Fluid Mechanics and Flight Mechanics

Efficient robust aerodynamic design optimization method for high-speed NLF airfoil

  • ZHAO Huan ,
  • GAO Zhenghong ,
  • XIA Lu
Expand
  • 1. School of Aeronautics and Astronautics, Sun Yat-sen University, Guangzhou 510275, China;
    2. School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received date: 2020-10-19

  Revised date: 2021-12-27

  Online published: 2020-12-25

Supported by

National Natural Science Foundation of China(12102489)

Abstract

The advanced high-speed and high-lift Natural-Laminar-Flow (NLF) airfoil has played an important role in improving the aerodynamic performance of the new generation of High-Altitude Long Endurance (HALE) Unmanned Air Vehicles (UAV). However, shock waves and separation bubbles are likely to occur on the surface of this kind of airfoil, which are very sensitive to the aerodynamic characteristics such as fluctuation of Mach number and angle of attack. The aerodynamic shape designed with the traditional method has low robustness, and is thus difficult to be used in engineering practice. Although the Robust Aerodynamic Design Optimization (RADO) method is a very promising solution, it encounters the difficulty of large computational cost. In this paper, we study the key technologies affecting the efficiency of RADO and develop a sparse PC reconstruction algorithm based on the Adaptive Forward-Backward Selection (AFBS) method, greatly improving the efficiency of Uncertainty Quantification (UQ) and RADO. We also develop an efficient RADO method considering multi-parameter uncertainty, which solves the difficulty of the traditional airfoil design method that requirements for high-lift design, NLF design, and supercritical design cannot be met simultaneously. Finally, we successfully apply the proposed methods to design a class of robust high-speed NLF airfoils with significant characteristics. Results demonstrate that compared with the classical Global Hawk UAV airfoil, the airfoils designed with the proposed methods can provide better aerodynamic performance, larger low-drag range and more robust performance, which validate the effectiveness of the proposed RADO method and advantages of the proposed method over the deterministic optimization method.

Cite this article

ZHAO Huan , GAO Zhenghong , XIA Lu . Efficient robust aerodynamic design optimization method for high-speed NLF airfoil[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022 , 43(1) : 124894 -124894 . DOI: 10.7527/S1000-6893.2020.24894

References

[1] XIU D B, KARNIADAKIS G E. Modeling uncertainty in flow simulations via generalized polynomial chaos[J]. Journal of Computational Physics, 2003, 187(1): 137-167.
[2] HICKS R M, CLIFF S E. An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers:NASA TM-102840[R]. Washington,D.C.: NASA, 1991.
[3] FUJINO M, YOSHIZAKI Y, KAWAMURA Y. Natural-laminar-flow airfoil development for a lightweight business jet[J]. Journal of Aircraft, 2003, 40(4): 609-615.
[4] GREEN B E, WHITESIDES J L, CAMPBELL R L, et al. Method for the constrained design of natural laminar flow airfoils[J]. Journal of Aircraft, 1997, 34(6): 706-712.
[5] 黄江涛, 高正红, 白俊强, 等. 应用Delaunay图映射与FFD技术的层流翼型气动优化设计[J]. 航空学报, 2012, 33(10): 1817-1826. HUANG J T, GAO Z H, BAI J Q, et al. Laminar airfoil aerodynamic optimization design based on Delaunay graph mapping and FFD technique[J]. Acta Aeronautica et Astronautica Sinica, 2012, 33(10): 1817-1826(in Chinese).
[6] SELIG M S, GUGLIELMO J J. High-lift low Reynolds number airfoil design[J]. Journal of Aircraft, 1997, 34(1): 72-79.
[7] ZHAO K, GAO Z H, HUANG J T. Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method[J]. Applied Mathematics and Mechanics, 2014, 35(2): 191-202.
[8] ZHU J, GAO Z H, ZHAN H, et al. A high-speed nature laminar flow airfoil and its experimental study in wind tunnel with nonintrusive measurement technique[J]. Chinese Journal of Aeronautics, 2009, 22(3): 225-229.
[9] LI J, GAO Z H, HUANG J T, et al. Robust design of NLF airfoils[J]. Chinese Journal of Aeronautics, 2013, 26(2): 309-318.
[10] LIEBECK R H. Design of subsonic airfoils for high lift[J]. Journal of Aircraft, 1978, 15(9): 547-561.
[11] ZHAO H, GAO Z H. Uncertainty-based design optimization of NLF airfoil for high altitude long endurance unmanned air vehicles[J]. Engineering Computations, 2019, 36(3): 971-996.
[12] NAJM H N. Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics[J]. Annual Review of Fluid Mechanics, 2009, 41(1): 35-52.
[13] ZANG T A, HEMSCH M J, HILBURGER M W, et al. Needs and opportunities for uncertainty-based multidisciplinary design methods for aerospace vehicles:NASA/TM-2002-211462[R]. Washington, D.C.: NASA Langley Research Center, 2002.
[14] KEANE A J. Comparison of several optimization strategies for robust turbine blade design[J]. Journal of Propulsion and Power, 2009, 25(5): 1092-1099.
[15] KEANE A J. Cokriging for robust design optimization[J]. AIAA Journal, 2012, 50(11): 2351-2364.
[16] HOSDER S, WALTERS R, PEREZ R. A non-intrusive polynomial chaos method for uncertainty propagation in CFD simulations[C]//44th AIAA Aerospace Sciences Meeting and Exhibit. Reston: AIAA, 2006.
[17] SHAH H, HOSDER S, WINTER T. Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions[J]. Reliability Engineering & System Safety, 2015, 138: 59-72.
[18] PADRON A S, ALONSO J J, ELDRED M S. Multi-fidelity methods in aerodynamic robust optimization[C]//18th AIAA Non-Deterministic Approaches Conference. Reston: AIAA, 2016.
[19] KIM N H, WANG H Y, QUEIPO N V. Efficient shape optimization under uncertainty using polynomial chaos expansions and local sensitivities[J]. AIAA Journal, 2006, 44(5): 1112-1116.
[20] SHIMOYAMA K, LIM J N, JEONG S, et al. Practical implementation of robust design assisted by response surface approximation and visual data-mining[J]. Journal of Mechanical Design, 2009, 131(6): 061007.
[21] DODSON M, PARKS G T. Robust aerodynamic design optimization using polynomial chaos[J]. Journal of Aircraft, 2009, 46(2): 635-646.
[22] ZHAO H, GAO Z H, XU F, et al. Review of robust aerodynamic design optimization for air vehicles[J]. Archives of Computational Methods in Engineering, 2019, 26(3): 685-732.
[23] ZHAO H, GAO Z H, GAO Y, et al. Effective robust design of high lift NLF airfoil under multi-parameter uncertainty[J]. Aerospace Science and Technology, 2017, 68: 530-542.
[24] HUANG J T, GAO Z H, ZHAO K, et al. Robust design of supercritical wing aerodynamic optimization considering fuselage interfering[J]. Chinese Journal of Aeronautics, 2010, 23(5): 523-528.
[25] PAIVA R M, CRAWFORD C, SULEMAN A. Robust and reliability-based design optimization framework for wing design[J]. AIAA Journal, 2014, 52(4): 711-724.
[26] LEE S H, CHEN W. A comparative study of uncertainty propagation methods for black-box-type problems[J]. Structural and Multidisciplinary Optimization, 2008, 37(3): 239-253.
[27] JANSSEN H. Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence[J]. Reliability Engineering & System Safety, 2013, 109: 123-132.
[28] LEE S H, CHEN W, KWAK B M. Robust design with arbitrary distributions using Gauss-type quadrature formula[J]. Structural and Multidisciplinary Optimization, 2009, 39(3): 227-243.
[29] RAUHUT H, WARD R. Sparse Legendre expansions via l1-minimization[J]. Journal of Approximation Theory, 2012, 164(5): 517-533.
[30] BLATMAN G, SUDRET B. Adaptive sparse polynomial chaos expansion based on least angle regression[J]. Journal of Computational Physics, 2011, 230(6): 2345-2367.
[31] ZHAO H, GAO Z H, XU F, et al. An efficient adaptive forward-backward selection method for sparse polynomial chaos expansion[J]. Computer Methods in Applied Mechanics and Engineering, 2019, 355: 456-491.
[32] 黄江涛, 刘刚, 高正红, 等. 飞行器多学科耦合伴随体系的现状与发展趋势[J]. 航空学报, 2020, 41(5): 623404. HUANG J T, LIU G, GAO Z H, et al. Current situation and development trend of multidisciplinary coupled adjoint system for aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(5): 623404(in Chinese).
[33] YAO W, CHEN X, LUO W, et al. Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles[J]. Progress in Aerospace Sciences, 2011, 47(6): 450-479.
[34] SCHUE··LLER G I, JENSEN H A. Computational methods in optimization considering uncertainties-An overview [J]. Computer Methods in Applied Mechanics & Engineering, 2008, 198(1): 2-13.
[35] COOK L W, JARRETT J P. Robust airfoil optimization and the importance of appropriately representing uncertainty[J]. AIAA Journal, 2017, 55(11): 3925-3939.
[36] ZHAO H, GAO Z, XU F, et al. Adaptive multi-fidelity sparse polynomial chaos-Kriging metamodeling for global approximation of aerodynamic data[J]. Structural and Multidisciplinary Optimization, 2021, 64(2): 829-858.
[37] CHATTERJEE T, CHAKRABORTY S, CHOWDHURY R. A critical review of surrogate assisted robust design optimization[J]. Archives of Computational Methods in Engineering, 2019, 26(1): 245-274.
[38] BERAN P, STANFORD B. Uncertainty quantification in aeroelasticity[J]. Annual Review of Fluid Mechanics, 2017, 49(1): 361-386.
[39] 赵轲, 高正红, 黄江涛, 等. 基于混沌多项式方法的翼型流场不确定性分析及稳健设计研究[J]. 力学学报, 2014, 46(1): 10-19. ZHAO K, GAO Z H, HUANG J T, et al. Uncertainty quantification and robust design of airfoil based polynomial chaos technique[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 10-19(in Chinese).
[40] CAMERON R H, MARTIN W T. The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals[J]. Annals of Mathematics, 1947, 48(2): 385-392.
[41] CANDES E J. The restricted isometry property and its implications for compressed sensing[J]. Comptes Rendus Mathematique, 2008, 346(9-10): 589-592.
[42] 赵欢, 高正红, 王超, 等适用于高速层流翼型的计算网格研究[J]. 应用力学学报, 2018, 35(2): 351-357. ZHAO H, GAO Z H, WANG C, et al. Research on the computing grid of high speed laminar airfoil[J]. Chinese Journal of Applied Mechanics, 2018, 35(2): 351-357(in Chinese).
[43] SHI Y, MADER C A, HE S, et al. Natural laminar-flow airfoil optimization design using a discrete adjoint approach[J]. AIAA Journal, 2020, 58(11): 4702-4722.
[44] 赵欢. 基于代理模型的高效气动优化与气动稳健设计方法研究[D].西安: 西北工业大学, 2020. ZHAO H. Research on surrogate-based efficient aerodynamic optimization and robust aerodynamic design methods[D]. Xi'an: Northwestern Polytechnical University, 2020(in Chinese).
Outlines

/