Morison model and force

Morison model

The Morison model is generally designed to incorporate in the simulation second order wave loads on a structure coming from drag and inertial effects such as viscous effects or turbulence. The Morison model is also used in case of a small body compared to the wave length. In the FRyDoM framework, the Morison model can be applied to any offshore structure. A Morison model can be composed of multiple Morison elements, corresponding to a cylinder with drag and added mass coefficients. The following figure represents the definition a Morison structure applied on a platform. A Morison element is defined by a couple of two points (represented by red dots) corresponding to the extremity of the cylinder and a discretization.

Morison model

Fig. 10 Example of an Morison model for a platform

Morison force on a Morison element

Each Morison element is associated to a local frame located at the middle of the Morison element. By default, this local frame has its third axis \(\mathbf{e3}\) parallel to the direction of the Morison element, the first axis \(\mathbf{e1}\) is parallel to the horizontal plane XY and \(\mathbf{e2}\) is defined such that the frame \((\mathbf{e1}, \mathbf{e2}, \mathbf{e3})\) is orthonormal direct.

The Morison force in the local frame coordinates is defined as follows:

\[f_M^i = \rho V \left[\dot{u}^i + C_a^i \left(\dot{u}^i - \ddot{X}^i\right)\right] + \frac{1}{2} \rho D L C_d^i \left(u^i - \dot{X}^i\right)\left|u^i - \dot{X}^i\right|\]

where

  • \(i\) can be 1 or 2,
  • \(f^i\) is the force component along the ith axis,
  • \(C_a^i\) is the added mass, along the ith axis,
  • \(C_d^i\) is the drag coefficient, along the ith axis,
  • \(\rho\) is the water density,
  • \(V, D\) and \(L\) are the volume, diameter and length of the Morison element respectively,
  • \(u^i\) is the flow velocity,
  • \(\dot{X}^i\) is the absolute velocity of the center at the middle of the Morison element,

In this formulation, anisotropic Morison element can be represented by a set of anisotropic definition of the added mass and drag coefficients in function of the axis direction.