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Flow control of weakly non-parallel flows: application to trailing vortices

Published online by Cambridge University Press:  01 June 2017

F. Viola ,
E. Pezzica ,
G. V. Iungo ,
F. Gallaire  and
S. Camarri Open the ORCID record for S. Camarri [Opens in a new window]
F. Viola
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
E. Pezzica
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
G. V. Iungo
Affiliation:
Wind Fluids and Experiments (WindFluX) Laboratory, University of Texas at Dallas, Richardson, TX 75080, USA
F. Gallaire*
Affiliation:
Laboratory of Fluid Mechanics and Instabilities, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
S. Camarri
Affiliation:
Department of Civil and Industrial Engineering, University of Pisa, Pisa 56122, Italy
*
†Email address for correspondence: francois.gallaire@epfl.ch
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Abstract

A general formulation is proposed to control the integral amplification factor of harmonic disturbances in weakly non-parallel amplifier flows. The sensitivity of the local spatial stability spectrum to a base-flow modification is first determined, generalizing the results of Bottaro et al. (J. Fluid Mech., vol. 476, 2003, pp. 293–302). This result is then used to evaluate the sensitivity of the overall spatial growth to a modification of the inlet flow condition. This formalism is applied to a non-parallel Batchelor vortex, which is a well-known model for trailing vortices generated by a lifting wing. The resulting sensitivity map indicates the optimal modification of the inlet flow condition enabling the stabilization of the helical modes. It is shown that the control, formulated using a single linearization of the flow dynamics carried out on the uncontrolled configuration, successfully reduces the total spatial amplification of all convectively unstable disturbances.

JFM classification

Flow Control: Flow Control Flow Control: Instability control Vortex Flows: Vortex instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 822 , 10 July 2017 , pp. 342 - 363
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Copyright
© 2017 Cambridge University Press 

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