Literature Survey of Wind Turbine Aeroelastic Stability

A literature survey of wind turbine aeroelastic stability is presented. The subject received early interest as the emergent wind industry looked to lessons from the helicopter industry. There has not been a utility-scale turbine with flutter problems, but there is a concern over the behavior of larger, more flexible turbines. Blades of innovative design with bend-twist coupling and tip sweep are also a concern. Much of the aerodynamic modeling was formulated in the 1930s by Theodorsen. Modern authors have developed finite element structural models for eigenvalue solutions to the stability models. Calculations for a 1.5 MW turbine blade with bend-twist coupling show flutter speed at twice the rotor rotational speed. Comparisons were made to standard turbine aeroelastic codes showing good agreement, and the possibility of using these codes to check for flutter

Literature Survey of Wind Turbine Aeroelastic Stability

A literature survey of wind turbine aeroelastic stability is presented. The subject received early interest as the emergent wind industry looked to lessons from the helicopter industry. There has not been a utility-scale turbine with flutter problems, but there is a concern over the behavior of larger, more flexible turbines. Blades of innovative design with bend-twist coupling and tip sweep are also a concern. Much of the aerodynamic modeling was formulated in the 1930s by Theodorsen. Modern authors have developed finite element structural models for eigenvalue solutions to the stability models. Calculations for a 1.5 MW turbine blade with bend-twist coupling show flutter speed at twice the rotor rotational speed. Comparisons were made to standard turbine aeroelastic codes showing good agreement, and the possibility of using these codes to check for flutter

Comparison of upwind and downwind operation of the NREL Phase VI Experiment

Wind tunnel data are presented comparing upwind versus downwind operation of the National Renewable Energy Laboratory\u27s Phase VI wind turbine. Power was not reduced as expected with downwind operation, which may be attributed to inboard three-dimensional effects. Average flap bending loads were reduced with downwind coning and compared well with prediction. Blade fatigue loads were increased with downwind operation; however, fatigue was mitigated with an aerodynamic tower shroud (fairing). The shroud needs to remain aligned with the freestream, demonstrated by an increase in fatigue loads from a 10° error in shroud alignment. Pressure data were acquired of the tower wake at the rotor location with and without the shroud installed. The bare-tower wake data compared well with previously published work. The shroud wake data at 10° error in alignment showed velocity reduction and turbulence approaching the bare tower values. Downwind operation, with an aligning tower shroud, should be considered for future designs given the load benefits of downwind coning

Gilbert ROUGET : Initiatique vôdoun : Images du rituel (vol. 1) ; Initiatique vôdun : Musique du rituel (vol. 2) (Sonagrammes et transcriptions musicales de Jean Schwarz et Tran Quâng Hai en collaboration avec l’auteur)

Cette œuvre magistrale de Gilbert Rouget est la suite logique d’Un roi africain et sa musique de cour (1996). En effet, après les rituels royaux, ce sont à ceux pratiqués dans le cadre plus général du culte des vôdoun au Bénin du Sud que l’auteur a décidé de consacrer cet ouvrage important. Mais, alors que celui-là constituait un seul livre homogène, dans lequel étaient insérés deux disques compacts, celui-ci se compose de deux volumes : un livre et un dossier, comportant deux disques compact..

Collisional Cascades in Planetesimal Disks II. Embedded Planets

We use a multiannulus planetesimal accretion code to investigate the growth of icy planets in the outer regions of a planetesimal disk. In a quiescent minimum mass solar nebula, icy planets grow to sizes of 1000--3000 km on a timescale t = 15-20 Myr (a/30 AU)^3 where a is the distance from the central star. Planets form faster in more massive nebulae. Newly-formed planets stir up leftover planetesimals along their orbits and produce a collisional cascade where icy planetesimals are slowly ground to dust. The dusty debris of planet formation has physical characteristics similar to those observed in beta Pic, HR 4796A, and other debris disks. We derive dust masses for small particles, 1 mm and smaller, and large particles, 1 mm and larger, as a function of the initial conditions in the planetesimal disk. The dust luminosities derived from these masses are similar to those observed in Vega, HR 4796A, and other debris disks. The calculations produce bright rings and dark gaps. Bright rings occur where 1000 km and larger planets have recently formed. Dark gaps are regions where planets have cleared out dust or shadows where planets have yet to form.Comment: to be published in the Astronomical Journal, January 2004; 7 pages of text; 17 figures at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-figures.pdf; 2 animations at http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-movies.htm

Collisional Cascades in Planetesimal Disks I. Stellar Flybys

We use a new multiannulus planetesimal accretion code to investigate the evolution of a planetesimal disk following a moderately close encounter with a passing star. The calculations include fragmentation, gas and Poynting-Robertson drag, and velocity evolution from dynamical friction and viscous stirring. We assume that the stellar encounter increases planetesimal velocities to the shattering velocity, initiating a collisional cascade in the disk. During the early stages of our calculations, erosive collisions damp particle velocities and produce substantial amounts of dust. For a wide range of initial conditions and input parameters, the time evolution of the dust luminosity follows a simple relation, L_d/L_{\star} = L_0 / [alpha + (t/t_d)^{beta}]. The maximum dust luminosity L_0 and the damping time t_d depend on the disk mass, with L_0 proportional to M_d and t_d proportional to M_d^{-1}. For disks with dust masses of 1% to 100% of the `minimum mass solar nebula' (1--100 earth masses at 30--150 AU), our calculations yield t_d approx 1--10 Myr, alpha approx 1--2, beta = 1, and dust luminosities similar to the range observed in known `debris disk' systems, L_0 approx 10^{-3} to 10^{-5}. Less massive disks produce smaller dust luminosities and damp on longer timescales. Because encounters with field stars are rare, these results imply that moderately close stellar flybys cannot explain collisional cascades in debris disk systems with stellar ages of 100 Myr or longer.Comment: 33 pages of text, 12 figures, and an animation. The paper will appear in the March 2002 issue of the Astronmomical Journal. The animation and a copy of the paper with full resolution figures are at S. Kenyon's planet formation website: http://cfa-www.harvard.edu/~kenyon/p

Density waves in debris discs and galactic nuclei

We study the linear perturbations of collisionless near-Keplerian discs. Such systems are models for debris discs around stars and the stellar discs surrounding supermassive black holes at the centres of galaxies. Using a finite-element method, we solve the linearized collisionless Boltzmann equation and Poisson's equation for a wide range of disc masses and rms orbital eccentricities to obtain the eigenfrequencies and shapes of normal modes. We find that these discs can support large-scale `slow' modes, in which the frequency is proportional to the disc mass. Slow modes are present for arbitrarily small disc mass so long as the self-gravity of the disc is the dominant source of apsidal precession. We find that slow modes are of two general types: parent modes and hybrid child modes, the latter arising from resonant interactions between parent modes and singular van Kampen modes. The most prominent slow modes have azimuthal wavenumbers $m=1$ and $m=2$. We illustrate how slow modes in debris discs are excited during a fly-by of a neighbouring star. Many of the non-axisymmetric features seen in debris discs (clumps, eccentricity, spiral waves) that are commonly attributed to planets could instead arise from slow modes; the two hypotheses can be distinguished by long-term measurements of the pattern speed of the features.Comment: 17 pages, 11 figures, accepted for publication in Monthly Notices of the Royal Astronomical Societ