Hopf Bifurcation Calculations for a Symmetric Airfoil in Transonic Flow

Badcock, K. J.; Woodgate, M.; Richards, B. E.

doi:10.2514/1.9584

Cited by 39 publications

(29 citation statements)

References 12 publications

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“…The testcase corresponds to the "heavy case" described in Ref. 24 The traces of the pitching and plunging modes for increasing reduced velocity are shown in Fig. 2.…”

Section: Aerofoil Resultsmentioning

confidence: 99%

Model Reduction of High-Fidelity Models for Gust Load Alleviation

Ronch

Tantaroudas

Badcock

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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A systematic approach to the model reduction of high-fidelity fluid-structure-flight models and the subsequent flight control design for very flexible aircraft is considered. The test case is for an unmanned aerial vehicle. The full order model involves the geometricallyexact nonlinear beam equations coupled with a linear aerodynamic model. A nonlinear reduced order model is derived to reduce the computational cost and dimension of the full order nonlinear system while retaining the ability to predict nonlinear effects. The approach uses information on the eigenspectrum of the coupled system Jacobian matrix and projects the system through a series expansion onto a small basis of eigenvectors representative of the full order dynamics. The small dimension model is then used to design control laws for applications sush as load alleviation. Results are presented for an aerofoil section and an unmanned aerial vehicle model to illustrate the approach.

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“…The testcase corresponds to the "heavy case" described in Ref. 24 The traces of the pitching and plunging modes for increasing reduced velocity are shown in Fig. 2.…”

Section: Aerofoil Resultsmentioning

confidence: 99%

Model Reduction of High-Fidelity Models for Gust Load Alleviation

Ronch

Tantaroudas

Badcock

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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“…Towards this end, direct flutter tools, which establish a nonlinear set of algebraic equations for the flutter point based upon general information about Hopf-point solutions (Griewank and Reddien, 1983) (a small oscillatory perturbation about a steady state equilibrium), were developed by Morton and Beran (1999) and extended by Badcock and Woodgate (2010), and Badcock et al (2004). Gradients of the directly computed flutter speed with respect to a large number of design variables were obtained by Stanford and Beran (2011) for aeroelastic optimization.…”

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confidence: 99%

Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization

Stanford

Beran

2013

Journal of Fluids and Structures

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a b s t r a c tThe usefulness of flutter as a design metric is diluted for wings with destabilizing (softening) nonlinearities, as a stable high-amplitude limit cycle (subcritical) may exist for flight speeds well below the flutter point. It is thus desired to design aeroelastic structures such that the post-flutter behavior is as benign (i.e., supercritical) as possible, among the other constraints commonly considered in the optimization process. In order to account for these metrics in an accurate and efficient manner, direct tools are utilized to first locate the Hopf-point (flutter speed), and then to obtain a nonlinear perturbation solution via the method of multiple scales. The latter scheme provides a scalar variable whose sign and magnitude dictate the nature of the limit cycle. The accuracy of these methods is demonstrated with a high-aspect-ratio highly flexible wing, modeled with nonlinear beam finite elements and the ONERA dynamic stall tool. Stiffness and inertial design variables are allowed to vary spatially throughout the wing, in order to conduct gradient-based optimization of the limit cycle under flutter and mass constraints. The resulting wing structure demonstrates strongly supercritical behavior, as well as several design conflicts between linear (flutter) and nonlinear (limit cycles) sensitivities, which are not present in the uniform baseline wing.Published by Elsevier Ltd.

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“…The application of direct bifurcation tracking methods to large systems in aerodynamics has mainly been limited to enclosed or internal flows. However, a few studies do exist, primarily concerned with bifurcation tracking of transonic flows of aeroelastic systems such as those by Badcock et al [19,20,21,22]. These studies focused on the computation of the stability limit of aeroelastic systems.…”

Section: Introductionmentioning

confidence: 99%

Development of an efficient bifurcation tracking method

2017

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractThe buffet onset boundary is associated with a change in stability of the flow solution. The buffet onset boundary has been computed for a NACA 0012 aerofoil using a modified bifurcation tracking method. The algorithm combines the projection aspect of the Recursive Projection Method with two different direct bifurcation tracking methods. This considerably reduces the cost of the bifurcation tracking methods by solving for the bifurcation point on a small subspace of the system containing only the least stable dynamics. The method has been extended to allow the boundary to be computed as geometrical parameters, camber and thickness, are changed. This enables rapid evaluation of the effect of different aerofoil designs on the boundary. Results are presented comparing the full bifurcation tracking methods to their projected equivalent and show that although the projected methods lack the numerical accuracy of the full counterpart, the trends of the boundaries agree well.

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Hopf Bifurcation Calculations for a Symmetric Airfoil in Transonic Flow

Cited by 39 publications

References 12 publications

Model Reduction of High-Fidelity Models for Gust Load Alleviation

Model Reduction of High-Fidelity Models for Gust Load Alleviation

Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization

Development of an efficient bifurcation tracking method

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