1. EXT1 - External wrapping

This component can be used to model additional weight or buoyancy modules attached to a riser line. The specified additional weight and buoyancy are used to adjust the average properties of the segment.

1.1. Data group identifier

NEW COMPonent EXT1

1.2. Component type identifier

CMPTYP-ID

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

1.3. Mass and volume

AMS AE RGYR FRAC

  • AMS: real: Mass per unit length \(\mathrm {[M/L]}\)

  • AE: real: Buoyancy volume/length \(\mathrm {[L^2]}\)

  • RGYR: real: Radius of gyration around local x-axis \(\mathrm {[L]}\)

  • FRAC: real: Fraction of the segment that is covered \(\mathrm {[1]}\)

    • 0 <= FRAC <= 1

The resulting properties of the segment with external wrapping are:

Mass / length:

  • \(\mathrm {AMS_{res}=AMS_{cs}+AMS_{ext}\times FRAC}\)

Resulting radius of gyration:

  • \(\mathrm {RGYR_{res}=(AMS_{cs}\times RGYR_{cs}^2+AMS_{ext}\times RGYR_{ext}^2\times FRAC)/(AMS_{cs}+AMS_{ext}\times FRAC)}\)

Resulting external area for buoyancy:

  • \(\mathrm {AE_{res}=AE_{cs}+AE_{ext}\times FRAC}\)

Where:

  • cs denotes the original cross section properties; i.e. without wrapping.

  • ext denotes the properties of the wrapping given in this data group.

  • res denotes the resulting average segment properties

um ii fig121
Figure 1. Description of external wrapping

1.4. Hydrodynamic coefficients

CDX CDY AMX AMY CDLX CDLY

  • CDX: real: Drag force coefficient in tangential direction \(\mathrm {[F/((L/T)^2\times L)]}\)

  • CDY: real: Drag force coefficient in normal direction \(\mathrm {[F/((L/T)^2\times L)]}\)

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

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

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

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

The coefficients specified for the external wrapping are added directly to the coefficients specified for the pipe.

The drag forces per unit length acting in the local x-direction is computed as:

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

In the case of an axis symmetric cross section the drag force per unit length, \(\mathrm {F_n}\), acting normal to the local x-axis is computed by assuming that the instantaneous drag force direction is parallel to the instantaneous transverse relative velocity component

  • \(\begin{array}{l}\mathrm {F_n=(CDY_R+FRAC\times CDY)(VRELY^2+VRELZ^2)}\\+\mathrm {(CDLY_R+FRAC\times CDLY)\sqrt{VRELY^2+VREZ^2}}\end{array}\)

In the case of a cross section with 2 symmetry planes the drag force per unit length in the local y and z directions are computed as:

  • \(\mathrm {F_y=(CDY_R+FRAC\times CDY)VRELY\times VRELY+(CDLY_R+FRAC\times CDLY)VRELY}\)

  • \(\mathrm {F_z=(CDZ_R+FRAC\times CDZ)VRELZ\times VRELZ+(CDLZ_R+FRAC\times CDLZ)VRELZ}\)

Where:

  • \(\mathrm {CDX_R,CDY_R,CDZ_R}\): are the input quadratic drag force coefficients of the riser in local x,y and z-directions

  • \(\mathrm {CDLX_R,CDLY_R,CDLZ_R}\): are the input linear drag force coefficient of the riser in local x,y and z-directions

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

  • \(\mathrm {CDLX,CDLY}\): are the input linear drag force coefficients of the external wrapping in local x andy-directions

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

For an axis symmetric pipe with external wrapping the input drag force coefficient in normal direction can be calculated as:

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

The added mass per unit length in normal direction can be calculated as:

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

where:

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

  • \(\mathrm {D}\): outer diameter of the external wrapping

  • \(\mathrm {D_R}\): outer diameter of the pipe

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

  • \(\mathrm {C_{dnR}}\): normal drag coefficient of the pipe

  • \(\mathrm {C_{mn}}\): normal added mass coefficient of the external wrapping

  • \(\mathrm {C_{mnR}}\): normal added mass coefficient of the pipe