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Transient energy analysis of a spatially interconnected model for 3D Poiseuille flow
Publikationstyp
Conference Paper
Date Issued
2010
Sprache
English
Author(s)
Institut
Start Page
2557
End Page
2562
Article Number
5530564
Citation
Proceedings of the 2010 American Control Conference, ACC 2010 : Baltimore, Maryland, USA, 30 June - 2 July 2010. - Piscataway, NJ, 2010. - 5530564 2557-2562 (2010-01-01)
Contribution to Conference
Publisher DOI
Scopus ID
Publisher
IEEE
In this paper a new model for 3D Poiseuille flow is presented. The model is based on applying a combined spectral-finite difference approach on the velocity-vorticity formulation of the Navier-Stokes equations. In 3D the dominating feature of the problem is non-normality of the eigenvectors. One measure to assess the non-normality is the transient energy response. The model is validated by comparing the maximum transient energy for two different cases; for both cases the Reynolds number is fixed at 5000, in the first case the span-wise spatial frequency is set to zero and the stream-wise spatial frequency is varied from 0.1 to 2, while for the second case the stream-wise frequency is set to zero and the span-wise frequency is varied from 0.1 to 3. It is known that for the first case the system is stable, while the second case is highly non-normal with maximum transient energy reaching 4500. It is observed that the model predicts both of these characteristics. Next, as a first step towards controller synthesis, a stabilizing state feedback controller is designed to minimize the transient energy response, by minimizing the induced L 2-norm. The closed loop response shows that the energy is reduced by the factor of 30. © 2010 AACC.
DDC Class
600: Technik
620: Ingenieurwissenschaften