Investigation of an optimal control approach in the context of compressible boundary region equations

Omar Es-Sahli, Adrian Sescu, Mohammed Afsar, Yuji Hattori, Makoto Hirota

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Abstract

High-amplitude freestream disturbances, as well as surface roughness elements, trigger streamwise oriented vortices and streaks of varying amplitudes in laminar boundary layers, which can lead to secondary instabilities and ultimately to transition to turbulence. In the present work, we aim at deriving and numerically testing an optimal control algorithm in an attempt to reduce the growth of these streamwise vortices and eventually mitigate the frictional drag in a compressible boundary layer. We analytically reduce the compressible Navier-Stokes equations to the boundary region equations (BRE) in a high Reynolds number asymptotic framework, based on the assumption that the streamwise wavenumber of the streaks is much smaller than the cross-flow wavenumbers. Then, we utilize the method of Lagrange multipliers to derive the adjoint compressible boundary region equations, and the associated optimality conditions. The wall transpiration velocity represents the control variable, whereas the wall shear stress or the vortex energy designates the cost functional. We report and discuss results for different Mach numbers, wall conditions, and spanwise separations.
Original languageEnglish
Number of pages1
Publication statusPublished - 22 Nov 2020
Event73rd Annual Meeting of the APS Division of Fluid Dynamics - Online Event, Chicago, United States
Duration: 22 Nov 202024 Nov 2020
http://meetings.aps.org/Meeting/DFD20

Conference

Conference73rd Annual Meeting of the APS Division of Fluid Dynamics
Abbreviated titleAPS-DFD 2021
Country/TerritoryUnited States
CityChicago
Period22/11/2024/11/20
Internet address

Keywords

  • boundary region equations
  • asymptotic analysis
  • Computational Fluid Dynamics (CFD)

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