1. CRS1 - Axisymmetric cross section

The following is a CRS1 cross section example. Subsequent sections provide details and further options.

'**********************************************************************
 NEW COMPONENT CRS1
'**********************************************************************
'                             units:  Mg kN m C
'cmptyp-id temp alpha beta
 Xaxdmp    /    /     /
'ams         ae        ai   rgyr   ast wst dst thst rextcnt rintcnt
 0.3         0.0415    0    0.080  /   /   /   /    /       /
'iea  iej  igt ipress imf harpar
 3    1    1   0      0   0
'
' Axial force/strain of tensioner
' Fx     eps=L/L0-1=x/L0   (L0=1 m, x is tensioner stroke)
  1000    0.0   &
  1100    5.0   &
  1400   10.0
'ei              gas
 2.84E8          0
'gtminus
 2.19E8
'DAMP chtype1 [chtype2 chtype3 chtype4]
 DAMP  AXDMP
'idmpaxi expdmp
 1       1.737
'dmpaxi
 30.00
' icode=2 => dimensionless hydrodynamic force coefficients
'cqx  cqy    cax  cay    clx  cly    icode  d       scfkn  scfkt
 0    1.0    0    1.0      0    0    2      230E-3  1.0    1.0
'tb              ycurmx
 1600            0.1

1.1. Data group identifier

NEW COMPonent CRS1

1.2. Component type identifier

CMPTYP-ID TEMP ALPHA BETA
  • CMPTYP-ID: character(8): Component type identifier

  • TEMP: real, default: 0: Temperature at which the specification applies \(\mathrm {[Temp]}\)

  • ALPHA: real, default: 0: Thermal expansion coefficient \(\mathrm {[Temp^{-1}]}\)

  • BETA: real, default: 0: Pressure expansion coefficient \(\mathrm {[1/(F/L^2)]}\)

    • BETA gives the expansion of an element with zero effective tension from the difference between the internal and the external pressure.

um ii fig62
Figure 1. Axis symmetric cross section

1.3. Mass and volume

AMS AE AI RGYR AST WST DST THST R_EXTCNT R_INTCNT
  • AMS: real: Mass/unit length \(\mathrm {[M/L]}\)

  • AE: real: External cross-sectional area \(\mathrm {[L^2]}\)

  • AI: real: Internal cross-sectional area \(\mathrm {[L^2]}\)

  • RGYR: real: Radius of gyration about local x-axis \(\mathrm {[L]}\). Dummy for bar elements, i.e. IEJ = 0: zero bending stiffness.

  • AST: real: Cross-section area for stress calculations \(\mathrm {[L^2]}\)

    • The default value is calculated as seen below

  • WST: real: Cross-section modulus for stress calculations \(\mathrm {[L^3]}\)

    • The default value is calculated as seen below

  • DST: real: Diameter for stress calculations \(\mathrm {[L]}\)

    • The default value is calculated as seen below

  • THST: real: Thickness for stress calculations \(\mathrm {[L]}\)

    • The default value is calculated as seen below

  • R_EXTCNT: real, default: 0: External contact radius \(\mathrm {[L]}\)

  • R_INTCNT: real, default: 0: Inner contact radius \(\mathrm {[L]}\)

AE is used to calculate buoyancy.

AI is used to calculate additional mass of internal fluid if present. Otherwise AI is dummy or see below.

Default values of the stress calculation parameters will be calculated from AE and AI if AE > AI. A homogenous cylinder shaped cross-section is assumed:

  • AST \(\mathrm {=AE-AI}\)

  • WST \(\mathrm {=\pi (D_e^4-D_i^4)/(32D_e)}\)

  • DST \(\mathrm {=D_e}\)

  • THST \(\mathrm {=(D_e-D_i)/2}\)

    • where \(\mathrm {D_e=\sqrt{\frac{4AE}{\pi }}}\) and \(\mathrm {D_i=\sqrt{\frac{4AI}{\pi }}}\)

The outer and inner contact radii of the cross section, R_EXTCNT and R_INTCNT, are used for

The default values of R_EXTCNT and R_INTCNT are zero in the present version.

1.4. Stiffness properties classification

IEA IEJ IGT IPRESS IMF HARPAR
  • IEA: integer, default: 1: Axial stiffness code

    • 1 - constant stiffness

    • N - table with N pairs of tension-elongation to be specified

    • N >= 2

  • IEJ: integer, default: 0:

    • 0 - zero bending stiffness

    • 1 - constant stiffness

    • N - table with N pairs of bending moment - curvature to be specified

    • N >= 2

  • IGT: integer, default: 0: Torsion stiffness code

    • 0 - zero torsional stiffness

    • 1 - constant stiffness

    • -1- non-symmetric constant stiffness

    • N - symmetric, (N positive) pairs specified

    • -N- general torsion/relation (non-symmetric) N pairs specified

    • |N| >= 2

  • IPRESS: integer, default: 0: Pressure dependency parameter related to bending moment

    • 0 - no pressure dependency

    • 1 - linear dependency (not implemented)

    • NP - NP sets of stiffness properties to be given, corresponding to a table of NP pressure values (not implemented)

      • 2 <= NP <= 10

  • IMF: integer, default: 0: Hysteresis option in bending moment/curvature relation

    • 0 - no hysteresis

    • 1 - hysteresis generated by an internal friction moment at reversed curvature

  • HARPAR: real, default: 0: Hardening parameter for kinematic/isotropic hardening

    • 0 <= HARPAR <= 1

    • Only to be given if IEJ > 1 and IMF = 1

IEJ and IGT must both be zero or both greater than zero to assure stability in the FEM analysis.

Note that:

  • IPRESS=0 in this version.

  • IMF=0, IMF=1 is implemented in present version.

  • IMF \(\mathrm {\neq }\) 0 should be used with care as the analysis can become unstable.

1.5. Bending-torsion geometric coupling specification

This data group is optional, and will only be applied for IEJ=1, IGT=1, and IMF=0.

BTGC
  • BTGC: character(4): bending-torsion coupling identifier.

If the BTGC identifier is present, geometric coupling between torsion and bending is accounted for.

1.6. Axial stiffness. Case 1, IEA=1

EA
  • EA: real > 0: Axial stiffness \(\mathrm {[F]}\)

1.7. Axial stiffness. Case 2, IEA=N

EAF(1) ELONG(1) . . . EAF(N) ELONG(N)
  • EAF(1): real: Axial force corresponding to relative elongation ELONG(1) \(\mathrm {[F]}\)

  • ELONG(1): real: Relative elongation ()

  • .

  • .

  • .

The pairs of EAF and ELONG must be given in increasing order on a single input line.

um ii fig70
Figure 2. Axial force corresponding to relative elongation

1.8. Bending stiffness properties

The amount of input depends upon the parameters IEJ, IPRESS and IMF according to the table below:

  • Case: 0, IEJ: 0, IPRESS: 0, Allowed IMF-values: 0, Data required: None.

  • Case: 1a, IEJ: 1, IPRESS: 0, Allowed IMF-values: 0, Data required: EI, GAs.

  • Case: 1b, IEJ: 1, IPRESS: 0, Allowed IMF-values: 1, Data required: EI, MF.

  • Case: 2, IEJ: 1, IPRESS: 1, Allowed IMF-values: 0, Data required: Not implemented.

  • Case: 3, IEJ: N, IPRESS: 0, Allowed IMF-values: 0, 1, Data required: CURV(I): I=1,N. BMOM(I): I=1,N.

  • Case: 4, IEJ: N1, IPRESS: N2, Allowed IMF-values: 0, Data required: Not implemented.

1.9. Bending stiffness. Case 1a, IEJ=1 IPRESS=0 IMF=0

EI GAs
  • EI: real > 0: Bending stiffness \(\mathrm {[FL^2]}\)

  • GAs: real: Shear stiffness \(\mathrm {[F]}\)

The shear stiffness, GAs, is an optional input parameter. Specified GAs > 0 will include shear deformation. This requires that all stiffness properties are constant, i.e. IEA = 1, IEJ = 1, IGT = 1

1.10. Bending stiffness. Case 1b, IEJ=1 IPRESS=0 IMF=1

EI MF SF
  • EI: real: Bending stiffness \(\mathrm {[FL^2]}\)

  • MF: real: Internal friction moment, see figure below. \(\mathrm {[FL]}\)

  • SF: real, default: 10.: Internal friction moment stiffness factor. \(\mathrm {[-]}\)

The default value of SF corresponds to the earlier fixed value of 10.0.

um ii fig71
Figure 3. Internal friction moment description

1.11. Bending stiffness. Case 2, IEJ=1 IPRESS=1 (Not implemented)

EI(1) PRESS(1) EI(2) PRESS(2) MF(1) MF(2)
  • EI(1): real: Bending stiffness \(\mathrm {[FL^2]}\)

  • PRESS(1): real: Pressure at which the above values apply \(\mathrm {[F/L^2]}\)

  • EI(2): real: See description above

  • PRESS(2):

  • MF(1): real: Internal friction moment for pressure PRESS(1)

  • MF(2): real: Internal friction moment for pressure PRESS(2)

PRESS(1) < PRESS(2)

MF(1) and MF(2) dummy for IMF = 0

um ii fig72
Figure 4. Bending stiffness around y-axis as function of pressure

Values at other pressure levels than PRESS(1) and PRESS(2) are obtained by linear interpolation/ extrapolation.

1.12. Bending stiffness description. Case 3 IEJ=N IPRESS=0

Tabulated curvature/bending moment relation. This specification consists of two different input lines. For IMF \(\mathrm {\neq }\) 0 cfr. Bending stiffness. Case 4.

Curvature
CURV(1) ... CURV(N)
  • CURV(1): real: Curvature values for which bending moment is specified \(\mathrm {[1/L]}\)

  • .

  • .

  • .

  • CURV(N): To be specified in increasing order

CURV=1/CURVATURE RADIUS

Bending moment, y-axis
BMOMY(1) BMOMY(N)
  • BMOMY(1): real: Bending moment around y-axis \(\mathrm {[FL]}\) corresponding to curvature values given above in `Curvature'.

  • BMOMY(N)

CURV(1), BMOMY(1) have to be zero. Positive slope required, i.e.: BMOMY(I+1) > BMOMY(I).

um ii fig74
Figure 5. Bending moment around y-axis as function of curvature

1.13. Bending stiffness. Case 4 IEJ=N1, IPRESS=N2 (Not implemented)

This specification consists of three different input lines.

Curvature
CURV(1) ... CURV(N)
  • CURV(1): real: Curvature values for which bending moment is specified \(\mathrm {[1/L]}\)

  • .

  • .

  • .

  • CURV(N): To be specified in increasing order

CURV=1/CURVATURE RADIUS

CURV(1) has to be zero

Pressure
PRESS(1) ... PRESS(N)
  • PRESS(1): real: Pressure levels for which bending moment is specified \(\mathrm {[F/L^2]}\)

  • PRESS(N):

Bending moment, y-axis
BMOMY(1,1) BMOMY(N1,N2)
  • BMOMY(1,1): real: Bending moment at curvature I and pressure J \(\mathrm {[FL]}\).

  • BMOMY(N1,N2)

BMOMY(1,J), J=1,N2 have to be zero, see also the figure below. Positive slope with increasing curvature is required, i.e.: BMOMY(I+1,J) > BMOMY(I,J).

um ii fig75
Figure 6. Bending moment around y-axis as function of curvature and pressure

1.14. Torsion stiffness

No data required for IGT=0.

Constant torsion stiffness. Case 1 |IGT|=1
GT- GT+
  • GT-: real > 0: Torsion stiffness \(\mathrm {[FL^2/Radian]}\)

  • GT+: real: D.o. for positive twist. Dummy if IGT=1

Nonlinear torsion stiffness. Case 2 |IGT|=N
TMOM(1) TROT(1) . . . TMOM(N) TROT(N)
  • TMOM(1): real: Torsion moment \(\mathrm {[FL]}\)

  • TROT(1): real: Torsion angle/length \(\mathrm {[Radian/L]}\)

  • .

  • .

  • .

  • TMOM(N):

  • TROT(N): real:

If IGT is positive TMOM(1) and TROT(1) have to be zero. TROT must be given in increasing order.

1.15. Damping specification

This data group is optional. It enables the user to specify cross sectional damping properties of the following types:

  • mass proportional damping

  • stiffness proportional damping

  • axial damping properties

Specification of mass and stiffness proportional damping specification will overrule corresponding damping specification given on global level as input to Dynmod data group Time integration and damping parameters.

Data group identifier and selection of damping types
DAMP CHTYPE1 CHTYPE2 CHTYPE3 CHTYPE4
  • DAMP: character(4): Data group identifier (the text DAMP)

  • CHTYPE1: character(5):

    • =MASPR: Mass proportional damping

    • =STFPR: Stiffness proportional damping

    • =AXDMP: Local axial damping model

    • =AXFRC: Local axial friction model

  • CHTYPE2: character(5): Similar to CHTYPE1

  • CHTYPE3: character(5): Similar to CHTYPE1

  • CHTYPE4: character(5): Similar to CHTYPE1

Between one and four damping types may be selected. The order of the damping type selection is arbitrary.

In the following the damping parameters for the selected damping types is described. The input lines have to be given in one block and in the order described below. Skip input for damping types which are not selected.

Parameters for mass proportional damping, if MASPR is specified
A1T A1TO A1B
  • A1T: real: Factor for mass proportional damping in axial dofs.

  • A1TO: real, default: A1T: Factor for mass proportional damping in torsional dofs.

  • A1B: real, default: A1TO: Factor for mass proportional damping in bending dofs.

The element mass proportional damping matrix is computed by:

\(\mathrm {\boldsymbol{\mathrm {c_m}}=a_{1t}\boldsymbol{\mathrm {m}}_t+a_{1to}\boldsymbol{\mathrm {m}}_{to}+a_{1b}\boldsymbol{\mathrm {m}}_b}\)

where \(\boldsymbol{\mathrm {m}}\) is the local mass matrix and the subscripts t, to and b refer to axial, torsional and bending contributions, respectively.

Parameters for stiffness proportional damping, if STFPR is specified
A2T A2TO A2B  DAMP_OPT
  • A2T: real: Factor for stiffness proportional damping in axial dofs.

  • A2TO: real, default: A2T: Factor for stiffness proportional damping in torsional dofs.

  • A2B: real, default: A2TO: Factor for stiffness proportional damping in bending dofs.

  • DAMP_OPT: character(4), default: TOTA: Option for stiffness contribution to Rayleigh damping

    • = TOTA: Stiffness proportional damping is applied using total stiffness, i.e. both material and geometric stiffness

    • = MATE: Stiffness proportional damping is applied using material stiffness only

The element stiffness proportional damping matrix is computed by:

\(\mathrm {\boldsymbol{\mathrm {c_k}}=a_{2t}\boldsymbol{\mathrm {k}}_t+a_{2to}\boldsymbol{\mathrm {k}}_{to}+a_{2b}\boldsymbol{\mathrm {k}}_b}\)

where \(\boldsymbol{\mathrm {k}}\) is the local stiffness matrix and the subscripts t, to and b refer to axial, torsional and bending contributions, respectively.

Parameters for local axial damping, if AXDMP is specified

The local axial damping model is written:

\(\mathrm {F=C(\varepsilon )\times |\dot {\varepsilon }|^P\times sign(\dot {\varepsilon })}\)

where:

  • \(\mathrm {F}\): damping force

  • \(\mathrm {C}\): damping coefficient (strain dependent)

  • \(\mathrm {\varepsilon }\): relative elongation

  • \(\mathrm {\dot {\varepsilon }}\): strain velocity

  • \(\mathrm {P}\): exponent for strain velocity (P >= 1)

IDMPAXI EXPDMP
  • IDMPAXI: integer: Damping coefficient code

    • = 1: Constant damping coefficient

    • = N: Table with N pairs of damping coefficient - elongation to be specified.

    • N >= 2

  • EXPDMP: real: Exponent for strain velocity

IDMPAXI = 1

DMPAXI
  • DMPAXI: real: Damping coefficient (constant)

IDMPAXI >1

DMPAXI(1) ELONG(1) . . . . . . . . DMPAXI(IDMPAXI) ELONG(IDMPAXI)
  • DMPAXI(1): real: Damping coefficient corresponding to relative elongation ELONG(1)

  • ELONG(1): real: Relative elongation ( )

ELONG must be given in increasing order for the pairs of DMPAXI and ELONG . All pairs are given on a single input line

Parameters for local axial friction, if AXFRC is specified
FRCAXI(1) ELONG(1) FRCAXI(2) ELONG(2)
  • FRCAXI(1): real: Static friction force corresponding to elongation ELONG(1)

  • ELONG(1): real: Relative elongation ( )

  • FRCAXI(2): real, default: FRCAXI(1): Dynamic friction force corresponding to elongation ELONG(2)

  • ELONG(2): real, default: 1.1 x ELONG(1): Relative elongation ( )

ELONG(2) > ELONG(1)

1.16. Hydrodynamic load type identification, One optional input line

CHLOAD
  • CHLOAD: character: = HYDR - Text to identify hydrodynamic coefficients

Required if non-Morison loads are to be specified
Load type identification if CHLOAD=HYDR, One input line
CHTYPE
  • CHTYPE: character: Hydrodynamic load type

    • = NONE: No hydrodynamic load

    • = MORI: Load based on Morisons generalized equation. Sea surface penetration formulation

    • = MORP: As MORI, but improved by taking into account partially submerged cross-section

    • = MACF: Load based on MacCamy-Fuchs potential equations and quadratic drag load

    • = POTN: Potential flow with quadratic drag load coefficients

    • = TVIV: Time domain VIV load.

    • = HNET: Net properties and hydrodynamic added mass coefficients for net

The option POTN currently is under testing. Potential flow forces are only available for irregular time domain analysis.
The option TVIV is currently under development and some load options are restricted.
Hydrodynamic force coefficients if CHTYPE=MORI or CHTYPE=MORP

Interpretation of hydrodynamic coefficients are dependent on the input parameter ICODE. Input of dimensional hydrodynamic coefficient is specified giving ICODE=1 while input of nondimensional of hydrodynamic coefficients for circular cross sections is specified giving ICODE=2.

CHTYPE=MORP is similar to CHTYPE=MORI but with thre key differences:

  • the load calculated at a cross-section is reduced in proportional with the instantaneous wet portion of the cross-section

  • the Froude-Krylov term used longitudinal direction in Morison’s equation is replaced by the product of the dynamic pressure and the submerged area at each end of the element.

  • if the specified value for external area (AE) is zero, neither hydrostatic nor hydrodynamic loads will act on the cross section. Definitions of dimensional/nondimensional hydrodynamic force coefficients for a fully submerged cross section are given below

CQX CQY CAX CAY CLX CLY ICODE D SCFKN SCFKT
  • CQX: real: Quadratic drag coefficient in tangential direction

    • ICODE=1: CQX=CDX: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\)

    • ICODE=2: CQX=Cdt: nondimensional drag force coefficient

  • CQY: real: Quadratic drag coefficient in normal direction

    • ICODE=1: CQY=CDY: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\)

    • ICODE=2: CQY=Cdn: nondimensional drag force coefficient

  • CAX: real: Added mass per unit length in tangential direction

    • ICODE=1: CAX=AMX: added mass \(\mathrm {[M/L]}\)

    • ICODE=2: CAX=Cmt: nondimensional added mass coefficient

  • CAY: real: Added mass per unit length in normal direction

    • ICODE=1: CAY=AMY: added mass \(\mathrm {[M/L]}\)

    • ICODE=2: CAY=Cmn: nondimensional added mass coefficient

  • CLX: real: Linear drag force coefficient in tangential direction

    • ICODE=1: CLX=CDLX: dimensional linear drag coefficient \(\mathrm {[F/((L/T)\times L)]}\)

    • ICODE=2: CLX=CdtL: nondimensional linear drag force coefficient

  • CLY: real: Linear drag force coefficient in normal direction

    • ICODE=1: CLY=CDLY: dimensional linear drag force coefficient \(\mathrm {[F/((L/T)\times L)]}\)

    • ICODE=2:CLY=CdnL: nondimensional linear drag force coefficient

  • ICODE: integer, default: 1: ICODE Code for input of hydrodynamic force coefficients

    • ICODE=1: Dimensional coefficients

    • ICODE=2: Nondimensional coefficients

  • D: real, default:\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Hydrodynamic diameter of the pipe \(\mathrm {[L]}\).

    • Default value is calculated from external cross-sectional area given as input in data section Mass and volume

    • Note that the hydrodynamic diameter is used for time domain VIV loads and for marine growth and is a key parameter in VIVANA.

  • SCFKN: real, default: 1: Scaling factor for the Froude-Krylov term in Morison’s equation in normal direction

  • SCFKT: real, default: 1: Scaling factor for the Froude-Krylov term in Morison’s equation in tangential direction. Only the values 0.0 and 1.0 are permitted.

Definition of hydrodynamic force coefficients

The tangential force which is a friction force per unit length acting in local x-axis, \(\mathrm {Ft}\) is computed by:

\(\mathrm {Ft=CDX\times VRELX\times |VRELX|+CDLX\times VRELX}\)

The drag force per unit length acting normal to the local x-axis, \(\mathrm {F_n}\), is computed by assuming that the instantaneous drag force direction is parallel to the instantaneous transverse relative velocity component:

\(\mathrm {F_n=CDY(VRELY^2+VRELZ^2)+CDLY\times \sqrt{VRELY^2+VRELZ^2}}\)

where:

  • \(\mathrm {CDX,CDY}\): are the dimensional quadratic drag force coefficients in local x- and y-directions (i.e. tangential and normal directions)

  • \(\mathrm {CDLX,CDLY}\): are the dimensional linear drag force coefficients in local x- and y-directions

  • \(\mathrm {VRELX,VRELY,VRELZ}\): are relative water velocities in local x,y and z-directions

The nondimensional hydrodynamic force coefficients for a circular cross section are defined according to the following expressions:

  • \(\mathrm {CDX=\frac{1}{2}\rho S_WC_{dt}}\)

  • \(\mathrm {CDY=\frac{1}{2}\rho DC_{dn}}\)

  • \(\mathrm {CDLX=\rho \sqrt{gS_W}\times S_W^2C^L_{dt}}\)

  • \(\mathrm {CDLY=\rho \sqrt{gD}\times D^2C^L_{dt}}\)

  • \(\mathrm {AMX=\rho \frac{\pi D^2}{4}C_{mt}}\)

  • \(\mathrm {AMY=\rho \frac{\pi D^2}{4}C_{mn}}\)

where:

  • \(\mathrm {\rho }\): water density

  • \(\mathrm {g}\): acceleration of gravity

  • \(\mathrm {S_W}\): cross sectional wetted surface \(\mathrm {(=\pi D)}\)

  • \(\mathrm {D}\): hydrodynamic diameter of the pipe

  • \(\mathrm {C_{dt}}\): nondimensional quadratic tangential drag coefficient

  • \(\mathrm {C_{dn}}\): nondimensional quadratic normal drag coefficient

  • \(\mathrm {C^L_{dt}}\): nondimensional linear tangential drag coefficient

  • \(\mathrm {C^L_{dn}}\): nondimensional linear normal drag coefficient

  • \(\mathrm {C_{mt}}\): nondimensional tangential added mass coefficient

  • \(\mathrm {C_{mn}}\): normal added mass coefficient

    • (\(\mathrm {C_{mn}}\) is normally equal to 1.0 for a circular cross section)

Note that if the specified value for external area (AE) is zero, neither hydrostatic nor hydrodynamic loads will act on the cross section

Hydrodynamic force coefficients if CHTYPE=MACF

MacCamy-Fuchs frequency-dependent hydrodynamic loads on a stationary vertical circular cylinder will be applied for CHTYPE=MACF. MacCamy-Fuchs forces are pre-computed based on the element position after static calculation. MacCamy-Fuchs forces are only available for irregular time domain analysis.

Quadratic drag may also be applied on cross-sections with MacCamy-Fuchs loading.

Hydrodynamic force coefficients
CQX CQY CAX ICODE D
  • CQX: real: Quadratic drag coefficient in tangential direction

    • ICODE=1: CQX=CDX: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\)

    • ICODE=2: CQX=Cdt: nondimensional drag force coefficient

  • CQY: real: Quadratic drag coefficient in normal direction

    • ICODE=1: CQY=CDY: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\)

    • ICODE=2: CQY=Cdn: nondimensional drag force coefficient

  • CAX: real, default: 0.0: Added mass per unit length in tangential direction

    • ICODE=1: CAX=AMX: added mass \(\mathrm {[M/L]}\)

    • ICODE=2: CAX=Cmt: nondimensional added mass coefficient

  • ICODE: integer: Code for input of hydrodynamic drag coefficients

    • ICODE=1: Dimensional coefficients

    • ICODE=2: Nondimensional coefficients

  • D: real, default:\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Hydrodynamic diameter of the pipe \(\mathrm {[L]}\).

    • Default value is calculated from external cross-sectional area given as input in data section Mass and volume

Simplified radiation force

The horizontal radiation loads is based on an added mass coefficient and a damping coefficient.

 CAY DAMP IRACOD
  • CAY: real, default: 0.0: Added mass per unit length in normal direction

    • IRACOD=1: CAY=AMY: added mass \(\mathrm {[M/L]}\)

    • IRACOD=2: CAY=Cmn: nondimensional added mass coefficient

  • DAMP: real, default: 0.0: Damping in normal direction

    • IRACODE=1: DAMP=CDa: dimensional damping coefficient \(\mathrm {[F/((L/T)\times L)]}\)

    • IRACODE=2: DAMP=CDan: nondimensional damping coefficient

  • IRACODE: integer, default: 1: Code for input of simplified radiation force coefficients

    • IRACODE=1: Dimensional coefficients

    • IRACODE=2: Nondimensional coefficients

The nondimensional hydrodynamic added mass coeffcient and the damping coefficient are defined according to the following expressions:

  • \(\mathrm {CDa=\rho \sqrt{gD}\times D^2CD_{an}}\)

  • \(\mathrm {AMY=\rho \frac{\pi D^2}{4}C_{mn}}\)

The input CHTYPE=MACF is extended in Riflex 4.13 and is not compatible with earlier versions of Riflex.
Hydrodynamic force coefficients if CHTYPE=POTN

Frequency-dependent added mass, radiation damping, and excitation forces based on the first order potential flow solution will be applied for CHTYPE=POTN. The radiation and diffraction coefficients are to be given by a separate input file specified under the data group Potential flow library specification.

Quadratic drag may also be applied on cross-sections with potential flow loading.

CQX CQY ICODE D SCFKT
  • CQX: real: Quadratic drag coefficient in tangential direction

    • ICODE=1: CQX=CDX: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\)

    • ICODE=2: CQX=Cdt: nondimensional drag force coefficient

  • CQY: real: Quadratic drag coefficient in normal direction

    • ICODE=1: CQY=CDY: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\)

    • ICODE=2: CQY=Cdn: nondimensional drag force coefficient

  • ICODE: integer, default: 1: ICODE Code for input of hydrodynamic force coefficients

    • ICODE=1: Dimensional coefficients

    • ICODE=2: Nondimensional coefficients

  • D: real, default:\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Hydrodynamic diameter of the pipe \(\mathrm {[L]}\).

    • Default value is calculated from external cross-sectional area given as input in data section Mass and volume

  • SCFKT: real, default: 1: Scaling factor for the Froude-Krylov term in Morison’s equation in tangential direction. Only the values 0.0 and 1.0 are permitted.

Hydrodynamic force coefficients if CHTYPE=TVIV

Under implementation. Some load options are restricted.

CQX CQY CAX CAY CLX CLY ICODE D SCFKN SCFKT

See the description above for Hydrodynamic force coefficients.

Time domain VIV load options and coefficients, 2 or 3 input lines.

CHTVIV NMEM CHH
  • CHTVIV: character(8): Time domain VIV load option

    • = CF: Cross-flow VIV loads only

    • = CFIL: Cross-flow and in-line VIV loads calculated independently. Restricted option

    • = IL: In-line VIV loads only. Restricted option

  • NMEM: integer > 0, default: 500: Number of time steps used in calculation of standard deviation

  • CHH: real >= 0, default: 0.0: Higher harmonic load coefficient (nondimensional). Restricted option

Cross-flow VIV load coefficients. The following input line is given if CHTVIV is CF or CFIL:

CV FNULL FMIN FMAX
  • CV: real >= 0: Vortex shedding force coefficient for the (instantaneous) cross-flow load term (nondimensional)

  • FNULL: real > 0: Natural cross-flow vortex shedding frequency (nondimensional)

  • FMIN: real > 0: Minimum cross-flow vortex shedding frequency (nondimensional)

  • FMAX: real > FMIN: Maximum cross-flow vortex shedding frequency (nondimensional)

Independently calculated in-line load coefficients. Restricted option. The following input line is given if CHTVIV is CFIL or IL:

CVIL FNULIL FMINIL FMAXIL
  • CVIL: real >= 0: Vortex shedding force coefficient for the (instantaneous) in-line load term (nondimensional)

  • FNULIL: real > 0: Natural in-line vortex shedding frequency (nondimensional)

  • FMINIL: real > 0: Minimum in-line vortex shedding frequency (nondimensional)

  • FMAXIL: real > FMINIL: Maximum in-line vortex shedding frequency (nondimensional)

The VIV parameters are nondimensional and independent of ICODE.
VIV parameters for pure CF are shown in Table 1.
Table 1. Suggested VIV empirical parameters used for CHTVIV=CF, i.e. Cross flow only. CQY and CAY are nondimensional drag force and added mass coefficients in normal direction.

Flow conditions

Structure type

Parameters

CV

CQY

CAY

FNULL

FMIN

FMAX

Constant current

Bare riser section

1.3

1.0

1.0

0.13

0.10

0.26

Buoyancy section (Lb/Lr=1/2)

Bare riser

1.2

0.9

1.0

0.18

0.10

0.22

Buoyancy element

0.08

0.3

1.0

0.10

0.05

0.15

Buoyancy section (Lb /Lr=1/1)

Bare riser

0.8

1.2

1.0

0.18

0.10

0.26

Buoyancy element

0.5

0.6

1.0

0.10

0.05

0.15

Vessel motion induced VIV

Bare riser & buoyancy section

0.8

1.2

1.0

0.216

0.10

0.26

Lb/Lr is the ratio between the length of the buoyancy element and the bare riser section, see Figure 7.
TVIV cf lblr ration
Figure 7. Ratio between the length of the buoyancy element and the bare riser section
Net properties and hydrodynamic added mass coefficients if CHTYPE=HNET

A complete net is normally modelled bye a set of segments where each segment represents a net panel, and is specified by a cable/bar cross section with equivalent properties.

The net properties and hydrodynamic added mass coefficients are specified for segment end 1. The derived drag and lift coefficients and the specified added mass coefficients are scaled according to the actual net width which is found by linear interpolation between specified net width at segment end 1 and segment end 2. This also applies to the specified unit mass and external area.

CHTYPE=HNET may only be used with bar elements (No bending and torsional stiffness to be specified)
The net load model requires that the net plane is defined. The net plane is the plane containing the updated local element X-axis and the fixed reference vector specified in the input group LOCAL ELEMENT AXIS.
If the specified value for external area (AE) is zero, neither hydrostatic nor hydrodynamic loads will act on the cross section
Net and segment properties
SN WIDTH1 WIDTH2 REDVEL
  • SN: real >= 0 <=1: Solidity ratio (the ratio between thread area and net area) \(\mathrm {[-]}\)

  • WIDTH1: real >= 0: Net width at segment end 1 \(\mathrm {[L]}\)

  • WIDTH2: real >= 0: Net width at segment end 2 \(\mathrm {[L]}\)

  • REDVEL: real >= 0 <= 1: Reduced current velocity factor (the ratio between reduced current speed and ambient current speed due to upstream net shadowing effects \(\mathrm {[-]}\)

Note that only one of the input variables WIDTH1 or WIDTH2 can be specified with the value 0.

The drag and lift coefficient \(\mathrm {[F/((L/T)^2\times L^2)]}\) are calculated based on the net solidity (SN) according to the following equations:

Direction independent drag force coefficient:

  • \(\mathrm {C_{D0}=\frac{1}{2}\rho \times 0.04}\)

Direction dependent drag force coefficient:

  • \(\mathrm {C_{D1}=\frac{1}{2}\rho \times (-0.04+SN-1.24SN^2+13.7SN^3)cos(\alpha)}\)

Direction dependent lift force coefficient:

  • \(\mathrm {C_l=\frac{1}{2}\rho \times (0.57SN-3.54SN^2+10.1SN^3)sin(2\alpha})\)

where:

  • \(\mathrm {\rho }\): is the water density

  • \(\mathrm {SN}\): is the net solidity ratio

  • \(\mathrm {\alpha }\): angle between the flow direction and the net normal vector in the direction of the flow

Note that the equations for drag and lift coefficients are valid for the solidity ratio range [0.13,0.32], see netloads in the Theory manual.

Hydrodynamic force coefficients
CAX CAY ICODE D
  • CAX: real: Added mass per length, tangential direction \(\mathrm {[M/L]}\)

    • ICODE=1: CAX=AMX: added mass \(\mathrm {[M/L]}\)

    • ICODE=2: CAX=Cmt: nondimensional added mass coefficient

  • CAY: real: Added mass per length, normal direction \(\mathrm {[M/L]}\)

    • ICODE=1: CAY=AMY: added mass \(\mathrm {[M/L]}\)

    • ICODE=2: CAY=Cmn: nondimensional added mass coefficient

  • ICODE: integer, default: 1: ICODE Code for input of hydrodynamic force coefficients

    • ICODE=1: Dimensional coefficients

    • ICODE=2: Nondimensional coefficients

  • D: real, default:\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Equivalent hydrodynamic diameter to be used for nondimensional added mass coefficients \(\mathrm {[L]}\).

    • Default value is calculated from external cross-sectional area given as input in data section Mass and volume

1.17. Aerodynamic load type identification, One optional input line

CHLOAD
  • CHLOAD: character: = WIND - Text to identify wind coefficients

Load type identification if CHLOAD=WIND, One input line
CHTYPE
  • CHTYPE: character: Type of load coefficients

    • = MORI: Morison-like loading, Drag term

Drag coefficients if CHTYPE=MORI, One input line
CDXAERO CDYAERO ICODE D
  • CDXAERO: real: Quadratic drag coefficient in tangential direction

    • ICODE=1: CDXAERO=CDXa: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\)

    • ICODE=2: CDXAERO=Cdta: non-dimensional drag force coefficient

  • CDYAERO: real: Quadratic drag coefficient in normal direction

    • ICODE=1: CDYAERO=CDYa: dimensional drag force coefficient \(\mathrm {[F/((L/T)^2\times L)]}\)

    • ICODE=2: CDYAERO=Cdna: non-dimensional drag force coefficient

  • ICODE: integer, default: 1: Code for input of aerodynamic force coefficients

    • ICODE=1: Dimensional coefficients

    • ICODE=2: Nondimensional coefficients

  • D: real, default:\(\sqrt{\mathrm {\frac{4}{\pi }(AE)}}\): Aerodynamic diameter of the pipe \(\mathrm {[L]}\).

    • Default value is calculated from external cross-sectional area given as input in data section Mass and volume

    • Dummy for ICODE=1

The tangential force which is a friction force per unit length acting in local x-axis, \(\mathrm {F_t}\) is computed by:

\(\mathrm {F_t=CDXa\times VRELX\times |VRELX|}\)

The drag force per unit length acting normal to the local x-axis, \(\mathrm {F_n}\), is computed by assuming that the instantaneous drag force direction is parallel to the instantaneous transverse relative velocity component:

\(\mathrm {F_n=CDYa(VRELY^2+VRELZ^2)}\)

where:

  • \(\mathrm {CDXa,CDYa}\): are the dimensional quadratic drag force coefficients in local x- and y-directions (i.e. tangential and normal directions)

  • \(\mathrm {VRELX,VRELY,VRELZ}\): are relative wind velocities in local x,y and z-directions

The nondimensional aerodynamic force coefficients for a circular cross section are defined according to the following expressions:

  • \(\mathrm {CDXa=\frac{1}{2}\rho _aS_WC_{dta}}\)

  • \(\mathrm {CDYa=\frac{1}{2}\rho _aDC_{dna}}\)

where:

  • \(\mathrm {\rho _a}\): air density

  • \(\mathrm {S_W}\): cross sectional perimeter \(\mathrm {(=\pi D)}\)

  • \(\mathrm {D}\): aerodynamic diameter of the pipe

  • \(\mathrm {C_{dta}}\): nondimensional quadratic tangential drag coefficient

  • \(\mathrm {C_{dna}}\): nondimensional quadratic normal drag coefficient

1.18. Capacity parameter

TB YCURMX
  • TB: real: Tension capacity \(\mathrm {[F]}\)

  • YCURMX: real: Maximum curvature \(\mathrm {[1/L]}\)

These parameters are dummy in the present version