Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction

V Kitsios; N A Buchmann; C Atkinson; J S Frederiksen; J Soria

doi:10.1007/978-3-319-06260-0_5

Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction

V Kitsios
, N A Buchmann
, C Atkinson
, J S Frederiksen
, J Soria

Mechanical & Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter (Book) › Research › peer-review

1 Citation (Scopus)

Abstract

Koopman modes are presented for a leading edge separated aerofoil flow
with turbulent recirculation. The specific flow configuration is a NACA 0015 aerofoil at an angle of attack of 18◦ and a chord based Reynolds number of 3 × 104. This decomposition approximates the evolution of a nonlinear system by a linear operator, the eigenvectors of which represent the spatial form of the fluctuations, and the eigenvalues represent the associated temporal frequencies and growth rates. Proper orthogonal decomposition (POD) modes are used to create a reduced rank linear operator from which the Koopman modes are determined. The sensitivity to the number of PODmodes used in the rank reduction is assessed. The dominant frequencies identified by the Koopman eigenvalues coincide with the dominant frequencies determined from a Fourier analysis of probe histories.

Original language	English
Title of host publication	Instability and Control of Massively Separated Flows
Subtitle of host publication	Proceedings of the International Conference on Instability and Control of Massively Separated Flows, held in Prato, Italy, from 4-6 September 2013
Editors	Vassilis Theofilis, Julio Soria
Place of Publication	Cham Switzerland
Publisher	Springer
Pages	39-44
Number of pages	6
ISBN (Print)	9783319062594
DOIs	https://doi.org/10.1007/978-3-319-06260-0_5
Publication status	Published - 2015

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10.1007/978-3-319-06260-0_5

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Kitsios, V., Buchmann, N. A., Atkinson, C., Frederiksen, J. S., & Soria, J. (2015). Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction. In V. Theofilis, & J. Soria (Eds.), Instability and Control of Massively Separated Flows: Proceedings of the International Conference on Instability and Control of Massively Separated Flows, held in Prato, Italy, from 4-6 September 2013 (pp. 39-44). Springer. https://doi.org/10.1007/978-3-319-06260-0_5

Kitsios, V ; Buchmann, N A ; Atkinson, C et al. / Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction. Instability and Control of Massively Separated Flows: Proceedings of the International Conference on Instability and Control of Massively Separated Flows, held in Prato, Italy, from 4-6 September 2013. editor / Vassilis Theofilis ; Julio Soria. Cham Switzerland : Springer, 2015. pp. 39-44

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title = "Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction",

abstract = "Koopman modes are presented for a leading edge separated aerofoil flow with turbulent recirculation. The specific flow configuration is a NACA 0015 aerofoil at an angle of attack of 18◦ and a chord based Reynolds number of 3 × 104. This decomposition approximates the evolution of a nonlinear system by a linear operator, the eigenvectors of which represent the spatial form of the fluctuations, and the eigenvalues represent the associated temporal frequencies and growth rates. Proper orthogonal decomposition (POD) modes are used to create a reduced rank linear operator from which the Koopman modes are determined. The sensitivity to the number of PODmodes used in the rank reduction is assessed. The dominant frequencies identified by the Koopman eigenvalues coincide with the dominant frequencies determined from a Fourier analysis of probe histories.",

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Kitsios, V, Buchmann, NA, Atkinson, C, Frederiksen, JS & Soria, J 2015, Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction. in V Theofilis & J Soria (eds), Instability and Control of Massively Separated Flows: Proceedings of the International Conference on Instability and Control of Massively Separated Flows, held in Prato, Italy, from 4-6 September 2013. Springer, Cham Switzerland, pp. 39-44. https://doi.org/10.1007/978-3-319-06260-0_5

Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction. / Kitsios, V; Buchmann, N A; Atkinson, C et al.
Instability and Control of Massively Separated Flows: Proceedings of the International Conference on Instability and Control of Massively Separated Flows, held in Prato, Italy, from 4-6 September 2013. ed. / Vassilis Theofilis; Julio Soria. Cham Switzerland: Springer, 2015. p. 39-44.

Research output: Chapter in Book/Report/Conference proceeding › Chapter (Book) › Research › peer-review

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T1 - Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction

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AU - Buchmann, N A

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AU - Frederiksen, J S

AU - Soria, J

PY - 2015

Y1 - 2015

N2 - Koopman modes are presented for a leading edge separated aerofoil flow with turbulent recirculation. The specific flow configuration is a NACA 0015 aerofoil at an angle of attack of 18◦ and a chord based Reynolds number of 3 × 104. This decomposition approximates the evolution of a nonlinear system by a linear operator, the eigenvectors of which represent the spatial form of the fluctuations, and the eigenvalues represent the associated temporal frequencies and growth rates. Proper orthogonal decomposition (POD) modes are used to create a reduced rank linear operator from which the Koopman modes are determined. The sensitivity to the number of PODmodes used in the rank reduction is assessed. The dominant frequencies identified by the Koopman eigenvalues coincide with the dominant frequencies determined from a Fourier analysis of probe histories.

AB - Koopman modes are presented for a leading edge separated aerofoil flow with turbulent recirculation. The specific flow configuration is a NACA 0015 aerofoil at an angle of attack of 18◦ and a chord based Reynolds number of 3 × 104. This decomposition approximates the evolution of a nonlinear system by a linear operator, the eigenvectors of which represent the spatial form of the fluctuations, and the eigenvalues represent the associated temporal frequencies and growth rates. Proper orthogonal decomposition (POD) modes are used to create a reduced rank linear operator from which the Koopman modes are determined. The sensitivity to the number of PODmodes used in the rank reduction is assessed. The dominant frequencies identified by the Koopman eigenvalues coincide with the dominant frequencies determined from a Fourier analysis of probe histories.

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M3 - Chapter (Book)

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BT - Instability and Control of Massively Separated Flows

A2 - Theofilis, Vassilis

A2 - Soria, Julio

PB - Springer

CY - Cham Switzerland

ER -

Kitsios V, Buchmann NA, Atkinson C, Frederiksen JS, Soria J. Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction. In Theofilis V, Soria J, editors, Instability and Control of Massively Separated Flows: Proceedings of the International Conference on Instability and Control of Massively Separated Flows, held in Prato, Italy, from 4-6 September 2013. Cham Switzerland: Springer. 2015. p. 39-44 doi: 10.1007/978-3-319-06260-0_5

Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction

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