基于欧拉法流线的三维表面水滴撞击特性计算方法

doi:10.7527/S1000-6893.2025.32751

Abstract

Abstract:

The computation of droplet impingement characteristics on three-dimensional surface is the primary task for ice accretion analysis and anti-icing/de-icing system design for an aircraft and its engine. To overcome the shortcomings of the traditional Eulerian method and Lagrangian method， a streamline-based Eulerian method was established to obtain three-dimensional surface water droplet impingement characteristic. This method only solves the momentum equation to derive the velocity distribution， and does not require calculating the droplet continuity equation. Droplet streamlines are generated via backward integration from the vertices of the three-dimensional surface mesh， allowing impingement characteristics to be calculated without predetermination for droplet release locations or tracking a large number of droplet trajectories. The proposed method is applied to compute droplet collection efficiencies on a three-dimensional sphere， a spinner， and an engine inlet. The results show high computational efficiency and good agreement with the data in the literature， thereby confirming the feasibility and effectiveness of the streamline-based Eulerian method for three-dimensional droplet impingement analysis. This work can provide reference for the ice accretion analysis and anti-icing/de-icing system design of aircraft and engines.

Key words: aircraft icing, droplet impingement characteristic, Eulerian method, Lagrangian method, engine

CLC Number:

V248.1

Xiaobin SHEN, Zekun YE, Jingyu ZHAO, Jietao GUO, Guiping LIN. A three-dimensional surface water droplet impingement characterization method based on Eulerian streamlines[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(11): 632751.

Figures/Tables 15

Fig.1

Table 1

Comparison of calculation methods for water droplet impingement characteristics

项目	传统拉格朗日法	传统欧拉法	欧拉流线法
理论与水滴运动计算	根据牛顿第二定律建立水滴受力运动方程；确定水滴释放位置积分获得水滴轨迹	将水滴看作连续介质建立连续性方程、动量方程，获得水滴容积系数分布、速度场	采用欧拉框架获得水滴速度场；基于速度场，从壁面节点开始进行反向积分获得水滴流线
控制方程	$d u d t = K u a - u$	$∇ ⋅ (ρ d α u) = 0$ $∇ ⋅ (ρ d α u u) = ρ d α K (u a - u)$	$∂ u ∂ t + u ⋅ ∇ u = K u a - u$
收集系数计算法	根据撞击到壁面的水滴轨迹计算收集系数	根据壁面处的水滴容积分数、速度获得收集系数	根据撞击到壁面的水滴流线计算收集系数
方法特点	① 水滴受力运动过程描述清晰，较易添加大水滴与冰晶动力学效应；② 二维简单表面的计算较为简便、高效；③ 复杂表面的水滴释放位置难以确定，三维轨迹计算量大、效率低	① 对于三维与复杂表面计算效率也很高；② 可获得整个计算域的水滴分布特性，并一次性得到所有三维表面的水滴收集系数；③ 控制方程高度非线性，易出现水滴容积分数奇异点	① 仅求解欧拉法动量方程避免水滴容积分数奇异点的出现；② 在水滴速度场上积分获得流线，适用于复杂三维表面；③ 既有欧拉框架下的水滴速度计算，又有拉格朗日框架下轨迹、收集系数的计算，过程较烦琐

Table 1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Table 2

Fig.10

Fig.11

Fig.12

Fig.13

References 40

[1]	高郭池，张波，全敬泽，等. 正常类飞机自然结冰试飞适航审定技术［J］. 航空学报， 2024， 45（1）： 128531.
	GAO G C， ZHANG B， QUAN J Z， et al. Airworthiness certification technology of normal aircraft natural icing flight test［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（1）： 128531 （in Chinese）.
[2]	赵宾宾，张恒，李杰. 翼型结冰状态复杂分离流动数值模拟综述［J］. 航空学报， 2023， 44（1）： 627211.
	ZHAO B B， ZHANG H， LI J. Review of numerical simulation on complex separated flow of iced airfoil［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（1）： 627211 （in Chinese）.
[3]	李概奇，田骏丹，吴晶峰，等. 新研民用涡轴发动机结冰适航试验［J］. 航空学报， 2025， 46（12）： 131388.
	LI G Q， TIAN J D， WU J F， et al. Icing airworthiness test on a newly developed civil turbo-shaft engine［J］. Acta Aeronautica et Astronautica Sinica， 2025， 46（12）： 131388 （in Chinese）.
[4]	易贤，任靖豪，赖庆仁，等. 大型飞机全尺寸多段翼结冰特性计算和试验［J］. 航空学报， 2025， 46（5）： 531575.
	YI X， REN J H， LAI Q R， et al. Icing characteristics of full-scale multi-element configurations of large aircraft： Computation and experiment［J］. Acta Aeronautica et Astronautica Sinica， 2025， 46（5）： 531575 （in Chinese）.
[5]	杨倩，郭晓峰，李芹，等. 基于POD和代理模型的热气防冰性能预测方法［J］. 航空学报， 2023， 44（1）： 626992.
	YANG Q， GUO X F， LI Q， et al. Hot air anti-icing performance estimation method based on POD and surrogate model［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（1）： 626992 （in Chinese）.
[6]	石达志，桑为民，李世杰，等. 基于LBM的结冰表面水滴撞击特性数值模拟［J］. 航空学报， 2023， 44（S2）： 729192.
	SHI D Z， SANG W M， LI S J， et al. Numerical simulation of water droplet impact characteristics on icing surfaces based on LBM［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（S2）： 729192 （in Chinese）.
[7]	LAURENDEAU E， BOURGAULT-COTE S， OZCER I A， et al. Summary from the 1st AIAA ice prediction workshop［C］∥AIAA AVIATION 2022 Forum. Reston： AIAA， 2022.
[8]	IULIANO E， BRANDI V， MINGIONE G， et al. Water impingement prediction on multi-element airfoils by means of eulerian and Lagrangian approach with viscous and inviscid air flow［C］∥44th AIAA Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 2006.
[9]	WRIGHT W B. User manual for the NASA Glenn ice accretion code LEWICE： Version 2.0［R］. Washington，D.C.： NASA， 1999.
[10]	SHEN X B， XIAO C H， NING Y J， et al. Research on the methods for obtaining droplet impingement characteristics in the Lagrangian framework［J］. Aerospace， 2024， 11（3）： 172.
[11]	BOURGAULT Y， BOUTANIOS Z， HABASHI W G. Three-dimensional eulerian approach to droplet impingement simulation using FENSAP-ICE， Part 1： Model， algorithm， and validation［J］. Journal of Aircraft， 2000， 37（1）： 95-103.
[12]	WIROGO S， SRIRAMBHATLA S. An eulerian method to calculate the collection efficiency on two and three dimensional bodies［C］∥41st Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 2003.
[13]	王利平，王福新，刘洪. 过冷大水滴环境粒径分布模拟方法研究进展［J］. 航空学报， 2024， 45（S1）： 730570.
	WANG L P， WANG F X， LIU H. Research progress on simulation methods of drop diameter distribution in supercooled large drop icing conditions［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（S1）： 730570 （in Chinese）.
[14]	刘宗辉，卜雪琴，包佳仪，等. 部分融化冰晶撞击表面临界破碎速度实验［J］. 航空学报， 2025， 46（14）： 131558.
	LIU Z H， BU X Q， BAO J Y， et al. Experiment on critical fragmentation velocity of partially melted ice particles impacting a rigid surface［J］. Acta Aeronautica et Astronautica Sinica， 2025， 46（14）： 131558 （in Chinese）.
[15]	XIE L， LI P Z， CHEN H， et al. Robust and efficient prediction of the collection efficiency in icing accretion simulation for 3D complex geometries using the Lagrangian approach I： An adaptive interpolation method based on the restricted radial basis functions［J］. International Journal of Heat and Mass Transfer， 2020， 150： 119290.
[16]	SENGUPTA B， ESMAEILIFAR E， SADEGH ARAGHIZADEH M， et al. Rotor-fuselage-intake aerodynamics and icing using vortex and eulerian-Lagrangian computational fluid dynamics methods［J］. AIAA Journal， 2025， 63（3）： 909-930.
[17]	ZHU C X， TAO M J， ZHAO N， et al. Study of droplet shadow zone of aircraft wing with diffusion effects［J］. AIAA Journal， 2019， 57（8）： 3339-3348.
[18]	王昭力，曾涛，周志宏，等. TVD格式在水滴流场数值模拟中的应用［J］. 航空学报， 2022， 43（12）： 627010.
	WANG Z L， ZENG T， ZHOU Z H， et al. Application of TVD scheme in numerical simulation of water droplet field［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（12）： 627010 （in Chinese）.
[19]	WU J， XU Q Y， WU F， et al. Droplet collection efficiency regularity of NACA0012 airfoil based on the eulerian method［J］. Aerospace， 2023， 10（5）： 412.
[20]	TONG X L， LUKE E. Eulerian simulations of icing collection efficiency using a singularity diffusion model［C］∥43rd AIAA Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 2005.
[21]	LIU Y， QU J G， YI X， et al. A Monte Carlo Lagrangian droplet solver with backpropagation neural network for aircraft icing simulation［J］. Transactions of Nanjing University of Aeronautics and Astronautics， 2023， 40（5）： 566-577.
[22]	曾涛，王昭力，熊华杰，等. 复杂构型水滴收集率的拉格朗日快速算法研究［J］. 航空动力学报， 2025， 40（7）： 20220539.
	ZENG T， WANG Z L， XIONG H J， et al. Research on a fast Lagrangian algorithm for water droplet collection efficiency in complex configurations［J］. Journal of Aerospace Power， 2025， 40（7）： 20220539 （in Chinese）.
[23]	任靖豪，王强，李维浩，等. 基于梯度下降的水滴收集率计算方法［J］. 航空学报， 2023， 44（4）： 126381.
	REN J H， WANG Q， LI W H， et al. A prediction algorithm of collection efficiency based on gradient descent method［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（4）： 126381 （in Chinese）.
[24]	BELLOSTA T， BALDAN G， SIRIANNI G， et al. Lagrangian and Eulerian algorithms for water droplets in in-flight ice accretion［J］. Journal of Computational and Applied Mathematics， 2023， 429： 115230.
[25]	WANG S， LOTH E. Droplet impact efficiency on aerodynamic surfaces with a globally eulerian/locally Lagrangian method［J］. Journal of Aircraft， 2017， 54（1）： 104-113.
[26]	ZAYNI M K， BLANCHET M， LAURENDEAU E. Lagrangian particle tracking for ice accretion applications［C］∥AIAA Aviation Forum and Ascend 2024. Reston： AIAA， 2024.
[27]	郑梅，冯丽娟，秦娜，等. 短舱防冰系统三维内外流耦合计算方法［J］. 航空学报， 2023， 44（1）： 627425.
	ZHENG M， FENG L J， QIN N， et al. 3D computational method for conjugate heat transfer between internal and external flow of nacelle anti-icing system［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（1）： 627425 （in Chinese）.
[28]	吴佩佩，晏涛，马赛强，等. 发动机唇口电热防冰系统性能仿真［J］. 航空动力学报， 2020， 35（10）： 2056-2063.
	WU P P， YAN T， MA S Q， et al. Numerical simulation of performance of engine lip electro-thermal anti-icing system［J］. Journal of Aerospace Power， 2020， 35（10）： 2056-2063 （in Chinese）.
[29]	TORMEN D， ZANON A， DE GENNARO M. Ice protection system design for the next generation civil tiltrotor engine intake［J］. SAE Technical Paper Series， 2023， 1： 2023-1-1374.
[30]	JUNG S K， MYONG R S. A second-order positivity-preserving finite volume upwind scheme for air-mixed droplet flow in atmospheric icing［J］. Computers & Fluids， 2013， 86： 459-469.
[31]	BLANCHET M， BOURGAULT-COTE S， LAURENDEAU E. Conservative hyperbolic droplet solver for aircraft icing［C］∥AIAA Aviation 2022 Forum. Reston： AIAA， 2022.
[32]	陈希，招启军. 考虑遮蔽区影响的旋翼三维水滴撞击特性计算新方法［J］. 航空学报， 2017， 38（6）： 120745.
	CHEN X， ZHAO Q J. New method for predicting 3-D water droplet impingement on rotor considering influence of shadow zone［J］. Acta Aeronautica et Astronautica Sinica， 2017， 38（6）： 120745 （in Chinese）.
[33]	SOTOMAYOR-ZAKHAROV D， BANSMER S. Finite-volume Eulerian solver for simulation of particle-laden flows for icing applications［J］. Computers & Fluids， 2021， 228： 105009.
[34]	BOURGAULT Y， HABASHI W G， DOMPIERRE J， et al. A finite element method study of Eulerian droplets impingement models［J］. International Journal for Numerical Methods in Fluids， 1999， 29（4）： 429-449.
[35]	LU Y J， SUN Q Q， CHOI K S， et al. Joint effects of virtual surfaces on anti-icing and drag reduction［J］. AIAA Journal， 2025， 63（4）： 1502-1511.
[36]	GAO X， QIU B R， WANG Z J， et al. Influence of spinner shape on droplet impact over rotating spinners［J］. Aerospace， 2023， 10（1）： 68.
[37]	BIDWELL C， STANLEY MOHLER Y R. Collection efficiency and ice accretion calculations for a sphere， a swept MS（1）-317 wing， a swept NACA-0012 wing tip， an axisymmetric inlet， and a Boeing 737-300 inlet［C］∥33rd Aerospace Sciences Meeting and Exhibit. Reston： AIAA， 1995.
[38]	JIA W， ZHANG F. Numerical investigation of supercooled large droplets impingement characteristics of the rotating spinner［J］. International Journal of Aerospace Engineering， 2024， 2024（1）： 1683744.
[39]	ZANON A， PAGE J， TORMEN D， et al. 1st AIAA Ice Prediction Workshop： AIT numerical simulation results［C］∥AIAA Aviation 2022 Forum. Reston： AIAA， 2022.
[40]	IULIANO E， MINGIONE G， DE DOMENICO F， et al. An eulerian approach to three-dimensional droplet impingement simulation in icing environment［C］∥AIAA Atmospheric and Space Environments Conference. Reston： AIAA， 2010.

工况	Case-131	Case-132
MVD/μm	20.36	20.36
马赫数Ma	0.232 8	0.231 2
静温/K	283.15	279.63
静压/Pa	95 492	95 492
进气质量流量/（kg·s^-1）	7.80	10.41

A three-dimensional surface water droplet impingement characterization method based on Eulerian streamlines

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 15

References 40

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	Yuhan ZHANG, Lei FU, Ruoyang LIU, Ning MA, Ming ZHANG, Xu DONG, Zhenyu LI, Dakun SUN, Xiaofeng SUN. Effect of a drooped intake on performance of compressor [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(7): 632676-632676.
[2]	Haideng ZHANG, Yun WU, Yingwei TIAN, Nan TANG, Yueren ZUO. Research progress and prospect of swirl/total pressure combined distortion test and evaluation [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(7): 632790-632790.
[3]	Aohua CHEN, Linquan CHEN, Qiu WU, Junwei LI, Qiang LI, Yi LI. Influence of combustion chamber cavity on structural damping characteristics of solid rocket motors [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(6): 132527-132527.
[4]	Donghuan WANG, Hai JIN, Dongkai WAN, Jun WANG, Hong XIAO. Real-time monitoring and evaluation method for aero-engine performance degradation based on performance digital twin [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(5): 132459-132459.
[5]	Faning SHAO, Chao YANG, Pingting CHEN, Feilong WANG, Weichen ZHAO, Bo NING, Junkui MAO. Warm-up characteristics and thrust impact of aero-engines based on fluid-thermal-solid coupled simulation [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(2): 132104-132104.
[6]	Zhen JIA, Chendi LI, Kunyu WEI, Hongda DONG, Xiaofan HE. Speed spectrum development method for engine fan disk [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(2): 232110-232110.
[7]	Wei TIAN, Yanfei LIU, Shaoping ZHANG, Wangyang ZHANG, Dongzhe ZHANG, Huiming GUO, Zuojun LI. Research progress and application of lattice materials in aero-engines [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(11): 432073-432073.
[8]	Ying WANG, Yang LI, Chaoqian CHENG, Zongxia JIAO. Thermal load analysis for aeroengine oil system with extended flight profile [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(1): 632005-632005.
[9]	Xueqi CHEN, Zuoxiang ZHANG, Dong WANG, Yanhong MA, Jie HONG. Loading of intermediate bearing-support structure and its impact on structural integrity [J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(1): 232061-232061.
[10]	Fang ZHANG, Weibin XIANG, Kai XIAO, Siqi XIAO, Liang XIANG, Bing WANG. Simulation and experiment of attitude control propulsion system’s dynamic characteristics [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(S1): 732329-732329.
[11]	Haiyu ZHAO, Li ZHOU, Wenjian DENG, Zhanxue WANG. Aerodynamic interference effects of propfan engine inlet and contra-rotating propfan [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(8): 631042-631042.
[12]	Feiteng LUO, Zhenming QU, Haitao LI, Xinke LI, Dahao YAO, Wenjuan CHEN, Yaosong LONG, Baoxi WEI, Yanjin MAN, Fujiang YANG, Qiang CHENG, Wubin KONG. Research progress and key issues of inlet pre-injection at hypersonic condition [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(8): 631189-631189.
[13]	Guanwei YAO, Gaowen LIU, Yan CHEN, Xiaozhi KONG, Aqiang LIN. Forward design of high-performance turbine low-radius pre-swirl system [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(7): 130832-130832.
[14]	Yihao XU, Pengcheng DONG, Junchao ZHENG, Chunqing TAN, Hailong TANG. Overall performance optimization method of adaptive cycle propulsion system [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(7): 130987-130987.
[15]	Wenfeng DING, Nian WAN, Biao ZHAO, Yucan FU, Jiuhua XU. Research status and tendency of advanced manufacturing theory and technology in aerospace [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(6): 531309-531309.