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A multi-objective airfoil shape optimization study using mesh morphing and response surface method

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Abstract

Here, a distinct procedure was adopted to optimize the shape of the NACA 0012 airfoil profile for Reynolds number, Mach number, and angle of attack equal to 2e6, 0.15, and 10.24 deg, respectively. The airfoil shape was appropriately parameterized, and mesh morphing tools were used to bypass the remeshing process. Computational fluid dynamic (CFD) simulations were carried out for all combinations of selected parameters. Response surfaces were constructed for the drag and lift coefficients of the airfoil based on several statistical criteria. Subsequently, the Pareto front was used to solve the multi-objective optimization problem. Eventually, three single-objective types of optimization problems were studied. A 10 % reduction in drag coefficient was estimated for the drag minimization problem, a 22 % improvement in lift coefficient was found in case of lift maximization problem, and a 6 % reduction in drag coefficient was determined in the lift constrained drag minimization problem.

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Abbreviations

A :

Reference area

a :

Coefficient in the regression equation

c :

Chord length of the airfoil

C d :

Drag coefficient

C l :

Lift coefficient

C p :

Specific heat capacity

C p :

Pressure coefficient

C f :

Skin friction coefficient

F d :

Drag force

F l :

Lift force

M :

Mach number

n :

Exponent in the regression equation

p :

Pressure

R :

Gas constant

R 2 :

Coefficient of determination

Re :

Reynolds number

S :

Sutherland constant

T :

Temperature

u :

Velocity component

V ∞ :

Velocity magnitude at the free-stream

x, y :

Cartesian coordinates

Yu, Yi, Yt :

Airfoil parameters

α :

Angle of attack

λ :

Thermal conductivity

μ :

Dynamic viscosity

ρ :

Density

i, j :

Tensor indices

0 :

Reference value

∞ :

Free-stream condition

‘:

Turbulent fluctuation

*:

Non-dimensional quantity

2D :

Two-dimensional

CAD :

Computer aided design

CFD :

Computational fluid dynamics

CFD-O :

CFD based optimization

DOE :

Design of experiment

FFD :

Free form deformation

MMO :

Mesh morpher/optimizer

NACA :

National advisory committee for aeronautics

NSGA :

Non-dominated sorting genetic algorithm

RANS :

Reynolds averaged Navier-Stokes

RBF :

Radial basis function

RSM :

Response surface methodology

SST :

Shear stress transport

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Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the ministry of Education-Korea (No. 2018R1 D1A1B07046034).

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Authors and Affiliations

  1. School of Mechanical Engineering, Pusan National University, 2, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan, 46241, Korea

    Hariharan Kallath, Jun Seok Lee, Foster Kwame Kholi, Man Yeong Ha & June Kee Min

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  1. Hariharan Kallath
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  2. Jun Seok Lee
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  3. Foster Kwame Kholi
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  4. Man Yeong Ha
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Correspondence to June Kee Min.

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Recommended by Editor Yang Na

Hariharan Kallath received his M.S. in Ocean Engineering from the Indian Institute of Technology, Chennai, and Mechanical Engineering degree from The Institution of Engineers (India), Kolkata. He is currently doing a Ph.D. at the School of Mechanical Engineering, Pusan National University, in Busan, South Korea. His research interest includes energy systems related to aircraft thermal management.

June Kee Min received his Ph.D. degree from Korea Advanced Institute of Science and Technology, Korea, in 1999. Currently, he is a Professor at the School of Mechanical Engineering at Pusan National University in Busan, Korea. His research interest is on the development of advanced CFD models for various complicated flow and heat transfer problems.

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Kallath, H., Lee, J.S., Kholi, F.K. et al. A multi-objective airfoil shape optimization study using mesh morphing and response surface method. J Mech Sci Technol 35, 1075–1086 (2021). https://doi.org/10.1007/s12206-021-0221-0

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