Modeling physical uncertainties in dynamic stall induced fluid–structure interaction of turbine blades using arbitrary polynomial chaos Jeroen A.S. Witteveen, Sunetra Sarkar * , Hester Bijl Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands Received 31 May 2006; accepted 2 January 2007 Available online 20 February 2007 Abstract A nonlinear dynamic problem of stall induced flutter oscillation subject to physical uncertainties is analyzed using arbitrary polyno- mial chaos. A single-degree-of-freedom stall flutter model with torsional oscillation is considered subject to nonlinear aerodynamic loads in the dynamic stall regime and nonlinear structural stiffness. The analysis of the deterministic aeroelastic response demonstrated that the problem is sensitive to variations in structural natural frequency and structural nonlinearity. The effect of uncertainties in these param- eters is studied. Arbitrary polynomial chaos is employed in which appropriate expansion polynomials are constructed based on the statistical moments of the uncertain input. The arbitrary polynomial chaos results are compared with Monte Carlo simulations. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Dynamic stall; Stall flutter; Structural nonlinearity; Uncertainty quantification; Polynomial chaos expansion; Arbitrary uncertainties 1. Introduction Aeroelastic stability remains an important concern for the design of wind turbine rotors, more so with the use of increasingly flexible blades. Increased flexibility some- times brings in complex oscillation modes which could be potentially dangerous to the structure [1,2]. Moreover, wind turbine rotors often have to operate at large angles of attack, past the stall angle of the profile, i.e., in the dynamic stall regime. The resulting flow is largely sepa- rated and viscous effects are important. The physical pro- cess of dynamic stall involves growth and evolution of the leading edge vortex structure and its subsequent shed- ding from the body into the near wake, all of which have significant influence on the aerodynamic loads. This paper presents an algorithm which can be used to investigate the stall induced oscillation of a two-dimensional profile when one or more system parameters are varied randomly. 1.1. Aeroelasticity and stall flutter One of the interesting problems in aeroelasticity is the study of stability of a structure in wind. Flutter is a dynamic aeroelastic instability of a structure subjected to aerodynamics forces. Classical flutter involves interaction of vibration modes to transfer energy to and from the vibrating systems. Many researchers have investigated linear and nonlinear flutter problems using analytical methods such as Galerkin approach, direct integration, harmonic balance method, perturbation methods, etc. [3]. A traditional approach to a flutter problem (both experi- mental and numerical) uses bending-torsion or bending- torsion-edgewise modes of a blade profile and have been widely used in the aeroelastic community [4–7]. Thus, an infinite dimensional problem is replaced by a two or three degrees-of-freedom system. This will not give an exact pre- diction of the critical airspeed, etc., but will indicate the 0045-7949/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2007.01.004 * Corresponding author. Tel.: +31 152785169; fax: +31 152787077. E-mail address: S.Sarkar@tudelft.nl (S. Sarkar). www.elsevier.com/locate/compstruc Computers and Structures 85 (2007) 866–878