A compressible boundary layer optimal control approach using nonlinear boundary region equations

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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High-amplitude free-stream turbulence and large surface roughness elements can excite a laminar boundary layer sufficiently enough to cause streamwise oriented vortices to form. The latter is accompanied by streaks of varying amplitudes that ‘wobble’ through inviscid secondary instabilities and, ultimately, transition to turbulence. In this paper, we formu- late a mathematical framework for the optimal control of compressible boundary layers to suppress the growth rate of the streamwise vortex system before breakdown occurs. This has a commensurate impact on the wall shear stress and heat transfer at the wall. Flow instabilities are introduced either through roughness elements equally separated in the spanwise direction or via free-stream disturbances. The compressible Navier-Stokes equations are reduced to the boundary region equations (BRE) in a high Reynolds number asymptotic framework wherein the streamwise wavelengths of the disturbances are assumed to be much larger than the spanwise and wall-normal counterparts. The method of La- grange multipliers is used to derive the adjoint compressible boundary region equations via an appropriate transformation of the original constrained optimization problem into an unconstrained form. In the present formulation, the wall transpiration velocity represents the control variable while the wall shear stress or the vortex energy represents the cost functional. Our study shows that this kind of control approach induces a significant reduc- tion in the kinetic energy and wall shear stress of the boundary layer flow. Contour plots visually demonstrate how the primary instabilities gradually flatten out as more control iterations are applied.
Original languageEnglish
Title of host publicationAIAA Aviation 2021 Forum
Place of PublicationReston, VA.
Number of pages17
Publication statusPublished - 2 Aug 2021
EventAIAA Aviation 2021 Virtual Event - Virtual, United States
Duration: 2 Aug 20216 Aug 2021


ConferenceAIAA Aviation 2021 Virtual Event
Abbreviated titleAIAA 2021
Country/TerritoryUnited States
Internet address


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


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