Modeling physical uncertainties in dynamic stall induced fluid-structure interaction of turbine blades using arbitrary polynomial chaos

A nonlinear dynamic problem of stall induced flutter oscillation subject to physical uncertainties is analyzed using arbitrary polynomial 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 parameters 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.

[1]  Chris L. Pettit,et al.  Uncertainty in Aeroelasticity Analysis, Design, and Testing , 2004 .

[2]  Earl H. Dowell,et al.  Nonlinear aeroelasticity in rotorcraft , 1993 .

[3]  Thomas W. Strganac,et al.  Aeroelastic Response of a Rigid Wing Supported by Nonlinear Springs , 1998 .

[4]  David A. Peters,et al.  Toward a Unified Lift Model for Use in Rotor Blade Stability Analyses , 1985 .

[5]  D. Xiu,et al.  Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos , 2002 .

[6]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[7]  Dan Borglund,et al.  Robust Aeroelastic Stability Analysis Considering Frequency-Domain Aerodynamic Uncertainty , 2002 .

[8]  Wright-Patterson Afb,et al.  Polynomial Chaos Expansion Applied to Airfoil Limit Cycle Oscillations , 2004 .

[9]  B. H. K. Lee,et al.  Effects of structural nonlinearities on flutter characteristics of the CF-18 aircraft , 1989 .

[10]  G. Karniadakis,et al.  Long-Term Behavior of Polynomial Chaos in Stochastic Flow Simulations , 2006 .

[11]  Hester Bijl,et al.  Stall Induced Vibration and Flutter in a Symmetric Airfoil , 2006 .

[12]  Roger Ghanem,et al.  Stochastic Finite Elements with Multiple Random Non-Gaussian Properties , 1999 .

[13]  R. Ibrahim,et al.  Influence of joint relaxation on deterministic and stochastic panel flutter , 2005 .

[14]  Fabrice Poirion,et al.  On some stochastic methods applied to aeroservoelasticity , 2000 .

[15]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[16]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[17]  Ramana V. Grandhi,et al.  Optimization of a wing structure for gust response and aileron effectiveness , 2003 .

[18]  N. Wiener.  The Homogeneous Chaos , 1938 .

[19]  Henry T. Y. Yang,et al.  Reliability and nonlinear supersonic flutter of uncertain laminated plates , 1993 .

[20]  N. Sri Namachchivaya,et al.  Stochastic Dynamics of a Nonlinear Aeroelastic System , 2006 .

[21]  Jeroen A. S. Witteveen,et al.  Modeling Arbitrary Uncertainties Using Gram-Schmidt Polynomial Chaos , 2006 .

[22]  Rick Lind,et al.  Robust Flutter Margin Analysis that Incorporates Flight Data , 1998 .

[23]  Bryan E. Richards,et al.  Non-linear analysis of stall flutter based on the ONERA aerodynamic model , 2003, The Aeronautical Journal (1968).

[24]  Peter Dunn,et al.  Nonlinear Stall Flutter and Divergence Analysis of Cantilevered Graphite/Epoxy Wings , 1990 .

[25]  Vincent J. Harrand,et al.  Computational and Experimental Investigation of Limit Cycle Oscillations of Nonlinear Aeroelastic Systems , 2002 .

[26]  P. K. Chaviaropoulos.  Flap/lead–lag aeroelastic stability of wind turbine blade sections , 1999 .

[27]  Chris L. Pettit,et al.  Spectral and multiresolution Wiener expansions of oscillatory stochastic processes , 2006 .

[28]  Stuart J. Price,et al.  The post-Hopf-bifurcation response of an airfoil in incompressible two-dimensional flow , 1996 .

[29]  S. J. Price,et al.  NONLINEAR AEROELASTIC ANALYSIS OF AIRFOILS : BIFURCATION AND CHAOS , 1999 .

[30]  Marianna A. Shubov,et al.  MATHEMATICAL MODELING AND ANALYSIS OF FLUTTER IN BENDING-TORSION COUPLED BEAMS, ROTATING BLADES, AND HARD DISK DRIVES , 2004 .

[31]  Chris L. Pettit,et al.  Uncertainty Quantification in Aeroelasticity: Recent Results and Research Challenges , 2004 .

[32]  G. Karniadakis,et al.  An adaptive multi-element generalized polynomial chaos method for stochastic differential equations , 2005 .

[33]  Yuan-Cheng Fung,et al.  An introduction to the theory of aeroelasticity , 1955 .

[34]  W. T. Martin,et al.  The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals , 1947 .

[35]  Gene H. Golub,et al.  Matrix computations , 1983 .

[36]  Marianna A. Shubov,et al.  Flutter Phenomenon in Aeroelasticity and Its Mathematical Analysis , 2006 .

[37]  George E. Karniadakis,et al.  Beyond Wiener–Askey Expansions: Handling Arbitrary PDFs , 2006, J. Sci. Comput..

[38]  Earl H. Dowell,et al.  Comparison of Theory and Experiment for Nonlinear Flutter and Stall Response of Helicopter Blade , 1991 .

[39]  Thomas Y. Hou,et al.  Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics , 2006, J. Comput. Phys..

[40]  K. Bathe.  Finite Element Procedures , 1995 .

[41]  Spyros G. Voutsinas,et al.  Viscous and Aeroelastic Effects on Wind Turbine Blades. The VISCEL Project. Part II: Aeroelastic Stability Investigations , 2003 .

[42]  N. Wiener,et al.  Nonlinear Problems in Random Theory , 1964 .

[43]  R. Ghanem,et al.  Uncertainty propagation using Wiener-Haar expansions , 2004 .

[44]  Rene F. Swarttouw,et al.  Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.

[45]  Robert H. Scanlan,et al.  A Modern Course in Aeroelasticity , 1981, Solid Mechanics and Its Applications.

[46]  D. Xiu,et al.  Modeling uncertainty in flow simulations via generalized polynomial chaos , 2003 .

[47]  Efstratios Nikolaidis,et al.  Engineering Design Reliability Handbook , 2004 .

[48]  Chris L. Pettit,et al.  Effects of Uncertainty on Nonlinear Plate Aeroelastic Response , 2002 .

[49]  W. Gautschi.  Orthogonal Polynomials: Computation and Approximation , 2004 .

[50]  Humberto Contreras,et al.  The stochastic finite-element method , 1980 .

[51]  N. C. Nigam,et al.  Applications of Random Vibrations , 1994 .

[52]  P. G. Migliore,et al.  Feasibility Study of Pultruded Blades for Wind Turbine Rotors , 2000 .