A Novel Aerodynamic Shape Optimization Approach for Three-Dimensional Turbulent Flows

Osusky, Lana; Zingg, David W.

doi:10.2514/6.2012-58

Cited by 12 publications

(11 citation statements)

References 27 publications

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“…The particular test considered is the well-studied ONERA M6 wing [31]. This geometry has been studied by numerous authors [32,33,34,35,36,8,10] due to the simple, well defined geometry and the availability of experimental data.…”

Section: Resultsmentioning

confidence: 99%

“…The gradient produced by the discrete adjoint is exact in the discrete sense and can thus be verified with great precision using the complex-step method [5]. The discrete adjoint approach is also widely used in aerodynamic shape optimization [6,7,8,9,10,11,12]. The implementation of either continuous or discrete adjoint methods in a complex CFD code remains a challenging time-consuming task.…”

Section: Introductionmentioning

confidence: 99%

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Automatic Differentiation Adjoint of the Reynolds-Averaged Navier-Stokes Equations with a Turbulence Model

Lyu

Kenway

Paige

et al. 2013

21st AIAA Computational Fluid Dynamics Conference

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This paper presents an approach for the rapid implementation of an adjoint solver for the ReynoldsAveraged Navier-Stokes equations with a Spalart-Allmaras turbulence model. Automatic differentiation is used to construct the partial derivatives required in the adjoint formulation. The resulting adjoint implementation is computationally efficient and highly accurate. The assembly of each partial derivative in the adjoint formulation is discussed. In addition, a coloring acceleration technique is presented to improve the adjoint efficiency. The RANS adjoint is verified with complex-step method using a flow over a bump case. The RANS-based aerodynamic shape optimization of an ONERA M6 wing is also presented to demonstrate the aerodynamic shape optimization capability. The drag coefficient is reduced by 19% when subject to a lift coefficient constraint. The results are compared with Euler-based aerodynamic shape optimization and previous work. Finally, the effects of the frozenturbulence assumption on the accuracy and computational cost are assessed.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Automatic Differentiation Adjoint of the Reynolds-Averaged Navier-Stokes Equations with a Turbulence Model

Lyu

Kenway

Paige

et al. 2013

21st AIAA Computational Fluid Dynamics Conference

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show abstract

“…The fidelity of the models used for aerodynamic shape optimization has also been increasing, and it is now possible to use computational fluid dynamics (CFD) to optimize a design with respect to hundreds of design variables using both Euler [15,16,17,18] and NavierStokes models [19,20,21]. In the design of transonic wings it is particularly important to use high-fidelity models to correctly predict the drag due to viscous and compressibility effects.…”

Section: Introductionmentioning

confidence: 99%

Multipoint High-Fidelity Aerostructural Optimization of a Transport Aircraft Configuration

Kenway

Martins

2014

Journal of Aircraft

308

184

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This paper presents multi-point high-fidelity aerostructural optimizations of a long-range wide-body transonic transport aircraft configuration. The aerostructural analysis employs Euler CFD with a 2 million cell mesh and a structural finite element model with 300 000 degrees of freedom. The coupled adjoint sensitivity method is used to efficiently compute gradients, enabling the use of gradient-based optimization with respect to hundreds of aerodynamic shape and structural sizing variables. The NASA Common Research Model is used as the baseline configuration, together with a wingbox structure that was designed for this study. Two design optimization problems are solved: one where takeoff gross weight is minimized, and another where fuel burn is minimized. Each optimization uses a multi-point formulation with 5 cruise conditions and 2 maneuver conditions. Each of the optimization problems have 476 design variables, including wing planform, airfoil shape, and structural thickness variables. Optimized results are obtained within 36 hours of wall time using 435 processors. The resulting optimal configurations are discussed and analyzed for the aerostructural trade-offs resulting from each objective. The takeoff gross weight minimization results in a 4.2% reduction in takeoff gross weight with a 6.6% fuel burn reduction, while the fuel-burn optimization resulted in an 11.2% fuel burn reduction with no significant change in the takeoff gross weight.

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“…The geometry and specifications are given by the Aerodynamic Design Optimization Discussion Group [2]. The fuselage and tail are deleted from the original CRM, and the root of the remaining wing is moved to the symmetry plane.…”

Section: A Initial Geometrymentioning

confidence: 99%

“…The benchmark problems range from the optimization of a two-dimensional airfoil using the Euler equations, to threedimensional shape optimization using the Navier-Stokes. In this paper, we present the results of the most complex benchmark problem among the four test cases: the lift-constrained drag minimization of the Common Research Model (CRM) wing with flow governed by the Reynolds-Averaged Navier-Stokes equations (RANS) [2].…”

Section: Introductionmentioning

confidence: 99%

RANS-based Aerodynamic Shape Optimization Investigations of the Common Research Model Wing

Lyu

Kenway²,

Martins³

2014

52nd Aerospace Sciences Meeting

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The aerodynamic shape optimization of transonic wings requires Reynolds-averaged Navier-Stokes (RANS) modeling due to the strong nonlinear coupling between airfoil shape, wave drag, and viscous effects. While there has been some research dedicated to RANS-based aerodynamic shape optimization, there has not been an benchmark case for researchers to compare their results. In this investigations, a series of aerodynamic shape optimizations of the Common Research Model wing defined for the Aerodynamic Design Optimization Workshop are presented. The computational fluid dynamics solves Reynolds-averaged Navier-Stokes equations with a Spalart-Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with a discrete adjoint method that computes the derivatives of the aerodynamic forces. The drag coefficient at the nominal flight condition is minimized subject to lift, pitching moment and geometric constraints. A multilevel acceleration technique is used to reduce the computational cost. A total of 768 shape design variables are considered, together with a grid with 28.8 million cells. The drag coefficient of the optimized wing is reduced by 8.5% relative to the baseline. The single-point design has a sharp leading edge that is prone to flow separation at off-design conditions. A more robust design is achieved through a multipoint optimization, which achieves more reliable performance when lift coefficient and Mach number are varied about the nominal flight condition. To test the design space for local minima, randomly generated initial geometries are optimized, and a flat design space with multiple local minima was observed.

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A Novel Aerodynamic Shape Optimization Approach for Three-Dimensional Turbulent Flows

Cited by 12 publications

References 27 publications

Automatic Differentiation Adjoint of the Reynolds-Averaged Navier-Stokes Equations with a Turbulence Model

Automatic Differentiation Adjoint of the Reynolds-Averaged Navier-Stokes Equations with a Turbulence Model

Multipoint High-Fidelity Aerostructural Optimization of a Transport Aircraft Configuration

RANS-based Aerodynamic Shape Optimization Investigations of the Common Research Model Wing

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