Analysis of Aeroelastic System Under Random Gust With Parametric Uncertainties Using Polynomial Chaos Expansion

2012 ◽  
Author(s):  
S. Venkatesh ◽  
Sunetra Sarkar ◽  
Ajit Desai
Keyword(s):  
Potential Flow ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Polynomial Chaos Expansion ◽  
The Body ◽  
Limit Cycle Oscillation ◽  
Chaos Expansion ◽  
Aeroelastic System ◽  
Flutter Speed ◽  
Wake Model

In the design of wind turbine structures, aeroelastic stability is of utmost importance. It becomes even more crucial when there are uncertainties involved in it. A symmetric airfoil with its pitch-plunge flexibility is considered under potential flow. The potential flow model is justified as the classical flutter model involves unseparated flow over the body so that inviscid assumptions are valid. In the present study of aeroelastic system, nonlinear parameters have been considered as it can stabilize the diverging growth of a flutter oscillation. Quantification of aleatoric uncertainties present in the system has been done by modeling them as a Gaussian parameters. The epistemic uncertainty present in the system has also been reduced by considering unsteady vortex lattice method (UVLM) instead of the rigid wake model of Wagner. In this model, the wake is free to evolve and also the shape of airfoil has been considered. The present study involves usage of UVLM code on a NACA 0012 airfoil. The values of the linear flutter speed predicted by using UVLM code is in close agreement with that of the fixed wake model of Lee et al. When the structural nonlinearities are present, the system exhibits a self sustained oscillation of constant amplitude called as Limit Cycle Oscillation (LCO) even beyond the linear flutter speed. In the present study, a horizontal gust is modeled with a given spectra by superposition of a set of sinusoidal components which is a standard practice. This gust has then been applied on the airfoil along with the structural uncertainties. A spectral uncertainty quantification tool called Polynomial Chaos Expansion is used to quantify the effect of uncertainty propagation and calculate the response statistics. A non-intrusive version of the method using stochastic projection approach is used to capture the time histories and plot the PDFs at various time instants of all the realizations with Monte Carlo Simulation as a reference solution. The evolution of PCE coefficients in the time domain along with its ensemble variations has also been looked into in the present study.

scholarly journals Bifurcation Analysis with Aerodynamic-Structure Uncertainties by the Nonintrusive PCE Method

2017 ◽  
Vol 2017 ◽  
pp. 1-17
Author(s):  
Linpeng Wang ◽  
Yuting Dai ◽  
Chao Yang
Keyword(s):  
Polynomial Chaos ◽  
Aerodynamic Force ◽  
Polynomial Chaos Expansion ◽  
Limit Cycle Oscillation ◽  
Structure Parameters ◽  
Chaos Expansion ◽  
Aeroelastic Model ◽  
Aerodynamic Parameters ◽  
Cycle Oscillation ◽  
The Time Domain

An aeroelastic model for airfoil with a third-order stiffness in both pitch and plunge degree of freedom (DOF) and the modified Leishman–Beddoes (LB) model were built and validated. The nonintrusive polynomial chaos expansion (PCE) based on tensor product is applied to quantify the uncertainty of aerodynamic and structure parameters on the aerodynamic force and aeroelastic behavior. The uncertain limit cycle oscillation (LCO) and bifurcation are simulated in the time domain with the stochastic PCE method. Bifurcation diagrams with uncertainties were quantified. The Monte Carlo simulation (MCS) is also applied for comparison. From the current work, it can be concluded that the nonintrusive polynomial chaos expansion can give an acceptable accuracy and have a much higher calculation efficiency than MCS. For aerodynamic model, uncertainties of aerodynamic parameters affect the aerodynamic force significantly at the stage from separation to stall at upstroke and at the stage from stall to reattach at return. For aeroelastic model, both uncertainties of aerodynamic parameters and structure parameters impact bifurcation position. Structure uncertainty of parameters is more sensitive for bifurcation. When the nonlinear stall flutter and bifurcation are concerned, more attention should be paid to the separation process of aerodynamics and parameters about pitch DOF in structure.

scholarly journals Analysis of a Nonlinear Aeroelastic System with Parametric Uncertainties Using Polynomial Chaos Expansion

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Ajit Desai ◽  
Sunetra Sarkar
Keyword(s):  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Stochastic Bifurcation ◽  
Parametric Uncertainties ◽  
Chaos Expansion ◽  
Aeroelastic Stability ◽  
Aeroelastic System ◽  
Important Concern ◽  
Stochastic Framework ◽  
Flutter Boundary

Aeroelastic stability remains an important concern for the design of modern structures such as wind turbine rotors, more so with the use of increasingly flexible blades. A nonlinear aeroelastic system has been considered in the present study with parametric uncertainties. Uncertainties can occur due to any inherent randomness in the system or modeling limitations, and so forth. Uncertainties can play a significant role in the aeroelastic stability predictions in a nonlinear system. The analysis has been put in a stochastic framework, and the propagation of system uncertainties has been quantified in the aeroelastic response. A spectral uncertainty quantification tool called Polynomial Chaos Expansion has been used. A projection-based nonintrusive Polynomial Chaos approach is shown to be much faster than its classical Galerkin method based counterpart. Traditional Monte Carlo Simulation is used as a reference solution. Effect of system randomness on the bifurcation behavior and the flutter boundary has been presented. Stochastic bifurcation results and bifurcation of probability density functions are also discussed.

scholarly journals Uncertainty Quantification of a Nonlinear Aeroelastic System Using Polynomial Chaos Expansion With Constant Phase Interpolation

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Ajit Desai ◽  
Jeroen A. S. Witteveen ◽  
Sunetra Sarkar
Keyword(s):  
Dynamical System ◽  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Turbine Blades ◽  
Flexible Structures ◽  
Period Doubling ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Aeroelastic System ◽  
Phase Interpolation

The present study focuses on the uncertainty quantification of an aeroelastic instability system. This is a classical dynamical system often used to model the flow induced oscillation of flexible structures such as turbine blades. It is relevant as a preliminary fluid-structure interaction model, successfully demonstrating the oscillation modes in blade rotor structures in attached flow conditions. The potential flow model used here is also significant because the modern turbine rotors are, in general, regulated in stall and pitch in order to avoid dynamic stall induced vibrations. Geometric nonlinearities are added to this model in order to consider the possibilities of large twisting of the blades. The resulting system shows Hopf and period-doubling bifurcations. Parametric uncertainties have been taken into account in order to consider modeling and measurement inaccuracies. A quadrature based spectral uncertainty tool called polynomial chaos expansion is used to quantify the propagation of uncertainty through the dynamical system of concern. The method is able to capture the bifurcations in the stochastic system with multiple uncertainties quite successfully. However, the periodic response realizations are prone to time degeneracy due to an increasing phase shifting between the realizations. In order to tackle the issue of degeneracy, a corrective algorithm using constant phase interpolation, which was developed earlier by one of the authors, is applied to the present aeroelastic problem. An interpolation of the oscillatory response is done at constant phases instead of constant time and that results in time independent accuracy levels.

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