Dynamic Similarity of Wind Turbine's Tower-Nacelle System and its Scaled Model

Abstract

A paper presents analysis of dynamic similarity between full-scale wind turbines tower-nacelle system and its laboratory model. As a reference real-world structure, Vensys 82 wind turbine was assumed. Complete and partial similarity criteria were both introduced. Considering laboratory model to be equipped with tuned mass damper horizontally arranged at the top, partial similarity of one pair of points (tower tips) motions will be satisfactory. On the basis of similarity conditions, laboratory model parameters were determined so that data acquired for the model may be referred to real-world structure.

Study of vibration control using laboratory test rig of wind turbine tower-nacelle system with MR damper based tuned vibration absorber

“…Based on all the assumptions, constraints and thorough analyses results that are covered in [19][20][21], Ti Gr. 5 rod was selected to model wind turbine tower, while Lord Co. RD 1097-1 [17] was utilized as TVA MR damper.…”

“…Excitation signal is generated by LDS Dactron 7 and amplified by the Modal Shop 2100E21-400 unit 8. Such a laboratory test rig gives the possibility to model wind turbine tower vibration under several excitation sources [19][20][21]. (Fig.…”

Wind turbine's tower-nacelle model with magnetorheological tuned vibration absorber

“…These are as follows [10]: (a) possibility to apply to the nacelle a horizontal disturbance load of changeable maximum value, and changeable maximum travel stroke, according to the shaker specifications and testing conditions' requirements, (b) possibility to unplug the disturbance load from the nacelle after vibration excitation, to acquire free vibration response of first bending mode (and possibly also second bending mode), (c) value of bending mode(s) frequency(ies) should be reasonably low, to cope with time delays of feedback loop (MR damper and sensors/conditioners time constants, sampling period, etc.) while being reasonably high to cope with shaker and sensors operating ranges; thus the first bending frequency should be located at 3÷5 Hz range, (d) adequate damping ratio of system's first bending mode(s) to limit tower deflection amplitude while MR TVA system is not active or MR damper was locked / applied current to high (limit due to MR damper stroke and tower bending strength) and applied disturbance load is adequately high to observe reasonably big tower deflection amplitude for active MR TVA system (minimum reasonable MR damper operation displacement amplitude constraint), (e) reasonably high yield strength (Re) of tower material and reasonably high tower section modulus in bending (limit due to high bending torque at tower bottom section), (f) mass of the nacelle has to be adequately high to lower values of bending frequencies of the tower-nacelle system, while maintaining reasonably high factor of safety for tower buckling, (g) mass of the absorber has to be adequately high to enable reduction of tower deflection amplitude, while respecting limited MR damper stroke, (h) MR damper resistance force constraints: minimal and maximal, (i) MR damper maximum piston velocity, (j) maximum shaker force, and maximum shaker stroke limitations (the primary shaker for the nacelle excitation), (k) height of the laboratory test rig is limited by the laboratory ceiling height of 3.29 m, considering future possibility to lay rig down on the horizontally moving platform, modelling excitation of seismic-type, or seawaves-type (for buoy floating wind turbine model); also, a second, horizontal excitation applied to the tower, to be realised by the other shaker, should be a possible option, (l) mass of the laboratory test rig is limited by the foundation specification -cyclic dynamic loads should be minimised to eliminate the risk of foundation motion, (m) the laboratory setup, including its mechanical hardware, shaker, and MR damper used should be of commercially available type to fit within budget limitations, and possess adequate reliability and repeatability of operation characteristics, (n) at least partial dynamic similarity (similarity of motions of one pair of points -tower tips) between full-scale wind turbine's tower-nacelle system, and its laboratory model, has to be fulfilled [11], which adds additional constraints to the above requirements.…”

“…As dynamic similarity analysis [11] resulted in conclusion that number of parameters to be determined is greater than number of equations to fulfil, some experimental setup parameters (concerning e.g. scale of the model, cross-section shape) may be assumed arbitrary.…”

“…2, respectively. As a next stage, calculation analysis for these configurations was conducted with full continuousdiscrete analytical approach (infinite number of modes) based on [8] and utilised in [11], discrete frequency method applied for the 1 st bending mode only [10], and method using Comsol Multiphysics FEM tower-nacelle model embedded within MATLAB/Simulink environment with TVA (MR TVA) model build there (analysis of the first two bending modes) [10].…”