Aeroelastic analysis of a wind turbine blade using the harmonic balance method

In this paper, a new modified harmonic balance method is presented for the nonlinear aeroelastic analysis of two degree-of-freedom airfoils. Using this method, the nonlinear problem is first translated into a minimization problem, and the Particle Swarm Optimization which has high calculation efficiency is adopted to solve the problem. The proposed method is used to solve the nonlinear aeroelastic behavior of supersonic airfoil, with the unsteady aerodynamic load evaluated by the piston theory. Three examples of nonlinear aeroelasticity with significantly different coefficients are prepared, in which the frequencies and amplitudes of the limit cycles are obtained. The results show that the present current method is computationally more efficient.

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Unsteady Analysis of Wind Turbine Flows Using the Harmonic Balance Method

51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition ◽

10.2514/6.2013-1107 ◽

2013 ◽

Cited By ~ 3

Author(s):

Jason Howison ◽

Kivanc Ekici

Keyword(s):

Wind Turbine ◽

Harmonic Balance ◽

Harmonic Balance Method ◽

Balance Method

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Unsteady Turbomachinery Simulations Using Harmonic Balance on a Discontinuous Galerkin Discretization

Volume 2C: Turbomachinery ◽

10.1115/gt2018-77204 ◽

2018 ◽

Cited By ~ 2

Author(s):

Mayank Sharma ◽

Nathan A. Wukie ◽

Matteo Ugolotti ◽

Mark G. Turner

Keyword(s):

Discontinuous Galerkin ◽

Turbine Blade ◽

Harmonic Balance ◽

Complex Geometry ◽

Time Integration ◽

Harmonic Balance Method ◽

Balance Method ◽

Galerkin Discretization ◽

Runge Kutta ◽

Unsteady Problems

The Harmonic Balance method is well suited for analyzing unsteadiness in turbomachinery flows comprised of a few dominant frequencies. A harmonic condition is imposed on the temporal derivatives through a Fourier transform operation. The solution is then reinterpreted as a time-domain problem, where several instances of time (lying within the largest period) are solved for simultaneously with the enforcement of the time-harmonic condition providing coupling between time instances. A discontinuous Galerkin discretization is used together with overset grids to provide higher-order spatial accuracy and flexibility in representing complex geometry. In this work, the discontinuous Galerkin infrastructure is extended for unsteady problems with a Harmonic Balance method and a Diagonally Implicit Runge-Kutta time-integrator. Verification results are presented for both time integration approaches in addition to results for a turbine blade with unsteadiness driven by a prescribed unsteady inlet boundary condition. Comparisons of results from the Harmonic Balance and Diagonally Implicit Runge-Kutta approaches are very close, with some small discrepancies that require further investigation. Significantly, rapid convergence from the Newton solver is obtained for the Harmonic Balance approach applied to the Euler equations for the turbine blade problem. Solutions converged by 8–10 orders of magnitude are obtained in between 5 and 16 Newton steps.

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The Role of Structural Nonlinearities in Wind Turbine Blade Aeroelastic Analysis

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition ◽

10.2514/6.2011-995 ◽

2011 ◽

Cited By ~ 1

Author(s):

Brian Freno ◽

Robert Brown ◽

Paul Cizmas

Keyword(s):

Wind Turbine ◽

Turbine Blade ◽

Wind Turbine Blade ◽

Aeroelastic Analysis ◽

Structural Nonlinearities

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Aerodynamic and structural optimization of wind turbine blade with static aeroelastic effects

International Journal of Low-Carbon Technologies ◽

10.1093/ijlct/ctz057 ◽

2019 ◽

Vol 15 (1) ◽

pp. 55-64

Author(s):

Jie Zhu ◽

Xiaohui Ni ◽

Xiaomei Shen

Keyword(s):

Structural Optimization ◽

Wind Turbine ◽

Turbine Blade ◽

Optimization Method ◽

Wind Turbine Blade ◽

Analysis Model ◽

Element Analysis ◽

Design Variables ◽

Aeroelastic Analysis ◽

Static Aeroelasticity

Abstract With the increasing size of wind turbine blade, the aeroelastic analysis becomes an essential step in the blade design process. The scope of this paper is to investigate the static aeroelastic effects between the fluid–structure interaction and improve the blade performances. First, the rigid and flexible blades are used to analyze the effects of static aeroelasticity on the blade aerodynamic and structural performances through a blade element momentum model coupled with 3D finite element analysis model. Based on this, a multi-objective aerodynamic and structural optimization method is proposed aiming at increasing the annual energy production and reducing blade mass, key parameters of the blade are employed as design variables, and various design requirements including strain, deflection, vibration and buckling limits are considered as constraints. Finally, a commercial 1.5 MW wind turbine blade is applied as a case study, and the optimization results show great improvements for the aerodynamic and structural performances of the blade.

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Dynamic and Aeroelastic Analyses of a Wind Turbine Blade Modeled as a Thin-Walled Composite Beam

Volume 6B: Energy ◽

10.1115/imece2014-38679 ◽

2014 ◽

Cited By ~ 1

Author(s):

Serhat Yilmaz ◽

Seher Eken ◽

Metin O. Kaya

Keyword(s):

Wind Turbine ◽

Turbine Blade ◽

Transverse Shear ◽

Natural Frequencies ◽

Equations Of Motion ◽

Wind Turbine Blade ◽

Mode Shapes ◽

Box Beam ◽

Aeroelastic Analysis ◽

Thin Walled

In this paper, dynamic and aeroelastic analysis of a wind turbine blade modeled as an anisotropic composite thin-walled box beam is carried out. The analytical formulation of the beam is derived for the flapwise bending, chordwise bending and transverse shear deformations. The derivation of both strain and kinetic energy expressions are made and the equations of motion are obtained by applying the Hamilton’s principle. The equations of motion are solved by applying the extended Galerkin method (EGM) for anti-symmetric lay-up configuration that is also referred as Circumferentially Uniform Stiffness (CUS). As a result various coupled vibration modes are exhibited. This type of beam features two sets of independent couplings: i) extension-torsion coupling, ii) flapwise/chordwise bending-flapwise/chorwise transverse shear coupling. For both cases, the natural frequencies are validated by making comparisons with the results in literature and effects of coupling, transverse shear, ply-angle orientation, and rotational speed on the natural frequencies are examined and the mode shapes of the rotating thin-walled composite beams are further obtained. Blade element momentum theory (BEMT) is utilized to model the wind turbine blade aerodynamics. After combining the structural and the aerodynamic models, the aeroelastic analysis are performed and flutter boundaries are obtained.

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