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Airfoil optimization based on multi-objective bayesian

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Abstract

This paper proposes a novel aerodynamic optimization framework for airfoils, which utilizes OpenFOAM, an open-source computational fluid dynamics software, and a Bayesian network to achieve efficient optimization of airfoil aerodynamic performance. Aerodynamic analysis of the NACA 4-digit airfoil was performed by adopting the Spalart-Allmaras turbulence model to solve the Reynolds-averaged Navier—Stokes equations. With the use of this framework, the optimal lift-to-drag ratio can be found by using a small number of objective evaluations. The optimal angle of attack and aerodynamic shape can be obtained under different thicknesses. Finally, after various aerodynamic objectives are arranged and combined, the Pareto fronts were obtained by the multi-objective Bayesian algorithm. Compared with the original NACA four-digit airfoil, the lift-to-drag ratio of the airfoil after single-objective optimization is greatly improved as the thickness increases, and the airfoil after multi-objective optimization achieves different Pareto sets according to different sailing phases.

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Abbreviations

t :

Maximum thickness

y th :

Distribution of thickness

y c :

Mean camber line

m :

Maximum camber

p :

Position of maximum camber

c :

Chord length

L :

Lift

c l :

Lift coefficient

\({c_{{l_{datum}}}}\) :

Datum of lift coefficient

D :

Drag

c d :

Drag coefficient

\({c_{{d_{datum}}}}\) :

Datum of drag coefficient

c l/c d :

Lift-to-drag ratio

c f :

Friction drag coefficient

c p :

Pressure drag coefficient

α :

Angle of attack

ρ :

Local density

v :

Incoming flow velocity

S :

Cross-sectional area of the airfoil

ds :

Differential of S

p :

Pressure acting on the surface ds

p o :

Pressure away from the surface ds

\({{\bf{\hat t}}}\) :

Tangent direction vector of the surface ds

î:

Unit direction vector of the incoming flow

\({{\bf{\hat n}}}\) :

Normal direction vector of the surface ds

f :

Objective function

X :

Search space

Data :

Dataset

D 1:t :

Observed set

x i x j :

Ones in the existing dataset

x test i x test j :

New observations

p(f):

Prior probability distribution

p(D 1,t):

Marginal likelihood distribution

μ :

Mean

σ 2 :

Variance

I :

Unit vectors

Re :

Reynolds number

N :

Training points of MOBO

GP :

Gaussian process

Ac :

Acquisition function

UCB :

Upper confidence bound

SA :

Spalart-allmaras turbulence model

AOA :

Angle of attack

RANS :

Reynolds-averaged Navier-Stokes

CFD :

Computational fluid dynamics

BO :

Bayesian optimization

MOBO :

Multi-objective bayesian optimization

GA :

Genetic algorithm

NSGA :

Non-dominated sorting genetic algorithm

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Acknowledgments

This work is supported by the Natural Science Foundation of Jiangsu Province BK20201302 and the Fundamental Research Funds for the Central Universities No. 30919011401.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Ruo-Lin Liu, Xin-Yi Yuan & Wei-Tao Wu

  2. Beijing Institute of Electronic System Engineering, Beijing, 100854, China

    Qiang Zhao

  3. National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing, 210094, China

    Xian-Jun He & Ming-Yu Wu

Authors
  1. Ruo-Lin Liu
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  4. Xin-Yi Yuan
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Corresponding author

Correspondence to Ming-Yu Wu.

Additional information

Mingyu Wu received his B.S. in electrical engineering and automation from Nanjing University of Science and Technology, Nanjing, China in 2018. He is currently a Ph.D. student at the National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing, China. His current research interests include aerodynamics shape optimization, guidance and control, and machine learning.

Ruolin Liu received her B.S. in mechanical engineering from the Northeastern University, Shenyang, China, in 2020. She is currently a postgraduate student in aerospace, Nanjing University of Science and Technology, Nanjing, China. Her current research interests include aerodynamics shape optimization, machine learning, and trajectory design of guidance rockets.

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Liu, RL., Zhao, Q., He, XJ. et al. Airfoil optimization based on multi-objective bayesian. J Mech Sci Technol 36, 5561–5573 (2022). https://doi.org/10.1007/s12206-022-1020-y

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  • DOI: https://doi.org/10.1007/s12206-022-1020-y

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