深度动态失速数值模拟方法验证与确认

doi:10.7527/S1000-6893.2025.32671

Abstract

Abstract:

Dynamic stall is a common unsteady aerodynamic phenomenon encountered by rotorcraft and wind turbines， and its numerical simulation is of significant value for engineering prediction and mechanism analysis. However， current research predominantly compares a single simulation with experimental data and lacks an in-depth analysis of the discrepancies caused by various numerical parameters， leading to ambiguous reliability boundaries and limiting the capability of Computational Fluid Dynamics （CFD） to transition from a reproductive tool to a predictive one. Focusing on the pitching oscillation of a NACA0012 airfoil in a deep dynamic stall state， the effects of epistemic uncertainty introduced by key modeling choices were evaluated and quantified. The discrepancies in simulation results caused by key parameters， including grid types， turbulence models， pressure-velocity coupling methods， and boundary conditions， were systematically investigated， and the consistency of the numerical simulation with experimental data was assessed using time-history curves and hysteresis loops. The results indicate that with a proper configuration of modeling parameters， the simulation can closely approximate the experimental data， exhibiting higher fidelity， particularly during the critical stall-vortex evolution phase. Through a systematic comparative analysis of parameter combinations， a numerical simulation modeling reference scheme with high stability and accuracy was established， and by using interval quantification methods， the uncertainty band for the aerodynamic coefficients of the benchmark case was established. This provides practical guidance for subsequent numerical simulation studies of dynamic stall.

Key words: dynamic stall, rotorcraft, aerodynamic characteristics, NACA0012 airfoil, Computational Fluid Dynamics (CFD)

CLC Number:

V219

Jiayi LI, Haiqing SI, Hao DONG, Jingxuan QIU, Tianyu XIA. Verification and validation of deep dynamic stall numerical simulation method[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(6): 132671.

Figures/Tables 23

Fig.1

Table 1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

Fig.13

Fig.14

Fig.15

Fig.16

Fig.17

Fig.18

Fig.19

Fig.20

Table 2

Periodic fluctuations and fitting errors in numerical simulation results

统计量	RMSE/ $10 - 3$	绝对误差上限/ $10 - 2$	绝对误差下限/ $10 - 2$	绝对误差平均值/ $10 - 19$
$C L$	$4.48$	$3.99$	$- 9.02$	$- 8.00$
$C D$	$2.36$	$1.82$	$- 3.55$	$1.09$
$C m$	$2.12$	$3.31$	$- 1.61$	$0.246$

Table 2

Fig.21

References 38

[1]	CHEN B， ZHANG Z L， HUA X G， et al. Enhancement of flutter stability in wind turbines with a new type of passive damper of torsional rotation of blades［J］. Journal of Wind Engineering and Industrial Aerodynamics， 2018， 173： 171-179.
[2]	井思梦，赵国庆，招启军，等. 翼型动态失速气动力二次峰值数值模拟研究［J］. 南京航空航天大学学报（自然科学版）， 2022， 54（2）： 191-202.
	JING S M， ZHAO G Q， ZHAO Q J， et al. Numerical research on secondary peak of aerodynamic forces of airfoil under dynamic stall［J］. Journal of Nanjing University of Aeronautics and Astronautics （Natural Science Edition）， 2022， 54（2）： 191-202 （in Chinese）.
[3]	招启军，井思梦，赵国庆，等. 旋翼翼型动态失速机理及非定常设计研究进展［J］. 空气动力学学报， 2021， 39（6）： 70-84.
	ZHAO Q J， JING S M， ZHAO G Q， et al. Review of research progress on dynamic stall mechanism and unsteady design of rotor airfoils［J］. Acta Aerodynamica Sinica， 2021， 39（6）： 70-84 （in Chinese）.
[4]	张卫国，李国强，李栋，等. 旋翼翼型动态风洞试验技术研究［J］. 实验流体力学， 2023， 37（2）： 78-93.
	ZHANG W G， LI G Q， LI D， et al. Research on dynamic wind tunnel test technology of rotor airfoil［J］. Journal of Experiments in Fluid Mechanics， 2023， 37（2）： 78-93 （in Chinese）.
[5]	LEISHMAN J G， NGUYEN K Q. State-space representation of unsteady airfoil behavior［J］. AIAA Journal， 1990， 28（5）： 836-844.
[6]	张夏阳，高陈诚，招启军，等. 前飞状态可变弯度翼型/旋翼气动特性［J］. 航空学报， 2024， 45（24）： 630609.
	ZHANG X Y， GAO C C， ZHAO Q J， et al. Aerodynamic characteristics of variable-camber airfoil/rotor in forward flight［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（24）： 630609 （in Chinese）.
[7]	井思梦，招启军，杨柳青，等. 直升机旋翼动态失速研究新进展［J］. 南京航空航天大学学报（自然科学版）， 2025， 57（2）： 205-225.
	JING S M， ZHAO Q J， YANG L Q， et al. New progress in research on dynamic stall of helicopter rotors［J］. Journal of Nanjing University of Aeronautics and Astronautics （Natural Science Edition）， 2025， 57（2）： 205-225 （in Chinese）.
[8]	王清. 旋翼动态失速力学机理及气动外形优化研究［D］. 南京：南京航空航天大学， 2017.
	WANG Q. Investigations on dynamic stall mechanism and aerordynamic shape optimization of rotor［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2017 （in Chinese）.
[9]	井思梦. 旋翼动态失速流动机理及翼型非定常设计研究［D］. 南京：南京航空航天大学， 2024.
	JING S M. Research on dynamic stall flow physics of rotor and unsteady design of rotor airfoil［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2024 （in Chinese）.
[10]	JING S M， LU F， MA L， et al. Dynamic stall mechanisms of pitching airfoil： IDDES study across different Mach numbers［J］. Applied Sciences， 2025， 15（13）： 7309.
[11]	JING S M， ZHAO G Q， GAO Y， et al. Effects of leading edge radius on stall characteristics of rotor airfoil［J］. Aerospace， 2024， 11（6）： 470.
[12]	卞威. 旋翼非定常气动特性高精度模拟方法及桨/涡干扰机理研究［D］. 南京：南京航空航天大学， 2024.
	BIAN W. Investigations on high-precision numerical simulation method of rotor unsteady aerodynamic characteristics and blade vortex interaction mechanism［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2024 （in Chinese）.
[13]	招启军，赵国庆，王清，等. 先进旋翼设计空气动力学［M］. 北京：科学出版社， 2020.
	ZHAO Q J， ZHAO G Q， WANG Q， et al. Advanced rotor design aerodynamics［M］. Beijing： Science Press， 2020 （in Chinese）.
[14]	李游. 基于介质阻挡放电等离子体的旋翼流动分离主动控制研究［D］. 南京：南京航空航天大学， 2023.
	LI Y. Active control study of rotor flow separation based on dielectric barrier discharge plasma［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2023 （in Chinese）.
[15]	罗楠. 基于气动力代理模型的后缘襟翼旋翼振动载荷分析［D］. 南京：南京航空航天大学， 2023.
	LUO N. Aerodynamic surrogate modeling approach for trailing-edge flaps rotor vibration analysis［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2023 （in Chinese）.
[16]	CAMACHO E A R， SILVA A R R， MARQUES F D. Predicting airfoil dynamic stall loads using neural networks［J］. Aerospace Science and Technology， 2025， 165： 110466.
[17]	RAUL V， LEIFSSON L. Multifidelity aerodynamic shape optimization for airfoil dynamic stall mitigation using manifold mapping［J］. Journal of Computational Science， 2024， 75： 102213.
[18]	LUO D H， LU B X， GENG H C， et al. Dynamic stall control of an offshore wind turbine airfoil using a leading-edge microcylinder［J］. Ocean Engineering， 2024， 313： 119695.
[19]	GONG J Y， PENG W Q， LUO Z B， et al. Comparison of aerodynamic characteristics of wing dynamic stall under three typical jets control［J］. Chinese Journal of Aeronautics， 2025， 38（6）： 103284.
[20]	梁霄，张培红，王瑞利，等. PBX9502冲击Hugoniot曲线的参数标定和不确定度量化［J］. 弹道学报， 2024， 36（1）： 104-110.
	LIANG X， ZHANG P H， WANG R L， et al. Parameter calibration and uncertainty quantification of shock Hugoniot curve of PBX9502［J］. Journal of Ballistics， 2024， 36（1）： 104-110 （in Chinese）.
[21]	段于辉，张建新，冯春早，等. 虑及认知不确定性的曲线加筋壁板承载性能智能预测方法［J］. 兵器装备工程学报， 2025， 46（8）： 259-266.
	DUAN Y H， ZHANG J X， FENG C Z， et al. Intelligent prediction method for load-carrying of curvilinearly stiffened panel considering epistemic uncertainty［J］. Journal of Ordnance Equipment Engineering， 2025， 46（8）： 259-266 （in Chinese）.
[22]	杨懿宸，郑友琦，朱庆福，等. 基于启明星临界实验装置的小型铅堆确定论中子学计算方法研究及验证［J］. 原子能科学技术， 2025， 59（3）： 644-655.
	YANG Y C， ZHENG Y Q， ZHU Q F， et al. Deterministic neutronics calculation method of small lead-cooled reactor based on Venus-Ⅱ criticality experimental facility and its verification［J］. Atomic Energy Science and Technology， 2025， 59（3）： 644-655 （in Chinese）.
[23]	陈江涛，肖维，赵炜，等. 计算流体力学验证与确认研究进展［J］. 力学进展， 2023， 53（3）： 626-660.
	CHEN J T， XIAO W， ZHAO W， et al. Advances in verification and validation in computational fluid dynamics［J］. Advances in Mechanics， 2023， 53（3）： 626-660 （in Chinese）.
[24]	National Research Council， Division on Engineering and Physical Sciences， Board on Mathematical Sciences and Their Applications， et al. Assessing the reliability of complex models： Mathematical and statistical foundations of verification， validation， and uncertainty quantification［M］. Washington， D.C.： National Academies Press， 2012.
[25]	李耀. 基于民机真实飞行数据的CFD验证与确认研究［D］. 南京：南京航空航天大学， 2022.
	LI Y. CFD verification and validation research based on real flight data of civil aircraft［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2022 （in Chinese）.
[26]	AIAA. Recommended practice for code verification in computational fluid dynamics ：AIAA R-141-2021［S］. Reston： AIAA， 2021.
[27]	GHIA U， BAYYUK S， HABCHI S， et al. The AIAA code verification project： Test cases for CFD code verification［C］∥ 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Reston： AIAA， 2010.
[28]	夏侯唐凡，陈江涛，邵志栋，等. 随机和认知不确定性框架下的CFD模型确认度量综述［J］. 航空学报， 2022， 43（8）： 25716.
	XIAHOU T F， CHEN J T， SHAO Z D， et al. Model validation metrics for CFD numerical simulation under aleatory and epistemic uncertainty［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（8）： 25716 （in Chinese）.
[29]	熊芬芬，李泽贤，刘宇，等. 基于数值模拟的工程设计中参数不确定性表征方法研究综述［J］. 航空学报， 2023， 44（22）： 28611.
	XIONG F F， LI Z X， LIU Y， et al. A review of characterization methods for parameter uncertainty in engineering design based on numerical simulation［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（22）： 28611 （in Chinese）.
[30]	李原，尹凡夫，高伟，等. 基于改进LB动态失速模型的翼型非线性气弹分析［J］. 太阳能学报， 2023， 44（7）： 402-408.
	LI Y， YIN F F， GAO W， et al. Nonlinear aeroelastic analysis of 2D airfoil based on modified LB dynamic stall model［J］. Acta Energiae Solaris Sinica， 2023， 44（7）： 402-408 （in Chinese）.
[31]	MCALISTER K W， PUCCI S L， MCCROSKEY W J， et al. An experimental study of dynamic stall on advanced airfoil section. Volume 2： Pressure and force data： USAAVRADCOM-TR-82-A-8-VOL-2［R］. Washington D.C.： NASA， 1982.
[32]	MANI M R， DORGAN A J. A perspective on the state of aerospace computational fluid dynamics technology［J］. Annual Review of Fluid Mechanics， 2023， 55： 431-457.
[33]	王年华，常兴华，马戎，等. HyperFLOW软件非结构网格亚跨声速湍流模拟的验证与确认［J］. 力学学报， 2019， 51（3）： 813-825.
	WANG N H， CHANG X H， MA R， et al. Verification and validation of HyperFLOW solver for subsonic and transonic turbulent flow simulations on unstructured/hybrid grids［J］. Chinese Journal of Theoretical and Applied Mechanics， 2019， 51（3）： 813-825 （in Chinese）.
[34]	CELIK I B， GHIA U， ROACHE P J， et al. Procedure for estimation and reporting of uncertainty due to discretization in CFD applications［J］. Journal of Fluids Engineering， 2008， 130（7）： 1-4.
[35]	刘超群. Liutex-涡定义和第三代涡识别方法［J］. 空气动力学学报， 2020， 38（3）： 413-431.
	LIU C Q. Liutex-third generation of vortex definition and identification methods［J］. Acta Aerodynamica Sinica， 2020， 38（3）： 413-431 （in Chinese）.
[36]	李朋华，邱明，公平，等. 保持架间隙对角接触球轴承气帘效应的影响［J/OL］. 航空动力学报，（2025-02-18）［2025-08-11］. .
	LI P H， QIU M， GONG P， et al. Influence of cage clearance on air curtain effect of angular contact ball bearing［J/OL］. Journal of Aerospace Power，（2025-02-18）［2025-08-11］. （in Chinese）.
[37]	验证、确认和不确定性量化数学基础委员会，数学科学及其应用委员会，工程和物理科学部，等. 复杂模型的可靠性评估：验证、确认和不确定度量化的数学与统计基础［M］. 陈坚强，吴晓军，赵炜，等译. 北京：国防工业出版社， 2023.
	Committee on Mathematical Foundations of Verification， Validation， and Quantification Uncertainty， Board on Mathematical Sciences and Their Applications， Division on Engineering and Physical Sciences， et al. Assessing the reliability of complex models： Mathematical and statistical foundations of verification， validation， and uncertainty quantification［M］. CHEN J Q， WU X J， ZHAO W， et al， translated. Beijing： National Defense Industry Press， 2023 （in Chinese）.
[38]	MCCROSKEY W J， MCALISTER K W， CARR L W， et al. An experimental study of dynamic stall on advanced airfoil sections. Volume 1： Summary of the experiment： USAAVRADCOM-TR-82-A-8-VOL-1［R］. Washington D.C.： NASA， 1982.

网格	背景网格节点数	前景网格节点数	网格单元数/10⁴	重叠处网格面积比
G1	234×234	437×110	10.18	1.001 6
G2	285×285	481×148	15.12	1.003 5
G3	351×351	589×180	22.78	0.998 2
G4	432×432	777×205	34.41	1.002 9
G5	529×529	949×250	51.48	1.001 6
G6	651×651	1 153×309	77.73	1.002 3

Verification and validation of deep dynamic stall numerical simulation method

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 23

References 38

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Wangqing ZHU, Chenkai CAO, Guoqing ZHAO, Qinghua ZHU, Haoyu HU. Aerodynamic interference of scissor tail rotor and influence of unconventional layout parameters [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(S1): 732181-732181.
[2]	Lingling CHEN, Yang ZHANG, Yongqiang SHI, Qingzhen YANG. Film cooling performance/nozzle performance/infrared radiation characteristics of a vector nozzle [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(8): 631139-631139.
[3]	He JIA, Wei JIANG, Wenlong BAO, Xin XU, Wei RONG, Li YU. Transonic/supersonic aerodynamic characteristics and fluid-structure interaction mechanism of flexible parachutes for planetary exploration [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(1): 630369-630369.
[4]	Guangning LI, Kunpeng LEI, Xiaomin AN, Min XU, Yong XU. Numerical flight simulation of an airfoil with time varing Mach number effect acrossing transonic region [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(S1): 730875-730875.
[5]	Qi LIU, Yongjie SHI, Zhiyuan HU, Guohua XU. Parameter effects analysis on aerodynamic and aeroacoustic characteristics of coaxial rigid rotor [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 528856-528856.
[6]	Dazhi SUN, Xi CHEN, Weicheng BAO, Wei BIAN, Qijun ZHAO. Interferences of high-speed helicopter fuselage on aerodynamic and aeroacoustic source characteristics of propeller [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 529142-529142.
[7]	Yurou DAI, Jian LI, Xiaopeng XUE, Wei RONG. Aerodynamic characteristics of supersonic disk-gap-band parachute with different reefing ways [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(7): 128811-128811.
[8]	Guoqiang LI, Kuihui SONG, Chen QIN, Guangyin ZHAO, Linxin WU, Yongdong YANG. Test on active control of airfoil dynamic stall based on trailing edge flap [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(3): 128699-128699.
[9]	Xiayang ZHANG, Chencheng GAO, Qijun ZHAO, Jiahui LIANG. Aerodynamic characteristics of variable-camber airfoil/rotor in forward flight [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(24): 630609-630609.
[10]	Li LI, Yihua LIANG, Yong YANG, Junsheng WU. WiseCFD V2023: A software framework with open architecture to support verification and validation and credibility assessment of CFD software [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(20): 630440-630440.
[11]	Bin LI, Zenan ZHANG, Fei JIA, Jian SUN, Yanju LIU, Jinsong LENG. Research status and development trend of morphing wingtip technology [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(19): 30042-030042.
[12]	Yihui HAN, Jun HU, Yong YU, Jianqiao YU. Wind tunnel experimental verification of aerodynamic control force of cross⁃shaped flexible control surface [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(13): 129280-129280.
[13]	Siyuan CHANG, Yao XIAO, Guangli LI, Zhongwei TIAN, Kaikai ZHANG, Kai CUI. Effect of wing dihedral and anhedral angles on hypersonic aerodynamic characteristics of high-pressure capturing wing configuration [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(8): 127349-127349.
[14]	Wenbo CAO, Yilang LIU, Weiwei ZHANG. Accelerated convergence method for fluid dynamics solvers based on reduced⁃order model and gradient optimization [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(6): 127090-127090.
[15]	Wenlong BAO, He JIA, Xiaopeng XUE, Xuejiao HUANG, Shuyi GAO, Wei RONG, Qi WANG, Zhuangzhi WU. Influence of ‘windows’ structure on inflation process of ringsail parachute [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(5): 226936-226936.