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Hampering Görtler vortices via optimal control in the framework of nonlinear boundary region equations

Published online by Cambridge University Press:  01 June 2018

Adrian Sescu Open the ORCID record for Adrian Sescu [Opens in a new window]  and
M. Z. Afsar
Adrian Sescu*
Affiliation:
Department of Aerospace Engineering, Mississippi State University, Mississippi State, MS 39762, USA
M. Z. Afsar
Affiliation:
Mechanical and Aerospace Engineering, University of Strathclyde, 16 Richmond St, Glasgow G1 1XQ, UK
*
†Email address for correspondence: sescu@ae.msstate.edu
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Abstract

The control of streamwise vortices in high Reynolds number boundary layer flows often aims at reducing the vortex energy as a means of mitigating the growth of secondary instabilities, which eventually delays the transition from laminar to turbulent flow. In this paper, we aim at utilizing such an energy reduction strategy using optimal control theory to limit the growth of Görtler vortices developing in an incompressible laminar boundary layer flow over a concave wall, and excited by a row of roughness elements with spanwise separation of the same order of magnitude as the boundary layer thickness. Commensurate with control theory formalism, we transform a constrained optimization problem into an unconstrained one by applying the method of Lagrange multipliers. A high Reynolds number asymptotic framework is utilized, wherein the Navier–Stokes equations are reduced to the boundary region equations, in which wall deformations enter the problem through an appropriate Prandtl transformation. In the optimal control strategy, the wall displacement or the wall transpiration velocity serves as the control variable, while the cost functional is defined in terms of the wall shear stress. Our numerical results indicate, among other things, that the optimal control algorithm is very effective in reducing the amplitude of the Görtler vortices, especially for the control based on wall displacement.

JFM classification

Boundary Layers: Boundary layer control Flow Control: Control theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 848 , 10 August 2018 , pp. 5 - 41
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Copyright
© 2018 Cambridge University Press 

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