Optimal control of Gortler vortices by means of local wall deformations

Adrian Sescu, Mohammed Afsar

Research output: Contribution to conferenceAbstract

Abstract

We explore an optimal control strategy in the framework of high Reynolds number asymptotics in which the growth of Gortler vortices is reduced by local wall deformations. The Gortler vortices are excited by a row of roughness elements that enter the analysis through upstream conditions derived previously using an asymptotic analysis (Goldstein et al., J. Fluid Mech., 613, pp. 95-124, 2011). Since the leading order Navier-Stokes equations reduce to the boundary region equations (BRE) in a transverse region that scales on the local boundary layer thickness, they are parabolic in the streamwise direction, and may be solved by marching downstream. Wall deformations are introduced into the BREs via a Prandtl transformation for an arbitrary streamwise/spanwise wall surface shape. The vortex energy is then controlled using an optimal control algorithm formulated in the framework of the Lagrange multipliers method, wherein the solution to the adjoint equations are determined by an arbitrary variation in the Lagrangian, in which the cost functional is associated with the local energy of the Gortler vortices. Our numerical results indicate that the optimal control algorithm is very effective in reducing the amplitude of the Gortler vortices.

Conference

ConferenceThe 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics
Abbreviated titleAPS DFD17
CountryUnited States
CityDenver
Period19/11/1721/11/17
Internet address

Fingerprint

Vortex flow
Asymptotic analysis
Lagrange multipliers
Navier Stokes equations
Boundary layers
Reynolds number
Surface roughness
Fluids

Keywords

  • Gortler vortices
  • optimal control strategy
  • vortex energy

Cite this

Sescu, A., & Afsar, M. (2017). Optimal control of Gortler vortices by means of local wall deformations. Abstract from The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States.
Sescu, Adrian ; Afsar, Mohammed. / Optimal control of Gortler vortices by means of local wall deformations. Abstract from The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States.1 p.
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abstract = "We explore an optimal control strategy in the framework of high Reynolds number asymptotics in which the growth of Gortler vortices is reduced by local wall deformations. The Gortler vortices are excited by a row of roughness elements that enter the analysis through upstream conditions derived previously using an asymptotic analysis (Goldstein et al., J. Fluid Mech., 613, pp. 95-124, 2011). Since the leading order Navier-Stokes equations reduce to the boundary region equations (BRE) in a transverse region that scales on the local boundary layer thickness, they are parabolic in the streamwise direction, and may be solved by marching downstream. Wall deformations are introduced into the BREs via a Prandtl transformation for an arbitrary streamwise/spanwise wall surface shape. The vortex energy is then controlled using an optimal control algorithm formulated in the framework of the Lagrange multipliers method, wherein the solution to the adjoint equations are determined by an arbitrary variation in the Lagrangian, in which the cost functional is associated with the local energy of the Gortler vortices. Our numerical results indicate that the optimal control algorithm is very effective in reducing the amplitude of the Gortler vortices.",
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Sescu, A & Afsar, M 2017, 'Optimal control of Gortler vortices by means of local wall deformations' The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States, 19/11/17 - 21/11/17, .

Optimal control of Gortler vortices by means of local wall deformations. / Sescu, Adrian; Afsar, Mohammed.

2017. Abstract from The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States.

Research output: Contribution to conferenceAbstract

TY - CONF

T1 - Optimal control of Gortler vortices by means of local wall deformations

AU - Sescu, Adrian

AU - Afsar, Mohammed

PY - 2017/11/20

Y1 - 2017/11/20

N2 - We explore an optimal control strategy in the framework of high Reynolds number asymptotics in which the growth of Gortler vortices is reduced by local wall deformations. The Gortler vortices are excited by a row of roughness elements that enter the analysis through upstream conditions derived previously using an asymptotic analysis (Goldstein et al., J. Fluid Mech., 613, pp. 95-124, 2011). Since the leading order Navier-Stokes equations reduce to the boundary region equations (BRE) in a transverse region that scales on the local boundary layer thickness, they are parabolic in the streamwise direction, and may be solved by marching downstream. Wall deformations are introduced into the BREs via a Prandtl transformation for an arbitrary streamwise/spanwise wall surface shape. The vortex energy is then controlled using an optimal control algorithm formulated in the framework of the Lagrange multipliers method, wherein the solution to the adjoint equations are determined by an arbitrary variation in the Lagrangian, in which the cost functional is associated with the local energy of the Gortler vortices. Our numerical results indicate that the optimal control algorithm is very effective in reducing the amplitude of the Gortler vortices.

AB - We explore an optimal control strategy in the framework of high Reynolds number asymptotics in which the growth of Gortler vortices is reduced by local wall deformations. The Gortler vortices are excited by a row of roughness elements that enter the analysis through upstream conditions derived previously using an asymptotic analysis (Goldstein et al., J. Fluid Mech., 613, pp. 95-124, 2011). Since the leading order Navier-Stokes equations reduce to the boundary region equations (BRE) in a transverse region that scales on the local boundary layer thickness, they are parabolic in the streamwise direction, and may be solved by marching downstream. Wall deformations are introduced into the BREs via a Prandtl transformation for an arbitrary streamwise/spanwise wall surface shape. The vortex energy is then controlled using an optimal control algorithm formulated in the framework of the Lagrange multipliers method, wherein the solution to the adjoint equations are determined by an arbitrary variation in the Lagrangian, in which the cost functional is associated with the local energy of the Gortler vortices. Our numerical results indicate that the optimal control algorithm is very effective in reducing the amplitude of the Gortler vortices.

KW - Gortler vortices

KW - optimal control strategy

KW - vortex energy

UR - http://www.apsdfd2017.org/

UR - http://meetings.aps.org/Meeting/DFD17/Session/F16.7

M3 - Abstract

ER -

Sescu A, Afsar M. Optimal control of Gortler vortices by means of local wall deformations. 2017. Abstract from The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States.