Worst-Case Gust-Response Analysis for Typical Airfoil Section with Control Surface

Abstract

This paper determines the worst-case gust response of a typical airfoil section with a control surface. Matched filter theory is employed in order to compute the gust that produces a maximum response. These results are compared with a tuned one-minus-cosine gust, one of the standard representations of discrete gusts. It is found that the responses obtained by the matched filter theory are about twice as large as those obtained using the one-minus-cosine gust. Moreover, it is found that the hinge stiffness of the control surface can affect the plunging motion. Nomenclature= aerodynamic force vector caused by the gust,frequency response function of airplane h = plunge displacement, 2bn h y (t) = unit impulse response I α , I β = mass moment of inertia about elastic axis, control surface hinge J 0 (k), J 1 (k) = Bessel function of the first kind K = arbitrary constant k = reduced frequency, ωb/U L = scale of turbulence L G = lift caused by gust L M = lift caused by wing motion L M C , L M NC = lift of the circulatory flow, noncirculatory flow M G α , M G β = moment caused by gust M M α , M M β = moment caused by wing motion m = airfoil total mass n = gust gradient distance in chords p, s = Laplace variable R = ratio of standard deviations S α , S β = static moment T i = aerodynamic coefficient t = time t 0 , τ 0 = arbitrary time shift U= airspeed w G = upwash caused by gust w 0.75c = downwash at 75% chord w 1 − cos = maximum velocity of discrete gust

Active flap control with the trailing edge flap hinge moment as a sensor: using it to estimate local blade inflow conditions and to reduce extreme blade loads and deflections

“…A complete model should also include the unsteady hinge moment contribution of varying gust fields and changes in the relative wind speed of the airfoil. Nonetheless, the contribution of both can be neglected for our application, as discussed in Kanda and Dowell (2005) and Leishman (2006, p. 457).…”

“…In this study, we follow an approach used in Kracht et al (2015). The observer model is comprised of three submodels: a nonlinear M H-g model, a linear hinge model (that esti-matesM H-A andM H-I ) and a signal model.…”

“…We note that other signal models can be used, such as, e.g., a bank of independent harmonic oscillators (Kracht et al, 2015), if the wind conditions for a particular site are known with a certain degree of accuracy.…”

Load mitigation for wind turbines by a passive aeroelastic device

“…( 10) does not lead to a state space form of the model governing equations. To correct for this, Kanda and Dowell (2005) proposed to assume the upwash caused by the gust as constant over the section, which means that the circulatory contribution caused by the sectional motion is the same as the one due to the gust, an assumption that is acceptable for reduced frequencies s 1. This way, αG can be expressed as…”

A note on typographical errors defining Theodorsen's coefficients for aeroelastic analysis

“…Since Theodorsen's work was published, his theory has been used by researchers to develop methodologies in linear and nonlinear aeroelasticity and a large number of works have been published by the scientific community (Alighanbari, 1995; Ko et al., 1998; Bueno et al., 2014; Zhang and Behal, 2016). Among these works, several papers were disclosed with typographical errors in Theodorsen's coefficients (Edwards et al., 1979; Karpel, 1981; Kanda and Dowell, 2005; Li et al., 2010; Vasconcellos et al., 2012; Abdelkefi et al., 2012). The quality of these works is not questionable.…”