Research Papers: Techniques and Procedures

Adjoint-Based Aerodynamic Shape Optimization for Low Reynolds Number Airfoils

[+] Author and Article Information
Juanmian Lei

School of Aerospace,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: leijm@bit.edu.cn

Jiandong He

School of Aerospace,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: chrishe1900@gmail.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 14, 2015; final manuscript received September 8, 2015; published online October 5, 2015. Assoc. Editor: Moran Wang.

J. Fluids Eng 138(2), 021401 (Oct 05, 2015) (6 pages) Paper No: FE-15-1171; doi: 10.1115/1.4031582 History: Received March 14, 2015; Revised September 08, 2015

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.

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Jameson, A. , 1988, “ Aerodynamic Design Via Control Theory,” J. Sci. Comput., 3(3), pp. 233–260. [CrossRef]
Yamamoto, K. , and Inoue, O. , 1995, “ Applications of Genetic Algorithm to Aerodynamic Shape Optimization,” AIAA Paper No. 95-1650-CP.
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.
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. [CrossRef]
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.
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. [CrossRef]
Pines, D. J. , and Bohorquez, F. , 2006, “ Challenges Facing Future Micro-Air-Vehicle Development,” J. Aircr., 43(2), pp. 290–305. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Kagemoto, H. , 2014, “ Why Do Fish Have a “Fish-Like Geometry”?” ASME J. Fluids Eng., 136(1), p. 011106. [CrossRef]
Hicks, R. M. , and Henne, P. A. , 1978, “ Wing Design by Numerical Optimization,” J. Aircr., 15(7), pp. 407–412. [CrossRef]
Roe, P. L. , 1981, “ Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes,” J. Comput. Phys., 43(2), pp. 357–372. [CrossRef]
Venkateswaran, S. , and Merkle, C. , 1995, “ Dual Time Stepping and Preconditioning for Unsteady Computations,” AIAA Paper No. 95-0078.
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. [CrossRef]
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. [CrossRef]
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.
Selig, M. S. , 1995, Summary of Low Speed Airfoil Data, SoarTech, Ann Arbor, MI.


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Fig. 1

Optimization procedure

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Fig. 10

Comparison of the immediate drag coefficient between baseline and optimized configuration

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Fig. 9

Comparison of the immediate lift coefficient between baseline and optimized configuration

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Fig. 8

History of the time-averaged lift and drag coefficients during optimization

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Fig. 7

Comparison of the baseline and optimized configuration

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Fig. 6

Comparison of the time-averaged drag coefficients of NACA64A010 airfoil with the experimental data

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Fig. 5

Comparison of the time-averaged lift coefficients of NACA64A010 airfoil with the experimental data

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Fig. 4

Comparison of the time-averaged lift coefficients of NACA0012 airfoil with the experimental data

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Fig. 3

CL history of NACA0012 airfoil at Re = 10,000 and α = 6 deg

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Fig. 2

Close-up view of the NACA0012 airfoil grid

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Fig. 11

Comparison of the immediate lift to drag ratio between baseline and optimized configuration



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