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. 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 seafloor contact (unless IBTANG = -9;original flat bottom formulation) pipe-in-pipe contact Tubular contact point specification 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. 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. \(\mathrm {[1]}\) The default value of SF corresponds to the earlier fixed value of 10.0. 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 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). 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). 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 stiffness 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 stiffness 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 Note: 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. Restricted option. = HNET: Net properties and hydrodynamic added mass coefficients for net Note that the option POTN currently is under testing. Potential flow forces are only available for irregular time domain analysis. Note that the option TVIV is currently under development. 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: - \(\mathrm {CDa=\rho \sqrt{gD}\times D^2CD_{an}}\) - \(\mathrm {AMY=\rho \frac{\pi D^2}{4}C_{mn}}\) NOTE: 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 Restricted option. Under implementation. 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. If a number is found instead of CHTVIV, the input is read in the old input format. CHTVIV NMEM CHH CHTVIV: character(8): Time domain VIV load option = CF: Cross-flow VIV loads only = CFIL_1: Cross-flow VIV loads and cross-flow induced in-line VIV loads = CFIL: Cross-flow and in-line VIV loads calculated independently = IL: In-line VIV loads only 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) Cross-flow VIV load coefficients. The following input line is given if CHTVIV is CF, CFIL_1 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) Cross-flow induced in-line load coefficients. The following input line is given if CHTVIV is CFIL_1: CVIL ALPHIL CVIL: real >= 0, default: 0.0: Vortex shedding force coefficient for (instantaneous) in-line load term (nondimensional) ALPHIL: real >= 0, default: 0.0: Nondimensional parameter giving freedom to in-line excitation frequency Independently calculated in-line load coefficients. 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 old format (deprecated functionality) for time domain VIV load options and coefficient, 1 inputline. Note that this input format will be removed in later versions. CV FNULL FMIN FMAX NMEM CVIL ALPHIL CHH CV: real >= 0: Vortex shedding force coefficient for the (instantaneous) cross-flow load term (nondimensional) FNULL: real > 0: Natural vortex shedding frequency (nondimensional) FMIN: real > 0: Minimum vortex shedding frequency (nondimensional) FMAX: real > FMIN: Maximum vortex shedding frequency (nondimensional) NMEM: integer > 0: Number of time steps used in calculation of standard deviation CVIL: real >= 0, default: 0.0: Vortex shedding force coefficient for (instantaneous) in-line load term (nondimensional) ALPHIL: real >= 0, default: 0.0: Nondimensional parameter giving freedom to in-line excitation frequency CHH: real >= 0, default: 0.0: Higher harmonic load coefficient (nondimensional) Specifying CVIL, ALPHIL and CHH as zero will give excitation only in the updated cross-flow direction. 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. NOTE: 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