Thanks for your quick response.
About the tower:
I have replaced the tapered tower in the WP1.5MW with a uniform tower, with EI= 1.3710e+11 Nm^2 at all stations along the length ( 82.4 m). Accordingly, I have calculated the mode shape coefficients using “Modes” code and incorporated in the tower structural properties used for OpenFAST simulations.
Regarding M_eqTwr = 33/140 * M_twr:
Eq 3 and Eq 10 from the paper below has answers for choosing 33/140 factor;
The paper doesn’t say anything about the damping though.
About aerodynamic damping:
In OpenFAST model, I have set the “TwrAero” to False, meaning aerodynamic forces on tower are not calculated, just like the case in my in-house model.
Talking of the ‘tower motion’, I have considered it in the aerodynamic force calculations, which could provide aerodynamic damping. The relative wind velocity at each instant at each airfoil is calculated as,
- V_rel^2 = [ (V_wind – V_twr)(1-a) ]^2 + [ r(omega)*(1+a’) ]^2
- Thrust = 0.5rhoAV_rel^2Cx (at each section)
Infact calculated induction factors, are calculated using BEMT and the algorithm in the the paper ( Ning, S. A., “A simple solution method for the blade element momentum equations with guaranteed convergence,” Wind
Energy, Vol. 17, No. 9, 2014, pp. 1327–1345 ).
Am I missing to capture anything more that could add aerodynamic damping?
I have used a PI controller, with rotor speed error ( = omega_t – omega_rated ) as the feedback for the controller. ( NO tower motion measurements are considered for feedback in controller ) Again, in OpenFAST controller also, tower acceleration feedback is NOT considered.
One difference between controllers (FAST vs In-house) is that FAST controller has implemented gain scheduling but I have used a single set of gains (Kp, Ki) values for the controller across the operating region in my model. But, I have verified through step disturbance analysis that the chosen gains are capable of maintaining the system at the operating point for the entire region3 (V_rated to V_cutoff) with a reasonable step response. (Fig1 - in previous post).
I agree that the pitch action (rate of it ) could play a vital role in tower oscillations, but, the picture (Fig3 in the previous post) suggest the pitch action is almost same between OpenFAST and in-house code.
I will have to look at in more detail.