航空学报2026，Vol.47Issue(5)：41-54,14.DOI:10.7527/S1000-6893.2025.32452
基于预解分析的低雷诺数翼型优化设计方法
A resolvent-analysis-based optimization design method for airfoils at low Reynolds number
摘要
Abstract
Control of flow separation at high angles of attack plays a crucial role in enhancing the aerodynamic perfor-mance of airfoils at low Reynolds number,as well as in reducing flow-induced structural vibrations and noise.To ad-dress the inefficiency of current empirical trial-and-error and a posteriori based flow control methods,we propose a novel approach that integrates resolvent analysis with airfoil optimization design to achieve passive surface deformation control of unsteady flows.First,we construct an input-output dynamical model of the flow system.The excitation with the strongest response(i.e.,forcing modes),the states with the highest receptivity(i.e.,response modes)and the amplification between them(i.e.,resolvent gains)under harmonic inputs at varying frequencies can be identified through resolvent analysis.Second,a quantitative correlation between the resolvent gain and flow stability is estab-lished.When the flow system satisfies the rank-1 approximation condition,a reduction in the maximum resolvent gain directly corresponds to an improvement in flow stability.Finally,an efficient shape optimization framework is devel-oped,with the objective function defined as the minimization of the maximum gain,and the optimization process com-bining a penalty function approach with the nonlinear conjugate gradient method.The NACA0012 airfoil under the de-sign condition Ma=0.1,Re=200,angle of attack 18° is selected as the test case,and the two optimized airfoils are ob-tained by varying the penalty parameters.The computational results demonstrate that,under the condition of no loss or even an improvement in aerodynamic performance at small angles of attack,the maximum resolvent gain of the two airfoils is reduced by 63.49%and 54.44%,respectively.The flow stability at supercritical angles of attack is signifi-cantly enhanced,with the amplitude of lift fluctuations attenuating by an average of 16.20%and 13.79%.Addition-ally,the time-averaged drag coefficient decreases by 2.44%and 1.84%,respectively.Analysis of the flow field evolu-tion reveals that the alternating generation and shedding of leading-edge and trailing-edge separation vortices at high angles of attack lead to significant lift oscillations.The shape optimization effectively suppresses flow separation,achieving a synergistic improvement in both the aerodynamic performance and flow stability of the optimized airfoils.This study provides new theoretical guidance for airfoil separation flow control and establishes a resolvent-analysis-based shape optimization design method that is anticipated to be applicable to separation flow problems involving vari-ous types of flow instabilities.关键词
大攻角分离/预解分析/外形优化/被动控制/线性失稳Key words
flow separation at high angles of attack/resolvent analysis/shape optimization/passive control/linear instability分类
航空航天引用本文复制引用
袁昊,寇家庆,张伟伟..基于预解分析的低雷诺数翼型优化设计方法[J].航空学报,2026,47(5):41-54,14.基金项目
国家重点研发计划(2024YFB3310401) （2024YFB3310401）
陕西省自然科学基础研究计划(2025JC-YBQN-087) （2025JC-YBQN-087）
中央高校基本科研业务费专项资金(G2024KY05101) National Key Research and Development Program of China(2024YFB3310401) （G2024KY05101）
Natural Science Basic Research Program of Shaanxi(2025JC-YBQN-087) （2025JC-YBQN-087）
Fundamental Research Funds for the Central Universities(G2024KY05101) （G2024KY05101）
