8.1.13. Theory

This section discusses the theory applicable to the Hydrodynamic Pressure Mapping Add-on for the mapping of pressures from a Hydrodynamic Diffraction system.

8.1.13.1. Hydrodynamic and Hydrostatic Pressures on Surfaces

The real and imaginary parts of the incident, diffracted, radiated and hydrostatic-varying pressure components calculated in the Hydrodynamic Diffraction analysis are used to evaluate the total hydrodynamic pressure at each structure node for the specified incident wave amplitude and phase angle:

(8–1)

Where Pθ is the total hydrodynamic pressure at the required phase angle θ, with θ=0° when the incident wave crest passes the center of gravity of the structure; is the specified incident wave amplitude; and Pr and Pi are the real and imaginary parts, respectively, of the summed hydrodynamic (incident, diffracted, radiated and hydrostatic-varying) pressure components.

Where hydrostatic pressure is also included, the total pressure P is the summation of the hydrodynamic and hydrostatic parts:

(8–2)

Where the hydrostatic pressure Ps is calculated as:

(8–3)

In which ρ and g are the water density and acceleration due to gravity, respectively, as specified in the Hydrodynamic Diffraction analysis; and z is the depth of the structure node below the waterline in the Static Structural axis system (after any Axis Transformation has been applied).

8.1.13.2. Inertia and Viscous Drag Forces on Line Bodies

Distributed loads on submerged Line Bodies are calculated using the Morison equation:

(8–4)

Where:

F is the total Morison force per unit length;

D is the Line Body diameter (which should take into account any marine growth);

Cd is the viscous drag coefficient;

uf is the flow velocity normal to the Line Body (comprising the diffracted wave particle velocity and any defined current);

us is the structure velocity normal to the Line Body;

and are the flow and structure accelerations, respectively, normal to the Line Body;

A is the cross-sectional area of the Line Body;

is the added mass coefficient, from which:

(8–5)

Where Cm is the inertia coefficient. Setting Cm =0.0 turns off loading due to the diffracted wave and added mass effects (second and third terms of Equation 8–4); otherwise the valid range of values are Cm ≥1.0. Similarly, viscous drag (first term of Equation 8–4) can be ignored by setting Cd =0.0. For non-cylindrical cross sections, the Morison equation is applied separately in each direction normal to the Line Body.

The Hydrodynamic Pressure Mapping Add-on determines whether the ends of each beam element are above or below the local water surface and loads the Line Body accordingly. For elements that cut the water surface the loading is applied over the wetted length only.