Fluid Mechanics and Flight Mechanics

Discrete adjoint-based optimization approach for laminar flow wings

  • YANG Tihao ,
  • WANG Yiwen ,
  • WANG Yutong ,
  • SHI Yayun ,
  • ZHOU Zhu
Expand
  • 1. School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China;
    2. Unmanned System Research Institute, Northwestern Polytechnical University, Xi'an 710072, China;
    3. School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China;
    4. China Aerodynamics Research and Development Center, Mianyang 621000, China

Received date: 2021-07-20

  Revised date: 2021-09-22

  Online published: 2022-01-26

Supported by

National Natural Science Foundation of China (11902320, 12002284)

Abstract

Laminar flow is one of the key technologies in the future development of green aviation, while an efficient and reliable design optimization approach for problems with a large number of design variables is the key to promoting the industrial application of the laminar flow technique. Based on the high-fidelity RANS solver, and combined with the quasi-three-dimensional laminar boundary layer equation, Drela-Giles and C1 criteria, a transition prediction method, which can simultaneously capture Tollmien-Schlichting (TS) and Crossflow (CF) instabilities, is established. Comparison of the simulation results with typical wind tunnel and flight tests shows the reliability of the simulation approach. An accurate intermittency function is obtained by strictly interpolating the surface values to eliminate the numerical noise for the aerodynamic forces simulation. The coupled adjoint equation considering transition is derived accurately, and solved efficiently by combining the matrix-free technique, the chain rule, the hybrid reverse automatic differentiation, and the Coupled Krylov (CK) algorithm. Finally, the discrete adjoint-based laminar flow wings optimization method is built. The optimization of a wing-body configuration with typical characteristics of regional airliners demonstrates that the transition is effectively delayed, with 10.48% of the total drag reduced. The optimization results reveal that the gradient-based laminar flow wings optimization framework can deal with complex three-dimensional laminar flow wings optimization problems with multiple transition mechanisms.

Cite this article

YANG Tihao , WANG Yiwen , WANG Yutong , SHI Yayun , ZHOU Zhu . Discrete adjoint-based optimization approach for laminar flow wings[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022 , 43(12) : 126132 -126132 . DOI: 10.7527/S1000-6893.2021.26132

References

[1] ARNAL D, ARCHAMBAUD J P. Laminar-turbulent transition control:NLF, LFC, HLFC[C]//Advances in Laminar-Turbulent Transition Modeling, 2008.
[2] DE'POMPEIS R, CINQUETTI P, MARTINI P I S. Development and certification flight test on the piaggio P.180 avanti aircraft:A general overview:SAE Technical Paper 911003[R]. Warrendale:SAE International,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] CROUCH J. Modeling transition physics for laminar flow control[C]//38th Fluid Dynamics Conference and Exhibit. Reston:AIAA, 2008.
[5] EPPINK J L. The effect of forward-facing steps on stationary crossflow instability growth and breakfown[C]//AIAA Aerospace Sciences Meeting, 2018.
[6] ARNAL D, CASALIS G. Laminar-turbulent transition prediction in three-dimensional flows[J]. Progress in Aerospace Sciences, 2000, 36(2):173-191.
[7] KRUMBEIN A, KRIMMELBEIN N, SCHRAUF G. Automatic transition prediction in hybrid flow solver, part 1:Methodology and sensitivities[J]. Journal of Aircraft, 2009, 46(4):1176-1190.
[8] KRUMBEIN A, KRIMMELBEIN N, SCHRAUF G. Automatic transition prediction in hybrid flow solver, part 2:Practical application[J]. Journal of Aircraft, 2009, 46(4):1191-1199.
[9] LIAO W, MALIK M R, LEE-RAUSCH E M, et al. Boundary-layer stability analysis of the mean flows obtained using unstructured grids[J]. Journal of Aircraft, 2015, 52(1):49-63.
[10] SHI Y, GROSS R, MADER C A, et al. Transition prediction based on linear stability theory with the RANS solver for three-dimensional configurations[C]//Proceedings of the AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, 2018.
[11] ARNAL D. Transition prediction in transonic flow[M]//Symposium transsonicum III. Berlin:Springer Berlin Heidelberg, 1989:253-262.
[12] PERRAUD J, ARNAL D, CASALIS G, et al. Automatic transition predictions using simplified methods[J]. AIAA Journal, 2009, 47(11):2676-2684.
[13] YANG T H, ZHONG H, CHEN Y F, et al. Transition prediction and sensitivity analysis for a natural laminar flow wing glove flight experiment[J]. Chinese Journal of Aeronautics, 2021, 34(8):34-47.
[14] 杨体浩, 白俊强, 史亚云, 等. 考虑吸气分布影响的HLFC机翼优化设计[J]. 航空学报, 2017, 38(12):121158. YANG T H, BAI J Q, SHI Y Y, et al. Optimization design for HLFC wings considering influence of suction distribution[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(12):121158(in Chinese).
[15] 史亚云, 郭斌, 刘倩, 等. 基于能量观点的混合层流优化设计[J]. 北京航空航天大学学报, 2019, 45(6):1162-1174. SHI Y Y, GUO B, LIU Q, et al. Hybrid laminar flow optimization design from energy view[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(6):1162-1174(in Chinese).
[16] HAN Z H, CHEN J, ZHANG K S, et al. Aerodynamic shape optimization of natural-laminar-flow wing using surrogate-based approach[J]. AIAA Journal, 2018, 56(7):2579-2593.
[17] KENWAY G K W, MADER C A, HE P, et al. Effective adjoint approaches for computational fluid dynamics[J]. Progress in Aerospace Sciences, 2019, 110:100542.
[18] JAMESON A. Aerodynamic design via control theory[J]. Journal of Scientific Computing, 1988, 3(3):233-260.
[19] BREZILLON J, DWIGHT R P. Applications of a discrete viscous adjoint method for aerodynamic shape optimisation of 3D configurations[J]. CEAS Aeronautical Journal, 2012, 3(1):25-34.
[20] ALBRING T, SAGEBAUM M, GAUGER N R. New results in numerical and experimental fluid mechanics X[C]//19th STAB/DGLR Symposium Munich. Cham:Springer International Publishing, 2014.
[21] HE P, MADER C A, MARTINS J R R A, et al. An aerodynamic design optimization framework using a discrete adjoint approach with OpenFOAM[J]. Computers & Fluids, 2018, 168:285-303.
[22] 陈颂, 白俊强, 史亚云, 等. 民用客机机翼/机身/平尾构型气动外形优化设计[J]. 航空学报, 2015, 36(10):3195-3207. CHEN S, BAI J Q, SHI Y Y, et al. Aerodynamic shape optimization design of civil jet wing-body-tail configuration[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(10):3195-3207(in Chinese).
[23] 白俊强, 雷锐午, 杨体浩, 等. 基于伴随理论的大型客机气动优化设计研究进展[J]. 航空学报, 2019, 40(1):522642. BAI J Q, LEI R W, YANG T H, et al. Progress of adjoint-based aerodynamic optimization design for large civil aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(1):522642(in Chinese).
[24] 黄江涛, 张绎典, 高正红, 等. 基于流场/声爆耦合伴随方程的超声速公务机声爆优化[J]. 航空学报, 2019, 40(5):122505. HUANG J T, ZHANG Y D, GAO Z H, et al. Sonic boom optimization of supersonic jet based on flow/sonic boom coupled adjoint equations[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(5):122505(in Chinese).
[25] ZHANG P F, LU J, WANG Z D, et al. Adjoint-based optimization method with linearized SST turbulence model and a frozen gamma-theta transition model approach for turbomachinery design[C]//Proceedings of ASME Turbo Expo 2015:Turbine Technical Conference and Exposition, 2015.
[26] KHAYATZADEH P, NADARAJAH S. Aerodynamic shape optimization of natural laminar flow (NLF) airfoils[C]//50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston:AIAA, 2012.
[27] HALILA G L, MARTINS J R, FIDKOWSKI K J. Adjoint-based aerodynamic shape optimization including transition to turbulence effects[J]. Aerospace Science and Technology, 2020, 107:106243.
[28] LANGTRY R B, MENTER F R. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes[J]. AIAA Journal, 2009, 47(12):2894-2906.
[29] LEE J D, JAMESON A. Natural-laminar-flow airfoil and wing design by adjoint method and automatic transition prediction[C]//47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2009.
[30] RASHAD R, ZINGG D W. Aerodynamic shape optimization for natural laminar flow using a discrete-adjoint approach[J]. AIAA Journal, 2016, 54(11):3321-3337.
[31] 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.
[32] SHI Y, MADER C A, HE S, et al. Natural laminar flow wing optimization using a discrete adjoint approach[J]. Structural and Multidisciplinary Optimization, 2021, 64(5):1-22.
[33] GLEYZES C, COUSTEIX J, BONNET J L. A calculation method of leading-edge separation bubbles[M]//Numerical and physical aspects of aerodynamic flows II. Berlin:Springer, 1984:173-192.
[34] SPALART P, ALLMARAS S. A one-equation turbulence model for aerodynamic flows[C]//30th Aerospace Sciences Meeting and Exhibit. Reston:AIAA, 1992.
[35] SHI Y Y, YANG T H, BAI J Q, et al. Research of transition criterion for semi-empirical prediction method at specified transonic regime[J]. Aerospace Science and Technology, 2019, 88:95-109.
[36] 杨体浩, 白俊强, 王丹, 等. 考虑发动机干扰的尾吊布局后体气动优化设计[J]. 航空学报, 2014, 35(7):1836-1844. YANG T H, BAI J Q, WANG D, et al. Aerodynamic optimization design for after-body of tail-mounted engine layout considering interference of engines[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(7):1836-1844(in Chinese).
[37] MACK L M. Special course on stability and transition of laminar flow:AGARD-709[R]. Pairs:AGARD, 1984.
Outlines

/