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Rigid type

This line segment type is used to model any type of riser made of homogenous material, such as steel pipes. Primary mechanical characteristics such as mass, axial stiffness, bending stiffness and torsion stiffness are derived using the cross-section geometry and material characteristics. Modelling of the line segments assigned this line type is based on beam elements featuring 6 degrees of freedom per node.

The rigid pipe type is a convenient way to define steel pipe or homogenous material pipe properties. The numerical model is similar to the Flexible pipe type. This is useful to model pipes with a uniform material, as the stiffnesses are calculated using the pipe geometry and the material properties, based on the following :

The axial stiffness equals E*A with E the Young modulus and A the steel cross area: A = Π * (OD-ID) / 4
The bending stiffness equals E*I with E the Young modulus and I the inertia: I = Π * (OD4-ID4) / 4
The torsion stiffness equals G*Ct with G equal to 8.08e10 and Ct = 2 * I

Mechanical properties

Outside diameter (mm) : This is the outside diameter of the rigid pipe. Additional layers increasing the nominal pipe diameter (e.g. coatings) are not usually considered here.
Wall thickness (mm) : This is the steel wall thickness of the rigid pipe.
Additional mass (kg/m) : This is the additional mass for any components or coatings on the pipe.
Buoyancy diameter (mm) : This is the equivalent buoyancy diameter for the rigid pipe. It will be used for the calculation of the buoyancy force exercised by the external fluid (proportional to external fluid density). If zero is entered, then the Hydrodynamic Diameter will be considered.
Internal cross section (mm) : This is the internal section where internal fluid can be present; then the internal fluid weight (according to its density and this internal cross section area) will be taken into account, as well as the internal pi*Si pressure effect.
Apparent weight (N/m) (see note below): This is the equivalent submerged weight of the rigid pipe with its internal fluid and any other coatings and accessories included. With this tick-box ticked, it is possible to prescribe the equivalent submerged weight of the rigid pipe filled with internal fluid. This is useful if the presence of accessories, coatings, marine growth etc make the implicit calculation of mass difficult.

Note

When apparent weight option is not ticked, the submerged weight of this pipe section will be calculated using : - the weight in air of the pipe itself (lineic mass) - the additional weight due to the internal fluid (using the internal fluid density and the internal cross section area) - and the buoyancy force exercised by the external fluid (using the external fluid density and the buoyancy diameter).

Damping

Damping parameters are entered to account for structural damping due to the pipe material or friction between layers in composite structures such as unbonded flexible pipes. Structural damping is based on the Rayleigh viscous damping model, where the achieved damping rate depends on the frequency of the dynamic deformation. Details about the Rayleigh damping formulation used are presented in the Theory section.

Coefficient type: Select either "Beta" or "Ksi". Ksi refers to the actual damping rate (i.e. damping value over critical damping value ratio). Enter for instance 0.01 rate if you wish to set a damping equal to 1% of the critical damping. The damping coefficient considered in the dynamic analysis is eventually defined through the Beta coefficient which depends on the structural damping rate Ksi and on a given frequency as follows as shown below.

\[ \beta = \frac{2\xi}{\omega} = \frac{\xi}{\pi f} \]

Ksi coefficients are automatically switched into Beta coefficients by considering the wave period (i.e. regular wave period or peak period with irregular waves) since the wave and resulting floater motion is expected to be the main source of motion for the line.
Rayleigh: With this option, a general damping coefficient will be applied to any material deformation; tension, bending and torsion.
By mechanism: With this option, a damping coefficient will be specified by the user for each type of deformation; tension, bending or torsion.

VIV

Damping rate: This is the structural damping rate for the flexible pipe used to compute the amplitude of excited modes, contributing to the power dissipation term in the energy balance equation. The value to be entered is the actual damping ratio (so a value of 0.01 should be entered if the damping ratio is 1%). This damping is only used in the VIV calculations: it is added to the hydrodynamic damping computed by DeepVIV.
Strakes efficiency: Tick-box activates this option: to define a strakes contribution to decrease the VIV contribution. Enter 0.01 for 1%. A value of 1.0 would mean no VIV is possible.

Finite element model

Binodal beam: Selects beam elements with linear interpolation function (2 nodes). Each node has 6 degrees of freedom (i.e. 3 translations and 3 rotations).

Note

Binodal beam elements are suitable for most applications. Accuracy of the analysis may be improved when needed in the line sections that experience significant curvature by refining the segmentation (number of beam elements along the line segment).
Trinodal beam : Selects beam elements with quadratic interpolation function (3 nodes). Each node has 6 degrees of freedom (i.e. 3 translations and 3 rotations). This allows improving the accuracy of the analysis without refining the segmentation (number of beam elements along the line segment).

Hydrodynamic properties (Morison coefficients)

More details about the Morison formulation used are presented in the Morison theory section.

Normal drag: This coefficient is used to calculate the drag loads acting on the line's beam elements in the direction orthogonal to the line. The default value is 1.2.
Normal inertia: This coefficient is used to calculate the inertia loads acting on the line's beam elements in the direction orthogonal to the line. The default value is 2.0.
Normal added mass: This coefficient is used to calculate the added mass loads acting on the line's beam elements in the direction orthogonal to the line. The default value is "-" meaning that the normal added mass coefficient is to be derived from the normal inertia coefficient considering that normal added mass coefficient = normal inertia coefficient - 1, which is valid for circular cross-section shapes. Replacing the default value "-" with any number would cause the normal added mass coefficient to be independent from the normal inertia coefficient.
Axial drag: This coefficient is used to calculate the drag loads acting on the line's beam elements in the direction tangent to the line.
Axial inertia: This coefficient is used to calculate the inertia loads acting on the line's beam elements in the direction tangent to the line.
Axial added mass: This coefficient is used to calculate the added mass loads acting on the line's beam elements in the direction tangent to the line. The default value is "-" meaning that the normal added mass coefficient is to be derived from the normal inertia coefficient considering that normal added mass coefficient = normal inertia coefficient - 1. Replacing the default value "-" with any number would cause the axial added mass coefficient to be independent from the normal inertia coefficient.
Hydrodynamic diameter (mm) : This is used to compute Morison forces acting on the rigid pipe.

Aerodynamic coefficients

Normal drag: This coefficient is used to calculate the drag loads acting on the line's beam elements in the direction orthogonal to the line. The default value is 1.2.
Axial drag: This coefficient is used to calculate the drag loads acting on the line's beam elements in the direction tangent to the line.

Stress post-processing

Corrosion thickness allowance (mm): This is the corrosion thickness considered for the rigid pipe. The corrosion thickness will be removed from the wall thickness (the internal diameter is increased) when computing the stresses.
Failure stress (Mpa) : The minimum tensile strength (stress) at room temperature prescribed by the specification or standard under which the material is purchased. This parameter is used for post-processing of DNV code checks and fatigue damage accounting for the Goodman correction.
SCF: This is the stress concentration factor to consider for the rigid pipe. This coefficient is applied to the nominal stress in the plain pipe materia to take into account a local stress raisers, in particular welds, such that (SCF * stress) is the corrected stress to be considered. (a value of 0 is in fact replaced with an SCF of 1).

Pipe material

Young Modulus (Gpa) : This is the Young modulus of the rigid pipe material. For steel, this value is of 210 and is the default value.
Poisson coefficient: This is the Poisson coefficient of the rigid pipe material. For steel, this value is of 0.3 and is the default value.
Mass density: This is the mass density of the pipe material. For steel, this value is of 7.85 and is the default value.

Thermal properties

In the case the effect of thermal expansion is required to be included, a value for expansion coefficient and reference temperature need to be added here. The reference temperature is that at which expansion is nil, and thus implies knowledge of the installation sequence, ambient temperature etc.