Modeling stochastic wind loads on vertical axis wind turbines

The Vertical AXIS Wind Turbine (VAWT) is a machine which extracts energy from the wind. Since random turbulence is always present, the effect of this turbulence on the wind turbine fatigue life must be evaluated. This problem 1s approached by numerically simulating the turbulence and calcu– latlng, In the time domain, the aerodynamic loads on the turbine blades. These loads are reduced to the form of power and cross spectral densities which can be used In standard linear structural analysls codes. The relative Importance of the turbulence on blade loads 1s determined. The most common des]gn for Vertical Axis Wind Turb]nes (VAWT’S) was first patented in 1931 by Darrleus, a Frenchman. Th]s “egg beater” shaped machine consists of one or more blades with air– foil cross sections attached to the top and bottom of a central shaft, or tower. To m]nlmize bending stresses In the blades while the turbine rotates, the blades usually have a characteristic tropos– klen, or “splnnlng rope,” shape. Torque is produced when the turb]ne rotor turns In the wind. Fig. 1 shows the 17 meter research VAWT at Sandla National Laboratories, Albuquerque, NM This turb]ne has the most common configuration of VAWT’S currently being built, two blades w]th a central tower and guy cables supporting the top of the rotor. The aerodynamic analysls of the VAWT 1s compli– cated by several factors Since the VAWT blade rotates through 360 degrees relatlve to the lncl– dent wind during each rotation, the rate of change of angle of attack 1s often much greater than experienced ]n other airfoil applications. But because the speed of the blade 1s normally much greater than the w]nd speed, the angle of attack varies between posltlve and negative values around zero degrees. The higher the w]nd speed, the greater the angle of attack excursions. When the winds become h]gh enough, the angles of attack become large enough that the alrfoll begins to stall dynamically. Research In VAWT aerodynamics 1s currently lnvestlgatlng both dynamic stall and p]tch rate effects. Aerodynrunlc analys]s using the streamtube momentum balance approach was the earnest and slm lest approach used to est]mate Y VAWT performance The vortex llftlng llne ap– preach has produced some better results, in an average sense, over a wider range of wlnd2cond]tlons, but 1s computatlonally expensive Both methods suffer from the lack of a valldated method of predicting dynemlc stall. Except for emplrlcal llft and drag curves from wind tunnel testing, accurate pltchlng airfoil, dynamic stall models do not exist. Most VAWT’S experience stall over a s]gnlflcant portion of the normal operat]ng range The loss of llft due to stall in high winds 1s considered benef]clal because It llmlts the maximum power that the drive train must trans– mlt, thereby holding down the turbine cost. The structural analysls of the VAWT must deal with the fact that the structure is rotating. Corlolls and centrifugal effects make the modes of vlbra– tlon complex, but the system remains l]near. Free v]bratlon analysls and aero lastlc analysis 5 are well developed and valldated The forced v]bratlon analysis of the VAWT rotor ]s developed, but agreement w]th field data from operating turbines 1s sometimes poor, especlall~ In the high w]nd speed, significant stall, regime It is not yet clear whether the source of the error 1s In the structural analysls or ]n the calculation of the aerodynem]c loads The relatively good agree– ment of the structural analysis to the data gathered at low wind speeds would seem to indicate that the problem may l]e in the aerodynamics. Fig. 1 Darrleus Vertical AXIS Wind Turb]ne (VAWT) at Sand]a National Laboratories, Albuquerque, NM Another possible source of error In previous load calculations 1s the assumption of a steady w]nd. Until now, all the aerodynamic loads have been calculated based on a constant emblent wind. The loads which result from this calculation are shown In Fig. 2. Tangential forces are def]ned as the component In the dlrect]on tangent to the path of the blade as It rotates and normal forces are normal to this path. The tangential forces pro– duce a net torque about the central tower while the normal forces produce no net energy. When a constant wind lS assumed, the forces repeat exactly for each rotor revolution. The frequency content of these forces 1s therefore limlted to Integer mult;ples of the turbine rotational speed (abbreviated as “per rev” frequencies). This approach will produce zero excltat]on at any frequency other than the per rev frequencies. This lS not totally unreasonable because the per rev frequency content of the loads 1s produced by the mean wind and the rotation of the rotor, and ]s therefore large compared to the turbulence induced, stochastic loads However, data collected from VAWT’S operat]ng in high winds have shown slgnlf]cant response at the structural resonant frequencies as well as at the per rev frequencies. The spectral content of the blade stress response shown in Flg 3 could never be predicted with loads calculated assuming e steady wind. By calculating the aerodynamic loads due to a turbulent wind, the loads will contain all fre– quencles, not only the per rev frequencies. These stochastic loads are described by their power spectral densities (psd’s) and cross spectral densltles (csd’s). Because the relationship between incident wind speed and blade forces is