State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span

In this paper, a low-order state-space adaptation of the unsteady lifting line model has been analytically derived for a wing of finite aspect ratio, suitable for use in real-Time control of wake-dependent forces. Each discretization along the span has between 1-6 states to represent the local unste...

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Main Authors: Zhu, Qiang, Izraelevitz, Jacob Samuel, Triantafyllou, Michael S
Other Authors: Massachusetts Institute of Technology. Department of Mechanical Engineering
Format: Article
Published: American Institute of Aeronautics and Astronautics (AIAA) 2019
Online Access:http://hdl.handle.net/1721.1/120112
https://orcid.org/0000-0002-1555-9136
https://orcid.org/0000-0002-4960-7060
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author Zhu, Qiang
Izraelevitz, Jacob Samuel
Triantafyllou, Michael S
author2 Massachusetts Institute of Technology. Department of Mechanical Engineering
author_facet Massachusetts Institute of Technology. Department of Mechanical Engineering
Zhu, Qiang
Izraelevitz, Jacob Samuel
Triantafyllou, Michael S
author_sort Zhu, Qiang
collection MIT
description In this paper, a low-order state-space adaptation of the unsteady lifting line model has been analytically derived for a wing of finite aspect ratio, suitable for use in real-Time control of wake-dependent forces. Each discretization along the span has between 1-6 states to represent the local unsteady wake effects, rather than remembering the entire wake history which unnecessarily complicates controller design. Sinusoidal perturbations to each system degree of freedom are also avoided. Instead, a state-space model is fit to individual indicial functions for each blade element, allowing the downwash and lift distributions over the span to be arbitrary. The wake geometry is assumed to be quasi steady (no roll up) but with fully unsteady vorticity. The model supports time-varying surge (a nonlinear effect), dihedral, heave, sweep, and twist along the span. Cross-coupling terms are explicitly derived. This state-space model is then validated through comparison with an analytic solution for elliptic wings, an unsteady vortex lattice method, and experiments from the literature.
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spelling mit-1721.1/1201122024-06-26T20:28:47Z State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span Zhu, Qiang Izraelevitz, Jacob Samuel Triantafyllou, Michael S Massachusetts Institute of Technology. Department of Mechanical Engineering Izraelevitz, Jacob Samuel Triantafyllou, Michael S In this paper, a low-order state-space adaptation of the unsteady lifting line model has been analytically derived for a wing of finite aspect ratio, suitable for use in real-Time control of wake-dependent forces. Each discretization along the span has between 1-6 states to represent the local unsteady wake effects, rather than remembering the entire wake history which unnecessarily complicates controller design. Sinusoidal perturbations to each system degree of freedom are also avoided. Instead, a state-space model is fit to individual indicial functions for each blade element, allowing the downwash and lift distributions over the span to be arbitrary. The wake geometry is assumed to be quasi steady (no roll up) but with fully unsteady vorticity. The model supports time-varying surge (a nonlinear effect), dihedral, heave, sweep, and twist along the span. Cross-coupling terms are explicitly derived. This state-space model is then validated through comparison with an analytic solution for elliptic wings, an unsteady vortex lattice method, and experiments from the literature. 2019-01-22T18:53:08Z 2019-01-22T18:53:08Z 2017-01 2019-01-08T13:43:24Z Article http://purl.org/eprint/type/JournalArticle 0001-1452 1533-385X http://hdl.handle.net/1721.1/120112 Izraelevitz, Jacob S. et al. “State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span.” AIAA Journal 55, 4 (April 2017): 1279–1294 © 2016 The Authors https://orcid.org/0000-0002-1555-9136 https://orcid.org/0000-0002-4960-7060 http://dx.doi.org/10.2514/1.J055144 AIAA Journal Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf American Institute of Aeronautics and Astronautics (AIAA) Other repository
spellingShingle Zhu, Qiang
Izraelevitz, Jacob Samuel
Triantafyllou, Michael S
State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span
title State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span
title_full State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span
title_fullStr State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span
title_full_unstemmed State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span
title_short State-Space Adaptation of Unsteady Lifting Line Theory: Twisting/Flapping Wings of Finite Span
title_sort state space adaptation of unsteady lifting line theory twisting flapping wings of finite span
url http://hdl.handle.net/1721.1/120112
https://orcid.org/0000-0002-1555-9136
https://orcid.org/0000-0002-4960-7060
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