STUDY ON THE EVOLUTION CHARACTERISTICS OF SOLITARY WAVES AND INTERNAL VORTICES IN LIQUID FILM FLOW ON INCLINED WALLS

Wu Zhengren; Wang Qifeng; Lu Shijia; Dong Shuai; Liu Mei

doi:10.6052/0459-1879-24-031

Volume 56 Issue 7

Jul. 2024

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Theoretical and Applied Mechanics > 2024 > 56(7): 1983-1991. > DOI: 10.6052/0459-1879-24-031 CSTR: 32045.14.0459-1879-24-031

Wu Zhengren, Wang Qifeng, Lu Shijia, Dong Shuai, Liu Mei. Study on the evolution characteristics of solitary waves and internal vortices in liquid film flow on inclined walls. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(7): 1983-1991. DOI: 10.6052/0459-1879-24-031

Citation:

PDF (2978 KB)

STUDY ON THE EVOLUTION CHARACTERISTICS OF SOLITARY WAVES AND INTERNAL VORTICES IN LIQUID FILM FLOW ON INCLINED WALLS

Wu Zhengren^{*, †, ,},
Wang Qifeng^†,
Lu Shijia^†,
Dong Shuai^†,
Liu Mei^**

*.
Hebei Key Laboratory of Low Carbon and High Efficiency Power Generation Technology, North China Electric Power University, Baoding 071003, Hebei, China
†.
Department of Power Engineering, North China Electric Power University, Baoding 071003, Hebei, China
**.
Department of Economics and Management, North China Electric Power University, Baoding 071003, Hebei, China

Received Date: January 10, 2024
Accepted Date: June 16, 2024
Available Online: June 16, 2024
Published Date: June 17, 2024

Graphical Abstract

Abstract

Abstract

This paper investigates the evolution of solitary waves and internal vortices in a two-dimensional incompressible viscous liquid film flowing down an inclined wall under the influence of gravity. Using the method of small parameter perturbation and the traveling wave transformation, we first derive the general zeroth-order and first-order evolution equations for the film thickness on a non-smooth inclined substrate. These equations are then simplified and numerically solved using Mathematica. The analysis results show that in the waveform of the solitary wave, a capillary wave appears at the wavefront, and a fully open vortex forms at the trough of the capillary wave. Flow rate analysis indicates that it follows the same variation trend as the solitary wave profile and is positively correlated with the wave speed. For double-peak and triple-peak solitary waves, the flow rate of the preceding peak is greater than that of the subsequent peaks. When the wave speed increases beyond a certain critical value, vortices appear within the solitary wave peaks. Calculations show that this critical wave speed is directly proportional to the inclination angle. For double-peak and triple-peak solitary waves, further increase in wave speed results in vortices forming within the subsequent peaks as well. By analyzing the velocity distribution on the free surface, it is concluded that the generation of vortices is due to the combined effect of the velocity gradient of the vertical velocity at the wavefront and wave tail and the horizontal velocity exceeding the wave speed, with more wave peaks facilitating vortex formation. Analysis of the streaklines obtained in the moving coordinate system reveals that the vortex area is also proportional to the wave speed and rotates clockwise. Overall, it is inferred that the vortex starts to form at the surface of the solitary wave, with the fluid within the wave peaks rolling down along the wall.
- solitary wave,
- liquid film,
- vortex,
- wave speed

FullText(HTML)

References (38)

References

[1]	余夏静, 叶雪均. 液膜技术及其应用研究进展. 污染防治技术, 2011, 24(3): 69-72 (Yu Xiajing, Ye Xuejun. Advances on technique and application of liquid membrane separation process. Pollution Control Technology, 2011, 24(3): 69-72 (in Chinese) Yu Xiajing, Ye Xuejun. Advances on technique and application of liquid membrane separation process. Pollution Control Technology, 2011, 24(3): 69-72 (in Chinese)
[2]	黄悬悬, 王亦飞, 于广锁等. 垂直降膜, 鼓泡流动特性与传热机理研究进展. 高校化学工程学报, 2023, 37(3): 333-349 (Huang Xuanxuan, Wang Yifei, Yu Guangsuo, et al. Review on vertical falling film and bubbling flows and their heat transfer mechanisms. Journal of Chemical Engineering of Higher Educational Institutions, 2023, 37(3): 333-349 (in Chinese) doi: 10.3969/j.issn.1003-9015.2023.03.001 Huang Xuanxuan, Wang Yifei, Yu Guangsuo, et al. Review on vertical falling film and bubbling flows and their heat transfer mechanisms. Journal of Chemical Engineering of Higher Educational Institutions, 2023, 37(3): 333-349 (in Chinese) doi: 10.3969/j.issn.1003-9015.2023.03.001
[3]	胡玖琦, 王敬鑫, 朱春玲等. 风驱动下平板水膜表面波动特性实验研究. 南京航空航天大学学报, 2022, 54(2): 259-266 (Hu Jiuqi, Wang Jingxin, Zhu Chunling, et al. Experimental study on surface fluctuation characteristics of flat water film driven by airflow. Journal of Nanjing University of Aeronautics & Astronautics, 2022, 54(2): 259-266 (in Chinese) Hu Jiuqi, Wang Jingxin, Zhu Chunling, et al. Experimental study on surface fluctuation characteristics of flat water film driven by airflow. Journal of Nanjing University of Aeronautics & Astronautics, 2022, 54(2): 259-266 (in Chinese)
[4]	王振东. 孤立波与孤立子. 力学与实践, 2005, 27(5): 86-88 (Wang Zhendong. Solitary waves and solitons. Mechanics in Engineering, 2005, 27(5): 86-88 (in Chinese) doi: 10.3969/j.issn.1000-0879.2005.05.022 Wang Zhendong. Solitary waves and solitons. Mechanics in Engineering, 2005, 27(5): 86-88 (in Chinese) doi: 10.3969/j.issn.1000-0879.2005.05.022
[5]	刘梅, 王松岭, 吴正人. 非平整基底上受热液膜流动稳定性研究. 物理学报, 2014, 63(15): 154702 (Liu Mei, Wang Songling, Wu Zhengren. Stability of heated liquid film on an uneven substrate. Acta Physica Sinica, 2014, 63(15): 154702 (in Chinese) Liu Mei, Wang Songling, Wu Zhengren. Stability of heated liquid film on an uneven substrate. Acta Physica Sinica, 2014, 63(15): 154702 (in Chinese)
[6]	汪超, 杜伟, 杜鹏等. 内孤立波作用下潜深对潜体运动响应和载荷特性的影响研究. 力学学报, 2022, 54(7): 1921-1933 (Wang Chao, Du Wei, Du Peng, et al. Influence of diving depth on motion response and load characteristics of submerged body under action of internal solitary wave. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 1921-1933 (in Chinese) doi: 10.6052/0459-1879-21-649 Wang Chao, Du Wei, Du Peng, et al. Influence of diving depth on motion response and load characteristics of submerged body under action of internal solitary wave. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 1921-1933 (in Chinese) doi: 10.6052/0459-1879-21-649
[7]	Maksymov IS, Pototsky A. Solitary-like wave dynamics in thin liquid films over a vibrated inclined plane. Applied Sciences, 2023, 13(3): 1888 doi: 10.3390/app13031888
[8]	Pumir A, Manneville P, Pomeau Y. On solitary waves running down an inclined plane. Journal of Fluid Mechanics, 1983, 135: 27-50 doi: 10.1017/S0022112083002943
[9]	Kapitza PL, Kapitza SP. Wave flow of thin viscous fluid layers. Zh Eksp Teor Fiz, 1948, 18(1): 3-28
[10]	胡军, 胡国辉, 孙德军等. 沿平板下落薄膜流动的研究综述. 力学进展, 2005, 35(2): 161-169 (Hu Jun, Hu Guohui, Sun Dejun, et al. A review on thin films falling along an inclined plane. Advance in Mechanics, 2005, 35(2): 161-169 (in Chinese) Hu Jun, Hu Guohui, Sun Dejun, et al. A review on thin films falling along an inclined plane. Advance in Mechanics, 2005, 35(2): 161-169 (in Chinese)
[11]	Benjamin TB. Wave formation in laminar flow down an inclined plane. Journal of Fluid Mechanics, 1957, 2(6): 554-573 doi: 10.1017/S0022112057000373
[12]	Yih CS. Stability of Liquid Flow Down an Inclined Plane. World Scientific, 1991: 357-370
[13]	Benney D. Long waves on liquid films. Journal of Mathematics and Physics, 1966, 45(1-4): 150-155 doi: 10.1002/sapm1966451150
[14]	Gjevik B. Occurrence of finite-amplitude surface waves on falling liquid films. Physics of Fluids, 1970, 13(8): 1918-1925 doi: 10.1063/1.1693186
[15]	Nakaya C. Long waves on a thin fluid layer flowing down an inclined plane. Physics of Fluids, 1975, 18(11): 1407-1412 doi: 10.1063/1.861037
[16]	Lin S. Finite-amplitude stability of a parallel flow with a free surface. Journal of Fluid Mechanics, 1969, 36(1): 113-126 doi: 10.1017/S0022112069001546
[17]	Lin S. Finite amplitude side-band stability of a viscous film. Journal of Fluid Mechanics, 1974, 63(3): 417-429 doi: 10.1017/S0022112074001704
[18]	Kliakhandler IL. Inverse cascade in film flows. Journal of Fluid Mechanics, 2000, 423: 205-225 doi: 10.1017/S0022112000001786
[19]	Shkadov V, Kholpanov L, Malyusov V, et al. On nonlinear theory of wave flows of liquid film. Teor Osnovy Khim Tekh, 1970, 4: 859-867
[20]	Chang HC, Demekhin E, Kalaidin E, et al. Coarsening dynamics of falling-film solitary waves. Physical Review E, 1996, 54(2): 1467 doi: 10.1103/PhysRevE.54.1467
[21]	Joo S, Davis S. Instabilities of three-dimensional viscous falling films. Journal of Fluid Mechanics, 1992, 242: 529-547 doi: 10.1017/S0022112092002489
[22]	Wang X, Ehsan H, Abbas M, et al. Analytical solitary wave solutions of a time-fractional thin-film ferro- electric material equation involving beta-derivative using modified auxiliary equation method. Results in Physics, 2023, 48: 106411 doi: 10.1016/j.rinp.2023.106411
[23]	Chu YM, Arshed S, Sadaf M, et al. Solitary wave dynamics of thin-film ferroelectric material equation. Results in Physics, 2023, 45: 106201 doi: 10.1016/j.rinp.2022.106201
[24]	刚傲, 马玉祥, 牛旭阳等. 孤立波与水平板相互作用过程涡演化的研究//第三十届全国水动力学研讨会暨第十五届全国水动力学学术会议论文集 (上册). 合肥: 中国海洋出版社, 2019: 212-219 (Gang Ao, Ma Yuxiang, Niu Xuyang, et al. Study on vortex evolution in the interaction process between solitary wave and horizontal plate//Proceedings of the 30th National Conference on Hydrodynamics and the 15th National Conference on Hydrodynamics (Volume I). Hefei: China Ocean Press, 2019: 212-219 (in Chinese) Gang Ao, Ma Yuxiang, Niu Xuyang, et al. Study on vortex evolution in the interaction process between solitary wave and horizontal plate//Proceedings of the 30th National Conference on Hydrodynamics and the 15th National Conference on Hydrodynamics (Volume I). Hefei: China Ocean Press, 2019: 212-219 (in Chinese)
[25]	Kofman N, Mergui S, Ruyer-Quil C. Three-dimensional instabilities of quasi-solitary waves in a falling liquid film. Journal of Fluid Mechanics, 2014, 757: 854-887 doi: 10.1017/jfm.2014.506
[26]	王千, 刘桦, 房詠柳等. 孤立波与淹没平板相互作用的三维波面和水动力实验研究. 力学学报, 2019, 51(6): 1605-1613 (Wang Qian, Liu Hua, Fang Yongliu, et al. An experimental study of 3-D wave surface and hydrodynamic loads for interaction between solitary wave and submerged horizontal plate. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1605-1613 (in Chinese) doi: 10.6052/0459-1879-19-244 Wang Qian, Liu Hua, Fang Yongliu, et al. An experimental study of 3-D wave surface and hydrodynamic loads for interaction between solitary wave and submerged horizontal plate. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1605-1613 (in Chinese) doi: 10.6052/0459-1879-19-244
[27]	Zeng J, Wang Y, Li T, et al. Effect of structural parameters of corrugated plate on the evolution of solitary waves and liquid film thickness distribution. Chemical Engineering Science, 2023, 276: 118774 doi: 10.1016/j.ces.2023.118774
[28]	Miyara A. Numerical analysis on flow dynamics and heat transfer of falling liquid films with interfacial waves. Heat and Mass Transfer, 1999, 35(4): 298-306 doi: 10.1007/s002310050328
[29]	Yu Y. Study on hydrodynamics and heat transfer of solitary wave on film flow with CFD method. International Journal of Nuclear Energy Science and Technology, 2015, 9(1): 56-77 doi: 10.1504/IJNEST.2015.067838
[30]	马学虎, 薄守石, 兰忠等. 降液膜波动的影响因素分析. 高校化学工程学报, 2010, 24(1): 10-15 (Ma Xuehu, Bo Shoushi, Lan Zhong, et al. Analysis on wave flow of laminar-wavy falling liquid film. Journal of Chemical Engineering of Higher Educational Institutions, 2010, 24(1): 10-15 (in Chinese) doi: 10.3969/j.issn.1003-9015.2010.01.003 Ma Xuehu, Bo Shoushi, Lan Zhong, et al. Analysis on wave flow of laminar-wavy falling liquid film. Journal of Chemical Engineering of Higher Educational Institutions, 2010, 24(1): 10-15 (in Chinese) doi: 10.3969/j.issn.1003-9015.2010.01.003
[31]	Kunugi T, Kino C. Numerical simulation of oscillatory falling liquid film flows. Fusion Engineering and Design, 2003, 65(3): 387-392 doi: 10.1016/S0920-3796(03)00007-3
[32]	Vlachogiannis M, Bontozoglou V. Observations of solitary wave dynamics of film flows. Journal of Fluid Mechanics, 2001, 435: 191-215 doi: 10.1017/S0022112001003688
[33]	Malamataris N, Vlachogiannis M, Bontozoglou V. Solitary waves on inclined films: Flow structure and binary interactions. Physics of Fluids, 2002, 14(3): 1082-1094 doi: 10.1063/1.1449465
[34]	Chakraborty S, Nguyen PK, Ruyer-Quil C, et al. Extreme solitary waves on falling liquid films. Journal of Fluid Mechanics, 2014, 745: 564-591 doi: 10.1017/jfm.2014.91
[35]	庄礼贤, 尹协远, 马晖扬. 流体力学, 第二版. 合肥: 中国科学技术大学出版社, 2009: 78-84 (Zhuang Lixian, Yin Xieyuan, Ma Huiyang. Fluid Mechanics, 2nd Edition. Hefei: University of Science and Technology of China Press, 2009: 78-84 (in Chinese) Zhuang Lixian, Yin Xieyuan, Ma Huiyang. Fluid Mechanics, 2nd Edition. Hefei: University of Science and Technology of China Press, 2009: 78-84 (in Chinese)
[36]	黄德波. 水波理论基础. 北京: 国防工业出版社, 2011: 13-19
[37]	薄守石, 马学虎, 兰忠等. 溴化锂溶液垂直降膜过程中流动与传热的数值模拟. 化学反应工程与工艺, 2011, 27(2): 114-120 (Bo Shoushi, Ma Xuehu, Lan Zhong, et al. Numerical simulation of flow and heat transfer during vertical falling film process of lithium bromide solution. Chemical Reaction Engineering and Technology, 2011, 27(2): 114-120 (in Chinese) doi: 10.3969/j.issn.1001-7631.2011.02.004 Bo Shoushi, Ma Xuehu, Lan Zhong, et al. Numerical simulation of flow and heat transfer during vertical falling film process of lithium bromide solution. Chemical Reaction Engineering and Technology, 2011, 27(2): 114-120 (in Chinese) doi: 10.3969/j.issn.1001-7631.2011.02.004
[38]	薄守石, 马学虎, 兰忠等. 降液膜流动孤波中的涡流影响因素分析. 工程热物理学报, 2011, 32(10): 1703-1706 (Bo Shoushi, Ma Xuehu, Lan Zhong, et al. Numerical simulation on flow and heat transfer of LiBr solution along the vertical wall. Journal of Engineering Thermophysics, 2011, 32(10): 1703-1706 (in Chinese) Bo Shoushi, Ma Xuehu, Lan Zhong, et al. Numerical simulation on flow and heat transfer of LiBr solution along the vertical wall. Journal of Engineering Thermophysics, 2011, 32(10): 1703-1706 (in Chinese)

[1]	Huang Kai, Li Mingpeng. RESEARCH ON THE STRAIN RATE DEPENDENCE OF PHASE TRANSFORMATION PATTERN EVOLUTION IN NITI ALLOYS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(5): 1-9. DOI: 10.6052/0459-1879-25-055
[2]	Li Zhonghua, Li Zhihui, Wu Junlin. RESEARCH ON DSMC NUMERICAL METHOD OF PHASE TRANSITION IN VACUUM PLUME[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5): 1356-1365. DOI: 10.6052/0459-1879-23-419
[3]	Chong Tao, Mo Jianjun, Fu Hua, Li Tao, Luo Binqiang. PHASE TRANSITION AND SPALL BEHAVIOR OF TIN UNDER RAMP WAVE COMPRESSION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(1): 113-119. DOI: 10.6052/0459-1879-22-516
[4]	Li Xing, Gu Xin, Xia Xiaozhou, Chen Aijiu, Zhang Qing. PERIDYNAMIC THERMOMECHANICAL COUPLING MODEL WITH PHASE CHANGE AND SIMULATION OF FREEZING FAILURE OF POROUS MEDIA[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3310-3318. DOI: 10.6052/0459-1879-22-521
[5]	Zhou Ting, Kan Qianhua, Kang Guozheng, Qiu Bo. A MACROSCOPIC PHENOMENOLOGICAL CONSTITUTIVE MODEL FOR THE UNIAXIAL TRANSFORMATION RATCHETING OF SUPER-ELASTIC NiTi SHAPE MEMORY ALLOY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 588-596. DOI: 10.6052/0459-1879-17-116
[6]	Yaoming Zhang, Cuilian Sun, Yan Gu. The evaluation of nearly singular integrals in the boundary integral equations with variable transformation[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(2): 207-214. DOI: 10.6052/0459-1879-2008-2-2007-123
[7]	FINITE ELEMENT METHOD BASED ON ENTHALPY FORMULATION OF CONVECTION-DIFFUSION FOR LIQUID-SOLID PHASE CHANGE PROBLEMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1993, 25(1): 123-128. DOI: 10.6052/0459-1879-1993-1-1995-622
[8]	THE TRANSFORMATION OF THE PAPKOVICH-NEUBER (P-N) GENERAL SOLUTION AND OTHERS[J]. Chinese Journal of Theoretical and Applied Mechanics, 1991, 23(6): 755-758. DOI: 10.6052/0459-1879-1991-6-1995-902
[9]	一种描述形状记忆合金拟弹性变形行为的本构关系[J]. Chinese Journal of Theoretical and Applied Mechanics, 1991, 23(2): 201-210. DOI: 10.6052/0459-1879-1991-2-1995-827
[10]	THE PROBLEM OF BLOCK DIAGONALIZATION OF A COMPLEX ORTHOGONAL MATRIX AND ITS APPLICATION TO ISING MODEL PHASE TRANSITION[J]. Chinese Journal of Theoretical and Applied Mechanics, 1990, 22(2): 171-175. DOI: 10.6052/0459-1879-1990-2-1995-928

Cited By

Get Citation

PDF

XML

Article Metrics

Article views (103) PDF downloads (23)

STUDY ON THE EVOLUTION CHARACTERISTICS OF SOLITARY WAVES AND INTERNAL VORTICES IN LIQUID FILM FLOW ON INCLINED WALLS

Abstract

References

Related Articles

Catalog

Article Metrics

Related

Download Center

Author Center

STUDY ON THE EVOLUTION CHARACTERISTICS OF SOLITARY WAVES AND INTERNAL VORTICES IN LIQUID FILM FLOW ON INCLINED WALLS

Abstract

References

Related Articles

Catalog

Article Metrics

Related

Download Center

Author Center

Export File

Citation

Format

Content