Optimal Control of Unsteady Flows Using Time Accurate and Non-Linear Frequency Domain Methods

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of timeintegration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

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“…[7]- [13]. The goal of the current work is to extend the time-dependent adjoint formulation for static grids introduced in Ref.…”

Section: Introductionmentioning

confidence: 99%

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

Nielsen

Diskin

Yamaleev

2009

19th AIAA Computational Fluid Dynamics

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“…For some applications, such as turbomachinery, it is necessary to optimize a shape exposed to an unsteady flow. Recent work by Duta et al (2002) and Nadarajah et al (2003) has made excellent progress toward such a capability. Furthermore, high-fidelity multi-disciplinary optimization will become increasingly feasible.…”

Section: Challenges and Opportunitiesmentioning

confidence: 99%

Fifty Years of Aerodynamics: Successes, Challenges, and Opportunities

Nelson¹,

Zingg²

2004

Can. Aeronaut. Space J.

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“…As a result, several authors have developed timedependent adjoint implementations for a variety of problems. Nadarajah and Jameson [15] and Nadarajah et al [16] developed a continuous adjoint approach for control and design optimization of unsteady and periodic phenomena. Rumpfkeil and Zingg [17] developed a discrete adjoint approach for time-dependent aerodynamic flows.…”

Section: Literature Reviewmentioning

confidence: 99%

An Adjoint-based Derivative Evaluation Method for Time-dependent Aeroelastic Optimization of Flexible Aircraft

Kennedy

Martins²

2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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The goal of this paper is to develop techniques to enable the use of aeroelastic constraints within a high-fidelity design optimization framework. As a first-step towards this goal we have developed a fully-coupled aeroelastic analysis tool that includes a coupled structural and aerodynamic analysis as well as rigid-body degrees of freedom. This work departs from previous efforts in two important ways: first, we use solution techniques that are tailored for high-performance parallel computing; second, we implement a fully-coupled adjoint method using a coupled-Krylov approach for the evaluation of derivatives of time-dependent functions of interest. The coupled Newton-Krylov approach enables us to perform simulations in the full structural space without modal reduction. The timedependent adjoint approach enables us to evaluate the gradient of functions of interest for cases with hundreds or thousands of design variables in a cost similar to the time-dependent simulation. In order to demonstrate our framework, we verify the gradient accuracy of some preliminary simulations of three transport aircraft wings with increasing span subject to gust loads.

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Optimal Control of Unsteady Flows Using Time Accurate and Non-Linear Frequency Domain Methods

Cited by 40 publications

References 3 publications

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

Fifty Years of Aerodynamics: Successes, Challenges, and Opportunities

An Adjoint-based Derivative Evaluation Method for Time-dependent Aeroelastic Optimization of Flexible Aircraft

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