Practical considerations in aerodynamic design optimization

Jou, Wen‐Huei; Huffman, William P.; Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Hilmes, Craig L.; Johnson, F. T.

doi:10.2514/6.1995-1730

Cited by 35 publications

(12 citation statements)

References 10 publications

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“…In SAND, one views (1.1)-(1.2) as being posed in the form (1.3). Our observations apply to various reduced basis SQP approaches to (1.3), such as those described in [8,10,13,16]. These approaches have been widely studied and go back at least as far as [1].…”

Section: The Multigrid Algorithmmentioning

confidence: 97%

Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations

Lewis

Nash

2005

SIAM J. Sci. Comput.

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Abstract. We discuss a multigrid approach to the optimization of systems governed by differential equations. Such optimization problems appear in many applications and are of a different nature than systems of equations. Our approach uses an optimization-based multigrid algorithm in which the multigrid algorithm relies explicitly on nonlinear optimization models as subproblems on coarser grids. Our goal is not to argue for a particular optimization-based multigrid algorithm, but instead to demonstrate how multigrid can be used to accelerate nonlinear programming algorithms. Furthermore, using several model problems we give evidence (both theoretical and numerical) that the optimization setting is well suited to multigrid algorithms. Some of the model problems show that the optimization problem may be more amenable to multigrid than the governing differential equation. In addition, we relate the multigrid approach to more traditional optimization methods as further justification for the use of an optimization-based multigrid algorithm.

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Section: The Multigrid Algorithmmentioning

confidence: 97%

Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations

Lewis

Nash

2005

SIAM J. Sci. Comput.

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“…Zingg et al (2005) discuss floating thickness constraints to help maintain structural integrity and a cross-sectional area constraint to optimize for fuel volume. Area constraints have also been discussed by Drela (1990), Jou et al (1995), and Venkataraman (1996). However, neither thickness nor area constraints demonstrated the ability to control surface oscillations that appeared in some design cases.…”

Section: Introductionmentioning

confidence: 99%

Curvature constraints for airfoil shape optimization in turbulent flow

Kolla¹,

Yokota²,

Lassaline³

et al. 2008

Can. Aeronaut. Space J.

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Abstract. This paper illustrates how surface curvature constraints are incorporated within a two-dimensional optimization method to control geometric oscillations along aerodynamically optimized airfoils. Two treatments were developed; each bounds the surface curvature of an airfoil with upper and lower limits. The first treatment maintains the overall shape of the airfoil while minimizing the local oscillations by applying symmetric curvature bounding. The second treatment bounds an airfoil within a prescribed curvature space. It strongly controls the geometric surface oscillations; however, it does allow an airfoil to be significantly altered from its original shape versus the first method. Both treatments are effective in reducing geometric oscillations along the airfoil surface while maintaining the overall aerodynamic performance.Résumé. Dans cet article, on montre comment les contraintes de la courbure de la surface sont intégrées dans le contexte d'une méthode d'optimisation à deux dimensions pour contrôler les oscillations géométriques le long des surfaces portantes optimisées pour l'aérodynamisme. Deux traitements ont été développés, chacun fixant la courbure du profil d'aile portante dans des limites supérieures et inférieures. Le premier traitement conserve la forme de la surface portante dans son ensemble tout en minimisant les oscillations locales en appliquant une limite de courbure symétrique. Le second traitement fixe les limites de la surface portante à l'intérieur d'un espace de courbure prescrit. Ce dernier contrôle fortement les oscillations géométriques de surface, tout en permettant de transformer de façon significative la surface portante par rapport à sa forme initiale contrairement à la première méthode. Les deux traitements sont efficaces pour réduire les oscillations géométriques le long de la surface portante tout en maintenant la performance aérodynamique dans son ensemble. [Traduit par la Rédaction] 7

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“…(11), (12)), where u is the solution of (15), (16). The semi-discrete version of the control spaces (10)- (12) are…”

Section: Problem Descriptionmentioning

confidence: 99%

“…The papers [1][2][3][4][5][6][7][8][9][10][11] present a sample of recent activities in the former category and References [12][13][14][15][16][17] illustrate activities in the latter category. To the authors' knowledge, the present paper documents the ÿrst approach to the optimal boundary control of unsteady compressible viscous ows.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of unsteady compressible viscous flows

Collis

Ghayour

Heinkenschloss

et al. 2002

Numerical Methods in Fluids

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SUMMARYThe control of complex, unsteady ows is a pacing technology for advances in uid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical ow control systems. However, most of the prior work in this area has focused on incompressible ow which precludes many of the important physical ow phenomena that must be controlled in practice including the coupling of uid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two-dimensional compressible Navier-Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter-rotating viscous vortices above an inÿnite wall which, due to the self-induced velocity ÿeld, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall-normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the in uence of control regularization for each case.

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Practical considerations in aerodynamic design optimization

Cited by 35 publications

References 10 publications

Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations

Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations

Curvature constraints for airfoil shape optimization in turbulent flow

Optimal control of unsteady compressible viscous flows

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