1. CRS2 - Double symmetric cross section

1.1. Data group identifier

NEW COMPonent CRS2

1.2. Component type identifier

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

  • TEMP: real: Temperature at which the specification applies

    • Dummy in present version

um ii fig89
Figure 1. Cross section with 2 symmetry planes

1.3. Mass and volume

AMS AE AI RGYR
  • AMS: real: Mass per 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 \(\mathrm {[L]}\)

AE is used to calculate buoyancy.

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

Note that the mass center is located along the local X-axis, i.e. at the origin of the local Y- and Z-axes.

1.4. Stiffness properties classification

IEA IEJ IGT IPRESS
  • IEA: integer, default: 0: 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

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

IPRESS=0 in this version of the program.

1.5. Bending-torsion geometric coupling specification

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

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 ()

  • .

  • .

  • .

  • EAF(N): real:

  • ELONG(N): real:

The pairs of EAF and ELONG must be given in increasing order. See also the figure Axial force corresponding to relative elongation.

1.8. Bending stiffness properties

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

  • Case: 0, IEJ: 0, IPRESS: 0, Data required: None.

  • Case: 1, IEJ: 1, IPRESS: 0, Data required: EJY, EZJ, MFY, MF2.

  • Case: 2, IEJ: 1, IPRESS: 1, Data required: Not implemented.

  • Case: 3, IEJ: N, IPRESS: 0, Data required: CURV(I): I=1,N. BMOMY(I): I=1,N. BMOMZ(I)

  • Case: 4, IEJ: N1, IPRESS: N2, Data required: Not implemented.

Thus, the following data are required for the respective cases:

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

EJY EJZ GAsZ GAsY
  • EJY: real > 0: Bending stiffness around local y-axis \(\mathrm {[FL^2]}\)

  • EJZ: real > 0: Bending stiffness around z-axis \(\mathrm {[FL^2]}\)

  • GAsZ: real: Shear stiffness in Z-direction \(\mathrm {[F]}\)

  • GAsY: real: Shear stiffness in Y-direction \(\mathrm {[F]}\)

The shear stiffness, GAsZ and GAsY, are optional input parameters.

Specified GAsZ>0 and GAsY>0 will include shear deformation. This requires that all stiffness properties are constant, i.e. IEA = 1, IEJ = 1, IGT = 1.

Note that the shear center is located along the local X-axis, i.e. at the origin of the local Y- and Z-axes.

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

EJY(1) EJZ(1) PRESS(1) EJY(2) EJZ(2) PRESS (2)
  • EJY(1): real: Bending stiffness around local y-axis \(\mathrm {[FL^2]}\)

  • EJZ(1): real: Bending stiffness around local z-axis \(\mathrm {[FL^2]}\)

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

  • EJY(2): real: Bending moments corresponding to 2nd pressure level, see description above

  • EJZ(2): real:

  • PRESS(2): real:

PRESS(1) < PRESS(2)

um ii fig93
Figure 2. 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.

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

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): real: To be specified in increasing order

CURV=1/CURVATURE RADIUS

Bending moment, y-axis
BMOMY(1) . . . BMOMY(N)
  • BMOMY(1): real: Bending moment around local y-axis \(\mathrm {[FL]}\)

  • .

  • .

  • .

  • BMOMY(N): real

Bending moment, z-axis
BMOMZ(1) . . . BMOMZ(N)
  • BMOMZ(1): real: Bending moment around local z-axis \(\mathrm {[FL]}\)

  • .

  • .

  • .

  • BMOMZ(N): real

CURV(1), BMOMY(1) and BMOMZ(1) have to be zero. See also the figure Bending moment around y-axis as function of curvature.

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

This specification consists of four different input lines.

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

  • .

  • .

  • .

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

CURV=1/CURVATURE RADIUS

CURV(1) has to be zero. See also the figure Bending moment around y-axis as function of curvature.

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

  • .

  • .

  • .

  • PRESS(N): real:

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

  • .

  • .

  • .

  • BMOMY(N1,N2):real:

BMOMY(1,J), J=1, N2 have to be zero.

Bending moment, z-axis
BMOMZ(1,1) . . . BMOMZ(N1,N2)
  • BMOMZ(I,J): real: Bending moment about local Z-axis at curvature I and pressure J \(\mathrm {[FL]}\).

  • .

  • .

  • .

  • BMOMZ(N1,N2):real:

BMOMZ(1,J), J=1, N2 have to be zero.

1.13. Torsion stiffness

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

  • GT+: real: D.o. for positive twist. Dummy for 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 \(\mathrm {[Radian/L]}\)

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

1.14. 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(6):

    • =MASPR: Mass proportional damping

    • =STFPR: Stiffness proportional damping axial, torsional and shear/bending degrees of freedom

    • =STFPR2:Stiffness proportional damping as STFPR, but separate coefficients in the shear/bending directions.

    • =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 and may be given in arbitrary order. Combination of STFPR and STFPR2 is not allowed!

In the following the damping parameters for the selected damping types is described. The order of 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 for bending and shear.

  • 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 stiffness proportional damping, if STFPR2 is specified
A2T A2TO A2BY A2BZ  DAMP_OPT
  • A2T: real: Factor for stiffness proportional damping in axial dofs.

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

  • A2BY: real, default: A2TO: Factor for stiffness proportional damping for bending around local Y-axis and shear in local Z-axis.

  • A2BZ: real, default: A2BY: Factor for stiffness proportional damping for bending around local Z-axis and shear in local Y-axis.

  • 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:

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

where \(\boldsymbol{\mathrm {k}}\) is the local stiffness matrix and the subscripts t, to, by and bz refer to axial, torsional, bending around local y-axis and bending around local y-axis, 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)

1.15. Hydrodynamic load type identification, One input line

CHLOAD
  • CHLOAD: character: = HYDR - Text to identify hydrodynamic load type

Note: Required if non-Morison loads are to be specified

Load type identification for 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: Load based on input of force transfer functions and retardation fuctions from 3rd party programs and quadratic drag load (Under development)

Note that the option POTN currently is under testing. Potential flow forces are only available for irregular time domain analysis.

Hydrodynamic force coefficients if CHTYPE=MORI or CHTYPE=MORP, submerged cross section

CHTYPE=MORP is similar to CHTYPE=MORI but with three 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. The external area for this purpose is assumed to be circular.

  • If the specified value for external area (AE) is zero, neither hydrostatic nor hydrodynamic loads will act on the cross section.

Definitions of dimensional hydrodynamic force coefficients for a fully submerged cross section are given below

CDX CDY CDZ CDTMOM AMX AMY AMZ AMTOR CDLX CDLY CDLZ SCFKN SCFKT
  • CDX: real: Drag force coefficient for local x-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDY: real: Drag force coefficient for local y-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDZ: real: Drag force coefficient for local z-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDTMOM: real: Drag force coefficient for local x-rotation. Not used in present version.

  • AMX: real: Added mass per length in x-direction \(\mathrm {[M/L]}\)

  • AMY: real: Added mass per length in y-direction \(\mathrm {[M/L]}\)

  • AMZ: real: Added mass per length in z-direction \(\mathrm {[M/L]}\)

  • AMTOR: real: Added mass for local x-rotation \(\mathrm {[ML^2/L]}\) Not used in present version.

  • CDLX: real, default: 0: Linear drag force coefficients in local x-direction \(\mathrm {[F/((L/T)\times L)]}\)

  • CDLY: real, default: 0: Linear drag force coefficients in local y-direction \(\mathrm {[F/((L/T)\times L)]}\)

  • CDLZ: real, default: 0: Linear drag force coefficients in local z-direction \(\mathrm {[F/((L/T)\times L)]}\)

  • 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.

The drag forces per unit length acting in the local coordinate system are computed as:

  • \(\mathrm {F_x=CDX\times VRELX\times VRELX+CDLX\times VRELX}\)

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

  • \(\mathrm {F_z=CDZ\times \sqrt{VRELY^2+VRELZ^2}\times VRELZ+CDLZ\times VRELZ}\)

where:

  • \(\mathrm {CDX,CDY,CDZ}\): are the input quadratic drag force coefficients in local x, y and z-directions

  • \(\mathrm {CDLX,CDLY,CDLZ}\): are the input linear drag force oefficients in local x, y and z-directions

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

The input quadratic drag force coefficients \(\mathrm {CDX}\), \(\mathrm {CDY}\) and \(\mathrm {CDZ}\) will normally be calculated as:

  • \(\mathrm {CDX=\frac{1}{2}\rho S_{2D}C_{dx}}\)

  • \(\mathrm {CDY=\frac{1}{2}\rho B_yC_{dy}}\)

  • \(\mathrm {CDZ=\frac{1}{2}\rho B_zC_{dz}}\)

where:

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

  • \(\mathrm {S_{2D}}\): cross sectional wetted surface

  • \(\mathrm {B_y,B_z}\): projected area per. unit length for flow in local y and z-direction, respectively

  • \(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and z-directions, respectively

The input added mass per. unit length \(\mathrm {AMX}\), \(\mathrm {AMY}\) and \(\mathrm {AMZ}\) can be calculated as:

  • \(\mathrm {AMX=\rho AC_{mx}}\)

  • \(\mathrm {AMY=\rho AC_{my}}\)

  • \(\mathrm {AMZ=\rho AC_{mz}}\)

where:

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

  • \(\mathrm {A}\): cross sectional area

  • \(\mathrm {C_{mx},C_{my},C_{mz}}\): nondimensional added mass coefficients in local x, y and z-directions, respectively

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 elements with MacCamy-Fuchs loading. McCamy Fuchs assumes that the cross-section is circular, so a single transverse quadratic drag coefficient is given (CDZ will be set to CDY).

CQX CQY 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

  • 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

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 CQZ ICODE D SCFKT
  • CQX: real: Quadratic drag coefficient in local x-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 local y-direction

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

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

  • CQZ: real: Quadratic drag coefficient in local z-direction

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

    • ICODE=2: CQZ=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 \(\mathrm {[L]}\).

    • 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.

1.16. Aerodynamic load type identification, One optional input line

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

1.17. Load type identification, One optional input line

CHTYPE
  • CHTYPE: character: Type of wind load coefficients

    • = MORI: Morison-like loading, Drag term

    • = AIRC: Air foil cross section to be specified (Not implemented)

    • = AIRF: Air foil cross section, Refers to a air foil library file

CHTYPE=MORI: Morison-like aerodynamic drag, One input line
CDXAERO CDYAERO CDZAERO
  • CDXAERO: real: Dimensional quadratic drag coefficient for local x-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDYAERO: real: Dimensional quadratic drag coefficient for local y-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDZAERO: real: Dimensional quadratic drag coefficient for local z-direction \(\mathrm {[F/((L/T)^2\times L)]}\)

The drag forces per unit length acting in the local coordinate system are computed as: - \(\mathrm {F_x=CDXAERO\times VRELX\times |VRELX|}\) - \(\mathrm {F_y=CDYAERO\times VRELY\times \sqrt{VRELY^2+VRELZ^2}}\) - \(\mathrm {F_z=CDZAERO\times VRELZ\times \sqrt{VRELY^2+VRELZ^2}}\)

where:

  • \(\mathrm {CDXAERO,CDYAERO,CDZAERO}\): are the input quadratic drag force coefficients in local x, y and z-directions

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

The input quadratic drag force coefficients \(\mathrm {CDX}\), \(\mathrm {CDY}\) and \(\mathrm {CDZ}\) will normally be calculated as:

  • \(\mathrm {CDXAERO=\frac{1}{2}\rho _{air}S_{2D}C_{dx}}\)

  • \(\mathrm {CDYAERO=\frac{1}{2}\rho _{air}B_yC_{dy}}\)

  • \(\mathrm {CDZAERO=\frac{1}{2}\rho _{air}B_zC_{dz}}\)

where:

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

  • \(\mathrm {S_{2D}}\): cross sectional surface area

  • \(\mathrm {B_y,B_z}\): projected area per. unit length for flow in local y and z-direction, respectively

  • \(\mathrm {C_{dx},C_{dy},C_{dz}}\): nondimensional drag coefficients in local x, y and z-directions, respectively

If the component is part of a wind turbine tower line, only the CDY component is used for tower shadow computation.

CHTYPE=AIRF: Coefficients on file. ID and chord length, One input line
CHCOEF CHORDL YFC ZFC ROTFAX
  • CHCOEF: character(32): Air foil coefficient identifier. Must be found on the air foil library file

  • CHORDL: real: Chord length of foil section. \(\mathrm {[L]}\)

    • It is used to scale the air foil load coefficients.

  • YFC: real, default: 0: Y-coordinate of foil origin \(\mathrm {[L]}\)

  • ZFC: real, default: 0: Z-coordinate of foil origin \(\mathrm {[L]}\)

  • ROTFAX: real, default: 0: Inclination of foil system \(\mathrm {[deg]}\)

The blade coordinate system and origin coincides with the elastic (local) \(\mathrm {(X_L,Y_L,Z_L)}\) coordinate system. The aerodynamic coordinate system \(\mathrm {(X_{AF},Y_{AF})}\) is located at (YFC,ZFC) referred to the local coordinate system, and is rotated about the blade x axis by the angle ROTFAX, as indicated in the figure below. The \(\mathrm {X_L}\) axis is pointing into the paper plane, while the \(\mathrm {Z_{AF}}\) is pointing out of plane. Note that the air foil coefficients has to be referred to the aerodynamic coordinate system as indicated by the corresponding angle of attack in the figure. For airfoil elements that are part of a wind turbine blade, the local \(\mathrm {X_L}\)-axis is pointing towards the blade tip.

Normally, the arodynamic twist and the structural twist are given as one input. The input is given as twist of the elastic local coordinate system (see Line and segment specification ). ROTFAX should normally be 0.

riflex um foil
Figure 3. Definition of foil center and inclination of foil system in the local cross section (strength).

In coupled analysis, a SIMO wind type with IWITYP >= 10 must be used if the case contains elements with wind force coefficients that are not on the blades of a wind turbine.

1.18. Capacity parameter

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

  • YCYRMX: real: Maximum curvature around local y-axis \(\mathrm {[1/L]}\)

  • ZCURMX: real: Maximum curvature around local z-axis \(\mathrm {[1/L]}\)

These parameters are dummy in the present version