Progress in Aerodynamic Shape Optimization Based on the Reynolds-Averaged Navier-Stokes Equations

Koo, David; Zingg, David W.

doi:10.2514/6.2016-1292

Cited by 12 publications

(6 citation statements)

References 30 publications

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“…The computational cost of evaluating the partial derivatives of an objective or constraint function is insensitive to the number of design variables, requiring only one flow solution and one adjoint solution. This method becomes the most practical one for the design of complex aerodynamic configurations [56,57] because it can deal with the optimization problems with 100-1000 design variables [58,59] or even more. The drawback of a gradient-based method is that the solution optimality can be sensitive to the initial guesses, and it can become trapped into a local minimum [60].…”

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confidence: 99%

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

et al. 2017

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A novel formulation of gradient-enhanced surrogate model, called weighted gradient-enhanced kriging, is proposed and used in combination with the cheap gradients obtained by the adjoint method to ameliorate the "curse of dimensionality". The core idea is to build a series of submodels with much smaller correlation matrices and then sum them up with appropriate weight coefficients, aiming to avoid the prohibitive cost associated with decomposing the large correlation matrix of a gradient-enhanced kriging. A self-contained derivation of the proposed method is presented, and then it is verified by surrogate modeling test cases. The present method is integrated into a surrogatebased optimizer and tested for design optimizations. It is further demonstrated for inverse design of a transonic wing, parameterized with a number of design variables in the range from 36 to 108, using Reynolds-averaged Navier-Stokes flow and adjoint solvers. It is observed that, for the wing design with 36 and 54 variables, the weighted and conventional gradient-enhanced kriging are comparable, and both are much more efficient than kriging without using any gradient. For the wing design with 72 and 108 variables, the cost of training a gradient-enhanced kriging increases rapidly and becomes prohibitive. In contrast, the cost of training a weighted gradient-enhanced kriging is kept in an acceptable level, which makes it more practical for higher-dimensional problems.

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confidence: 99%

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

et al. 2017

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“…Koo and Zingg [48] applied the algorithm to the CRM wing-body-tail configuration, in addition to several wingletted wings sized for the Boeing 737-900; these included a winglet up configuration, a wingtip fence configuration, and a split-tip configuration. Jetstream has also been used by Reist and Zingg [18] to design and study a lifting-fuselage configuration.…”

Section: Aerodynamic Shape Optimizationmentioning

confidence: 99%

Aerodynamic Shape Optimization of a Box-Wing Regional Aircraft Based on the Reynolds-Averaged Navier-Stokes Equations

Chau

2017

35th AIAA Applied Aerodynamics Conference

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The box wing is an unconventional aircraft configuration that has the potential to provide major savings in fuel consumption relative to the conventional cantilever wing. In order to further develop and evaluate this potential, high-fidelity aerodynamic shape optimization is applied to the aerodynamic design of a box wing and a cantilever wing, based on the Embraer E190 regional jet, with the latter serving as a performance baseline. The optimization framework consists of B-spline parameterization, free-form and axial deformation geometry control, an integrated mesh-movement scheme based on the theory of linear elasticity, a Newton-Krylov-Schur flow solver for the Reynolds-averaged Navier-Stokes equations, a gradient-based optimizer, and the discrete-adjoint method for gradient evaluation. Results indicate that a box-wing with a heightto-span ratio of 0.26 burns 7.61% less fuel at cruise than a conventional baseline of the same span and lift. Aerodynamic trends and trade-offs are investigated, and a weight sensitivity study is performed.ii Acknowledgements First and foremost, I would like to thank my supervisor, Professor David Zingg. I cannot thank him enough for the opportunity to work on such a state-of-the-art problem, which has proven to be challenging, but incredibly rewarding. I also have him to thank for the invaluable knowledge and experience that I have gained during these past few years. His passion for computational aerodynamics and environmentally-friendly aircraft design is something to be envied, and will always serve as a pillar of inspiration. I would also like to thank the UTIAS community for creating a welcoming and fun work environment. To the computational aerodynamics group, thank you for all of the helpful feedback you have given me over the years, and for making my late nights in the lab palatable. In particular, I would like to thank Dr. Shahriar Khosravi for the many interesting discussions on aerodynamics and structures, and Dr. Thomas Reist for his invaluable technical guidance and discussions on aircraft design.

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“…Lyu, Z.J. and others [7][8][9][10][11] introduced longitudinal trim consideration into gradient-based optimization by deriving adjoint equations for solving zero-pitching moment constraints. Rubén [12] applied Prandtl's lifting line theory to compute the lift distribution of wings and horizontal tails, optimizing the combination using genetic algorithms to achieve optimal lift distribution while considering longitudinal trim.…”

Section: Introductionmentioning

confidence: 99%

Aerodynamic Shape Optimization of Subsonic/Supersonic Flows Integrating Variable-Fidelity Longitudinal Trim Analysis

Wu,

Huang,

et al. 2024

Aerospace

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Most existing studies on aerodynamic shape optimization have not considered longitudinal trim under control surface deflection, typically achieving self-trim through a constraint of zero pitching moment or adjusting the optimized configuration for longitudinal trim. However, adjustments to the optimized configuration might introduce additional drag, reducing overall optimization benefits. In this paper, a novel approach of incorporating control surface deflection for longitudinal trim in aerodynamic optimization is proposed. Firstly, an aerodynamic computation program based on the high-order panel method was developed, introducing velocity perturbations on specific mesh surfaces to simulate actual control surface deflections. Subsequently, a comprehensive optimization framework was established, encompassing parametric modeling, aerodynamic computation, and variable-fidelity control surface deflection analysis. Finally, aerodynamic optimization analysis was conducted under both subsonic and supersonic conditions. Thirty-one design variables were selected with the trimmed lift-to-drag ratio in cruising condition as the objective function and the control surface deflection angle as the constraint. The results indicated an 8.52% increase in the trimmed lift-to-drag ratio compared to the baseline model under subsonic conditions and an 8.1% increase under supersonic conditions.

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Progress in Aerodynamic Shape Optimization Based on the Reynolds-Averaged Navier-Stokes Equations

Cited by 12 publications

References 30 publications

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

Aerodynamic Shape Optimization of a Box-Wing Regional Aircraft Based on the Reynolds-Averaged Navier-Stokes Equations

Aerodynamic Shape Optimization of Subsonic/Supersonic Flows Integrating Variable-Fidelity Longitudinal Trim Analysis

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