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Mapped Chebyshev Pseudo-Spectral Method for Dynamic Aero-Elastic Problem of Limit Cycle Oscillation

Mapped Chebyshev Pseudo-Spectral Method for Dynamic Aero-Elastic Problem of Limit Cycle Oscillation A mapped Chebyshev pseudo-spectral method is developed as one of the Fourier-spectral approaches and solves nonlinear PDE systems for unsteady flows and dynamic aero-elastic problem in a given time interval, where the flows or elastic motions can be periodic, nonperiodic, or periodic with an unknown frequency. The method uses the Chebyshev polynomials of the first kind for the basis function and redistributes the standard Chebyshev–Gauss–Lobatto collocation points more evenly by a conformal mapping function for improved numerical stability. Contributions of the method are several. It can be an order of magnitude more efficient than the conventional finite difference-based, time-accurate computation, depending on the complexity of solutions and the number of collocation points. The method reformulates the dynamic aero-elastic problem in spectral form for coupled analysis of aerodynamics and structures, which can be effective for design optimization of unsteady and dynamic problems. A limit cycle oscillation (LCO) is chosen for the validation and a new method to determine the LCO frequency is introduced based on the minimization of a second derivative of the aero-elastic formulation. Two examples of the limit cycle oscillation are tested: nonlinear, one degree-of-freedom mass–spring–damper system and two degrees-of-freedom oscillating airfoil under pitch and plunge motions. Results show good agreements with those of the conventional time-accurate simulations and wind tunnel experiments. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Aeronautical & Space Sciences Springer Journals

Mapped Chebyshev Pseudo-Spectral Method for Dynamic Aero-Elastic Problem of Limit Cycle Oscillation

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2018 by The Korean Society for Aeronautical & Space Sciences and Springer Nature Singapore Pte Ltd.
Subject
Engineering; Aerospace Technology and Astronautics; Fluid- and Aerodynamics
ISSN
2093-274X
eISSN
2093-2480
DOI
10.1007/s42405-018-0033-3
Publisher site
See Article on Publisher Site

Abstract

A mapped Chebyshev pseudo-spectral method is developed as one of the Fourier-spectral approaches and solves nonlinear PDE systems for unsteady flows and dynamic aero-elastic problem in a given time interval, where the flows or elastic motions can be periodic, nonperiodic, or periodic with an unknown frequency. The method uses the Chebyshev polynomials of the first kind for the basis function and redistributes the standard Chebyshev–Gauss–Lobatto collocation points more evenly by a conformal mapping function for improved numerical stability. Contributions of the method are several. It can be an order of magnitude more efficient than the conventional finite difference-based, time-accurate computation, depending on the complexity of solutions and the number of collocation points. The method reformulates the dynamic aero-elastic problem in spectral form for coupled analysis of aerodynamics and structures, which can be effective for design optimization of unsteady and dynamic problems. A limit cycle oscillation (LCO) is chosen for the validation and a new method to determine the LCO frequency is introduced based on the minimization of a second derivative of the aero-elastic formulation. Two examples of the limit cycle oscillation are tested: nonlinear, one degree-of-freedom mass–spring–damper system and two degrees-of-freedom oscillating airfoil under pitch and plunge motions. Results show good agreements with those of the conventional time-accurate simulations and wind tunnel experiments.

Journal

International Journal of Aeronautical & Space Sciences – Springer Journals

Published: May 7, 2018

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