NREL 5MW monopile OWT modelling details

Wind & Water General
3

Sir,

Sorry for my late reply. Yes, I do have FAST input files. Currently for my Mtech thesis, I was working on Platform model 2 i.e, Bottom fixed offshore wind turbine with foundation modeled as coupled springs. I have some doubts and I am asking it here for my clarification. Please correct me if my understanding is wrong.

  1. The NREL 5MW wind turbine was modeled with nonlinear beam elements in the FAST code. For the NREL 5MW wind turbine, the blade structural properties are defined at 49 locations along the blade from the blade root to tip. And for aerodynamic and structural forces calculation at nodes, the blade is discretizing into 17 nodes. And the support structure properties for both tower and monopile were defined at 13 locations along the support structure i.e, from the seabed (-20m) to tower top(87.6m). And the tower nodes above mean sea level was discretized into 20 nodes for aerodynamic and elastic forces calculation on the tower. Then for the calculation of hydrodynamic loading, into how many nodes the monopile has been discretized?

  2. FAST code uses Kane’s method for deriving the equation of motion. According to Kane’s method the equations of motion for a holonomic system is defined as
    Fr + F*r = 0 where Fr = Fr|aero + Fr|gravity + Fr|elastic + Fr|drivetrain + Fr|platform

     where  Fr|platform = -(Addedmass*qdd) + Fr|hydro + Fr|seismic ( If monopile OWT is under action of wind, wave and seismic effects)

  Fr|seismic is the seismic forces required to achieve the ground motion given by user and is caluclated as 

                    Fr|seismic = k * (PtfmDisp-X) + c * (PftmVel-XD)

where PtfmDisp and PtfmVel are desired displacement and velocity at the base of the monopile at seabed and X, XD are realized displacement and velocity.
Fr|hydro is calculated by using morison equation because D/l ratio is less than 0.2 for monopile substructure in seawater. And I have used JONSWAP spectrum for modeling irregular waves.

     And where F*r = F*r|hub + F*r|blades + F*r|tower + F*r|nacelle +F*r|platform

 (and what F*r|platform indicates then. Is it equals to mass of the (monopile+Platform mass) multiplied by input ground motion?)

The Addedmass term in the Fr|platform is added to Mass matrix and complete nonlinear equation of motion is written in matrix form as

M(q,u,t)*qdd = f(q,qd,u,ud,t)

where,

M = mass matrix depending on a nonlinear combination of displacements (q), control inputs (u), and time (t)
qdd = accelerations
f = forcing vector depending on a nonlinear combination of displacements (q), velocities (qd), control inputs (u), wind inputs (ud) (input disturbances), and time (t).

These non linear equations of motion is linearized to find the full system modes. So linearization of nonlinear equations of motion is done about several operating points and reducing the nonlinear equation to second order representation of
Mxdd + C xd + Kx = F(t) where xdd,xd, x are vectors of second derivative of DOF’s, first derivative of DOF’s and DOF’s
and it was further defined in first order representation and all the state matrices obtained are given to mbc post processing matlab scripts and averaged eigen values, eigen vectors are obtained. Can we stop the linearization at second order representation and can we get mass and stiffness matrices as out of mbc?

Sorry for posting such a lengthy question. Please correct me if my understanding is wrong.

Thank you.