: +1 713 255 0020

Email: [email protected]

SHEAR7 V4.6 USERGUIDE

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TABLE OF CONTENTS

1.0 SUMMARY OF NEW FEATURES OF VERSION 4.6 2.0 NEW FEATURES OF VERSION 4.5 AND VERSION 4.6 3.0 PROGRAM GENERAL DESCRIPTION 4.0 PROGRAM OPERATION AND EXECUTION 5.0 COMPUTATIONAL FLOW OF THE PROGRAM 6.0 SPECIFICATION OF OUTPUT FILES 7.0 SPECIFICATION OF INPUT DATA 8.0 INTERPRETATION OF SHEAR7 OUTPUT DATA 9.0 REFERENCES 10. 0 SAMPLE *.DAT FILES AND PLOTTING PROGRAMS 11.0 TROUBLESHOOTING V4.6 12.0 FILE MANAGEMENT AND *.DAT FILE CONVERSION PROGRAMS 13.0 APPENDICES

1: UNDERSTANDING LIFT COEFFICIENTS IN VERSIONS 4.3 THROUGH 4.6.

2: SECTIONAL DAMPING MODEL IN SHEAR7 3: FATIGUE DAMAGE AND RMS VALUES CALCULATION IN V4.5 AND

V4.6 4: MODELING STEEL CATENARY RISERS. 5: EXAMPLE USE OF THE AMPLITUDE CUTOFF 6: DAMAGE RATE PREDICTION WITH PARTIAL STRAKE COVERAGE


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1. SUMMARY OF NEW FEATURES OF VERSION 4.6 SHEAR7 version 4.6 introduces enhancements to version 4.5, while utilizing the same time sharing concept. In particular, V4.6 allows a vastly improved modeling of strakes, both partial and close to full coverage. The program enhancements include:

• Introduction of structural zone dependent reduced velocity bandwidth enabling vastly improved partial strake modelling;

• Adding the option to model hydrodynamic forces on strakes in terms of sectional damping as an alternative to predominantly negative fluctuating lift coefficient (lift curve);

• Introduction of material properties varying along the model (multiple sets of moduli of elasticity and S-N Curves supported); those are defined individually in each sectional zone;

• The numbers of the S-N Curves that can now be defined or/and used in a single *.dat file are unlimited.

• The maximum allowable number of S-N curve segments is increased to 10 (from 5 that was supported in older versions); 1 to 10 segments can be used in order to define each of the multiple S-N Curves.

In the view of introduction of the above new features the user mode definition that was available in version 4.5 was removed from version 4.6. Users that require that facility are recommended to use it with version 4.5 of the program. The hydrodynamic enhancements of the program (the first two bullet items in the list above) were added in order to enhance strake modeling capabilities of SHEAR7 (see Appendix 6) The structural enhancements were introduced in order to allow modeling multiple structural materials in the same model. That may include for example using different fatigue curves along different regions of a Top Tensioned Riser (TTR), modeling titanium stress joints often used on Steel Catenary Riser (SCR), etc. The above changes resulted in the following modifications to the input (*.dat) file, in comparison with that used in version 4.5 of the program (see also Sections 7 & 12):

• Bandwidth values are now structural zone specific; • A single value of the reduced velocity bandwidth is still used for all modes and zones during

the preliminary calculation; that value is the maximum bandwidth value of the zone specific values;

• The zone specific bandwidth is listed in front of the Strouhal Number or the Strouhal code in Block 2;

• The added mass coefficient is moved from its former position in front of the Strouhal Number or Code to the beginning of next line; it is placed in front of the three Sectional Damping coefficients;


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• The zone Modulus of Elasticity and the I.D (Identification NOT Inner Diameter). The number of the zone S-N Curve are listed in a new line added below the line defining the moment of inertia, mass and submerged weight;

• A new line is added at the top of Block 4: this specifies the number of the S-N Curves defined in Block 4 of the *.dat file;

• I.D.s of each of the S-N Curves defined are added in front of the number of segments used in the definition of each fatigue curve. There is no limit on the number of S-N Curves that can be defined in the *.dat file or a requirement that all of those curves must be used;

• The line specifying the number of user modes and all the optional lines used in the user-mode definition are removed from Block 5 of the *.dat file;

• A new line with a new code entry is added at the end of Block 5; if that code is equal to the default zero, the contents Item 13 of the *.out file is listed in that file, as it was in v4.5. When that code is equal to 1 or to 2, the printing of the contents of Item 13 is redirected to a new optional *.out1 file, which results in a smaller *.out file. When that code is equal to 1 only the new optional *.out1 file is generated. When that code is equal to 2, a new optional *.out2 file is generated together with the *.out1 file. The new optional *.out2 file is designed for research purposes and for post-processing in spreadsheets or in MATLAB. Only numbers are included in the optional *.out2 file.

• The entries for the global modulus of elasticity (Block 2) and for the global reduced velocity bandwidth (Block 5) are removed.

Shear7 identifies the power-in regions by using the Strouhal Frequency computed from the Strouhal Number (St) and the reduced velocity bandwidth (Vr). Lift coefficient (clift) values are used in those regions and they are listed for each mode and power-in node in item 13 of the *.out file. Outside the 1/St ± Vr/2 interval, Venugopal’s sectional damping is computed, depending on the reduced velocity Vr and on the Reynolds Number. That is the case for all versions of Shear7, including version 4.6. For strake models the values of lift coefficients are predominantly negative, with the exception of small positive regions close to A/D = 0.0. Traditionally Shear7 has taken advantage of this to model the vortex suppression action of strakes. Negative values of lift coefficients reduce the Power-In force and as such limit the resonant response. This is still the case in version 4.6 whenever a non-zero bandwidth is used in a straked zone, which has been designated power-in by the program. However, the capability of defining different “dVr and St” combinations in straked and bare structural zones will usually ensure that a straked zone is excluded from the “power in length” in favor of the adjacent bare zones. This will then force the straked zone to be “power-out” and as such contributes directly to the modal damping force. This has been shown to result in response predictions which are much closer to those measured in the NDP and Miami long cylinder experiments. See Appendix 6 for more details and references in the 2011 OMAE paper number 49817 [17]. When one wants to force a straked zone to not participate as a power-in region, then dVr should be set to zero. The zone then contributes only hydrodynamic damping, which is controlled by user-defined damping coefficients. Setting dVr to zero is primarily intended as a research tool and should not be used in normal fatigue damage predictions, because this assumes that the strakes perform with 100% efficiency. The recommended input for dVr for modeling strakes is presented in


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Appendix 6. It is the current recommendation to use a dVr=0.25, so as to provide some conservatism in response prediction. NOTE: In order to converge, Shear7 requires some positive lift values somewhere on the model. Accordingly, for models with full or almost full strake coverage convergence problems may arise when dVr=0.0 or is very small. If a convergence problem for the above reason is suspected, it is recommended to increase the straked zone bandwidth until convergence is achieved. 2. NEW FEATURES OF VERSION 4.5 & 4.6 SHEAR7 version 4.5 was the twelfth distribution of SHEAR7. The use of the program is similar to that of versions 4.0-4.4 but the way in which the program works has been changed considerably. This reflects the findings of recent research, in particular that of the MIT/DEEPSTAR program involving towing slender pipes in the Gulf Stream offshore Miami. The most significant modification introduced in version 4.5 involves a change in the way power-in regions are apportioned in time and space. In V4.4 and in all earlier versions of the program utilized a ‘competing modes’ model of Vortex Induced Vibrations (VIV), whereas all potentially responding modes competed among each other for power-in length on the riser. Whenever response in more than one mode was feasible, the whole power-in region was subdivided into individual power-in regions, one per mode. Any overlaps between modal power-in regions were removed. The greater the number of modes left above the cutoff power level, the smaller the individual power-in regions became. This had the effect of reducing the response of each mode. Recent research has shown that this in not seen on typical risers. Rather, each mode appears one at a time. Over a long period several modes may come and go, sharing the time that VIV is experienced. Each mode has a much larger power-in region than would be permitted by removing spatial overlap in power-in regions. Each mode has more power-in and responds with larger amplitude than would be predicted in the old method of response computation. More explanation is offered below and several relevant references from recent conference papers are listed in the Reference Section 9 [4, 5, 6, 12 &14]. 2.1 Time Sharing Concept SHEAR7 versions 4.5 and 4.6 utilize the concept of time-sharing between the modes, making spatial overlap elimination between the modes unnecessary. The concept of time sharing is based on observations from the Gulf Stream, Deepstar-funded, slender pipe experiments. The data revealed that VIV response is dominated by one single frequency at a time, with the response switching frequently among frequencies. The time sharing principle is illustrated for a low mode number example below. Similar to the way that previous program versions operated, the program first performs an initial modal power calculation using full bandwidth for the power-in region to form a basis for deciding relative modal dominance in the final modal calculation. In versions 4.5 and 4.6, after the initial power calculation, modes are allowed to respond with the full input bandwidth (power-in region) but the time over which they are allowed to respond is reduced in accordance with calculated time sharing probabilities. As the default, the time sharing probabilities are proportional to power ratios.


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The program still works in the frequency domain and it still uses the Modal Superposition Method. 2.1 Multiple zones when power-in regions are far apart For high mode number cases those modes that have power-in regions far away from each other may not interact significantly and, therefore may occur at the same time. This is because, during the propagation of transverse waves along the riser, the oscillation amplitude dissipates exponentially as the wave travels. Two power-in regions sufficiently far apart may occur at the same time, because they do not interfere with one another. The above possibility is allowed in versions 4.5 and 4.6, by allowing up to three independent time sharing zones on the riser. These zones are made independent by allowing the time sharing probabilities in each zone add up to one. These zones are treated independently. The way in which modes are assigned to zones depends on the amplitude of waves generated by the dominant mode. The dominant mode is still determined by a preliminary modal power computation. As waves travel away from the power-in region, they will damp out. Once they become small enough, they are no longer able to suppress local synchronization of the wake with locally generated vibration. The user sets this cutoff amplitude in the *.dat file. For example, an amplitude cutoff of 0.3 means that when the dominant mode waves have attenuated to 30% of their original value, they will no longer be able to suppress the formation of another modes power-in region. From that point and all points further away, a secondary zone is allowed to form. There are in principle two such regions on any riser, one above and one below the zone of influence of the dominant mode. Any modes with power-in regions in these zones are allowed to coexist in time with the primary zone defined by the dominant mode. Any location where the dominant mode amplitude is above the cutoff value, belongs to the primary zone. All modes in that zone are required to time share with the dominant mode. Outside of the primary zone secondary zones may exist. The higher the amplitude cutoff the smaller will be the primary zone and the more conservative the result.


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A recommended value for the dominant mode amplitude cutoff is 0.3. The higher the value, the more conservative the result, because more modes are likely to coexist in secondary zones. The maximum cutoff is one, in which case only modes sharing the same power-in region will time share in the primary zone. Very often this may be a single mode in zone one, but many modes in zones 2 and 3. Because the response from all the zones happens at the same time, the total response will be greater, than when only one zone exists. Setting the amplitude cutoff to 0.0 forces a single primary zone. Accordingly, three time sharing scenarios are possible:

• There is only one time sharing zone on the riser: this happens when the amplitude of the propagating dominant mode waves are above the cutoff value for all neighboring modes. This will typically be the case for low maximum mode number risers or when the amplitude cutoff is low(closer 0.0);

• There are two independent time sharing zones on the riser: this happens whenever the dominant mode amplitude drops below the cutoff only to one side of the power-in region of the dominant mode.

• There are three independent time sharing zones: This happens when secondary power-in zones exist to either side of the primary zone. This is most likely to happen in sheared cases with a high amplitude cutoff(closer to 1.0)

The *.out file lists the zones, the modes with power-in regions in each zone, and the time shared probability of occurrence of modes in each zone. 2.2 Changes in the Specification of Lift Coefficient Tables The user prepared common.cl file contains the lift coefficient data tables. Six CL data tables are provided with this issue of the program, two for bare riser sections and two for regions with strakes. In addition the user may add custom designed lift coefficient tables to the common.cl file. An appendix (Appendix 1) on the specification of CL tables is included with this guide. It is entitled “Understanding Lift Coefficients in V4.3 through V4.6”. The *.dat file allows zone-by-zone specification of lift coefficient tables and zone by zone specification of hydrodynamic damping coefficients. The line which tells the program how many lift coefficient tables it should read has been removed from the *.dat file. The number of tables is specified in the beginning of the common.cl file. This program has been calibrated against a variety of sub-critical data sets (Reynolds number<100,000). Six lift coefficient tables are provided in the common.cl, provided with the program. The table number is important, as it is used to specify which CL values are to be used in each zone. The tables currently provided with the program are described below: Table 1: This table is intended to be conservative for bare riseres. It depends only on A/D and not on reduced velocity. This table will yield results similar to that seen in version 4.2.


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Table 2: This table is based on the original Gopalkrishna data, and has been extended by Prof. Carl Martin Larsen of NTNU. It is a function of both Vr and A/D. It yields best fit predictions and is therefore not necessarily conservative. Table 3: This table is a very conservative model for strakes and it is now considered obsolete. It was created before data was available for the AIMS 25% high, 15 D pitch strakes. It is not a function of Vr and has positive values of CL for A/D up to 0.3. Table 4: Table 4 is a dummy table that is intended for editing by users, in cases where custom curves are preferred. It is also indicated by a comment note in the common.cl file. If further custom tables are required, they should be added as Table 7 and upwards. While doing that, the users should remember to increment by one the nCLtype number in line 2 of common.cl file every time an additional CL table is added to that file. Table 5: This table presents the recommended conservative strake model. It has substantial positive CL values up to A/D of 0.15 and negative CL values for larger vibration amplitudes. This table does not depend on Vr. Table 6: This table is based on the latest research [16] and on modeling experience that is subcritical model test data of the 25% high, 17.5D pitch. It is less conservative than Tables 5, or 3 and it should be only used for undamaged, ideal strakes that are not subject to marine growth fouling. Table 6 has a very small region of positive CL and small absolute values of negative CLs for larger vibration amplitudes. This table does not depend on Vr. There are substantial gaps in measured data and therefore there are significant gaps in calibration. In particular, we have little performance data for strakes at Reynolds numbers greater than 100,000. High Reynolds number rigid cylinder data is available, which indicates that significant VIV response is unlikely. 2.3 Changes in Recommended Strouhal Number High Reynolds number model test data are available from rigid short cylinder tests. Little data is available for high mode number cases. The user must, therefore, seek the best available advice in modeling Strouhal number for Reynolds number applications greater than 100,000. There is mounting evidence to indicate that 0.18 is slightly conservative over a wide range of sub-critical to super-critical Reynolds numbers. We now recommend that 0.18 be used for all cases. Users may set their own values as they have access to better measured data. In the program Strouhal number codes 100 and 300 are no longer available. Strouhal code 200, is still available. In this table the Strouhal number is constant at 0.17 up to Re=20,000 and then rises linearly to 0.24 at Re=90,000. St is constant at 0.24 above 90,000. This table is much more conservative than a constant value of 0.18 as recommended above. This table might be used if there is evidence that higher St values are warranted at higher Re values. 2.4 The Effect of Higher Harmonics on Fatigue Damage Recent Deepstar/MIT experiments have confirmed that higher harmonics in the response may increase damage rates by an order of magnitude in local parts of the riser. The test data was


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acquired at subcritical Reynolds numbers. The phenomenon has yet to be quantified at higher Reynolds numbers. For the present this program does not take the higher harmonics into account. An application note on how to take into account the effects of higher harmonic fatigue damage will be issued at a later date. This is a subject of current research, which should be monitored by users of the program. OMAE 2007 has a paper by Vikas Jhingran and J. Kim Vandiver, which describes the higher harmonic damage rate issue more fully [3]. The testing of strakes during the Miami offshore VIV experiments, revealed that 50% strake coverage was sufficient to eliminate the contributions of higher harmonics to the VIV response and fatigue damage [14, Vandiver et al]. 2.5 General Improvements to Input and Output Files Many small improvements have been made to the code and in the *.out file format. The time sharing probability entries have been added to the *.fat file. The *.scr file (a debugging file) was improved substantially with the v4.5 issue. An input data echo has been added at the beginning of that file in order to make easier the debugging of the input data. The new output *.dmg file includes a table listing unfactored Rayleigh fatigue damage rate values computed for each mode at each node on the riser. A new optional output *.out1 file was added with the introduction of version 4.6. That file can be used in order to decrease the size of the *.out file, by redirecting the printout of Item 13, to the *.out1 file. Item 13 or the optional *.out1 file include the listings of the lift coefficient, the non-dimensional frequency and the reduced velocity in the power-in zones. Generation of a few new error messages was included in version 4.6, in particular with regard to adding the new features. The messages appear in the command window, the *.out file and/or in the *.scr file. 2.6 Recommended Reduced Velocity Bandwidth (bare pipe: VR=0.4 to 0.7; strakes: VR=0.25) All modes in the same structural zone will use the same reduced velocity bandwidth. V4.5 introduced a single, global bandwidth value, which was previously called the single mode bandwidth. The modes that remain above the cutoff use the reduced velocity bandwidth, which the user specifies in the input *.dat file. The recent Miami-Deepstar tests reveal that for bare cylinders this bandwidth is on average equal to 0.4 [5, 6]. If one wishes to predict the mean value of measured response, then 0.4 is a good choice. If one wishes to be somewhat conservative in a design prediction of fatigue life, then a larger value might be used. 0.5 or 0.6 would be more conservative. 0.7 would be very conservative. The power-in for each mode is roughly proportional to bandwidth. The bandwidth has the effect of limiting the power-in length for each mode. The introduction of the common.cl file, in V4.3 allowed the user to provide a lift coefficient table in which the lift coefficient may be varied as a function of reduced velocity. It is typical to have very small lift coefficients at high and low reduced velocities, which has the same effect as imposing a limit on the power-in reduced velocity bandwidth. Table 2 does this, while table 1 does not. Since the CL table is centered on a value of normalized reduced frequency of 1.0, then a bandwidth of 0.4 means the power-in regions may vary from 0.8 to 1.2 in normalized reduced frequency. Reduced velocity and normalized reduced frequency are both printed in the *.out file. See Appendix 6 for more information on dVr values for straked zones.


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2.7 Multiple Structural Zones Multiple zones were introduced in Version 4.0. In V4.3 the maximum number of structural zones was 120, this limit has been removed, so as to permit one to model risers with frequent variations in hydrodynamic properties. An example might be the application of buoyancy modules or strakes on alternating riser joints. Within each zone one may specify the Strouhal number, lift coefficient reduction factor and lift coefficient table to be read from the common.cl file. One also sets the diameter, the moment of inertia, the mass/length and the linear tension variation within each structural zone. The last line in each structural zone lists the added mass coefficient and the three hydrodynamic damping coefficients. One should avoid using too many zones. Each zone should be many nodes in length. In version 4.6 the modulus of elasticity and the reduced velocity bandwidth became structural zone specific. Also, V4.6 now supports the use of multiple S-N Curves that are also structural zone specific. A new line is added to the definition of each structural zone in version 4.6. That line defines the data pertaining to the structural material used and the second of the new lines adds to the hydrodynamic properties of the zone. Accordingly, in version 4.6 each structural zone is defined by 6 lines:

• Lines 1 through 3 define the zone geometry, mass and submerged weight. • NEW line 4 defines the modulus of elasticity of the material used and the NEW I.D. Number

of the S-N Curve corresponding. • Lines 5 and 6 define the hydrodynamic properties of the zone, whereas:

• Ca, the added lift coefficient is moved to the beginning of line 6, just in front of the three Sectional Damping Coefficients; thus all the force coefficients used are now listed in the same line.

• Vr, the reduced velocity bandwidth, is added at the beginning of line 5, just in front of the Strouhal Number or Code.

2.8 Multiple S-N Curve Definitions Version 4.6 supports definitions of an unlimited number of S-N Curves that can be used in the same Shear7 model. The curves are defined in the way that is analogous to that used in the earlier versions of Shear7. The S-N Curve I.D numbers that start the definition of each S-N curve must be numbered consecutively. Definitions of S-N Curves that are not used on a particular model are allowed, which may be sometimes convenient. The number of segments that can be defined for any S-N Curve is between 1 and 10. The earlier program versions supported the maximum of 5 segments. Having said that, in a case a user requires a larger number of S-N Curve segments, a custom version supporting such a higher number can be compiled.


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As previously, a global Stress Concentration Factor (SCF) and any number of local SCFs can be defined (not to exceed the number of nodes in the structure). Also as previously, the selection(s) of (a) local SCF(s) at any node or set of nodes overwrite(s) any non-unity global SCF at that (those) nodes only. 2.9 Other Input Features The line pertaining to entry of the global value of the modulus of elasticity for the entire structure was removed from Block 2 of the version 4.6 *.dat file. Similarly, the line pertaining to entry of the global value of the reduced velocity bandwidth Vr for the entire structure was removed from Block 5 of version 4.6 *.dat file. Line or lines pertaining to the user entry mode were removed from Block 5, because the user mode facility is no longer supported by version 4.6. Modelers who require that facility are advised to use version 4.5. Options to generate new output *.out1 and *.out2 files were added with the introduction of version 4.6. The*.out1 file can be used in order to decrease the size of the *.out file, by redirecting the printout of Item 13, to the *.out1 file. Item 13 or the optional *.out1 file include the listings of the lift coefficient, the non-dimensional frequency and the reduced velocity in the power-in zones. The*.out2 file is designed to make possible post processing of lift coefficient and damping values. It gives a complete list of damping and lift coefficients for every mode at every node. This would be rarely needed for normal response prediction, but has use in research. See section 6.9 for details. Flags Controlling the Generation of Optional Output Files. Three lines in Block 5 *.dat file that were added in version 4.5 and the fourth one in version 4.6. The lines that include control flags for the generation (0=no, 1=yes) of the following output files are the following:

a. The *.scr file (a de-bugging file) b. The *.dmg file is available in versions 4.5 and 4.6; the option is to generate the *.dmg file

specifying the Rayleigh fatigue damage per year at each mode and node. This file contains unfactored (not multiplied by the probability of occurrence) Rayleigh fatigue damage values computed by SHEAR7. The time sharing probabilities are listed in row two of the *.dmg file, but this is for information only. In case a user wishes to perform their own fatigue calculations, she or he can decide whether or not to use the time sharing probabilities computed by SHEAR7.


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c. The *.fat file; the change is that the *.fat file was previously always generated; in versions 4.5 and 4.6 the user has a control over that generation in order to reduce the number of unwanted output files.

d. The *.out1 file; that new file can be used in order to decrease the size of the *.out file, by redirecting the printout of Item 13, to the *.out1 file. Item 13 or the optional *.out1 file include the listings of the lift coefficient, the non-dimensional frequency and the reduced velocity in the power-in zones.

e. The*.out2 file is designed for post processing of program results involving the fluctuating lift coefficient and the sectional damping computed.

2.10 Changes to the *.dat File To enable previous V4.5 *.dat files to run as Version 4.6 requires changing Block 2, Block 4 and Block 5 as shown below. Block 1, Block 3 (the current data) and the optional Block 6 (supplemental data) remain unchanged. Note both deletions and new insertions. A program called convert_v45_to_v46.exe is provided, which will convert version 4.5 files to version 4.6 input files. The formats of the common.cl file and that of the *.mds and *.cat files are unchanged. *** BLOCK 2. structural and hydrodynamic data *** 6 flag for structural model 1500.000 total length of the structure (ft) 100 number of spatial segments 30022.800 modulus of elasticity (ksi) 64.000 volume weight of the fluid (lbf/ft**3) 0.0000140000 kinematic viscosity of the fluid (ft**2/s) 0.00300 structural damping coefficient: 224809.0 effective tension at origin (lbf) 1 no. of zones to define sectional property 0.0000 1.0000 zone start and end point in x/L 84.00000 46.00000 42.00000 hydro strength inside diameter(in) 0.3233E+01 2296.140 166.870 inertia(ft^4)mass(lb/ft) sbmg wt(lb/ft) 30022.8 1 NEW: modulus of elasticity (ksi), NEW: S-N Curve I.D. No. 0.5 0.18 1.0 1 bandwidth, St code, Cl reduction factor, zoneCLtype 1.000 0.2 0.18 0.2 Ca, DampCoeff1, DampCoeff2, DampCoeff3 *** BLOCK 4. s-n and scf data *** 1 NEW: No. of S-N curves defined 1 1 NEW: S-N curve I.D., No. of S-N curve segments 0.0000 cut-off stress range (ksi) 0.4010E+01 0.1000E+09 stress range (ksi) cycles to failure 0.4700E+02 0.1000E+05 stress range (ksi) cycles to failure 1.000 global stress concentration factor 0 no. of local stress concentration positions *** BLOCK 5. computation/output option *** 1 calculation option(0=fn’s only,1=full calc, 2=imported modes) 0.0 1.0 0.1 response location definition for the *.out file 0 no. of user input modes 0.0 gravitational acceleration(ft/s**2) 0.4 reduced velocity bandwidth 0.05 0.3 power cutoff, dominant mode amplitude cut-off 1.0 power ratio exponent (1=power ratio;0=equal probabilities) 0 flag for importing nodal effective tension and mass, (0=no; 1=yes) 0 flag for writing the *.anm file (0=no, 1=yes) 0 flag for generating *.scr file, (0=no; 1=yes) 0 flag for generating *.dmg file, (0=no; 1=yes) 0 flag for generating *.fat file, (0=no; 1=yes) 0 *.out file selection: 0=*.out, 1=*.out1, 2=*.out1+*.out2


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Change1: The line defining the global modulus of elasticity is removed

The structural zone specific modulus of elasticity is now defined instead in the structural zone definition.

Change 2: A new material property line is added to the structural zone definition. This line

includes the modulus of elasticity and the new I.D. Number of the S.N. Curve used in the structural zone. The S-N Curves need not be called here in any specific order, any curve listed in Block 4 can be specified.

Change 3: the reduced velocity bandwidth Vr is now structural zone specific and it is

defined in the structural zones.

Change 4: The value of the added mass coefficient is moved one line down, and it is now listed in front of the sectional damping coefficients.

Change 5: A new line specifying the number of S-N Curves defined is added at the beginning

of Block 4. Any number of S-N Curves can be defined in Block 4. The Curves defined may or may not be called in the structural zone definition in Block 2.

Change 6: A new I.D. Number of the S-N Curve is added in front of the number of segments in the S-N Curve definition. The I.D. Numbers must be consecutive natural numbers

starting with 1. Thus the definition of the first S-N curve defined must use the ID = 1, the second S-N Curve defined must use the ID = 2, etc. (That requirement is similar and consistent with the definitions of lift curves in the common.cl file.)

Change 7: New, optional S-N Curves definitions may be added to Block 4. They have similar format to those used in the earlier versions of Shear7, with the exception of the additions of their I.D Numbers, as described in Change 6.

Change 8: The file lines defining the user mode entry are removed. This option is no longer

supported in version 4.6. Modelers requiring the use of that facility should use version 4.5 of the program.

Change 9: The line specifying the global entry of the reduced velocity bandwidth is removed. Reduced velocity bandwidth(s) is (are) now defined as the part of structural zone definition(s) in Block 2, see Change 3.

Change 10: New line specifying a flag entry for a generation or not, of a new optional *.out1

and *.out2 file; the *.out1 file can be used in order to decrease the size of the *.out file, by redirecting the printout of Item 13, to the *.out1 file. Item 13 of the *.out file or the **.out1 file include the listings of the lift coefficient, the non-dimensional frequency and the reduced velocity in the power-in zones.

The*.out2 file is designed for post processing of program results involving the fluctuating lift coefficient and the sectional damping. It lists these values along the entire model together with the non-dimensional frequency and the reduced velocity.


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3.0 PROGRAM GENERAL DESCRIPTION Introduction to the program: SHEAR7 is a mode superposition, VIV response prediction program, which evaluates which modes are likely to be excited by vortex shedding and estimates the steady state, cross-flow, VIV response in uniform or sheared flows. 3.1 Program Capabilities The program evaluates natural frequencies and mode shapes of cables and beams with linearly varying or slowly varying tension and with a variety of boundary conditions, including cantilevers and free hanging risers. The program is written so that additional structural models may be added to the list as they are developed. At this time, only the beam and cable models with constant or linearly varying tension and pinned ends have been extensively tested. Unknown bugs no doubt exist, especially for some of the less frequently used structural models. Let us know of them, please. The program is capable of evaluating the natural frequencies and mode shapes and VIV response of horizontal catenary cables, and uses an approximate structural model for inclined catenary cables. The user may choose to compute natural frequencies and mode shapes in a separate program, such as a finite element program, and provide them as input to SHEAR7 in a common.mds file. In this way, structures, which are not in the standard solution set of SHEAR7, may be evaluated. The SHEAR7 VIV response prediction includes Root Mean Square (RMS) displacement, velocity, acceleration, RMS stress and fatigue damage rate as well as local drag amplification coefficients. Global and local stress concentration factors may be applied to the riser being modeled. Cylinders are not required to be of constant cross-section. The user may also model sections of risers with VIV suppression devices, fairings or staggered buoyancy modules. Recommendations on how to model fairings or staggered buoyancy modules may be requested from the authors. 3.2 Cable or Beam Behavior (Tension or EI dominated) The distinction between the term cable and beam, as used here, is that cables do not have significant bending rigidity (i.e., their resistance to transverse deflection is dominated by tension), whereas beams under tension have significant bending stiffness. In the SHEAR7 *.out file a dimensionless parameter is computed so as to give the user a measure of beam versus tension dominated behavior. In general it is the highest frequency mode which is most affected by beam stiffness effects. See item 2.1 in the *.out file. 3.3 VIV Solution method SHEAR7 can be used to predict the cross flow, vortex-induced vibration response of a long cylinder with varying tension in a sheared flow. The basic solution technique used is modal analysis and power-balance iteration (to account for the non-linear relationship between response and lift coefficient. The physical assumption is that the power input (by lift force) and power output (through damping) for each mode should be in balance in a steady state. From initial values of lift and damping coefficients, this program finds the lift and damping coefficients in a balanced state through iteration. The converged lift and damping coefficients are used to compute cylinder response.


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3.4 Very Long Cylinder Limitations SHEAR7 is a mode superposition program and is not well suited to structures with large numbers of participating modes. Historically, we used a recommendation that not more than 100 participating modes be used. However, recent tests indicate that for long, slender and lightly damped structures higher numbers of modes may be used. In V4.5 the maximum number of modes was increased to 500 to facilitate higher mode number risers and the same limit is used in V4.6. The maximum allowable numbers of spatial segments, structural zones or fatigue curves defined are unlimited. The SHEAR7 program provides an estimate of a useful dimensionless parameter, nζ , consisting of the product of the mode number and the modal damping ratio. This parameter gives the user a measure of the relative importance of wave propagation behavior versus resonant mode behavior. When nζ is greater than 1, wave propagation behavior is common. When it is less than 0.2 standing waves are most often seen. 3.5 Coordinate System and Current Profile Specification The program assumes that the coordinate system used to specify the axial position along the cylinder is non-dimensional, beginning at x/L = 0.0 and ending at x/L = 1.0. The current profile values in the input *.dat file must be specified in terms of x/L coordinates and must begin with the lowest x/L value and proceed to the highest. It is recommended, but not required, that the minimum tension end be located at x/L = 0.0. The structural zones, the velocity profile, locations of SCF's and location of vibration suppression regions must always be specified in terms of the local x/L coordinate. Velocity profiles require a minimum of two points. The program will interpolate to all other locations. If the user has separately computed the tension distribution, it may be separately input via a common.cat file. This user provided data is then used in the computation of the natural frequencies and mode shapes. common.cat files are specified later in this guide. If mode shape information is provided with a common.mds file there must be a one to one match between mode shape data and the nodes in the structural model. common.cat and common.mds should not be used together. The common.mds will govern if both are called for. 3.6 Unit Systems One of two unit systems, English and SI, may be selected for use in the program. Once a unit system is chosen, however, the input data must be prepared consistently. If, for example, one chooses the English unit system, it must then be used for every dimensional input quantity. The correct unit to be used for each entry is noted in the sample input data files.


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4. 0 PROGRAM OPERATION AND EXECUTION 4.1 Program Execution Options: The SHEAR7 program has been developed in Fortran and has been compiled so as to run as a DOS executable file on PC's.V4.3 through V4.6 will run in the command window under Microsoft Windows. There are several ways to execute the program. Each is described below. 4.1.1 Execution-Direct Method: Place the SHEAR7V4.6.exe file in the same directory as the

input data files (which include the common.cl file). Double click on the executable and respond to the prompt to enter the root-name of the *.dat file. A batch file may also be made which contains as many entries as one wishes. It must be run from within the directory containing the input data files. On each line of the batch file one places the instruction ‘shear7v4.6 root-name’. This batch file will then run all of the entries. See the sample “datafile.bat” file on the distribution diskette. If the SHEAR7V4.6.exe file is not in the same directory with the data files, then the explicit path must be given to the SHEAR7V4.6.exe file in the batch file.

4.1.2 Execution-Specify a Shortcut to the Executable: You may also place a shortcut on the desktop and set the properties of the shortcut so that the proper paths to the executable and to the input data may be found. They may be in separate directories. The common.cl, common.cat and the common.mds files should be in the same directory as the rootname.dat files. The output files always accumulate in the same directory as the input *.dat files.

4.2 Program Solution Options The program contains a module for free vibration analysis and a module for computing response to vortex shedding. The user may elect to use both modules or each one individually. The free vibration subroutine calculates natural frequency, mode shape, and curvature for a wide variety of boundary conditions. The response module uses the results of the free vibration analysis or uses free vibration information computed separately and input via the common.mds file. 4.3 Choice of structural models The most frequently used and reliable are the pinned-pinned cable and beam models. A pinned-pinned beam model is available which allows for rotational springs at both ends. In addition a free-pinned beam with varying tension has been implemented in the program. The pinned end may have a rotational spring. These models with rotational springs are known to have numerical problems for some cases. The program reports when it is unable to find natural frequencies. These infrequently used options should be used with caution. 4.4 Input files A set of sample data files are provided for the user's convenience. These examples demonstrate a variety of capabilities of the program, such as calculation options, VIV suppression simulation, and boundary conditions, and may be used as models for similar user defined structures. The program may use up to four user-provided input files. Details of each are given in Section 6.

When the SHEAR7 program runs, it reads in data from an input data file of the form ``root-name.dat''. This file is always required.


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When calculation option 2 is used the program expects to find a file named "common.mds". Preparation of this file is described in the next few paragraphs. When the user specifies in the input data file the use of externally provided tension and mass per unit length data, the program expects to find a file named "common.cat". The preparation of this file is described in the discussion of input data under Block 5, Line 7. A second mandatory input data file is the common.cl file. The common.cl file included with the program distribution has several tables of lift coefficient. The user can add to the common.cl file her or his custom built tables of lift coefficients. This file is always required.

5.0 COMPUTATIONAL FLOW OF THE PROGRAM SHEAR7 models the dynamic response of flexible cylinders to vortex shedding. It is normally used to model cross-flow excitation and response, but may be used to model in-line motion with the substitution of appropriate parameters. In the following an ordinary cross-flow response in a sheared flow is assumed. It is further assumed that a *.dat input file has been prepared. 5.1 Read Input Data

The program reads the input data from a *.dat file. From the diameter, current and Strouhal inputs, a vector of Strouhal frequencies is found for every node on the riser, which are located in a dimensionless coordinate system which varies from 0 to 1.0.

5.2 Find Natural Frequencies and Mode Shapes

The program computes or reads from a user-provided common.mds file all the possible natural frequencies, which lie within the range of frequencies in the vector of Strouhal frequencies found in step one plus a multiple of higher frequencies to assist in the mode superposition calculation.

5.3 Maximum Number of Modes

The array sizes in the SHEAR7 program are set by means of parameter NMD, the maximum number of natural modes. The current setting for NMD is NMD=500.

If the maximum mode number required by SHEAR7 is greater than 500, the program will print out this number in the "root-name.out" file and abort. You will probably also see a message ("segmentation violation") on your computer screen. If you want to continue to run you must reduce the number of modes needed to less than 500 by shortening the length of the riser, reducing the maximum current, or increasing the tension. As a general rule, the program requires about three (3) times higher mode numbers in the mode summation than the highest frequency mode which is allocated a power-in region after the power level cut off is applied. This is referred to as the highest excited VIV mode. When this mode is above 15 or 20, the dominant response behavior is traveling waves [see Marcollo, OMAE, 2007]. In such cases, mode superposition will yield satisfactory results as long as the rule, including about three (3) times higher modes, is observed.


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5.4 Find Centers of Power-in Regions Every nodal point of coincidence between a natural frequencies and the Strouhal frequency vector is assumed to be the center of a power-in region associated with that natural frequency. Multiple occurrences of the same frequency are a single merged entity. The reduced velocity at each center point is simply 1/St at that point.

5.5 Define the Power-in Regions Using the Reduced Velocity Bandwidths: At this point the

program uses the user-selected reduced velocity bandwidth. Its recommended value is 0.4 to 0.7 (bare pipe), which has the following meaning. Around each center point a power-in region is defined. It extends to either side of the center by an amount determined by the reduced velocity bandwidth. The reduced velocity in each power-in region is allowed to vary by a fraction equal to one-half of the reduced velocity bandwidth. If the bandwidth is 0.4 then the reduced velocity may vary by plus or minus 20% to either side of the center. Another way of saying this is that the velocity may vary plus or minus 20% from the velocity at the center of the power-in region for each mode. Within each power-in region the excitation frequency stays constant and equal to the Strouhal frequency at the center point.

5.6 Determine the Modes Above the Power Cutoff Level: The power available to each mode is

computed. All values are divided by the largest to provide a ratio to the maximum, which varies from 0.0 to 1.0, and is reported in the *.out file. The power computation is based on the current profile, a computed modal force and a computed modal damping. The reduced velocity bandwidth together with the Strouhal number specified, the hydrodynamic diameter of the riser and the current profile are used in the determination of the modal power-in zones. A cutoff is applied and all modes above the cutoff are allowed to participate, each with its full power-in length. The allowed range for the cutoff is 0 to 1.0. When the power ratio cut-off is specified as 0.0 all modes are allowed to participate. The recommended value is 0.05.

All excitation frequencies with power ratios above this value are retained and the others are dropped. The ones remaining are identified by the mode number associated with the natural frequency unique to that zone. The mode with the power ratio of 1.0 is known as the dominant mode. The recommended value of 0.05 is much lower than earlier versions of the program. With earlier versions, setting this value to 1.0 forced single mode response. This was usually conservative. With V4.5 or 4.6 a low value is desirable so as to have several modes averaged over the length of the riser to smooth modal peaks and nodes. At each frequency the program conducts a single mode computation, so it is not necessary to force single mode response.

5.7 Dynamic Response Computation: At this point the program computes individually the

dynamic response due to the excitation in each power-in region. In doing so a modal damping value is determined at each excitation frequency in the computation. The damping is used to compute response, but it is also used to compute the rate of attenuation of vibration waves as they propagate away from the power-in region of the dominant mode. This program step requires iteration, because the proper lift coefficient and the damping are dependent on the A/D response amplitude which is not known at the start. The total response of the riser is the sum of the responses at each excitation frequency, weighted by the probability of occurrence at each frequency. The probability of occurrence is determined by the power ratio determined earlier in the computation.


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5.8 Determination of Primary and Secondary Modal Response Zones: The dominant mode is assumed to have a range of influence near its power-in region in which no other frequency may respond at the same time as the dominant mode. This is named the primary response zone. Within this zone only one modal excitation frequency at a time is allowed to be active. The limits of this zone are determined by the primary zone amplitude limit, a user-selected value. If that value is, for example, 0.3, then, as the waves generated in the dominant mode’s power-in region, propagate away from the source point on the riser, they begin to decay in amplitude due to damping. When the amplitude has decayed to 30% of the initial amplitude, that location is the end of the primary response zone. Beyond that point another power-in zone is allowed to exist at the same time. Such zones are known as ‘secondary’ power-in zones. There are at most two such zones, one above and one below the center of the dominant mode’s power-in region. The program puts a summary of all outputs in a *.out file. The detailed outputs at every node are written to a *.plt file, which is intended to be used in plotting results.

NOTE: The centers of the power in regions as discussed in this subsection as well as in the formula for the decay of the dominant mode amplitude in item 7.6.7, are the geometrical centers of the power-in regions that are computed utilizing the length coordinate x along the structure.

6.0 SPECIFICATION OF OUTPUT FILES Shear7 V4.5 or V4.6 will normally create three output files, *.out, and *.plt. *.mds file will also be generated unless the user supplies the mode frequencies and shapes in a common.mds file. Additional, optional files, ( *.anm, * .scr, *.dmg, *.fat, *.out1 & *.out2) can be created when specified by the user. See example scr1.dat and the description given later in this section. Each of the output file types is described below. 6.1 root-name.out (always created) A file which reproduces the input data and summarizes the analysis results from the SHEAR7 program. This file is explained more fully in Section 7.0. 6.2 root-name.plt (always created) A file for plotting the analysis results. There are seven columns. The displacement, is given in units of feet or meters and not in dimensionless units of A/D. The output columns are in the following order: Response location (x/L), RMS displacement (in feet or meters), RMS velocity (in ft/s or m/s), RMS acceleration (in ft/s2 or m/s2), RMS stress(N/m2 or ksi), damage rate(1/years) based on a Rayleigh model, and the drag coefficient amplification factor, Cf. Most of these quantities are also summarized in item 15 of the root-name.out file. 6.3 root-name.mds This file is created by the program when the internal eigensolver is used in calculation option 1, or when the user specifies calculation option 0 in order to only obtain the WKB mode output. When calculation option 2 is selected, then this file must be provided by the user and named common.mds. This is a file for natural frequency, mode shape, mode slope and mode curvature. The mode slope


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values are always required, even if all are set to 0.0, but they are used only in conjunction with structural (nmodels) 1 and 10 and only when gravity is to be included in the predicted RMS acceleration. The "*.mds" file consists of three blocks. One may see the structure of a typical *.mds file by running one of the example *.dat files and opening the *.mds file, which is created. An *.mds file has three blocks of data as described below. An excerpt from the "common.mds" file provided to run with input file "drill_riser_ext_modes.dat" is shown next. The excerpt below includes the complete data for Blocks 1 and 2 and the first few lines of Block 3. 11 201 (Block 1} 1 0.17993 {Block 2} 2 0.36101 3 0.54433 4 0.73101 5 0.92202 6 1.11851 7 1.32108 8 1.53085 9 1.74851 10 1.97460 11 2.21038 1 1 0.00000E+00 0.19339E-02 0.00000E+0 (Block 3) 1 2 0.19619E-01 0.19263E-02 -0.77101E-06 1 3 0.39159E-01 0.19182E-02 -0.82768E-06 1 4 0.58613E-01 0.19095E-02 -0.88344E-06 1 5 0.77975E-01 0.19003E-02 -0.93830E-06 Block 1: This block has one line with two numbers, the number of modes (in this case 11) and the number of nodes (in this case 201) used to specify the mode shape. The number of nodes is always the number of segments plus 1. Block 2: This block has a number of lines equal to the number of modes specified in the first block. Each line has two numbers, the first is the mode number and the second is the natural frequency (IN RADIANS/SECOND). The mode numbers and natural frequencies are presented in ascending order. Block 3: This block normally has five columns of numbers. A sixth column of x/L values is added for mode 1 only, when uneven nodal spacing is required. The first column is the mode number, the second the node number, the third, fourth and fifth the mode shape, mode slope and mode curvature. It begins lowest mode first and lowest node first and then lists the values for every node of that mode. Then the next mode is listed. The columns are in the following order: mode number, node number, mode shape, mode slope , and mode curvature The total number of lines in Block 3 is equal to the product of the number of modes and the number of nodes.

There is no blank line in between blocks.


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The mode shape is a normalized one, with the maximum amplitude being unity. The computed slope and curvature is based on this normalized mode shape. The slope and curvature are that which would result from a mode shape with unit amplitude. When the user chooses to provide the natural frequency, mode shape, slope and curvature, the above definitions and format must be followed. See example drill_riser_ext_modes.dat and its corresponding file, common.mds. Also read the instructions for calculation option 2 given in the description of the preparation of the input data file (Block 5, Line 1 of all input *.dat files) as specified in Section 7.6.1. 6.4 rootname.anm To enable creation of the *.anm file a ‘1’ should be entered next to “flag for MATLAB animation data output 1=yes;0=no)”. *.anm files are used by the MATLAB program s7movie.m. This program presents a time domain animation of the response of the system. This program and a subroutine called s7movie2.m must be in the MATLAB path. Upon running a GUI opens and asks the user for the *.anm file which you wish to animate. They can be very large files. The user should normally not request that the program create these files. Try example scr_import_tension.dat to see a demonstration of an animation file. You must have MATLAB to make use of *.anm files.

The MATLAB animation program gives the user the choice to see animations at one frequency at a time or of a superposition of many frequencies. SHEAR7 version 4.5 uses the concept of time sharing, which assumes one mode at a time from within the same response zone. Up to three response zones may occur as determined by the setting of the ‘primary zone amplitude limit’. A valid animation should use no more than one response frequency at a time, from within each response zone.

6.5 root-name.scr To enable creation of the *.scr file (a debugging file) a ‘1’ should be entered next to “flag for generating *.scr file (1=yes;0=no)”

The *.scr file generated by SHEAR7 version 4.5 or 4.6 is more user friendly and is intended to reveal at what point the program has execution problems. The data is written to the *.scr file as soon as it is computed by the program. In the case a program execution stops the user can estimate where the problem occurs by how far the execution is reported in the *.scr file. In particular, the first blocks of the *.scr file now contain an echo of the input data. The input echoes are written to the *.scr file almost immediately after the input has been read by SHEAR7. When the program crashes before writing anything in the *.out file, the point may be identified by seeing at what point the input data echo stops in the *.scr file. The problem is usually in the specification of the input data at that point. The *.scr file gives tabular summaries of preliminary and final computations. An example excerpt from execution of an example file is shown below. The table showing preliminary calculations pertains to the power-in regions, computed before the power cut-off is applied.


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A similar table pertaining to the final calculation stage corresponds to the final set of results. Please note that in the example shown only modes 2 and 4 are above the power cut-off, and accordingly the table reports zeros in the mode 3 column for all nodes, including those, where mode 3 was excited in the preliminary calculation. Both tables have been designed for scrolling and/or for easy export to a spreadsheet or other programs for plotting.

................ ................


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......... .........

The *.scr file also shows the program iteration history that is written to the file as soon as the iterations happen.

6.6 root-name.dmg To enable creation of the*.dmg file a ‘1’ should be entered next to “flag for generating *.dmg file (1=yes;0=no)”.


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This file includes 2 Blocks. Block 1 includes two lines. The first line lists the lowest and highest mode numbers for which Rayleigh fatigue damage per year is listed in Block 2. The second line in Block 1 includes the listing of the time sharing probabilities for each of the above modes.

Block 1:

Block 2:

……………………… ………………………

Block 2 includes the listing of unfactored (not multiplied by the time shared probability) Rayleigh fatigue damage per year computed for each of the above modes at each riser node. x/L node locations are listed in column 1 of Block 2, the Rayleigh damage results are listed in the remaining columns, each column listing corresponding to one of the modes. Whenever there are interruptions in the mode sequence numbers that make it above the power cut-off, zero time sharing probabilities are written to line 2 of Block 1 in the columns corresponding. In the *.dmg file output for the above example , modes 2 and 4 are above the power cut-off and this is why the time sharing probability is 0.0 in line 2 of Block 1. In this example the time sharing probabilities listed for modes 2 and 4 are each equal to 1.0, because these modes belong to different independent time sharing zones.

In the fatigue damage calculations that are used by SHEAR7 and reported in the *.out and the *.plt files the fatigue damage is multiplied by the time sharing probabilities listed in line 2 of Block 1 of the *.dmg file (same as those listed in Table 2.2.1 of the *.out file). The results listed in Block 2 of *.dmg are unfactored, so that the user can do his own post-processing.

6.7 root-name.fat To enable creation of the*.fat file a ‘1’ should be entered next to “flag for generating *.fat file (1=yes;0=no)”. This file is intended to be used externally to calculate fatigue damage by user-defined techniques. It contains the modal participation and frequency response characteristics of each mode. A new probability of occurrence column has been added. A MATLAB routine is available on request to process the *.fat file into a time series simulation of stress at any location. The time series information can be used to calculate damage rates via rainflow. The output of the time sharing probabilities was added to the *.fat table in the last column with the issue of SHEAR7 version 4.5.

6.8 root-name.out1 To enable creation of the *.out1 file ‘1’ or ‘2’ should be entered next to “*.out file selection: (0=*.out, 1=*.out1, 2=*.out1+*.out2)”. The reason for creating that file is to decrease the size of the *.out file, in particular for high aspect ratio models, where many oscillation modes can be present.


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With the above flag set to default zero no *.out1 file is generated, and the listing of Item 13 looks like it looked in Shear7v4.5 *.out file. With the flag set to ‘1’ or to ‘2’ the printout of Item 13 is redirected to the *.out1 file. Item 13 or the optional *.out1 file include the listings of the lift coefficient, the non-dimensional frequency and the reduced velocity in the power-in zones. Below is an example of the *.out1 file output. The format is identical to that used in Item 13 of the *.out file, whenever the *.out1 or the *out1 and *.out2 files are not generated, see Section 8. Lift coefficient for each mode. In the following, the lift coefficient Cl is the amplitude and not the RMS value. Iteration, change in Reynolds number, and user input Cl reduction in suppression zone are taken into account. mode number: 4 node number Cl Fn/Fvo VR --------------------------------------------------------- 5 0.6920 0.8661 4.81 6 0.6998 0.8663 4.81 7 0.6954 0.8665 4.81 8 0.6867 0.8667 4.81 9 0.6758 0.8670 4.81 10 0.6646 0.8672 4.80 11 0.6549 0.8674 4.80 12 0.6481 0.8676 4.80 13 0.6450 0.8678 4.80 14 0.6461 0.8680 4.80 15 0.6512 0.8883 4.69 16 0.6596 0.9189 4.53 17 0.6702 0.9517 4.38 18 0.6815 0.9869 4.22 19 0.6914 1.0248 4.07 20 0.6982 1.0657 3.91 21 0.6992 1.1100 3.75 22 0.6772 1.1582 3.60 23 0.6205 1.2108 3.44 24 0.5250 1.2683 3.29 25 0.3884 1.3316 3.13

6.9 root-name.out2 To enable creation of the *.ou2 file ‘2’ should be entered next to “*.out file selection: (0=*.out, 1=*.out1, 2=*.out1+*.out2)”. With the flag option ‘2’ both the *.out1 & the *.out2 are generated and the contents of Item 13 of the *.out file is redirected to the *.out1 file, as described in subsection 6.8. The *.out2 file includes only numbers and it contains entries pertinent to all the resonant modes for all nodes of the structure. The format of the *.ou2 file resembles those of the *.mds and the *.dmg files. The numbers are listed in 6 columns and include the following values listed from left to right:


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1. mode number 2. node number 3. lift coefficient value or code 4. sectional damping 5. non dimensional frequency 6. reduced velocity

The lift coefficient values, the non dimensional frequency and the reduced velocity are the same as those listed in the *.out1 file for all the power-in nodes of the resonant modes. Whenever the node is in the power-in region the lift coefficient is used and the sectional damping is zero. Whenever the node is outside the power-in zone, the lift coefficient is zero and sectional damping is used (see Appendix 2) if the node is submerged. In order to differentiate between an accidental zero value of the lift coefficient in a power-in zone, lift coefficient code = 99 is listed instead of the value zero used by the program outside the power-in regions. Whenever a node is out of water, zeros are listed in columns 4 to 6 of the *.out2 file. The units of the sectional damping values are:

(force/length)/velocity = (force/length)/(length/time) = force*time/length2

see Appendix 2. All other values in the *.out2 file are non-dimensional. The below is an example of a *.out2 listing for mode 4 (column 1) of a model: 4 1 99 0.0000 0.0000 0.00 4 2 99 0.0000 0.0000 0.00 4 3 99 0.0000 0.0000 0.00 4 4 99 0.0000 0.0000 0.00 4 5 0.6920 0.0000 0.8661 4.81 4 6 0.6998 0.0000 0.8663 4.81 4 7 0.6954 0.0000 0.8665 4.81 4 8 0.6867 0.0000 0.8667 4.81 4 9 0.6758 0.0000 0.8670 4.81 4 10 0.6646 0.0000 0.8672 4.80 4 11 0.6549 0.0000 0.8674 4.80 4 12 0.6481 0.0000 0.8676 4.80 4 13 0.6450 0.0000 0.8678 4.80 4 14 0.6461 0.0000 0.8680 4.80 4 15 0.6512 0.0000 0.8883 4.69 4 16 0.6596 0.0000 0.9189 4.53 4 17 0.6702 0.0000 0.9517 4.38 4 18 0.6815 0.0000 0.9869 4.22 4 19 0.6914 0.0000 1.0248 4.07 4 20 0.6982 0.0000 1.0657 3.91 4 21 0.6992 0.0000 1.1100 3.75 4 22 0.6772 0.0000 1.1582 3.60 4 23 0.6205 0.0000 1.2108 3.44 4 24 0.5250 0.0000 1.2683 3.29


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4 25 0.3884 0.0000 1.3316 3.13 4 26 99 15.6650 1.4015 2.97 4 27 99 90.8041 1.4792 2.82 4 28 99 238.6794 1.5466 2.69 4 29 99 449.8295 1.5726 2.65 4 30 99 710.4557 1.5996 2.60 4 31 99 1003.7813 1.6275 2.56 4 32 99 1310.9837 1.6564 2.52 4 33 99 1612.4006 1.6863 2.47 4 34 99 1888.6944 1.7174 2.43 In the above:

• nodes 1 through 4 are out of water; • nodes 5 through 25 are in a power-in region • nodes 26 through 34 are submerged, but they are outside the power-in region; code 99 in

column 3 is interpreted as a zero value of the lift coefficient. It is noted that requesting the printing of the *.out2 file is a convenient way of obtaining a listing of the non-dimensional frequencies and those of the reduced velocities outside the power-in regions. Cross-checking those values would usually be of an optional interest.


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7 SPECIFICATION OF INPUT DATA

For recommended parameter settings for bare riser, strakes, fairings or partial coverage cases see

Appendix 6. 7.1 Sample input data files: Sample input files are included on the distribution diskette for each example in the base verification set. Provisions are made so that SHEAR7 may be run in batch mode. See the sample datafile.bat file on the distribution CD. It will run every example data file as a single batch run. A typical input file, basic_beam_3.dat: The remainder of this discussion begins with a sample listing of an input file; in this case one for a beam with linearly varying tension, pinned ends and rotational springs. A line by line discussion of the entries of the data file is given. The text after each numerical entry is ignored, but must not extend beyond 80 characters, in which case the program will abort. The most common reason for program failure is to have input line lengths which are too long. When more than one number must be specified on a line, the numbers may be separated by spaces or spaces and commas. The information shown in red text below corresponds to changes required by V4.6 as compared with V4.5. Deletions of existing formats are shown as abcdefgh while new items added start with the word NEW: . *.dat files may be converted from version 4.5 format to version 4.6 format using the program convert45to46.exe, which is provided with the program. SHEAR7 Data file for a beam with rotational springs at top and bottom. File Name: basic_beam_3.dat *** BLOCK 1. unit system *** 1 flag for units (SI=0, or English=1) *** BLOCK 2. structural and hydrodynamic data *** 6 flag for structural model 1500.000 total length of the structure (ft) 100 number of spatial segments 30022.800 modulus of elasticity (ksi) 64.000 volume weight of the fluid (lbf/ft**3) 0.0000140000 kinematic viscosity of the fluid (ft**2/s) 0.00300 structural damping coefficient: 224809.0 effective tension at origin (lbf) 1 no. of zones to define sectional property 0.0000 1.0000 zone start and end point in x/L 84.00000 46.00000 42.00000 hydro strength inside diameter(in) 0.3233E+01 2296.140 166.870 inertia(ft^4)mass(lb/ft) sbmg wt(lb/ft) 30022.8 1 NEW: modulus of elasticity (ksi), NEW: S-N Curve I.D. No. 1.000 200 1.0 1 Ca St code Cl reduction factor, zoneCLtype 0.5 0.18 1.0 1 NEW: bandwidth, St code, Cl reduction factor, zoneCLtype 1.000 0.2 0.18 0.2 Ca, DampCoeff1, DampCoeff2, DampCoeff3 *** BLOCK 3. current data *** 6, 1.0 200 number of vel. pt., probability of occurrence, ID # 0.040 4.3000 location (x/L) and velocity (ft/s) 0.133 4.2900 location (x/L) and velocity (ft/s) 0.267 2.4200 location (x/L) and velocity (ft/s) 0.500 1.4900 location (x/L) and velocity (ft/s) 0.973 1.0100 location (x/L) and velocity (ft/s) 1.000 0.0 location (x/L) and velocity (ft/s) *** BLOCK 4. s-n and scf data *** 1 NEW: No. of S-N curves defined


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1 1 NEW: S-N curve I.D., No. of S-N curve segments 0.0000 cut-off stress range (ksi) 0.4010E+01 0.1000E+09 stress range (ksi) cycles to failure 0.4700E+02 0.1000E+05 stress range (ksi) cycles to failure 1.000 global stress concentration factor 0 no. of local stress concentration positions *** BLOCK 5. computation/output option *** 1 calculation option(0=fn’s only,1=full calc, 2=imported modes) 0.0 1.0 0.1 response location definition for the *.out file 0 no. of user input modes 0.0 gravitational acceleration(ft/s**2) 0.4 reduced velocity bandwidth 0.05 0.3 power cutoff, dominant mode amplitude cut-off 1.0 power ratio exponent (1=power ratio;0=equal probabilities) 0 flag for importing nodal effective tension and mass (0=no; 1=yes) 0 flag for writing the *.anm file,(0=no, 1=yes) 0 flag for generating *.scr file, (0=no; 1=yes) 0 flag for generating *.dmg file, (0=no; 1=yes) 0 flag for generating *.fat file, (0=no; 1=yes) 0 *.out file selection: 0=*.out, 1=*.out1, 2=*.out1+*.out2 *** BLOCK 6. Supp lemental data—frequently not used *** 0.10000E+07 rotational stiffness at x/L 1.0:lbf-ft/rad 0.10000E+07 rotational stiffness at x/L=0:lbf-ft/rad. if nmodel = 6 (pinned-pinned tensioned beam w/two rot springs), provide rotational stiffness at each end if nmodel = 9 (free-pinned (w/spring) beam w/varying tension, origin at free end), provide translational stiffness at x = L if nmodel = 19 (free-pinned (w/spring) beam w/o tension, origin at free end) provide translational stiffness at x = L if nmodel = 33 (inclined cable) provide chord inclination (angle) Next is a block by block description of the input data values such as those listed in the example above. The input data are divided into six blocks. The block identification lines in the data files are required. Each data file begins with two lines of user provided text, not to exceed 80 characters per line. 7.2 Line by line description of *.dat file entries The input data is organized into six blocks, so numbered in the *.dat files. They are described below. 7.2.1 Block 1. Unit System. By choosing 0 for SI units or 1 for English units the user selects a unit system which must be strictly adhered to for the entire data set. For each input quantity the dimensions are defined in the following descriptions of inputs. Always use the units consistent with the system designated in this line. 7.2.2 Block 2. Structural and Hydrodynamic Data 7.2.2.1 Option for the structural model: The flag “nmodel” is used in the program to specify which type of structure is to be modeled. The following structural models may be selected by entering the appropriate integer at this line in the input data file. Most applications are for beams under varying tension and use nmodel = 1. The example shown above is for nmodel 6, a beam with linearly varying tension, but also having rotational springs at the top and the bottom. However, there are many other models as described below. Models are grouped into four categories, A to D. Not all integers in a group, such as those


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in the group 0 to 9 have been used. This allows for additional models to be added later in each group. The names of example data files, which demonstrate each option, are provided below. These example data files are also conveniently summarized in an Excel spreadsheet, named EXAMPLES-v4.6_rev1.pdf, which is distributed with the program. A. 0 - 9, Cylinders with linearly varying tension: nmodel = 0, pinned-pinned cable, origin at minimum tension end. Examples are:

basic_cable.dat: English units, sheared flow nmodel = 1, pinned-pinned beam, origin at minimum tension end. Examples are: basic_beam_2.dat: SI units, sheared flow basic_beam_1.dat: English units, sheared flow nmodel=2, free-pinned beam, origin at free end nmodel=6, pinned-pinned beam with two rotational springs. basic_beam_3.dat: English units, fixed-fixed by two strong springs, sheared flow. In block 6, line 1 is for the spring constant at x/l=1.0 and line 2 is at x/l=0. nmodel=9, free-pinned (w/rotational spring) beam, varying tension, origin at free end B. 10 - 19: cylinders with constant tension nmodel=10, pinned-pinned cable, origin at either end nmodel=11, pinned-pinned beam, origin at either end nmodel=19, free-pinned (w/rotational spring) beam, origin at free end C. 20 - 29: cylinders with no tension nmodel = 22, free-pinned beam, origin at free end nmodel = 23, clamped-free beam, origin at clamped end nmodel = 24, clamped-pinned beam, origin at clamped end nmodel = 25, clamped-clamped beam, origin at either end nmodel = 26, sliding-pinned beam, origin at sliding end D. 30-33, Catenary cables with no bending stiffness


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nmodel = 30, constant tension, horizontal catenary nmodel = 33, constant tension, inclined catenary scr_inclined_cat.dat (unused numbers have been reserved for future use) The choice of which model to use is left to the user. In general, if the natural frequency, which is closest to the maximum vortex shedding frequency, is governed dominantly by tension, one may use finite cable models. If bending stiffness is important, use the finite beam model. The SHEAR7 program will estimate the relative importance of EI and T and will suggest in the *.out file whether a beam or a cable model should be used 7.2.2.2 Total cylinder length in (m) or (ft) 7.2.2.3 Number of segments in the structure (NS). The inverse of NS is the dimensionless spatial

resolution, DELX. The total number of nodes is NS+1. There used to be a limit of 2000 on NS, but that limit has been removed and accordingly the user can specify NS of her or his choice. If the user-input "NS" is 0, the program will automatically set it to 500. If the user-input "NS" is a non-zero positive integer it will be used in the program. Item 16 of the *.out file provides a recommended minimum number of segments that should be used, based on a requirement of ten nodes per minimum computed wave length.

7.2.2.4 Fluid density in (kg/m**3) or (lbf/ft**3). This is the density of the fluid surrounding the

cylinder. 7.2.2.5 Kinematic viscosity of the fluid in (m**2/s) or (ft**2/s). This is used to calculate the

Reynolds number. 7.2.2.6 Structural damping ratio. This is the structural damping ratio specified for the cable or

beam. It would correspond closely to the value that one might measure in a vacuum. For most cylinders under high tension in water, this value is usually very small (order of .003). Except for uniform flow cases the hydrodynamic damping is usually much larger. The value 0.01, for example, means the same as 1% of critical damping.

7.2.2.7 Effective tension at x/L=0 in (N) or (lbf). This is the effective tension in the cylinder. It is

common, but not required, that x/L=0.0 correspond with the minimum tension end of the cylinder.

7.2.2.8 Number of sectional zones and zone structural and hydrodynamic properties: The first line

in this group has one integer, the number of structural zones to be specified for the region. The structure may have multiple zones with different structural dynamic and hydrodynamic properties in each zone. Each zone requires five lines of input data as described below. If, for example, three zones are called for, then after one line with a 3 in it three groups of five lines of data must follow with no blank lines between groups. Each group must contain five lines of data as shown below.


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7.2.2.9 Line 1, 0.0 1.0 Zone 1 start and end point in x/L. The first line has two numbers specifying the beginning and end of the zone in x/L coordinates.

7.2.2.10 Line 2, 84. 46. 42. hydrodynamic diameter, outer and inner strength diameters in

meters or inches. The second line has the three diameters, necessary to describe the structure. The first is the outer hydrodynamic diameter of the cylinder in meters or inches. It is the outer diameter of the cylinder (the hydrodynamic diameter) and is used to compute the Strouhal frequency, added mass, hydrodynamic damping and lift force for this zone. The second and third numbers on the line are the outer and inner diameter for computing stress. Normally this would be the outer diameter of the strength member, which is not necessarily the cylinder hydrodynamic diameter, as in the case of a riser with flotation material surrounding the strength member. However, any other diameter can be selected as the stress diameter. That is because, the selection of the stress diameter affects only the dynamic stresses and the fatigue damage values computed, which are both computed at the stress diameter. For example, in a case where the controlling stress concentration factor occurs at the inside diameter, the user can specify the inside diameter as the stress diameter in the zone in question. The inner diameter (the third entry in that line) is needed for computing the cross sectional area of the strength material, and is used in nmodel 30, the horizontal catenary.

7.2.2.11 Line 3, 3.233 2296.1 166.8, “I” (ft**4 or m**4), mass/length in air (lbf/ft or

kg/m), tension variation(lbf/ft or N/m).

a. Effective area moment of inertia of the riser(I): This includes all tubulars. The units are in m**4 or ft**4. The product "EI" is the bending stiffness. "I" is used in computing the natural frequencies. It is input separately in this line and is not computed based on the strength OD and ID. This is because it is necessary to be able to account for the effect of other tubulars on the bending stiffness. However, in Item 4 of the *.out file, "I" is computed based on the OD and ID as given. This is useful as a check for simple cylindrical risers, in which case the input value and the computed values for "I" in these cases should be the same. The user may use the computed output as a way of obtaining "I" for simple cases, by first using an estimate of I in the input data file and then getting the computed value from the *.out file. The computed value is then substituted for the estimate on this input data line.

b. Mass or weight per unit length in air including contents: The second number in Line 3 is the mass or weight per unit length. It is in kg/m or lbf/ft, depending on the unit system in use. In normal operation the program computes the average mass per unit length and uses this value to find the natural frequencies and mode shapes. For two structural models (nmodels 1 and 10 the linearly varying tension beam or cable with pinned ends) it is possible to explicitly account for unusual tension and the mass variation by including it in the WKB integral. To account for the tension and mass variation one uses the common.cat file option. The common.cat file contains the tension and mass per unit length variations for the whole riser. These variations are used in a WKB solution for the natural frequencies and mode shapes, which assumes that properties are slowly varying. Sudden jumps in the mass/length will lead to errors. This is because the WKB method does not account for wave reflection at sudden changes in properties. It assumes slow variations in properties.


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c. Tension variation or weight in water per unit length: The third number is the tension variation per unit length. For sections of riser in the water this is the weight in water per unit length. This is also the effective tension variation per unit length in lbf/ft or N/m. This number specifies the amount the tension changes per unit length. The tension variation is assumed to be of the form T(x) = TO+TLINCO*x with TO being the tension at the beginning of the structural zone. TLINCO may be positive or negative. A positive sign indicates that the tension increases with increasing x/L. A negative sign means the tension decreases with increasing x/L. The effective tension in the riser may not be negative. If it is the program will print out a warning in the *.out file. It will give results but the natural frequencies may not be correct.

Therefore the origin of the global coordinate system assumed in this model may be at either the low or high tension end. It is recommended that x/L = 0 correspond to the low tension end, as this corresponds to a positive number as the linearly varying tension coefficient in this data line. However, the current profile must be specified in this same coordinate system. The current must be specified in the *.dat file, starting at the lowest value of x/L.

7.2.2.12 Line 4, 30022.8 1 modulus of elasticity (ksi), S-N Curve I.D. No.

a. Young's Modulus in (N/m**2) or (ksi). This is the actual Young's Modulus of the strength member for use in computing stress and damage rate. When calculation option 1 is in use it is also used in finding the natural frequencies and mode shapes. b. S-N Curve I.D. Number. This is the I.D. Number of the S-N Curve that is used in the fatigue calculation for the structural zone in question. The I.D. Number of any of the S-N Curves defined in Block 4 can be used.

7.2.2.13 Line 5, 0.5 0.18 1.0 1, zone’s Vr bandwidth., St. # or code, Cl reduction factor, and the CL table to be used. In this case table 1 is called for. The fourth line of the group defining each zone has four numbers in it, the reduced velocity bandwidth, the Strouhal number or code 200, the lift coefficient reduction factor, and the CL table that the program is supposed to use for that zone.

a. Reduced Velocity Bandwidth that is used in the current structural zone. The lock-in bandwidth is an input. The bandwidth is centered on a critical reduced velocity which is defined as, Vr,crit = 1/St. The double width of the band, expressed as a fraction of Vr,crit is the input specified on this line. Therefore, if the *.dat file specifies 0.4 as the lock-in bandwidth, then the band extends plus and minus 20% to either side of Vr,crit. Both the initial and final power calculations, for all modes, are based on the value of the reduced velocity bandwidth specified in the *.dat file. Example: If St = 0.2 then Vr,crit = 5.0. The lock-in bandwidth or power-in reduced velocity

band then extends to either side of Vr,crit according to the formula ,max , 12

rr

dVV Vr crit = +

,

,min . 12

rr

dVV Vr crit = −

. If the bandwidth is specified as 0.4 then the upper and lower

bounds of Vr are 5.0 + or - 20% or 4.0 to 6.0.


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A broader reduced velocity range increases the size and correlation length for each mode's power-in region. The bandwidth may be quite broad for low-density cylinders under low mode number lock-in conditions in nearly uniform flow. If the user wishes to be deliberately conservative, a value of 0.5 to 0.7 may be used. In sheared flow, with multiple modes remaining after applying the cutoff, the correlation length of the power-in region is shorter. In the Miami-Deepstar tests on a high mode number model, the observed reduced velocity bandwidth was approximately 0.4. [Swithenbank, Ph.D. thesis, MIT January 2007]. Other VIV model tests in uniform flow on flexible cylinders have also shown that the reduced velocity bandwidth is typically 0.25 to 0.35. Hence, 0.4 should work well for most cases. If the user wishes to be deliberately conservative, the one might use 0.5 to 0.7. The Strouhal number and reduced velocity bandwidth should be chosen while considering the CL tables. The peak lift coefficient in the CL table is assumed in SHEAR7 to occur at a frequency ratio value of 1.0. This value will correspond to , 1/ tVr crit S= . Frequency ratio is defined in Appendix 1 “Understanding Lift coefficients in V43 through V46”. The range of the frequency ratio and CL values appearing in the CL table should be at least as wide as the reduced velocity bandwidth. Frequency ratios and reduced velocities are now written to the *.out file for every node and mode in the power-in regions.

b. Strouhal Code: The Strouhal number, St, uniquely defines the relationship of flow velocity and cylinder diameter to the local vortex shedding frequency. For vibrating cylinders at subcritical Reynolds numbers, the Strouhal number varies between 0.14 and 0.18. Above about 100000 in Reynolds number the Strouhal number for stationary cylinders varies erratically in published data from about 0.2 to 0.5. Recent model tests reveal that the Strouhal number for freely vibrating cylinders varies from about 0.14 to 0.18 for Reynolds numbers varying from 20,000 to over 1 million. We recommend the use of 0.18 throughout the range as a conservative estimate of St. In the program the inverse of St is used as an estimate of Vr,crit, the critical reduced velocity at which the cylinder would achieve maximum response under lock-in conditions. The power-in region for each mode is centered on Vr,crit and has a reduced velocity double bandwidth, which is specified in the input data file. Hence, one's choice of St and the reduced velocity double bandwidth dictates the position of the power-in region for each mode.


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The Strouhal number may be specified as a number, such as 0.18, or user can select code 200. Code numbers 100 and 300 that were used in earlier versions are now disabled. If code 200 is specified, then a lookup table of Reynolds number versus Strouhal number is used as depicted in the figure. Code 200 is for a rough cylinder. Below Re=20,000 St=0.17, above Re=90,000, St=0.24. It varies linearly with Re between 20,000 and 90,000. This curve is very conservative. For most applications, St=0.18 is appropriate for all Reynolds numbers. c. Lift coefficient reduction factor The program allows the user to modify the lift coefficient iteration scheme. The lift coefficient reduction factor is multiplied by the Cl value in the Cl tables. Thus a value less than one reduces the value of Cl at all A/D and frequency ratio values by the same factor. A value of greater than 1.0 may be used to enhance the lift coefficient in the iteration.

In the *.out file the reported lift coefficient, includes the results of multiplying the lift coefficient table by this factor. A conservative default setting is 1.0 for all cases. Because SHEAR7 uses a non-linear response relationship in the iteration which determines the lift coefficient, the lift coefficient reduction factor does not have a linear effect on the predicted response amplitude. Because of the new capability to model the CL behavior directly, it should be rare that a reduction factor different from 1.0 is used.

d. Lift Coefficient Table to be used: This is the fourth number in the row. It specifies which Cl table from the common.cl table should be used. Table 1 results in conservative values of lift coefficient. Table 2, is based on curves which were fitted to the measured data on bare cylinders. It is less conservative, because it is based on mean values of measurements, and hence will produce mean value estimates.

Lift coefficient tables for modeling VIV suppression zones: In earlier versions of SHEAR7 the lift coefficient reduction factor was used to model strakes. This has been replaced by a

00.05

0.10.15

0.20.25

0.3

10000 100000 1000000 10000000

Stro

uhal

Num

ber

Reynolds Number

Strouhal Number versus Reynolds Number

St code 200


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superior method—using a Cl table customized to model the behavior of strakes, including some damping. CL Table 3 is an extremely conservative approximation to a riser with strakes. Table 5 is a less conservative approximation to the performance of 25% high, 15 D pitch strakes, manufactured by AIMS International.

Table 5 is based on sub-critical model tests of strakes 25% high and a pitch of approximately 15, manufactured by AIMS International. With 100% coverage, these strakes totally suppressed VIV at subcritical Reynolds numbers during the Miami and Lake Seneca Deepstar/MIT tests. Table 5 is intended to be conservative, but much less so than Table 3. Table 5 will result in hydrodynamic damping for A/D values greater than 0.15 in the power-in region, and will permit a maximum value of CL of 0.1 at an A/D=0. Thus this strake model will cause some positive power in at low A/D and substantial damping at A/D over 0.15. Typical response of a riser with partial strake coverage, will be driven mostly by the unprotected region, with the straked region providing damping. [See Jaiswal and Vandiver, OMAE2007]. See Appendix 6 for more details on modeling strakes in V4.6. The program now allows individual specification of CL behavior in different zones. The user can select a zoneCLtype from a given table that comes with the program or specify their own. This process is described in Appendix 1 : “Understanding Lift coefficients in V4.3 through V4.6” Table 4 is supplied as a dummy table for users to change. Further tables can also be added from Table 7 and upwards. Please remember to increment the number of CL tables listed in the common.cl file (nCLtype, line 2 in the common.cl) EACH and EVERY time you add a new custom table to that file.

Emulation of SHEAR7 V4.2 lift coefficient table. There is now one way to do this. In the zone specification indicate that CL table 1 is to be used. This table uses a CL versus A/D parabola to approximate the V4.2f CL table. The results of response calculations will be similar to that from V4.2f., when single mode response is specified.

7.2.2.14 Line 7, 1.0 0.2 0.18 0.2 , added mass coef, three hydrodynamic damping coefficients: for still water, low and high Vr regions.

a. Added mass coefficient: The added mass coefficient should be adjusted to account for external added mass as well as for the mass trapped in floodable voids in the cylinder, if not already included in the in air weight. A value of 1.0 implies an added mass equal to the mass displaced by a solid cylinder of the specified external hydrodynamic diameter. Note, added mass is known to be dependent on the reduced velocity [2, 7]. Therefore, no single value is known to be the best for this application. At the present time, the authors suggest choosing a value between zero and one and consistently staying with it.

The results are most sensitive to added mass when the density of the cylinder is low, such as neutrally buoyant risers. In this program the added mass primarily affects the predicted natural frequencies. SHEAR7 does not iterate to find the added mass for each mode and reduced velocity distribution. As a consequence the program is not ideally suited to replicate experimental results exactly at low mode number. This is of little practical importance in design. A variety of current profiles should be tested to cover the probable range of behavior that will be exhibited by the riser over its life.


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b. Three hydrodynamic damping coefficients: for still water, low and high Vr regions The user may specify the hydrodynamic damping in each zone. A doubling of the coefficients will double the hydrodynamic contribution to the damping contributed by that zone. This line has three numbers such as 0.2, 0.18 and 0.2, which are the standard bare cylinder values. These are, respectively, the still water, low and high reduced velocity region damping coefficients. If you change these numbers you will change the hydrodynamic damping for the zone when it is not part of the power-in region for a particular frequency. To learn more about hydrodynamic damping see the 2000 OTC paper number 11998 by Vikestad provided with the reference collection of papers, which may be obtained from the MIT SHEAR7 web site, http://web.mit.edu/shear7 When a section of the riser is not part of the power-in region, then the program will use the damping coefficients specified in that structural zone for the sectional damping calculations.

Caution: Do not attempt to model too much detail in the zones: The zone capability in Shear7 should not be used to include small structural details of the riser, such as the BOP, the LMRP, the flex joint and the slip joint. It is not yet known how to hydrodynamically model many of these structures and Shear7 does not model them dynamically. Hence, including such details in a Shear7 model only increases the likelihood of modeling and computation errors. A recommended approach is to include such structural details in the FEM calculations used to compute the mode shapes and natural frequencies of the riser, Only include zones in SHEAR7 that are needed to model the important hydrodynamics. Typically, zones should be used to distinguish between long segments, which have significant changes in diameter, damping, or require different lift coefficient tables, such as zones with strakes or fairings. Very short length features, which will not significantly alter the overall hydrodynamics, should be neglected.

Use Caution when using the internal eigensolver and multiple structural zones! The multiple zone feature in Shear7 may not give accurate natural frequency and mode shape information, especially at high mode number, when sudden changes in mass or stiffness occur in the riser model. This is because SHEAR7 ‘s internal eigensolver uses the WKB approximation, which assumes slowly varying properties, such as mass per unit length and moment of inertia, to estimate the natural frequencies and mode shapes. For example, buoyancy modules cause large jumps in mass and sudden changes in effective tension. Wave reflections at these boundaries are not modeled correctly by the WKB method. It is recommended that the natural frequencies and mode shapes of complex structures be computed using an external finite element program. The results can then be used to prepare a common.mds file for use with calculation option 2.

When the common.mds file option is used, the tension distribution, obtained from the structural zone data, is not used in the Shear7 computations. However, the mass distribution does influence the modal mass computation, which in turn is used to compute damping ratio. Similarly, the hydrodynamic diameter distribution influences the hydrodynamic lift and damping calculations. These lift and damping values are used in computing the modal response amplitude.


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7.2.3 Block 3, Specification of Current Profiles All version releases require that the first line of the velocity profile begin with the minimum value of x/L, which is usually 0.0 and increase from there to the maximum value of x/L for which the current is specified. The velocity profile does not need to be monotonic. However the program does not account for variations in current direction or for current reversal. It is recommended to put in the absolute value of a profile which has a current reversal. The velocity profile is assumed to come from a single direction and is perpendicular to the riser. If the flow is not perpendicular, it is recommended that the vector component of the current flow velocity which is perpendicular (normal) to the cylinder be used as input. This is valid up to about a 45 degree incidence angle. Recent research suggests that the VIV excitation diminishes rapidly with current angle greater than 45o to the riser [Swithenbank, 2007]. Although flow reversal is not allowed, the results from SHEAR7 are conservative, and for most cases realistic. The power-in region for any single mode is usually much shorter than the length of the entire profile. Within each power-in region the variation in flow direction is limited. Although the flow in two different power-in regions may have quite different directions, the damage rate due to each power-in region is computed separately and then summed, as if they were from the same direction. This produces a conservative result. The program recognizes three types of flow regions. They are: (1) an area not in the water, where there is neither added mass nor hydrodynamic damping. (2) a section in a flow region, which has associated with it hydrodynamic damping and added mass. (3) a section in still water, which also has added mass and hydrodynamic damping associated with it. Sections at one or both ends are assumed to be out of water if they are left out of the velocity profile specification. All submerged regions must be specified in the velocity profile whether in still or moving water. The following example profile is to illustrate this 6,1.0,200 number of vel. pt., probability of occurrence, profile ID 0.0, 0.0 location(x/L), velocity (m/s or ft/s) for first point 0.225 ,0.0 location (x/L), velocity (m/s or ft/s) of each succeeding point 0.2255, 3.8 0.35, 4.5 0.41, 5.8 0.449, 0.0 0.969, 0.0 Interpretation of this profile: There are 6 points specifying the profile as specified in line 1. The first specified point is at x/L = 0.0 with a velocity of 0.0. The second point is at x/L = 0.225 with a velocity of 0.0. Hence these first two points define a still water region. The profile then jumps quite suddenly to a value of 3.8 at x/L=0.2255 and rises linearly to 4.5 at x/L=0.35, and continues to increase until reaching 5.8 at x/L=0.41. The speed then drops linearly to 0.0 at x/L = 0.449. From


39

x/L = 0.449 to 0.969 the riser is again in still water. Between x/L = 0.969 and 1.0 the velocity profile is not specified and hence is interpreted as being out of the water. If a portion is out of water, its velocity should NOT be defined. In this way, the program interprets whether or not a node is in water, and is able to compute correctly the hydrodynamic damping and added mass. Specification of current data in Block 3 6,1.0,200 number of velocity points in profile, probability of occurrence, profile ID 0.04 , 4.30 location(x/L), velocity(m/s or ft/s) for first point (lowest x/L value 0.1333 , 4.29 location and velocity of each succeeding point 0.2667 , 2.42 location and velocity of each succeeding point 0.5000 , 1.49 location and velocity of each succeeding point 0.9733 , 1.00 location and velocity of each succeeding point 1.0 1.00 location and velocity of each succeeding point 7.2.3.1 Line 1 Block 3 specifies the current data. It always begins with a line with three numbers,

specifying the number of velocity points in profile, the probability of occurrence of the profile, and a user specified profile ID number.

a. The number of points specifying the profile: The profile is piecewise linear and must have at least two points.

b. annual probability of occurrence: This number must be between 0.0 and 1.0. It is the probability of the occurrence of this flow profile in one year. This quantity is multiplied by the computed damage rate before it is given in the output file. If one uses 1.0 in the input, the final damage rate is not affected.

c. flow profile ID: This number is reported in the output file to help users with profile bookkeeping. It is not used in the program.

7.2.3.2 Lines 2 through the end of the profile:

Each pair of points is used to define the profile. One pair of numbers per line, starting with the minimum value of x/L specifying the profile. The first number is the location in the x/L global coordinate system, which must be consistent with the coordinate system used to specify the tension. The second number is the flow speed in m/s or ft/s depending on the unit system. In a region in which the flow is specified, including zero speed, there is added mass and hydrodynamic damping. If a region is not specified at the top or bottom of the profile, it is assumed to be out of the water, and has no added mass or hydrodynamic damping. See Section 4.0 on specifying current profiles in this guide and the EXCEL file currents.xls for further description of velocity profile specifications.

7.5 Block 4. S-N and SCF data (example data follows): *** Block 4. S-N and scf data 1 NEW: No. of S-N curves defined 1 1 NEW: S-N curve I.D., No. of S-N curve segments 0.0000 cut-off stress range (ksi)


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0.4010E+01 0.1000E+09 stress range (ksi) cycles to failure 0.4700E+02 0.1000E+05 stress range (ksi) cycles to failure 1.000 global stress concentration factor 2 no. of local stress concentration positions 0.1000 1.400 location (x/L), stress concentration factor 0.7000 2.100 location (x/L, stress concentration factor

In V4.3 the x/L locations selected to apply SCF’s had to coincide EXACTLY with node locations. In V4.4 through V4.6 the user can now use approximate x/L locations using sufficient accuracy to identify the nearest node. The program now reports the stress and damage rate at the NEAREST nodes. Block 4 must include at least 1 S-N Curve definition, like in the example above. More curves can be defined optionally and they can but do not have to be used by the program. In other words Block 4 can include both required and redundant S-N Curve definitions. 7.5.1 Line 1: Number of S-N curves defined in Block 4 There is no limit on the number of S-N

Curves defined. The option of local specification of fatigue curves that can be structural zone specific is first introduced in V4.6. If only one S-N Curve is defined this number would be 1.

7.5.2 Line 2: S-N curve I.D., Number of SN curve line segments a. S-N curve I.D.: This number must start with 1 for any optional curves defined it must be incremented by 1. Each S-N Curve definition consists of at least 4 lines formatted like lines 2 through 5 in the example above. If more line segments are used to define any of the S-N Curves used, more lines must be added, while each of those lines is formatted like lines 4 or 5, see 6.4.2.b below.. b. Number of S-N Curve segments: For fatigue calculations the minimum number of S-N Curve segments is one. Most SN curves consist of one line segment on a log-log plot. Two SN pairs are needed to specify each SN curve line segment. Only two SN points (could) be used in all versions of SHEAR7 prior to 4.2f. Versions 4.2f through 4.5 allow for up to 5 line segments. In version 4.6 the above limit of the S-N curve segments is increased to 10, but program versions with arbitrarily higher maximum numbers can be complied on demand. Each of the S-N Curves defined in Block 4 can utilize any supported number of segments. Two segments require three S-N pairs, three segments require four S-N pairs, etc.

7.5.3 Line 3: Cutoff stress range, ksi or N/m**2. This is the stress range value on the curve where the number of cycles to failure is infinite. This is sometimes called the endurance limit. In seawater for most metals this is taken to be 0. 7.5.4 Lines 4 and 5 (for 1 line segment) Stress range in (N/m**2) or (ksi), and cycles to failure for point 1. These values are given one pair to each line. The first number is the stress range and the second is the number of cycles to failure corresponding to this stress range. This is followed by the next SN pair on the next line. On a log-log plot the S-N curve is assumed to be linear between these points. The stress range for the different points must be in increasing order.


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The sets of lines like those described in Sections 6.4.2 through 6.4.4 can be repeated in V4.6 in order to define additional S-N Curves. 7.5.5 Line 6 (in the example above): Global stress concentration factor: The RMS stress computed by SHEAR7 for the entire structure is multiplied by this value before the damage rate is computed. In cases where optional, local SCF values are defined, those optional SCF values OVERRIDE the global SCF value. 7.5.6 Line 7 (in the example above): Number of local stress concentration positions, followed by

x/L, SCF pairs: an example is given above where two local SCF's are specified. If SCFs are specified at approximate locations on the cylinder, the program will move the specified location to the nearest node. In version 4.3 the local SCF factors needed to be specified at exact nodal locations (lines 8 & 9 in the example).

Note (V.4.3 through V4.6): In cases where optional, local SCF values are defined, those optional SCF values OVERRIDE the global SCF value. Accordingly, if the user specifies a global SCF that differs from 1.0 and also specifies local, any SCF multiplications (if desired) of the local SCFs by the global SCF must be done manually and the resulting numbers must be used as input to the *.dat file (lines 8 & 9 in the example). It is easy to verify the above for any particular set of nodes by observing the effects of varying SCFs on the RMS stress values printed to the *.plt file. Example: If you use a global SCF of 2.0 in a 1001 node model and a local SCF value in node 11 is 3.0, the SCF values used at nodes 1 through 10 and 12 through 1001 are 2.0. At node 11 Shear7 would use the SCF value 3.0, not 6.0. If you wish that latter value were 6.0, you must enter 6.0 at node 11 location in the *.dat file.

7.6 Block 5. Computation/Output Options (example follows): *** BLOCK 5. computation/output option *** 1 calculation option(0=fn’s only,1=full calc, 2=imported modes) 0.0 1.0 0.1 response location definition for the *.out file 0 no. of user input modes 0.0 gravitational acceleration(ft/s**2) 0.4 reduced velocity bandwidth 0.7 0.65 power cutoff, dominant mode amplitude cut-off 1.0 power ratio exponent (1=power ratio;0=equal probabilities) 0 flag for importing nodal effective tension and mass (0=no; 1=yes) 0 flag for writing the *.anm file (0=no, 1=yes) 0 flag for generating *.scr file, (0=no; 1=yes) 0 flag for generating *.dmg file, (0=no; 1=yes) 0 flag for generating *.fat file, (0=no; 1=yes) 0 *.out file selection: 0=*.out, 1=*.out1, 2=*.out1+*.out2 7.6.1 Line 1: Calculation option, 0 will result in the natural frequencies and modes shapes only

being computed and put in a root-name.mds file. 1 is the normal use in which the program does the full natural frequency, mode shape and response computation. 2 is the response computation using externally prepared modal information placed in a file called common.mds.

7.6.1.1 Preparation of common.mds files for option2: The modal range defined in the common.mds file should be large enough so that it covers all possible excited modes in all current states to be used plus a multiple of around three (3)


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times higher modes. One way to determine the number of modes for the maximum current case is to first run the program with calculation option 1 and with a trial current profile which has the maximum current intended in all profiles to be used. SHEAR7 will use its internal model of, for example a beam with linearly varying tension to compute the required natural frequencies and mode shape information. By checking the root-name.mds file the user can determine the natural frequency(in rad/sec) of the highest mode used in the run. The user then prepares a common.mds file, typically using a finite element program. The FEA modes must have natural frequencies which are at least as large as the largest one found in the root-name.mds file after running under option 1. The user-prepared common.mds file must then contain the frequency, mode shape, mode slope and curvature for all modes which have natural frequencies up to the largest in the root-name.mds file, obtained by running the program in calculation option 1. Note that the natural frequencies listed in the root-name.mds are in radians/second. It is noted, that while generating common.mds files from FEA it is advisable to use slope and curvature values computed by the FEA programs and NOT TO USE simple deflection or/and slope numerical differentiation schemes in spreadsheets etc. The latter can lead to significant errors or even cause the program to stop, in particular when high mode numbers are excited. It is noted that, for example, both ABAQUS and ANSYS programs compute all the values required for the generation of the common.mds file.

If one is making many runs using calculation option 1, it may be advantageous to run the maximum current case first, rename the resulting root-name.mds file to common.mds, and then switch the calculation option to option 2 for all remaining computations. This saves the computation time of repeatedly computing the modal frequency and shape information. For a riser with high mode number this can be a significant fraction of the total computation time. The line by line specification of the common.mds file format is described in section 5.4 of this guide.

7.6.1.2 Specification of uneven nodal spacing: This was enabled in V4.3 but requires further

testing and should be checked carefully the first few times it is used. It requires special preparation of the common.mds file, described next. Non-uniform spacing can only be used for program calculation option 2, which requires the user to prepare in advance a common.mds file. In order to invoke the non-uniform spacing, the user provides the x/L values at each node as an additional sixth column of numbers in the mds file for the first mode only, as seen in the example on the next page. Note that if in the rootname.dat file the number of spatial segments is given as ‘n’ then the number of nodes at which one must give the x/L value is n+1. Node 1 and node n+1 specify the boundaries.

Example: (Format of mds file) ------- 23 201 <===== No. of Natural Modes, No. of Nodes 1 0.17976 <===== Mode number, natural frequency in radians/s 2 0.36067 " 3 0.54384 " 4 0.73044 " 5 0.92146 " 6 1.11794 " 7 1.32067 " 8 1.53060 "


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9 1.74825 " 10 1.97497 " 11 2.21075 " 12 2.45685 " 13 2.71325 " 14 2.98060 " 15 3.25966 " 16 3.55060 " 17 3.85403 " NEW INPUT 18 4.16997 " --------- 19 4.49903 " | 20 4.84122 " | 21 5.19716 " -------------- 22 5.56747 " x/L Values 23 5.95091 " -------------- |---------------------------------------------------------------------- | 1 1 0.00000E+00 0.19498E-02 0.00000E+00 0.00000000E+00 | 1 2 0.19781E-01 0.19422E-02 -0.77830E-06 0.50000000E-02 | 1 3 0.39481E-01 0.19340E-02 -0.83655E-06 0.10000000E-01 First| . Mode | . | . | 1 199 0.21998E-01 -0.10878E-02 0.21063E-06 0.99000000E+00 | 1 200 0.10956E-01 -0.10856E-02 0.22029E-06 0.99500000E+00 | 1 201 0.00000E+00 -0.10834E-02 0.00000E+00 0.10000000E+01 |---------------------------------------------------------------------- | 2 1 0.00000E+00 0.37499E-02 0.00000E+00 | 2 2 0.38038E-01 0.37339E-02 -0.18103E-05 | 2 3 0.75890E-01 0.37131E-02 -0.22883E-05 2nd | . Mode | . | . | 2 199 -0.42661E-01 0.21144E-02 -0.28219E-06 | 2 200 -0.21194E-01 0.21112E-02 -0.36373E-06 | 2 201 0.00000E+00 0.21071E-02 0.00000E+00 |---------------------------------------------------------------------- . |---------------------------------------------------------------------- | 23 1 0.00000E+00 0.28668E-01 0.00000E+00 | 23 2 0.28419E+00 0.26613E-01 -0.39914E-03 | 23 3 0.52770E+00 0.20757E-01 -0.73984E-03 Last | . Mode | . | . | 23 199 0.52016E+00 -0.23021E-01 -0.37423E-03 | 23 200 0.27003E+00 -0.25921E-01 -0.19325E-03 | 23 201 0.00000E+00 -0.26900E-01 0.00000E+00 |---------------------------------------------------------------------- ----------- ------------ ------------ ^ ^ ^ | | | Mode Shape Slope Curvature 7.6.2 Line 2, locations for output summary:

This line specifies the response locations at which a summary of the response is given in item 14 of the *.out file. This is meant for quick summary information only. It is not necessary to use a very fine spacing here. This line has three numbers corresponding to the beginning , ending and increment x/L values in the output table. This line does not affect the *.plt file which gives the output at all nodal points.

7.6.3 The user mode specification facility has been discontinued in V4.6 and the corresponding

data Entries (one + optional lines) have been removed from *.dat file. Users requiring that capability are advised to use V4.5.


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7.6.4 Line 3: Acceleration of gravity for tilt contamination estimation. If zero, then gravity is not included in the estimate of the RMS acceleration. If equal to the acceleration of gravity in the appropriate SI or English units, then the predicted RMS acceleration will include the effect of tilt at each point on a VERTICAL riser. This feature is implemented in structural models (nmodels) 1 and 10 only, the beam or cable with linearly varying tension. For all other nmodels the mode slope provided in the *.mds file will be zero. There must always be a column in the *.mds file for the slope. When preparing a common.mds file using a finite element program, it is normal to make the values in the modal slope column equal to 0.0, unless one wishes to have tilt included in the RMS acceleration.

7.6.5 The entry of the global reduced Velocity Bandwidth has been removed. In V4.6 structural

zone specific Reduced Velocity Bandwidth values are input in the Structural Zone definitions in Block 2.

7.6.6 Line 4 has two entries: The power ratio cutoff level is first:

The power cutoff level controls how many discrete modal power-in regions exist. In the program, the maximum input power and the corresponding mode is first identified. The input power level for each potentially excited mode is then divided by the maximum input power, resulting in a ratio of each mode's estimated input power to the maximum input power found for all modes evaluated. If this ratio for a particular mode is less than the cutoff value, this frequency will be excluded in the final response calculation.

The cutoff level is a number, which should always be positive and less than or equal to 1.0 When this number is very small, nearly all modal frequencies, potentially excited, will be identified and used in the response calculation. When set to 1.0, only the mode with the maximum available input power from the fluid will be included in the response calculation; in effect forcing the program to a single frequency lock-in calculation.

The higher the cutoff level, generally the more conservative the estimate, for low mode number cases. A value of 0.5 means that if any mode has a power level greater than 50% of the mode with the maximum power level, then the mode will be included in the response. The higher the cutoff level, the fewer the modes remaining in the analysis. Fewer modes, means that less smoothing will occur in the RMS predicted response over the length of the riser. A cutoff of one will result in a single frequency, single resonant mode computation. The RMS response and fatigue damage rate will typically have pronounced peaks and zeros corresponding to the absolute value of the mode shape. This has been found to not correspond to real data. Real measurements show some smoothing of the peaks, which suggests several frequencies participating in the response. The recommended value for this cutoff is 0.05 with the introduction of version 4.5 to allow response averaging over several frequencies. No matter what this level is set at, the preliminary power ratio of all modes is listed in the *.out file.

If several modes have input power comparable to maximum input power ratio, then a single mode response is not likely to occur. If there are two or more modes with an input power


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ratio greater than, for example, 0.9, then single mode lock-in is not likely. The more modes above 0.9 the less likely is single mode lock-in response. The setting of the cutoff value is a subject of active research. A setting of 0.5 to 0.7 was suggested with previous versions of SHEAR7, however, with the time sharing introduced in version 4.5 we now recommend using low power cut-off such as 0.05. This has the effect of smoothing the damage rate over the x/L range. For high mode number response, a low cutoff is the best approach, because substantial time sharing is likely to occur, resulting in considerable smoothing in the RMS response over the length of the riser.

7.6.7 Line 4, second entry: Primary zone amplitude limit.

The primary zone amplitude limit entry was first introduced in V4.5 together with time sharing. In addition to the occurrence of time sharing, it is recognized that those modes that have well separated power-in regions may be able to respond simultaneously. This is because waves created in one power-in region attenuate as they travel along the riser. If two power-in regions are sufficiently far apart, the waves generated in one will not be large enough to affect the excitation in the power-in region of the other. In such instances, they could both be allowed to occur at the same time. The possibility of independent and simultaneous occurrence of some modes has been accommodated in version 4.5 in an approximate way by allowing up to three independent time sharing zones on the riser. These zones are made independent by allowing the time sharing probabilities to add up to one, independently in each of the time sharing zones. The existence of secondary power-in zones is determined by the rate of decay of waves created by the dominant mode, as they travel away from the power-in region. The amplitude of the traveling wave decays exponentially with the distance traveled. The rate of decay depends on the distance traveled, the wavelength and the damping ratio as given in the following approximate formula.

where: AMM - dominant mode, M, amplitude at XM, the center of its own power-in region. AMN - dominant mode amplitude at XN, the center of the mode N’s power-in region. M - damping coefficient for mode M, the dominant mode XN - geometrical center on the riser of the power-in region for any mode, N. XM - geometrical center on the riser of the power-in region for the dominant mode M. L - length of the riser

When the wave from the power-in region of the dominant mode drops below a user-selected limit, then it is assumed that the wave is no longer large enough to disrupt the formation of a new power-in region at a different frequency. This is a subject of current research, but a reasonable value to choose for this limit is 0.3, which is to say that when the waves from the dominant mode excitation region decay to 30% of their initial value, one has entered a secondary zone in which VIV at a different frequency is allowed to exist simultaneously.

exp( / )MNM N M

MM

A M X X LA

πζ= − −


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This user-specified value for this amplitude limit must have a value between 0 and 1.0. The larger the value, the larger secondary zones will be, and more likely secondary power-in regions will be allowed to exist at the same time as the modes in the primary region. Hence, higher limits are more conservative. The primary zone amplitude limit is entered by the user in line 4 of Block 5 of the *.dat file. It must be between 0 and 1.0 and is recommended at 0.3, for the present. Power-in regions located close to that of the dominant mode will be associated with wave decay amplitudes that are close to 1.0 and will be in the primary zone. These modes will time share their probability of occurrence with the primary mode. All power-in regions, located where the amplitude has decayed to less than the user-assigned limit will belong to one or two secondary independent time-sharing zones, located on the riser each to either side of the primary time sharing zone. Three time sharing scenarios are possible:

• There is only one, primary time sharing zone on the riser: this happens when the amplitude of the dominant mode is greater than the limit set in the *.dat file everywhere on the riser.

• There are two independent time sharing zones on the riser: this happens whenever the amplitude of the waves from the dominant mode are smaller than the limit on only one side of the dominant power-in zone;

• There are three independent time sharing zones: when there are secondary zones on both sides of the primary time sharing zone.

The amplitude limit must not be smaller than 0.0 and not greater than 1.0.

Selecting a limit of 0.0 results in a single (primary) time sharing excitation zone on the riser; Setting the limit higher than 0.0 and smaller than 1.0 results in selecting from one to three independent time sharing excitation zones on the riser, a primary zone and up to two secondary zones; Setting the limit to 1.0 results in forcing only the dominant mode to be in the primary zone and all others in 1 or 2 secondary zones. An exception is when the current is uniform. All the modes share the same zone and more than one may be included in the primary zone, even if the limit is set to 1.0.

A detailed example is presented in Appendix 3. It shows an example in which a strong surface current is the source of a dominant power-in region corresponding to mode 48. A distant region, with low velocity but considerable length excites mode 10. Depending on the selection of the amplitude cutoff, mode 10 is excited in a secondary zone simultaneously with mode 48.

7.6.8 Line 5: Power Ratio exponent.

This entry was first introduced in V4.5. Further parametric investigation can be carried out by examining the effect of the power ratio exponent. With the exponent set to the recommended value of 1, the ranking ratios are equal to the power ratios. With a value of


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the exponent equal to 0.0, one gets all the ranking ratios equal to 1.0. Equal mode time sharing probabilities in each of the time sharing zones result. An example is shown at the end of APPENDIX 5.

7.6.9 Line 6: Is a common.cat file provided? (0 = NO, 1 = YES) If this flag is ‘0’ then the user need not prepare a common.cat file. If a ‘1’ is specified, then the user must prepare a file named common.cat file, containing the tension variation and the mass per unit length distribution. The common.cat file has three columns. An excerpt from the common.cat file provided with example scr1.dat is given here: 1 16560.00000 3.49485 2 17252.16992 3.49485 3 19644.23828 3.49485 4 25114.49805 3.49485 5 18115.56055 3.49485 6 16726.47852 3.49485 7 16799.23828 3.49485 8 16884.77344 3.49485 9 16982.9082 3.49485 10 17093.45312 3.49485 11 17216.18164 3.49485 12 17350.8418 3.49485

The first column is the x/L value of each node or the node number in ascending order. The number of entries must be equal to the number of segments specified in the *.dat file plus one. The second column is the tension at each node and the third is the mass/unit length at each node. The mass per unit length must include the added mass and the mass of contents and it must be in slugs/ft or kg/m, depending on the unit system being used. This allows the user to vary the mass/length in the WKB integral to find the natural frequencies and mode shapes. For best results one should not attempt to model abrupt changes in mass/length. The WKB integral in the program assumes slowly varying quantities and is unable to model wave reflection which occurs at large changes in mass per unit length. When a common.cat file is not desired put a "0" at the appropriate line in the input data file. When the common.cat file is not used, the program computes an average mass per unit length from the structural zone data and uses the average value to compute the natural frequencies and mode shapes.

7.6.10 Line 7: Flag for MATLAB animation (0 = No, 1= Yes) For creation of the , animation*.anm

file. *.anm files are used by the Matlab program s7movie.m. This program and a subroutine called s7movie2.m must be in the Matlab path. Upon running a GUI opens and asks the user for the *.anm file which you wish to animate. They can be very large files. This flag should be 0, unless one wishes to be able to be able to create a mode superposition time domain animation of the VIV. Try example scr_import_tension.dat to see a demonstration of an animation file. The *.anm files can also be quite large and should not be used unless needed.


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7.6.11 Line 8: Flag for the generation of the *.scr file (0 = no, 1= yes). Please see Section 5.4.5 for a brief description of new features added to the *.scr file that might be useful for identifying some errors in the *.dat files. It is advised to always generate *.scr files while building or de-bugging new models.

7.6.12 Line 9: Flag for the generation of the *.dmg file (0 = no, 1= yes). This file lists the Rayleigh

fatigue per year results for all resonant mode numbers at each node. See Section 5.4.6 for the detailed description. This fatigue damage rate has not been multiplied by the time sharing probability.

7.6.13 Line 10: Flag for the generation of the *.fat file (0 = no, 1= yes). The .fat file consists of the

total response amplitude and phase angle for every node for every response frequency. Combining this with mode shape information allows one to reconstruct times series of stress at every node for time domain fatigue damage computation purposes. This is useful when one wants to combine stress time histories from several sources, such as VIV and vessel motion.

7.6.14 Line 11: Flag for the generation of the *.out1 or the *.out1 and the *.out2 files (0=*.out,

1=*.out1, 2=*.out1+*.out2). The new *.out1 file can be used in order to decrease the size of the *.out file, by redirecting the printout of Item 13 (*.out file) , to the *.out1 file. For each power-in mode and node, Item 13 or the optional *.out1 file include the listings of the lift coefficient, the non-dimensional frequency and the reduced velocity in the power-in zones. The *.out2 file can be used for research purposes or for cross-checking. The *.out2 file includes the lift coefficient, the sectional damping, the non-dimensional frequency and the reduced velocity. Those are listed for the power-in modes at each node of the structure. 7.7 Block 6. Supplemental data: There are several structural models which require additional data. Most of them are cases with rotational or translational springs attached at one of the ends of the riser. When one of these “nmodels” , 6, 9, 19, or 33 are specified in Block 2, Line 1, then one or more additional data lines are inserted immediately after the Block 6 Header. Block 6. Supplemental Data, used only for nmodels:6, 9, 19, & 33. 0.10000E+07 rot stiffness at x=L:lbf-ft/rad 0.10000E+07 rot stiffness at x=0:lbf-ft/rad. The above two lines are rotational spring constants as used in example basic_beam_3.dat which is a beam with rotational springs at the ends. Any text written after the last item of data expected by the program will be ignored. Hence the following lines are placed in many of the sample *.dat files. if nmodel = 6 (pinned-pinned tensioned beam w/two rot springs) provide rotational stiffness at each end if nmodel = 9 (free-pinned (w/spring) beam w/varying tension, origin at free end) provide translational stiffness at x = L if nmodel = 19 (free-pinned (w/spring) beam w/o tension, origin at free end)


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provide translational stiffness at x = L if nmodel = 33 (inclined cable) provide chord inclination (angle)


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8.0 Interpretation of SHEAR7 Output Files As has been described previously, the seven possible output files from SHEAR7 are: "root-name.out", "root-name.plt", "root-name.scr", , “root-name.anm”, "root-name.dmg", "root-name.fat" and "root- name.mds". The ".out" file is discussed below. The presentation method used below is to list the complete results of running the example case “basic_beam_3.dat”. The output file “basic_beam_3.out” is listed below. Additional explanation is given in a bold typeface and placed at appropriate points throughout the example output file. The file begins with a notation, which includes the version number of SHEAR7 which was used to obtain the file. Immediately following is a complete listing taken from the input data file, which in this case was “basic_beam_3.dat” ****************************************************** ****************************************************** ** ** ** SSS H H EEEEE A RRRR 777777 ** ** S S H H E A A R R 7 ** ** S H H E A A R R 7 ** ** S H H E A A R R 7 ** ** S HHHHH EEEE AAAAA RRR 7 ** ** S H H E A A R R 7 ** ** S H H E A A R R 7 ** ** S S H H E A A R R 7 ** ** SSS H H EEEEE A A R R 7 ** ** ** ****************************************************** ****************************************************** Copyright 1994-2011 Massachusetts Institute of Technology Distributed by AMOG Consulting Version 4.6c 9:00 am 20 January 2011 Single Site License AMOG Consulting filename: basic_beam_3.out this is an output file from "SHEAR7" the input file name is: basic_beam_3.dat YOU HAVE INPUT: =============== *** BLOCK 1. unit system *** flag for units: 1 English *** BLOCK 2. structural and hydrodynamic data *** flag for structural model: 6


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total length of the structure (ft.): 1500.000 number of spatial segments: 100 volume weight of the fluid (lbf/ft**3): 64.000 kinematic viscosity of the fluid (ft**2/s): 0.1400E-04 structural damping coefficient: 0.00300 effective tension at origin (lbf): 224809.0 no. of zones to define sectional property: 1 start and end point of each zone in x/L: 0.0000 1.0000 hydrodynamic,strength,inside diameter(in) 84.000 46.000 42.000 inertia (ft**4) 0.3233E+01 mass (lbf/ft) 2296.140 sbmg wt (lbf/ft) 166.87 elastic modulus (ksi): 0.3002E+05 SN Curve I.D. No: 1 dVR, St code, Cl reduction factor, zoneCLtype: 0.500 0.180 1.000 1 added mass coeff, hydrodynamic damping factors: 1.000 0.200 0.180 0.200

In Block 2 the structural model is nmodel=6. This is a linearly varying tension beam with rotational springs on both ends. There is one structural zone with 5 lines of data. Note the zone specific bandwidth, the Strouhal code number has been set to 0.18 Also listed are the values of the Ca = 1.0 and the 3 damping coefficients, which correspond to the still water, low Vr and high Vr terms respectively. *** BLOCK 3. current data *** profile data pts: 6 probability: 0.100E+01 profile ID: 200 location (x/L) and velocity (ft/s): 0.040 4.3000 location (x/L) and velocity (ft/s): 0.133 4.2900 location (x/L) and velocity (ft/s): 0.267 2.4200 location (x/L) and velocity (ft/s): 0.500 1.4900 location (x/L) and velocity (ft/s): 0.973 1.0100 location (x/L) and velocity (ft/s): 1.000 1.0000 Unspecified regions are out of water.

Block 3 describes the current profile used. The high surface flow region begins at x/L = 0.04, because in this case the origin of the global coordinate system was put at the top of the riser. The tension of this riser increases as it goes deeper, indicating that the riser is positively buoyant. Also, since the region between x/L = 0.0 and 0.04 has not been mentioned above, it must be out of the water. *** BLOCK 4. s-n and scf data *** no. of S-N curves defined: 1 S-N Curve I.D. No. 1 no. of S-N curve segments: 1 cut-off stress range for this curve (ksi): 0.0000 stress range (ksi),cycles to failure: 0.4010E+01 0.1000E+09 stress range (ksi),cycles to failure: 0.4700E+02 0.1000E+05 global stress concentration factor: 1.000 no. of local stress concentration positions: 0 Block 4 lists the SN curve(s) defined and SCF data.


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*** BLOCK 5. computation/output option *** calculation option: 1 internal modes used in analysis response location definition: 0.0000 1.0000 0.1000 input gravitational acceleration (ft/sec**2): 0.000 cutoff to eliminate modes: 0.0500 primary zone amplitude limit: 0.3000 power value exponent used: 1.0000 flag for importing nodal tension & mass: 0 no flag for MATLAB animation data output: 0 no flag for generation *.scr file output: 0 no flag for generation *.dmg file output: 0 no flag for generation *.fat file output: 0 no flag for generation *.out_ file output: 0 *.out

Block 5 tells us that the calculation option selected is 1, for a complete natural frequency and mode shape computation as well as the VIV response computation. Gravity contributions due to tilt have not been included in the acceleration computation. If they had been included, it is always assuming the riser mean position is vertical. The power cut-off is set at 0.05, and the amplitude limit, which determines the beginning of any secondary power-in zones is set at 0.30. The power exponent is 1.0 which means the probability of modes is proportional to the power ratio for the mode. No *.cat file is expected, no *.anm file is to be created, but an *.scr trouble shooting file is created as output. No *.dmg file is created and no *.fat file is created. *.out file is generated.

cutoff to eliminate modes: 0.0500

A single value of the reduced velocity bandwidth is still used for all modes and zones during the preliminary calculation; that value is the maximum bandwidth value of the zone specific values. That maximum zone bandwidth used in the preliminary calculation is listed in the *.out file, Block 5 at the location corresponding to the echo of the global reduced velocity value that was used in V4.5. *** BLOCK 6. supplemental data *** rot stiffness at x=L: 0.10000E+07 lbf-ft/rad rot stiffness at x=0: 0.10000E+07 lbf-ft/rad. Lift Coefficient Data CL Table Set No.: 1 This CL Table used in the following sectional property zones: 1 Number of frequencies: 1 ndFreq aCL0 aCLmax CLmax CL0 CLfloor 0.10000E+01 0.11000E+01 0.30000E+00 0.70000E+00 0.30000E+00 -0.10000E+01 The supplemental data is the rotational spring constant information at each end, which is required because nmodel 6 was chosen. Immediately following the Block 6 input data is a listing of only those CL tables that have been called for in the *.dat file.


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Next in every *.out file comes the results of computations. THE RESULTS OF PROGRAM ANALYSIS =============================== 1. You have selected the following options: 1.1 CALCULATING NATURAL FREQUENCY and MODE SHAPE and VIV response with following structural model: pinned-pinned beam (w/two rot springs) (varying tension) 1.2 The English unit system 1.3 The following damping factors are used: 1 0.200 0.180 0.200 In 1.3 above are listed the zone number and the three damping model coefficient values 0.20, 0.180 and 0.20, which are the standard bare cylinder values. 2. Structural dynamic behavior. 2.1 String or beam? Tk^2/EIk^4 = 0.229E+00 When the above value is less than 30 you should use the beam model. Item 2.1 is a very useful check on the model being used. When this value is greater than 30, the bending stiffness, EI, does not significantly affect the natural frequency computation. Tension is dominant and therefore the user may want to use the cable structural model because it is computationally faster. In this example EI is important, and the beam model is necessary. 2.2 Modes in excitation bandwidth, natural frequency, modal ranking ratio, mode participation factors: F = force; L = length; T = time. modal modal modal power power ratio mode no. frequency force damping power ratio raised to (Hz) (F) (F*T/L) (F*L/T) to max the exponent ---------------------------------------------------------------------- 1 0.0176 0.000E+00 0.107E+05 0.000E+00 0.00000 0.000E+00 2 0.0426 0.105E+04 0.586E+04 0.936E+02 0.02886 0.289E-01 3 0.0788 0.321E+04 0.529E+04 0.975E+03 0.30074 0.301E+00 4 0.1277 0.601E+04 0.557E+04 0.324E+04 1.00000 0.100E+01 No. of potentially excited modes: 3


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Item 2.2 is a consequence of one of the most important steps in the program’s VIV modeling. In this step the program identifies all possible excited modes. In turn each one is assigned the full length power-in region, based on the reduced velocity bandwidth assigned in the input data file. Overlap with other power-in regions is ignored. Modal force, modal damping and modal power are computed and a ratio of modal power to the largest one is taken. The cutoff value assigned is compared to the power ratios and only those above the cutoff are retained for the final VIV analysis. In this case only Mode 3 and 4 are retained as they have a power ratio greater than 0.05 to Mode 4.. The last column lists the mode ranking ratios and is equal to the power ratios raised to the exponent input file, which was 1.0. The exponent value of 1.0 should be used in most cases. These are used to compute the modal time sharing probabilities, see Table 2.2.1. The modal time sharing probabilities are proportional to the mode ranking ratios. When the exponent of 1.0 is used, the last two columns in Table 2.2 list the same numbers.

Table 2.2 summarizes the results of the Preliminary Power Calculation. A single value of the reduced velocity bandwidth is still used for all modes and zones during the preliminary calculation. In each zone, straked or bare, the maximum CL value CLmax for any lift curve selected is used to compute the modal force and the modal power for each mode. The maximum mode amplitude a/D = 0.5, the Strouhal Number and ‘the maximum zone bandwidth used in the preliminary calculation’ are used for that purpose. 2.2.1 Results of the Mode Interaction Analysis: Based on the non-zero power-in lengths and the power cutoff value of: 0.05 the number of modes above cutoff is: 2 These modes are: Time Share Excitation Dominant Mode Probabilities: Zone # Amplitude: 3 0.2312 1 0.9551E+00 4 0.7688 1 0.1000E+01 -------- -------- Cumulative sum: 1.0000 Primary zone amplitude limit: 0.3000 Lowest And Highest Excited Mode Number Nmmin= 3 Nmmax= 4 The primary time sharing modes are those, whose centers of action fall close to that of the dominant mode. In this zone the dominant mode amplitude is greater than or equal to the primary zone amplitude limit. Wherever the dominant mode amplitude is smaller than the limit value, modal power-in regions are assigned to secondary time sharing zones. Zone number 1 in Table 2.2.1 is the primary time sharing zone. Secondary zones are numbered 2 or 3. The time share probabilities in each of the independent time sharing zones add up to 1.0. Please note that when there are many modes above cutoff, and if the number of nodes is not large enough, some of the modes that are above cutoff may not get any input power region, and therefore they may also be dropped out. These modes are insignificant to fluid input power.


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Table 2.2.1. lists those modes that exceed the power ratio mode cut-off value selected. These mode numbers are listed in column 1. Their time sharing probabilities, excitation zone numbers, and amplitude ratios values are listed in the remaining columns. The cumulative sum of the time sharing probabilities is listed at the bottom of the table. The dominant mode amplitude limit is also printed under the table for easier cross-reference with the amplitude ratios. 2.3 Ratio of change of vel to average vel: 1.65 The number of excited modes and the velocity ratio together provide insight as to the likelihood of lock-in. The velocity ratio is the change in velocity in the profile(Vmax-Vmin) divided by the spatial average velocity of the profile. Zero velocity regions are excluded from the average. This is a measure of the amount of shear in the profile. Both very large shears(greater than 1.2) and very small ones(less than .4) are known to provide particularly favorable conditions for single mode dominance as is the case here. 2.4 Finite or infinite system behavior? Dominant mode amplitude exponents: MODE WAVE Dominant_m to n# Dominant_m to n# NUMBER PROPAGATION DISTANCE MODE AMPLITUDE # PARAMETER RATIO EXPONENT n n*zeta_n DelX/L pi*zeta_m*m*|DelX|/L ---------------------------------------------------------------- 3 0.1353 0.1163 0.0459 4 0.1256 0.0000 0.0000 When the value n*zeta_n in the table is greater than 2, infinitely long structural behavior dominates. When this value is less than 0.2, spatial attenuation is small. The dominant mode amplitude exponents listed are those used in the computations of the amplitude values listed in Table 2.2.1. Please note, that for the dominant mode the |DelX|/L=0.0 and the mode amplitude value equals 1.0. Similarly, in uniform currents all the mode centers of action coincide, |DelX|/L=0.0 and the mode amplitude values also equal 1.0.

n is the mode number and nζ is the total modal damping including structural and hydrodynamic sources. The product nnζ is a measure of the spatial attenuation that occurs as a wave travels along a structure. It is therefore a measure of the dynamic length of the cable, independent of the real length. A cable is “long” in a dynamic sense when waves die out before reaching the far end. It is “short” when very little decay occurs and the waves reflect from the ends creating a standing wave pattern from end to end. Reference 1 explains how n*zeta, the product of the modal damping ratio and the mode number provides insight on the dynamic behavior of the system. Two new columns are added to this table in comparison with previous program versions. The formulae used to calculate all the numbers listed in Table 2.4 are quoted in the headings of each column. nnζ is used to compute the amplitude ratios listed


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in the new Table 2.2.1, the exponents used are now listed in Table 2.4. The last column lists the exponent used to compute the amplitude of waves from the dominant mode power-in region at the location of the center of the power-in region for the mode listed in the table. In this case the listed mode is the dominant mode, since only one mode exists above the power cutoff. 3. The ratio of the change of tension to the average tension: 0.7152 The bigger the ratio, the larger the variation in tension. 4. Structural Properties zone air mass mass ratio total mass inertia steel area hydro area slugs/ft slugs/ft ft**4 ft**2 ft**2 ----------------------------------------------------------------------- 1 0.714E+02 0.73 0.148E+03 0.323E+01 0.192E+01 0.385E+02 In the above table, if mass ratio is zero, it means that this zone is out of water.

Item 4. is a useful summary of the properties of a section, as computed internally using the data provided by the user. For example the inertia provided here is the area moment of inertia, I, as used to compute bending stiffness, EI. It is computed from the inside and outside diameters of the strength material for the zone. It is not necessarily the same as the I value provided by the user, which may account for other contributions such as internal tubulars. The steel area is the area defined by the strength diameters. The hydro area is the area of the cross-section with the specified hydrodynamic diameter. The total mass per unit length includes the computed added mass plus the mass per unit length given in the input data file and repeated here as the first column. The mass ratio is according to the definition in the literature: 2/m Dρ , where m does not include the added mass. However, structural mass, including trapped internal fluid mass is included if it was included in the mass/length in the input file. 5. Fundamental natural frequency = 0.017599(Hz) 6. Maximum flow velocity: 4.3000 ft/s Minimum flow velocity: 1.0000 ft/s 7. The highest Strouhal frequency is: 0.12163(Hz) at node: 5 The lowest Strouhal frequency is: 0.01929(Hz) at node: 101 8. Minimum wavelength corresponding to the maximum flow velocity= 750.00(ft) The minimum wavelength is computed based on the average tension in the structure and the maximum VIV frequency.


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9. Modal damping ratio "zeta", modal mass, and modal frequency for the mainly excited modes. mode no. damping ratio modal mass(slug) frequency (Hz) ------------------------------------------------------- 3 0.04509 107301.069 0.07878 4 0.03140 107434.283 0.12769 The modal damping ratio is the sum of the hydrodynamic damping computed in the program and the structural damping placed by the user in the input data file. 10. Information on mode overlap. There is mode overlap; the overlap part(s) Item 10 tells the user if the reduced velocity bandwidth which is being used resulted in overlapping power-in regions. Power-in regions normally overlap, when more than one mode is above the cutoff. 11. Modal Displacement Amplitude Mode No. Amplitude (ft or m) --------------------------------- 3 2.82116 4 3.39343 SHEAR7 is a mode superposition program. Item 11 gives the maximum magnitude of each resonant mode’s contribution to the final sum. It is the peak value and not an RMS value. In general this value will not exactly agree with the final response amplitude reported in Item 14. This is because the final response amplitude, even if at only one frequency, includes the contributions of resonant and non-resonant modes. 12. Modal excitation region. Mode No. No. of Nodes Length Ratio -------------------------------------- 3 13 0.129 4 14 0.139 Portion of the structure which is subject to flow is from 0.0400 L to 1.0000 L. Portion of the structure which is out of water is from 0.0000 L to 0.0400 L.


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The number of nodes reported above for each modal excitation region gives a direct measure of what fraction of the total length is used by that mode for power-in. The exact location of those nodes is found by seeing where the lift is applied in the next item. 13. Lift coefficient for each mode. In the following, the lift coefficient is the amplitude and not the RMS value. Iteration, change in Reynolds number, and user input Cl reduction in suppression zone are taken into account. mode number: 3 node number Cl Fn/Fvo VR -------------------------------------------- 18 0.6898 0.8119 6.84 19 0.6908 0.8431 6.59 20 0.6925 0.8767 6.34 21 0.6946 0.9132 6.08 22 0.6967 0.9528 5.83 23 0.6986 0.9961 5.58 24 0.6998 1.0434 5.32 25 0.6994 1.0955 5.07 26 0.6932 1.1530 4.82 27 0.6786 1.2169 4.57 28 0.6541 1.2723 4.37 29 0.6182 1.2938 4.29 30 0.5697 1.3160 4.22 mode number: 4 node number Cl Fn/Fvo VR -------------------------------------------- 5 0.6814 1.1548 4.81 6 0.6992 1.1551 4.81 7 0.6988 1.1554 4.81 8 0.6939 1.1557 4.81 9 0.6868 1.1559 4.81 10 0.6790 1.1562 4.80 11 0.6722 1.1565 4.80 12 0.6672 1.1568 4.80 13 0.6649 1.1571 4.80 14 0.6657 1.1574 4.80 15 0.6694 1.1845 4.69 16 0.6755 1.2252 4.53 17 0.6829 1.2689 4.38 18 0.6905 1.3159 4.22 The reported lift coefficients are those values which result from the lift coefficient iteration as a function of A/D and the frequency ratio. They include all applied factors such as the lift coefficient reduction factor. Also tabulated in the third column is the normalized frequency ratio, as used in the .CL table. The fourth column gives the local reduced velocity at each node. Whenever the user redirects Item 13 listing to the new, optional *.out1 file the above listing is printed in that file and item 13 of the *.out file list the following instead:


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“User requested that the contents of this item be redirected to an optionally generated file *.out1.” 14. RMS response and damage rate at specified locations. Modes used in mode superposition calculation are from mode 1 to mode 7. English units: displacement = feet; acceleration=ft/s^2; stress=ksi. RMS A/D is RMS displ /local hydro diameter 14.1 x/L RMS displ RMS A/D RMS acc RMS stress damage(1/years) -------------------------------------------------------------- 0.000 0.000 0.000 0.000E+00 0.784E-01 0.149E-05 0.100 2.176 0.311 0.132E+01 0.871E+01 0.737E+02 0.200 1.520 0.217 0.811E+00 0.529E+01 0.971E+01 0.300 1.402 0.200 0.883E+00 0.566E+01 0.157E+02 0.400 2.037 0.291 0.125E+01 0.804E+01 0.562E+02 0.500 0.989 0.141 0.297E+00 0.244E+01 0.798E+00 0.600 2.087 0.298 0.131E+01 0.818E+01 0.614E+02 0.700 1.177 0.168 0.725E+00 0.449E+01 0.634E+01 0.800 1.601 0.229 0.873E+00 0.550E+01 0.117E+02 0.900 2.105 0.301 0.128E+01 0.779E+01 0.492E+02 1.000 0.000 0.000 0.000E+00 0.000E+00 0.000E+00

Item 14 is the summary of the VIV computation. Column 1 in the table specifies sample output points as specified by the user in the *.dat file. Column 2 is the RMS response amplitude in real displacement units. Column 3 is Column 2 divided by the local diameter. If diameters change along the length one must beware as to the interpretation of this column. Columns 4, 5 and 6 are the RMS acceleration, stress and the fatigue damage rate. The fatigue damage rate is based on the RMS stress and the Rayleigh formula for damage rate, which assumes the stress comes from a narrow band random process. The damage rate shown in the last column above has been multiplied by the probability of occurrence of the current profile. 14.2 Maximum damage rate & its position for each excited mode Mode No. Location (x/L) damage rate upcrossing frequency (Hz) ---------------------------------------------------------------- 3 0.160 0.962E+00 0.07878 4 0.120 0.843E+02 0.12769 The individual maximum modal damage rates given above have not been multiplied by the probability of occurrence of the current profile. In addition these individual rates will not be exactly the same as that shown in the .plt files or given in the response table above. The reason is that these rates are only for the individual resonant mode and do not include the non-resonant contributions of other modes at the same frequency. These modal maximum damage rates and their locations are given only to assist the engineer in determining potential


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trouble spots associated with particular modes. This may be useful in determining which regions are candidates for VIV suppression. 14.3 The Overall Maximum RMS displacement (OMRD) is 2.300 ft OMRD occurs at x/L= 0.130 14.4 The Overall Maximum RMS Stress (OMRS) is 9.074 ksi OMRS occurs at x/L= 0.120 14.5 The Overall Maximum Fatigue Damage (OMFD) is 0.851E+02 OMFD occurs at x/L= 0.120

The overall maximum values given in 14.3, 14.4 and 14.5 above, result from searching every nodal point in the *.plt output file. These values include the contributions from all modes, resonant and non-resonant, and include the effect of the probability of occurrence of the current profile on the fatigue damage rate. 15. Re,St,and drag amplification factor x/L T (lb) V (ft/s) Re St Cf ------------------------------------------------------------- 0.000 224809.0 0.0000 0.0 0.180 1.000 0.100 249839.5 4.2935 2146774.2 0.180 1.766 0.200 274870.0 3.3550 1677500.0 0.180 1.607 0.300 299900.5 2.2883 1144141.6 0.180 1.575 0.400 324931.0 1.8891 944570.8 0.180 1.734 0.500 349961.5 1.4900 745000.0 0.180 1.459 0.600 374992.0 1.3885 694260.0 0.180 1.745 0.700 400022.5 1.2870 643520.1 0.180 1.514 0.800 425053.0 1.1856 592780.1 0.180 1.627 0.900 450083.5 1.0841 542040.2 0.180 1.750 1.000 475114.0 1.0000 500000.0 0.180 1.000 In the table, Cf is the drag amplification factor due to VIV response. The product of Cf and drag coefficient gives VIV amplified drag coefficient. T is effective tension.

Item 15 is a useful check for a variety of items. One may also verify that the effective tension variation has been modelled correctly by checking the second column in item 15. The local mean drag amplification factor, Cf, accounts for response caused amplification. This should be multiplied by the user chosen stationary cylinder CD value. The amplification factor depends on the rms A/D. This amplified CD value is a reasonable one to use in static configuration calculations which require an estimate of the mean drag coefficient, including the effects of VIV. 16. Computational resolution. The user-input number of spatial segments: 100


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The program-suggested number of spatial segments: 35 The above value is defined as below. It is assumed that the minimum wavelength equals twice of the structure length divided by the maximum mode number. It is also assumed that in each wavelength, 10 segments would be sufficient. The user-input number of spatial segments should be greater than or at least equal to the above program-suggested value. However, to adequately model the lift force distribution, the user-input number should not be too small. When the number of segments is small, the results can be sensitive to it.

Users should avoid defining structural zones that are very short in length and should ensure that each zone includes many nodes. This is especially relevant to third party software developers that provide automatic generation of SHEAR7 input files as output from their software.


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9. 0 REFERENCES Most of the following references and many others may be downloaded from the SHEAR7 research web site at MIT. http://web.mit.edu/shear7 or sending email to Prof. Vandiver, [email protected] 1. Jaiswal, V., Vandiver, J.K., “VIV Response Prediction for Long Risers with Variable Damping” OMAE2007-29353 , Proceedings of OMAE 2007: 26th International Conference on Offshore Mechanics and Artic Engineering, June 10-15, 2007, San Diego, USA 2. Jauvtis, N., and Williamson, C. H. K., “The effect of two degrees of freedom on vortex-induced vibration at low mass ratio”, J. Fluid Mech., vol. 509, pp. 23-62, 2004 3. Jhingran, V. and Vandiver, J.K., 2007, "Incorporating the Higher Harmonics in VIV Fatigue Predictions", Proceedings of OMAE2007, OMAE2007-29352 4. Marcollo, H., Vandiver, J.K., & Chaurasia, H, “Phenomena Observed in VIV Bare Riser Field Tests“, OMAE2007-29562, Proceedings of OMAE 2007: 26th International Conference on Offshore Mechanics and Artic Engineering, June 10-15, 2007, San Diego, USA 5. Swithenbank, S. and Vandiver, J.K., "Identifying the Power-in Region for Vortex-Induced Vibration on Long Flexible Cylinders", OMAE2007-29156, Proceedings of the 26th International Conference on Offshore Mechanics and Artic Engineering, June, 10-14, San Diego, CA., USA. 6. Swithenbank, S., “Dynamics of Long Flexible Cylinders at High-Mode Number in Uniform and Sheared Flow”, MIT Department of Mechanical Engineering, Doctoral dissertation, 2007, supervised by Prof. J. Kim Vandiver. 7. Vandiver, J.K., "Dimensionless Parameters Important to the Prediction of Vortex-Induced Vibration of Long, Flexible Cylinders in Ocean Currents", Journal of Fluids and Structures, July, 1993. 8. Vandiver, J. K. and Gonzalez, E., "Fatigue Life of Catenary Risers Excited by Vortex Shedding", Behavior of Offshore Structures Conference, Delft, Netherlands, July 1997. 9. Vandiver and Marcollo "High Mode Number VIV Experiments", IUTAM Symposium On Integrated Modeling of Fully Coupled Fluid-Structure Interactions Using Analysis, Computations, and Experiments, pp. 211-231, Rutgers University, June 1-6, 2003, Edited by H. Benaroya & T. Wei, Kluwer Academic Publishers, Dordrecht. 10. Vandiver, J.K. and Chung, T-Y., “Predicted and Measured Response of Flexible Cylinders in Sheared Flow”. Proc., ASME Winter Annual Meeting Symposium on Flow-Induced Vibration, Chicago, December 1988. 11. Vandiver, J. K., and Peoples, W. “The Effect of Staggered Buoyancy Modules on Flow-Induced Vibration of Marine Risers”, Proc. 2003 Offshore Technology Conference, OTC-15284


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12. Vandiver, J.K., Swithenbank, S.B., Jaiswal, V. and Jhingran V., 2006, “Fatigue damage from high mode number vortex-induced vibration”, Proceedings of OMAE2006, OMAE2006-9240 13. Vandiver, J.K., Marcollo, H., Swithenbank, S. and Jhingran, V., 2005, “High Mode Number Vortex-Induced Vibration Field Experiments”. Offshore Technology Conference OTC 17383. 14. Vandiver, J.K., Swithenbank, S., Jaiswal, V. and Marcollo, H. 2006, “The Effectiveness of Helical Strakes in the Suppression of High-Mode-Number VIV”, OTC 18276. 15. Vikestad, K., Larsen, C.M., and Vandiver, J.K., “Norwegian Deepwater Program: Damping of Vortex-Induced Vibration”, OTC Paper 11998, Proceedings of the Offshore Technology Conference, May 2000, Houston. 16. Marcollo, H.; Vandiver, J.K., OMAE2009-80028 Partial Strake Coverage Vortex-Induced Vibration benchmarking using Shear7v4.5. 17. Resvanis, T., Vandiver, J.K., 2011, Modelling Risers with Partial Strake Coverage, OMAE2011-49817.


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10. 0 SAMPLE *.DAT FILES AND PLOTTING PROGRAMS 10.1 For a complete listing of sample files see the EXCEL file named “EXAMPLES-v4.6_rev1.pdf” on the distribution CD. 10.2 UTILITY PLOTTING PROGRAMS (WITHIN MATLAB ENVIRONMENT) plotdgui-si.m This Matlab file will plot the rms displacement data in the .plt files for SI units. plotdgui-en.m This Matlab file will plot the rms displacement data in the .plt files for English units. plotvgui.m This Matlab file will plot the rms velocity data in the *.plt files. plotacgui This Matlab file will plot the rms acceleration data in the *.plt files. plotdrgui.m This Matlab file plots the damage rate in the *.plt file. plotskgui.m This Matlab file plots the rms stress in the *.plt file. s7movie.m and s7movie2.m are MATLAB files that create a time domain simulation of the response of the riser. Both files must be in the MATLAB path. Type s7movie in MATLAB to run. A GUI will pop open and ask you to select the *.anm file you wish to see animated. The user may check off the modes he wishes to include in the simulation or may choose to include all modes. The user must adjust the speed slider to some value greater than zero or the simulation will not run. This simulation reveals the spatial attenuation on long risers. The MATLAB animation files allow animations at single frequencies at a time or with a superposition of two or more excited nodes. With the introduction of time sharing single frequency animations are most common with V4.5 and above. Animations using multiple simultaneous frequencies are appropriate when the frequencies are selected from the primary and secondary response zones. Try the example scr_import_tension.dat to use the animation feature.


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11. TROUBLESHOOTING V4.5 & V4.6 The following should be checked if v4.5 is failing to run:

11.1 No Mode Found - When the program is unable to find a mode and stops, yielding no results. This problem is most often the result of having a rather short (low mode number) riser in a uniform current. Several factors are at play in this problem. They are the separation in natural frequencies close to the Strouhal frequency, the reduced velocity bandwidth, and the shear in the profile. The problem usually results when at all points on the riser the local computed shedding frequency, plus or minus the variation allowed by the reduced velocity bandwidth, does not include any natural frequencies. The solution is to increase the shear, or increase the reduced velocity bandwidth. In some cases the maximum velocity is so low that the vortex shedding frequency is less than the first natural frequency. Recommended practice:

1. Start with a substantial linearly sheared flow which goes from 0.0 speed to the greatest speed you will ever encounter.

2. Set the power cutoff to a low number, such as 0.01, so as to include all possible modes. 3. When you run the program the *.out file will tell you all of the possible excited modes and

their natural frequencies. 4. If you wish to try a uniform profile, use the Strouhal number you have selected to compute a

vortex shedding frequency for the velocity you are interested in. fvo=St*U/D. See what natural frequency is closest to it. Compute the ratio of the natural frequency to the shedding frequency.

5. Let R = fn/fvo . 6. Compute the reduced velocity range necessary to excite this mode. 7. dVr > 2*magnitude(1-1/R) 8. If dVr is unreasonably large, i.e. greater than say 0.5 or 0.7 then the program is trying to tell

you that indeed this may be a case for which lock-in will not happen, because the shedding frequency is not close enough to any available natural frequency. This will only happen for very low mode numbers, such as modes 1 or 2. For high modes dVr is large enough to overlap several natural frequencies.

11.2 Additional tips when the program fails to run

11.2.1 Enable the output of the *.scr file by putting a 1 rather than a 0 at the appropriate spot in block 5 in the *.dat file. Then look for the point in the *.scr file that reading input data failed. The program echoes the information in the *.dat file as it calls for it. When incorrectly formatted data is encountered the program stops at that point. This will give you a clue as to where to look in the*.dat file for the problem. Examples follow for typical problems. 11.2.2 a. Problems with the CL type: Check in the*.dat file that there is a value for zoneCLtype

in line 4 of each zone. This is found in Block 2


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*** BLOCK 2. structural and hydrodynamic data *** The zoneCLtype should be the 4th number in the 4th line of the zone, right after the CL reduction factor. In the 5th line in the specification for each zone should be the three damping coefficients.

b. Check that the right value for calculation option has been chosen.

c. Check that the new, V4.4 through V4.6 version of the common.cl file is used. After opening the file with Wordpad, Notepad, etc. you should see 6 columns in each CL data table. The new, last column should be labeled CLfloor. This column was not included in the old, V4.3 format of common.cl.

d. Check the *.scr file (and in the *.out) file that the sectional zone data are correctly interpreted by the program. In cases where the user (or a third party program) generates very large numbers of very short segments numerical resolution problems may arise, which may lead to errors and in some cases the program execution might stop. The cure is to increase the segment size and/or to make sure that the x/L values defining the sectional zone ends and/or the current velocity profiles coincide with the x/L coordinates of the nodes used.

11.2.3 Run the program with the calculation option = 1 (line 1, Block 5 of the *.dat file), nmodel=1 (line 1, Block 2 of the *.dat file), and compare the *.mds file generated with your common.mds file. Similar numbers of modes should be included in both files, the mode shape plots should look similar, if plotted in a spreadsheet, and the frequency increments should be regular and similar. It is better (and very slightly conservative) to include more modes in the common.mds file rather than less modes. Make sure that only lateral oscillation modes in the direction that is approximately transverse to the current direction are listed in your common.mds file. The result of Shear7 runs for the two models mentioned here should be similar in most cases. Make sure that the number of nodes you specify in block 2 of the *.dat file is the same as that used in your common.mds file.

11.2.4 Check the lengths of the smallest x/L increments in your model that define:

• Structural zones in BLOCK 2 of the *.dat file • Current profile in BLOCK 3 of the *.dat file

If any of those is shorter than the half of your element length, or even the element length, it is likely that your model is defined incorrectly. If you define your model in such a way, SHEAR7 would try to allocate both segment/zone ends to the same node and the program will crash. If you cannot see the complete model input echo in the *.scr file, or the echo is printed to the *.scr file, but your element properties are not, it is likely that either:

• you have (a) problem(s) described above in this item, or


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• there are errors or problems with any of Shear7 input files. Those include your *.dat file, your optional common.mds file, (problems like for example, but not necessarily those described in item 11.2.3). That can also mean that there are errors in your common.cl file or the optional common.cat file.

• Your model may be outside the cross-flow VIV range; check the omg_min and omg_max values (rad/s) listed in your *.scr file vs. the procedure described in Item 11.1 above. The omg_min and omg_max values (rad/s) are the ends of the oscillation frequency interval pertaining to your model and your current profile, in which cross-flow VIVs can happen. The same values are also displayed in the command window pertaining to your run, for load cases where you may not have cross-flow VIV oscillations. You will see those values displayed, if you run Shear7 in the command window.

All the files you need to run your model must be present in the same folder. If any of those files are missing, the program will not run. It is a good practice to always print *.scr file while debugging your models. It can help you identify those problems and also other problems that may arise during the execution of the program. The contents of the *.scr file is printed to that file during the step-by-step execution of Shear7. Accordingly, the place where that printing ends can help you to identify the calculation step where a problem has arisen. You can compare your incomplete *.scr file with a complete one and correlate the contents of the incomplete *.scr file with the description of the computational steps in Shear7 described in this User Guide.


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12.0 FILE MANAGEMENT AND*.DAT FILE CONVERSION PROGRAMS A program for automatic conversion of SHEAR7 V4.5 to V4.6dat files is provided. It is called convert_v45_to_v46.exe. This program will convert all of the *.dat files in a directory from V45 *.dat files to V4.6 *.dat files. The names of the files are not changed. Therefore, if you want to retain the original V4.5 *.dat files then put a copy in a separate directory. To use the program highlight the required .dat files in Windows, and drag them over the top of the convert_v45_to_v46.exe program then release.


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APPENDIX 6: DAMAGE RATE PREDICTION WITH PARTIAL STRAKE COVERAGE Recent experimental results in laboratory and field tests have shown that helical strakes can be very effective in reducing the VIV response of a long flexible structure, even when helical strakes do not cover 100% of the structure (i.e. partial coverage). SHEAR7v4.6 can be used to assess the effects of various partial strake coverages and the relative influence they have on the response. However, all of these experimental results which show the effectiveness of helical strakes only relate to helical strakes which:

• Have a specific geometry (strake height = 25% of diameter; Strake pitch = 17.5 diameters) • Are clean (do not have marine fouling) and are undamaged • It is also noted that the published experimental results have been obtained from mostly low

Reynolds number testing. The performance of strakes at high Reynolds numbers still remains somewhat less certain.

Modelling Partial Strake Coverage SHEAR7v4.6 allows the user to define a different Reduced Velocity Bandwidth (dVr) for each structural zone on the riser. Assigning straked zones smaller St and dVr will prevent a given mode’s power-in region; centered on a bare portion of the riser, from extending into the straked portion. This will then allow that straked portion to be power-out. This happens because the ‘jump’ in St values between the two structural zones (straked and bare) will change the localized

ratio considerably, forcing the power-in length to stop at the interface of the two zones. It is important to note that the inverse also applies, i.e. there will be modes that have power-in lengths covering only the straked portions of the riser with the bare zones being power-out (this is especially true in sheared currents). This is not a problem however because if the Straked Structural Zone uses the appropriate CL curve -one with very little positive lift- the total power into this mode will be very small and this mode will be cut-off, when more powerful bare regions exist elsewhere. The proposed modeling parameters were chosen by calibrating Shear7 with data from the 38m NDP riser which responded mostly in high mode numbers (10-15). Following this calibration, the same parameters were used to predict the response of the Deepstar-Miami II riser which responded at even higher mode numbers (~ 30). It will be shown that the parameters chosen from the initial calibration are well suited to predict the response of the Miami riser. More details can be found in [17] OMAE2011-49817. The recommended parameters for modeling partially strake covered risers are summarized in Table 6-1.

Table 6-1 Recommended Parameters for Partially Straked Risers for SHEAR7v4.6 Parameter Value

Bare regions Ca 1 St 0.18 Cl table 1 Damp. Coef 0.2, 0.18, 0.2 Vr bandwidth 0.4


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Straked regions Ca 2 St 0.10 Cl table 5 Damp. Coef 0.4, 0.5, 0. 2 Vr bandwidth 0.25 General Cl reduction factor 1 Primary Zone Ampl. Limit 0.3 Power Cutoff 0.05 Power Value Exponent 1 Figure 1 demonstrates the drastic difference in response predictions that these changes allowed. The figure shows how the predicted RMS displacement and Damage Rate vary along the length of the riser for the 50% straked NDP riser in a uniform current of 2.0 m/s. Note the exponentially decaying displacement in the straked portion of the riser. The .DAT file used to create the predictions in figure 1 is at the end of this appendix. Figure 2 compares the SHEAR7v4.5 and v4.6 predicted strain with the measured strain (1x) for the Miami riser with 50% strake coverage in the middle. Figure 3 show the results of modeling the entire NDP 50% Straked Riser dataset (Uniform + Sheared Flow) using this approach. The figure compares the predicted and measured damage rates. Every color corresponds to a different test case (current velocity) and the data points within each color group correspond to different sensor locations along the riser. In such plots of predicted vs. measured damage rates, when the points lie above the equality line (Dpred=Dmeas) the VIV prediction software is over-estimating the damage rates i.e. the program is being conservative. In general it is desirable that the predictions be conservative, but excessive conservativeness leads to unnecessarily expensive designs. Figure 4 compares the predicted and measured (1x) strains for 11 different tests from the Miami II experiments in various current profiles. It includes measured data and predictions for 3 different strake configurations: 50% strake coverage at the center, 40% strake coverage at the bottom and 25% strake coverage on either end. Most points in Figure 4 lie above the equality line (i.e. Shear7v4.6 is being conservative) and agree within one order of magnitude with the experimental results, in fact the majority of points are less than two times the measured value. A factor of 2 in strain corresponds to a factor of 23=8 in damage rates, roughly one order of magnitude, entirely


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consistent with what is seen in Figure 3. Only a few points have been under-predicted.

Fig 1 (left) comparison of SHEAR7v4.5 and v4.6 predicted RMS displacement along the NDP riser. (right) Comparison of predicted and measured damage rates along the riser (note: log scale).


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Fig 2 Comparison of SHEAR7v4.5 and V4.6 predicted strain and the 1x measured strain along the Miami riser when it had 50% strake coverage along its center. (test #: 20061023175030)


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Fig 3 Predicted vs. Measured Damage Rates for the 50% strake covered NDP riser in uniform (circular data points) and sheared flows (triangular data points).


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Fig 4 Predicted and Measured (1x) strain for the partially strake covered cases from the Miami II experiments.


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Modelling Full Strake Coverage The parameters listed under table 1, can also be used to mode fully straked risers. The results produced will generally be conservative as demonstrated in figures 5 & 6. Figure 5 compares the predicted and measured Damage Rate for the fully straked NDP riser in uniform flows. Figure 6 compares the predicted and measured Damage Rate for the fully straked NDP riser in sheared flows.

Fig 5 Measured and predicted Damage Rates for the 100% strake covered NDP riser in uniform flows


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Fig 6 Measured and predicted Damage Rates for the 100% strake covered NDP riser in sheared flows. Modelling Risers with partial fairings (weather-vaning) coverage Modeling a riser with fairings is very similar to the method used for strakes. The only real difference is that zones with fairings are not allowed to have any power-in (i.e. Fairings work perfectly). Fairings are a source of substantial damping which is reflected in the recommended coefficients. This represents an idealized method to model fairings. Future research is still needed to improve the ability to model fairings. The recommended parameters for risers with fairings for Shear7v4.6 is shown below in Table 6-2.


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Table 2 Recommended Parameters for Risers with Fairings for SHEAR7v4.6

Parameter Value Bare regions Ca 1 St 0.18 Cl table 1 Damp. Coef 0.2, 0.18, 0.2 Vr bandwidth 0.4 Regions with Fairings

Ca 2 St 0.10 Cl table 5 Damp. Coef 0.4 , 0.5 , 0. 4 Vr bandwidth 0.0 General Cl reduction factor 1 Primary Zone Ampl. Limit 0.3 Power Cutoff 0.05 Power Value Exponent 1

Strouhal number and Cl-table are irrelevant since the dVr=0 and the zone with the fairings is excluded from the Power-In region

Always “Power-out”


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Example .DAT input fileData file for testing SHEAR7 38m-NDP riser (SI units) File Name: NDP50Uni.dat *** BLOCK 1. unit system *** 0 flag for units *** BLOCK 2. structural and hydrodynamic data ***

10 flag for structural model 38.0 total length of the structure (m) 1000 number of spatial segments 1000 volume weight of the fluid (kg/m**3) 1.3E-06 kinematic viscosity of the fluid (m**2/s) 0.00300 structural damping coefficient: 5042 effective tension at origin (N) 2 no. of zones to define sectional property

0.0 0.5 zone start and end point in x/L 0.027 0.027 0.021 hydro strength inside diameter(m) 1.65405E-08 0.933 0.0 inertia(m^4) mass(kg/m) sbmg wt(kg/m) 2.25E+09 1 modulus of elasticity (N/m**2), S-N Curve I.D. No. 0.25 0.10 1.00 5 bandwidth, St code Cl reduction factor:, zoneCLtype 2.000 0.4 0.5 0.2 Ca, DampCoeff1, DampCoeff2, DampCoeff3 0.5 1.0 zone start and end point in x/L 0.027 0.027 0.021 hydro strength inside diameter(m) 1.65405E-08 0.933 0.0 inertia(m^4) mass(kg/m) sbmg wt(kg/m) 2.25E+09 1 modulus of elasticity (N/m**2), S-N Curve I.D. No. 0.4 0.18 1.00 1 bandwidth, St code, Cl reduction factor:, zoneCLtype 1.000 0.2 0.18 0.2 Ca, DampCoeff1, DampCoeff2, DampCoeff3 *** BLOCK 3. current data *** 2 1.00 4980 no. of profile data pts probability profile ID 0.000 2.000 1.000 2.000 *** BLOCK 4. s-n and scf data ***

1 No. of S-N curves defined 1 1 S-N curve I.D., No. of S-N curve segments 0.0000 cut-off stress range (N/m**2) 1.62e+07 1.00E+08 stress range (Pa) cycles to failure 3.49E+08 1.00E+04 stress range (Pa) cycles to failure

1.000 global stress concentration factor 0 no. of local stress concentration positions *** BLOCK 5. computation/output option *** 1 calculation option 0.00 1.00 0.1 response location definition 0.0 gravitational acceleration 0.05 0.3 power cutoff, primary zone amplitude limit 1.0 power value exponent (0 - equal probabilities;1 - power ratio) 0 flag for importing nodal effective tension and mass (0=no;1=yes) 0 flag for MATLAB animation data output (1=yes;0=no) 0 flag for generating *.scr file, (1=yes;0=no) 0 flag for generating *.dmg file, (1=yes;0=no) 0 flag for generating *.fat file, (1=yes;0=no) 0 flag for generating *.out1 file, (1=yes;0=no) *** BLOCK 6. supplemental data ***

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