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铝液滴撞击曲面的流动特性分析

李逢超 付宇 李超 杨建刚 胡春波

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Citation:

铝液滴撞击曲面的流动特性分析

李逢超, 付宇, 李超, 杨建刚, 胡春波

Flowing characteristics of aluminum droplets impacting curved surface

Li Feng-Chao, Fu Yu, Li Chao, Yang Jian-Gang, Hu Chun-Bo
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  • 为揭示高表面张力的铝液滴撞击弯曲壁面的铺展机制, 基于流体体积方法建立了铝液滴撞壁的数值计算模型, 通过分析韦伯数(We)、奥内佐格数(Oh)以及壁面曲率(k)对液滴碰壁过程的影响规律, 探索了铝液滴在曲面上的铺展特性与流动机理. 研究结果表明: 随着We的增大, 铝液滴的撞壁行为模式依次表现为黏附、反弹以及破碎射流; 由于铺展和回缩过程都会产生能量耗散, 因此液滴回缩速度要小于其铺展速度. 在撞壁过程中, 接触点处产生了两次压力峰和速度峰, 分别出现在撞壁时刻与即将反弹时刻. 随着k的增加, 液滴的最大铺展系数不断增加, 且在平面上最小, 但曲率变化对液滴铺展速度的影响并不突出. 基于计算结果, 通过引入k对铺展系数预测模型作出了修正. 同时, 基于能量守恒定律, 对铝液滴在曲面上的流动过程进行分析, 建立了多因素耦合作用下的铺展系数计算模型. 与撞击平面相比, 液滴在曲面上的铺展系数不仅与液滴的运动参数、壁面的润湿性有关, 还与壁面曲率与液滴曲率之比有关. 本文提出的两种预测模型均能为实际的工程应用提供参考依据.
    In order to reveal the mechanism of reaction between aluminum droplet and curved wall, a numerical calculation model based on the volume of fluid method of aluminum droplet impacting curved wall is established. By analyzing the influence law of Weber number, Ohnesorge number and wall curvature on the process of droplet impacting the wall, the spreading characteristics and flow mechanism of droplet on curved surface are studied. The results show that the flow characteristics of aluminum droplets after impacting the wall are affected not only by inertial force, surface tension, and viscous force, but also by the structure of the wall. The behavior patterns of the droplets contain adhesion, rebound and splash under different Weber numbers. Because energy dissipation is produced in both spreading process and retracting process, the retracting speed of droplet is always less than its spreading speed. During the flow of the droplet, there are two pressure peaks and velocity peaks at the contact point, while the two peaks appear respectively at the moment when the droplet impacts the wall and when the droplet is about to rebound. In the behavioral mode of rebound, as Ohnesorge number increases, the maximum spreading diameter of the droplet gradually decreases, and the contact time is shorter. In the behavioral mode of adhesion, the spreading radius of the droplets is of oscillatory decay. Within the same period, the maximum spreading coefficient of the larger-Ohnesorge number droplets is smaller, and the decay rate is faster and the oscillation period is shorter. With the increase of wall curvature, the maximum spreading coefficient of droplet increases and that on the plane is the minimum. Based on the calculation results, the empirical formula is revised. Compared with the previous formula, it can well predict the maximum spreading coefficient on the curved surface, whose average error is within 3%. Further, according to the conservation of energy, theoretical models which predict the maximum spreading coefficients when droplets impact a curved and plate wall are also established. Compared with the scenario on the plane, the spreading coefficient of droplet on the curved surface is related to not only the motion parameters of droplet and the wettability of wall surface, but also the ratio of wall curvature to droplet curvature. More importantly, the new theoretical model takes into account the coupling effects of Weber number, Reynolds number, curvature ratio and contact angle, so it has stronger applicability and better robustness. The research results in this work will provide the theoretical basis for practical engineering application.
      通信作者: 李超, lichao@nwpu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 52006169, 51876178)资助的课题.
      Corresponding author: Li Chao, lichao@nwpu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 52006169, 51876178).
    [1]

    Yi H, Qi L, Luo J, Zhang D, Li H, Hou X 2018 Int. J. Mach. Tools Manuf. 130–131 1

    [2]

    李涛 2020 博士学位论文 (济南: 山东大学)

    Li T 2020 Ph. D. Dissertation (Jinan: Shandong University) (in Chinese)

    [3]

    Rioboo R, Tropea C, Marengo M 2001 Atomization Sprays 11 155Google Scholar

    [4]

    Rioboo R, Marengo M, Tropea C 2002 Exp. Fluids 33 112Google Scholar

    [5]

    Mundo C, Sommerfeld M, Tropea C 1994 Int. J. Multiphase Flow 21 151

    [6]

    Stanton D W, Rutland C J 1996 SAE Trans. 105 960628

    [7]

    Xu H T, Liu Y C, He P, Wang H Q 1998 J. Fluids Eng. 120 593Google Scholar

    [8]

    Attané P, Girard F, Morin V 2007 Phys. Fluids 19 12101Google Scholar

    [9]

    宋云超 2013 博士学位论文 (北京: 北京交通大学)

    Song Y C 2013 Ph. D. Dissertation (Beijing: Beijing Jiaotong University) (in Chinese)

    [10]

    李大树 2015 博士学位论文 (北京: 中国石油大学)

    Li D S 2015 Ph. D. Dissertation (Beijing: China University of Petroleum) (in Chinese)

    [11]

    陈石, 王辉, 沈胜强, 梁刚涛 2013 物理学报 62 204702Google Scholar

    Chen S, Wang H, Shen S Q, Liang G T 2013 Acta Phys. Sin. 62 204702Google Scholar

    [12]

    梁刚涛, 郭亚丽, 沈胜强 2013 物理学报 62 024705Google Scholar

    Liang G T, Guo Y L, Shen S Q 2013 Acta Phys. Sin. 62 024705Google Scholar

    [13]

    黄虎, 洪宁, 梁宏, 施保昌, 柴振华 2013 物理学报 62 084702Google Scholar

    Huang H, Hong N, Liang H, Shi B C, Chai Z H 2013 Acta Phys. Sin. 62 084702Google Scholar

    [14]

    武冠杰 2019 博士学位论文 (西安: 西北工业大学)

    Wu G J 2019 Ph. D. Dissertation (Xi’an: Northwestern Polytechnical University) (in Chinese)

    [15]

    Pasandideh-Fard M, Chandra S, Mostaghimi J 2002 Int. J. Heat Mass Transfer 45 2229Google Scholar

    [16]

    尚超, 阳倦成, 张杰, 倪明玖 2019 力学学报 51 380Google Scholar

    Shang C, Yang Q C, Zhang J, Ni M J 2019 J. Theor. Appl. Mech. 51 380Google Scholar

    [17]

    Dou Y, Luo J, Qi L, Lian H, Huang J 2021 J. Mater. Process. Technol. 297 117268Google Scholar

    [18]

    Li C, Wu G, Li M, Hu C, Wei J 2020 Aerosp. Sci. Technol. 97 105639Google Scholar

    [19]

    Assael M J, Kakosimos K, Banish R M, Brillo J, Egry I, Brooks R, Quested P N, Mills K C, Nagashima A, Sato Y, Wakeham W A 2006 J. Phys. Chem. Ref. Data 35 285Google Scholar

    [20]

    Sarou-Kanian V, Millot F, Rifflet J C 2003 Int. J. Thermophys. 24 277Google Scholar

    [21]

    Wu G J, Ren Q B, Fu Y, Liu Y M, Hu C B 2018 J. Solid Rocket Technol. 41 677

    [22]

    Brackbill J U, Kothe D B, Zemach C 1992 J. Comput. Phys. 100 335Google Scholar

    [23]

    Balla M, Kumar Tripathi M, Sahu K C 2019 Phys. Rev. E 99 23107Google Scholar

    [24]

    唐鹏博, 王关晴, 王路, 石中玉, 李源, 徐江荣 2020 物理学报 69 024702Google Scholar

    Tang P B, Wang G Q, Wang L, Shi Z Y, Li Y, Xu J R 2020 Acta Phys. Sin. 69 024702Google Scholar

    [25]

    Akao F, Araki K, Mori S, Moriyama A 1980 Trans. ISIJ 20 737Google Scholar

    [26]

    Hatta N, Fujimoto H, Takuda H, Kinoshita K, Takahashi O 1995 ISIJ Int. 35 50Google Scholar

    [27]

    Samkhaniani N, Stroh A, Holzinger M, Marschall H, Frohnapfel B, Wörner M 2021 Int. J. Heat Mass Transfer 180 121777Google Scholar

    [28]

    Chandra S, Avedisian C T 1991 Proc. R. Soc. London, Ser. A 432 13Google Scholar

    [29]

    Pasandideh-Fard M, Qiao Y M, Chandra S, Mostaghimi J 1996 Phys. Fluids 8 650Google Scholar

  • 图 1  物理模型

    Fig. 1.  Schematic diagram of physical model.

    图 2  网格无关性验证

    Fig. 2.  Verification of grid independence.

    图 3  数值计算结果与实验结果[18]的对比

    Fig. 3.  Comparison of the numerical calculation results with the experimental data[18].

    图 4  铝液滴撞击曲面过程的压力与速度分布 (a) 压力云图; (b) 速度云图

    Fig. 4.  Pressure and velocity distribution of aluminum droplet impinging on concave surface: (a) Pressure contours; (b) velocity contours.

    图 5  固-液接触点的压力与速度变化规律

    Fig. 5.  Time evolution of the pressure and velocity of solid-liquid contact point.

    图 6  不同We下铝液滴在曲面上的铺展行为 (a) We = 0.7; (b) We = 2.7; (c) We = 10.8; (d) We = 43.3

    Fig. 6.  Spreading behavior of droplets on the surface at different impact We: (a) We = 0.7; (b) We = 2.7; (c) We = 10.8; (d) We = 43.3

    图 7  不同We下铝液滴铺展系数随时间的变化

    Fig. 7.  Time evolution of spreading coefficient of aluminum droplets under different We.

    图 8  铝液滴的铺展系数与中心高度系数随时间的变化规律 (a)铺展系数; (b)中心高度系数

    Fig. 8.  Time evolution of the spreading and center height coefficient of aluminum droplets of different sizes: (a) Spreading coefficient; (b) center height coefficient.

    图 9  铝液滴铺展系数和铺展速度随时间的变化规律 (a)铺展系数; (b)铺展速度

    Fig. 9.  Time evolution of the spreading coefficient and spreading velocity of droplets of different sizes: (a) Spreading coefficient; (b) spreading velocity.

    图 10  不同液滴温度下铺展系数随时间的变化规律

    Fig. 10.  Time evolution of the spreading coefficient of droplets of different temperatures.

    图 11  铝液滴最大铺展系数随温度的变化规律

    Fig. 11.  Variation of the maximum spreading coefficient of aluminum droplets with temperature.

    图 12  铝液滴撞击不同曲率壁面时铺展系数与中心高度系数的变化规律 (a) 铺展系数; (b)中心高度系数

    Fig. 12.  Time evolution of spreading and center height coefficient of aluminum droplet on different curvature surface: (a) Spreading coefficient; (b) center height coefficient.

    图 13  铝液滴撞击曲面时最大铺展系数随We的变化规律

    Fig. 13.  Variation of the maximum spreading coefficient with Weber number when aluminum droplet impinges on surface.

    图 14  修正的预测模型

    Fig. 14.  Modified prediction formula.

    图 15  铝液滴撞壁过程的形态变化 (a) 初始时刻; (b) 最大铺展时刻

    Fig. 15.  Deformation process of a droplet colliding with the wall: (a) The initial moment; (b) maximum spreading moment.

    表 1  主要物性参数

    Table 1.  Main physical properties.

    参数数值单位
    温度1000K
    压力101325Pa
    液滴密度2357kg/m3
    液滴黏度1.178×10–3Pa/s
    表面张力0.871N/m
    接触角161(°)
    下载: 导出CSV

    表 2  铝液滴物性参数随温度的变化

    Table 2.  Physical parameters properties of aluminum droplets at different temperatures.

    温度/K密度/
    (kg·m–3)
    黏度/
    (10–3 Pa·s–1)
    表面张力/
    (N·m–1)
    120022940.8650.834
    140022320.6940.797
    160021700.5890.760
    180021080.5180.723
    200020460.4670.686
    下载: 导出CSV

    表 3  铺展过程的特征参数

    Table 3.  Characteristic parameters of the spreading process.

    k$ {\beta }_{\mathrm{m}\mathrm{a}\mathrm{x}} $$ {h}_{\mathrm{m}\mathrm{i}\mathrm{n}} $t1/mst2/mstmax/ms
    01.3940.1920.60.92.3
    1671.4110.2420.60.82.2
    2501.4180.2570.60.82.2
    4001.4330.2810.60.82.3
    下载: 导出CSV

    表 4  预测模型的相对误差

    Table 4.  Relative error of prediction model

    kεReWeRelative error/%
    Hatta模型Samkhaniani模型Eq. (7)Eq.(32)
    1670.08324013.543.4533.911.2724.54
    1670.08332016.305.8054.130.3618.45
    1670.08340019.843.8374.511.1818.42
    1670.083480114.173.2387.611.0616.95
    2500.12524013.549.2929.482.8320.53
    2500.12532016.307.8450.370.2915.69
    2500.12540019.845.5468.871.4914.75
    2500.125480114.175.4685.671.2815.92
    4000.224013.5410.3524.341.5916.06
    4000.232016.308.6749.431.83615.33
    4000.240019.847.7367.431.6014.19
    4000.2480114.177.4579.430.9712.52
    下载: 导出CSV
  • [1]

    Yi H, Qi L, Luo J, Zhang D, Li H, Hou X 2018 Int. J. Mach. Tools Manuf. 130–131 1

    [2]

    李涛 2020 博士学位论文 (济南: 山东大学)

    Li T 2020 Ph. D. Dissertation (Jinan: Shandong University) (in Chinese)

    [3]

    Rioboo R, Tropea C, Marengo M 2001 Atomization Sprays 11 155Google Scholar

    [4]

    Rioboo R, Marengo M, Tropea C 2002 Exp. Fluids 33 112Google Scholar

    [5]

    Mundo C, Sommerfeld M, Tropea C 1994 Int. J. Multiphase Flow 21 151

    [6]

    Stanton D W, Rutland C J 1996 SAE Trans. 105 960628

    [7]

    Xu H T, Liu Y C, He P, Wang H Q 1998 J. Fluids Eng. 120 593Google Scholar

    [8]

    Attané P, Girard F, Morin V 2007 Phys. Fluids 19 12101Google Scholar

    [9]

    宋云超 2013 博士学位论文 (北京: 北京交通大学)

    Song Y C 2013 Ph. D. Dissertation (Beijing: Beijing Jiaotong University) (in Chinese)

    [10]

    李大树 2015 博士学位论文 (北京: 中国石油大学)

    Li D S 2015 Ph. D. Dissertation (Beijing: China University of Petroleum) (in Chinese)

    [11]

    陈石, 王辉, 沈胜强, 梁刚涛 2013 物理学报 62 204702Google Scholar

    Chen S, Wang H, Shen S Q, Liang G T 2013 Acta Phys. Sin. 62 204702Google Scholar

    [12]

    梁刚涛, 郭亚丽, 沈胜强 2013 物理学报 62 024705Google Scholar

    Liang G T, Guo Y L, Shen S Q 2013 Acta Phys. Sin. 62 024705Google Scholar

    [13]

    黄虎, 洪宁, 梁宏, 施保昌, 柴振华 2013 物理学报 62 084702Google Scholar

    Huang H, Hong N, Liang H, Shi B C, Chai Z H 2013 Acta Phys. Sin. 62 084702Google Scholar

    [14]

    武冠杰 2019 博士学位论文 (西安: 西北工业大学)

    Wu G J 2019 Ph. D. Dissertation (Xi’an: Northwestern Polytechnical University) (in Chinese)

    [15]

    Pasandideh-Fard M, Chandra S, Mostaghimi J 2002 Int. J. Heat Mass Transfer 45 2229Google Scholar

    [16]

    尚超, 阳倦成, 张杰, 倪明玖 2019 力学学报 51 380Google Scholar

    Shang C, Yang Q C, Zhang J, Ni M J 2019 J. Theor. Appl. Mech. 51 380Google Scholar

    [17]

    Dou Y, Luo J, Qi L, Lian H, Huang J 2021 J. Mater. Process. Technol. 297 117268Google Scholar

    [18]

    Li C, Wu G, Li M, Hu C, Wei J 2020 Aerosp. Sci. Technol. 97 105639Google Scholar

    [19]

    Assael M J, Kakosimos K, Banish R M, Brillo J, Egry I, Brooks R, Quested P N, Mills K C, Nagashima A, Sato Y, Wakeham W A 2006 J. Phys. Chem. Ref. Data 35 285Google Scholar

    [20]

    Sarou-Kanian V, Millot F, Rifflet J C 2003 Int. J. Thermophys. 24 277Google Scholar

    [21]

    Wu G J, Ren Q B, Fu Y, Liu Y M, Hu C B 2018 J. Solid Rocket Technol. 41 677

    [22]

    Brackbill J U, Kothe D B, Zemach C 1992 J. Comput. Phys. 100 335Google Scholar

    [23]

    Balla M, Kumar Tripathi M, Sahu K C 2019 Phys. Rev. E 99 23107Google Scholar

    [24]

    唐鹏博, 王关晴, 王路, 石中玉, 李源, 徐江荣 2020 物理学报 69 024702Google Scholar

    Tang P B, Wang G Q, Wang L, Shi Z Y, Li Y, Xu J R 2020 Acta Phys. Sin. 69 024702Google Scholar

    [25]

    Akao F, Araki K, Mori S, Moriyama A 1980 Trans. ISIJ 20 737Google Scholar

    [26]

    Hatta N, Fujimoto H, Takuda H, Kinoshita K, Takahashi O 1995 ISIJ Int. 35 50Google Scholar

    [27]

    Samkhaniani N, Stroh A, Holzinger M, Marschall H, Frohnapfel B, Wörner M 2021 Int. J. Heat Mass Transfer 180 121777Google Scholar

    [28]

    Chandra S, Avedisian C T 1991 Proc. R. Soc. London, Ser. A 432 13Google Scholar

    [29]

    Pasandideh-Fard M, Qiao Y M, Chandra S, Mostaghimi J 1996 Phys. Fluids 8 650Google Scholar

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出版历程
  • 收稿日期:  2022-03-11
  • 修回日期:  2022-03-31
  • 上网日期:  2022-08-30
  • 刊出日期:  2022-09-20

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