Special Topic: Anti-icing and De-icing Technology for Aeroengines

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

  • Xiaobin SHEN ,
  • Zekun YE ,
  • Jingyu ZHAO ,
  • Jietao GUO ,
  • Guiping LIN
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  • 1.School of Aeronautic Science and Engineering,Beihang University,Beijing 100191,China
    2.Hangzhou International Innovation Institute,Beihang University,Hangzhou 311115,China

Received date: 2025-09-03

  Revised date: 2025-10-20

  Accepted date: 2025-12-01

  Online published: 2025-12-09

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.

Cite this article

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 AERONAUTICAET ASTRONAUTICA SINICA, 2026 , 47(11) : 632751 -632751 . DOI: 10.7527/S1000-6893.2025.32751

References

[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202445(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 Sinica202445(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202344(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 Sinica202344(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202546(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 Sinica202546(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202546(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 Sinica202546(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202344(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 Sinica202344(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202344(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 Sinica202344(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]. Aerospace202411(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 Aircraft200037(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202445(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 Sinica202445(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202546(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 Sinica202546(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 Transfer2020150: 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 Journal202563(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 Journal201957(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202243(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 Sinica202243(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]. Aerospace202310(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 Astronautics202340(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202540(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 Power202540(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202344(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 Sinica202344(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 Mathematics2023429: 115230.
[25] WANG S, LOTH E. Droplet impact efficiency on aerodynamic surfaces with a globally eulerian/locally Lagrangian method[J]. Journal of Aircraft201754(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202344(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 Sinica202344(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202035(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 Power202035(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 Series20231: 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 & Fluids201386: 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201738(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 Sinica201738(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 & Fluids2021228: 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 Fluids199929(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 Journal202563(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]. Aerospace202310(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 Engineering20242024(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.
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