In the past decades, most of the research studies on airfoil shape design and optimization were focused on high Reynolds number airfoils. However, low Reynolds number airfoils have attracted significant attention nowadays due to their vast applications, ranging from micro-aerial vehicles (MAVs) to small-scale unmanned aerial vehicles. For low Reynolds number airfoils, the unsteady effects caused by boundary layer separation cannot be neglected. In this paper, we present an aerodynamic shape optimization framework for low Reynolds number airfoil that we developed based on the unsteady laminar N–S equation and the adjoint method. Finally, using the developed framework, we performed a test case with NACA0012 airfoil as a baseline configuration and the inverse of lift to drag ratio as the cost function. The optimization was carried out at Re = 10,000 and Ma = 0.2. The results demonstrate the effectiveness of the framework.

References

References
1.
Jameson
,
A.
,
1988
, “
Aerodynamic Design Via Control Theory
,”
J. Sci. Comput.
,
3
(
3
), pp.
233
260
.
2.
Yamamoto
,
K.
, and
Inoue
,
O.
,
1995
, “
Applications of Genetic Algorithm to Aerodynamic Shape Optimization
,”
AIAA
Paper No. 95-1650-CP.
3.
Reuther
,
J.
,
Jameson
,
A.
,
Farmer
,
J.
,
Martinelli
,
L.
, and
Saunders
,
D.
,
1996
,
Aerodynamic Shape Optimization of Complex Aircraft Configurations Via an Adjoint Formulation
,
Research Institute for Advanced Computer Science, NASA Ames Research Center
,
Reno, NV
.
4.
Jameson
,
A.
,
Martinelli
,
L.
, and
Pierce
,
N.
,
1998
, “
Optimum Aerodynamic Design Using the Navier–Stokes Equations
,”
Theor. Comput. Fluid Dyn.
,
10
(
1–4
), pp.
213
237
.
5.
Alonso
,
J. J.
,
Jameson
,
A.
,
Alonso
,
J.
,
Reuther
,
J. J.
,
Martinelli
,
L.
, and
Vassberg
,
J.
,
1998
, “
Aerodynamic Shape Optimization Techniques Based on Control Theory
,”
Proceedings of Control Theory
, CIME, International Mathematical Summer, Citeseer, pp.
21
27
.
6.
Shyy
,
W.
,
Berg
,
M.
, and
Ljungqvist
,
D.
,
1999
, “
Flapping and Flexible Wings for Biological and Micro Air Vehicles
,”
Prog. Aerosp. Sci.
,
35
(
5
), pp.
455
505
.
7.
Pines
,
D. J.
, and
Bohorquez
,
F.
,
2006
, “
Challenges Facing Future Micro-Air-Vehicle Development
,”
J. Aircr.
,
43
(
2
), pp.
290
305
.
8.
Nadarajah
,
S. K.
, and
Jameson
,
A.
,
2007
, “
Optimum Shape Design for Unsteady Flows With Time-Accurate Continuous and Discrete Adjoint Method
,”
AIAA J.
,
45
(
7
), pp.
1478
1491
.
9.
Rudmin
,
D.
,
Benaissa
,
A.
, and
Poirel
,
D.
,
2013
, “
Detection of Laminar Flow Separation and Transition on a NACA-0012 Airfoil Using Surface Hot-Films
,”
ASME J. Fluids Eng.
,
135
(
10
), p.
101104
.
10.
Lee
,
T.
, and
Su
,
Y.
,
2015
, “
Surface Pressures Developed on an Airfoil Undergoing Heaving and Pitching Motion
,”
ASME J. Fluids Eng.
,
137
(
5
), p.
051105
.
11.
Kagemoto
,
H.
,
2014
, “
Why Do Fish Have a “Fish-Like Geometry”?
ASME J. Fluids Eng.
,
136
(
1
), p.
011106
.
12.
Hicks
,
R. M.
, and
Henne
,
P. A.
,
1978
, “
Wing Design by Numerical Optimization
,”
J. Aircr.
,
15
(
7
), pp.
407
412
.
13.
Roe
,
P. L.
,
1981
, “
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
,”
J. Comput. Phys.
,
43
(
2
), pp.
357
372
.
14.
Venkateswaran
,
S.
, and
Merkle
,
C.
,
1995
, “
Dual Time Stepping and Preconditioning for Unsteady Computations
,”
AIAA
Paper No. 95-0078.
15.
Perez
,
R. E.
,
Jansen
,
P. W.
, and
Martins
,
J. R.
,
2012
, “
pyopt: a Python-Based Object-Oriented Framework for Nonlinear Constrained Optimization
,”
Struct. Multidiscip. Optim.
,
45
(
1
), pp.
101
118
.
16.
Ashraf
,
M.
,
Young
,
J.
, and
Lai
,
J. C. S.
,
2012
, “
Oscillation Frequency and Amplitude Effects on Plunging Airfoil Propulsion and Flow Periodicity
,”
AIAA J.
,
50
(
11
), pp.
2308
2324
.
17.
Cleaver
,
D. J.
,
Wang
,
Z.
, and
Gursul
,
I.
,
2010
, “
Vortex Mode Bifurcation and Lift Force of a Plunging Airfoil at Low Reynolds Numbers
,”
AIAA
2010-390.
18.
Selig
,
M. S.
,
1995
,
Summary of Low Speed Airfoil Data
,
SoarTech
,
Ann Arbor, MI
.
You do not currently have access to this content.