مطالعه وقوع پدیده کاویتاسیون با استفاده از روش شبکه بولتزمن چندفازی و با اعمال معادلات حالت مختلف

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی هوافضا، دانشکده مهندسی فناوری‌های نوین، دانشگاه شهید بهشتی، تهران، ایران

2 گروه مهندسی هوافضا، دانشکده مهندسی فناوری های نوین، دانشگاه شهید بهشتی، تهران، ایران

چکیده

در مطالعه حاضر، یک روش شبکه بولتزمن چندفازی برای شبیه‌سازی عددی جریان‌‌های کاویتاسیونی توسعه داده ‌شده‌است. برهم‌کنش و جدایش فازهای مایع و بخار با اعمال روش اختلاف دقیق صورت گرفته و جهت دستیابی به پایداری عددی با حداقل جریان‌های غیرفیزیکی و انطباق ترمودینامیکی بهتر نتایج عددی، از معادله‌های حالت مناسب استفاده ‌شده‌است. در این راستا، معادلات حالت مکعبی شان-چن و کارناهان-استارلینگ و معادله حالت غیرمکعبی پنگ-رابینسون اعمال شده‌اند. دقت و کارآیی الگوریتم با شبیه‌سازی وقوع کاویتاسیون همگن و غیرهمگن مطالعه شده و نتایج بدست‌آمده با نتایج دیگران مقایسه شده‌است. الگوریتم توسعه‌یافته برای بررسی وقوع و رشد حباب‌های کاویتاسیونی و دینامیک آن به کار گرفته شده و با استفاده از هر یک از معادلات حالت، تاثیر آب‌دوستی و آب‌گریزی سطوح دیواره بر پایداری عددی و نحوه برهم‌کنش بین جامد و سیال و اثرگذاری آن در چگونگی وقوع پدیده کاویتاسیون در گلوگاه یک نازل همگرا-واگرا مورد مطالعه قرارگرفته‌است. ارزیابی نتایج حاصل از روش حاضر با نتایج موجود در مراجع نشان می‌دهد که روش شبکه بولتزمن چندفازی با استفاده از یک معادله حالت مناسب، قابلیت و توانمندی بسیار خوبی برای شبیه‌سازی جریان‌های کاویتاسیونی در هندسه‌های کاربردی را دارا بوده و دینامیک پیچیده حباب‌های کاویتاسیونی را به‌خوبی تسخیر می‌کند.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Study of cavitation inception using multiphase lattice Boltzmann method with incorporating equations of state

نویسندگان [English]

  • Eslam Ezzatneshan 1
  • Hamed Vaseghnia 2
1 Aerospace Engineering Group, Dep. New Technologies Engineering, Shahid Beheshti University, Tehran, Iran
2 Aerospace Engineering Group, Faculty of New Technologies Engineering, Shahid Beheshti University, Tehran, Iran
چکیده [English]

In the present study, a multiphase lattice Boltzmann method is implemented for simulation of the cavitation bubbles dynamics and characteristics of cavitating flows. The effect of employing various equations of state is investigated on the computing of interaction forces and the phase separation between the liquid and its vapor in the cavitating flows. Herein, the cubic equations of state of Shan-Chen and Carnahan-Starling and the non-cubic equation of state of Peng-Robinson are applied and the exact difference method is imposed to improve the numerical stability. The efficiency of the present method is examined by comparison of the results obtained for the homogeneous and heterogeneous cavitation with those reported in the literature. Then, the implemented multiphase lattice Boltzmann method is used for studying the inception and growth of the cavitation bubbles in the throat of a venturi. The effect of hydrophobicity and hydrophobicity of the nozzle wall on the cavitation dynamics is investigated and a detailed discussion is made for the results from the physical point of view. Evaluation of the present results shows that the multiphase lattice Boltzmann method with incorporating an appropriate equation of state has an excellent capability for prediction of the bubble dynamics and cavitating flow characteristics in applied geometries.

کلیدواژه‌ها [English]

  • Cavitation inception
  • Multiphase lattice Boltzmann method
  • Equations of state
  • Exact difference method

مراجع

[1] C.E. Brennen, Cavitation and Bubble Dynamics, Oxford University Press,  (1995).
[2] W.A.S. S. Dabiri, D. D. Joseph, Cavitation in an orifice flow, Phys. Fluids, 19(072112) (2007).
[3] A.K. Gunstensen, D.H. Rothman, S. Zaleski, G. Zanetti, Lattice Boltzmann model of immiscible fluids, Physical Review A, 43(8) (1991) 4320-4327.
[4] D. H. Rothman and J. M. Keller, Immiscible Cellular-Automaton Fluids, Journal of Statistical Physics, 52(1119) (1988).
[5] X. Shan, H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Physical Review E, 47 (1993) 1815-1819.
[6] X. Shan, H. Chen, Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation, Physical Review E, 49(4) (1994) 2941-2948.
[7] a.G.D. Xiaowen Shan, Multicomponent Lattice-Boltzmann Model with Interparticle Interaction, Journal of Statistical Physics,, 81 (1995).
[8] P. Yuan, L. Schaefer, Equations of state in a lattice Boltzmann model, Physics of Fluids, 18(4) (2006) 042101.
[9] L.-S. Luo, Theory of the lattice Boltzmann method: Lattice Boltzmann models for nonideal gases, PHYSICAL REVIEW E, 62(4) (2000).
[10] W.R. Osborn, E. Orlandini, M.R. Swift, J.M. Yeomans, J.R. Banavar, Lattice Boltzmann Study of Hydrodynamic Spinodal Decomposition, Physical Review Letters, 75 (1995) 4031-4034.
[11] M.R. Swift, W.R. Osborn, J.M. Yeomans, Lattice Boltzmann simulation of nonideal fluids, Phys Rev Lett, 75(5) (1995) 830-833.
[12] E.O. Michael R. Swift, W. R. Osborn, and J. M. Yeomans, Lattice Boltzmann simulations of liquid-gas and binary fluid systems, PHYSICAL REVIEW E, 54(5041) (1996).
[13] L.-S. Luo, Unified Theory of Lattice Boltzmann Models for Nonideal Gases, Physical Review Letters, 81(8) (1998) 1618-1621.
[14] X.S.a.G.D.D. Xiaoyi He, Discrete Boltzmann equation model for nonideal gases, PHYSICAL REVIEW E, 57(1).
[15] S.C. Xiaoyi He, and Raoyang Zhang, A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh–Taylor Instability1, Journal of Computational Physics, 152 (1999) 642–663.
[16] R. Zhang, X. He, S. Chen, Interface and surface tension in incompressible lattice Boltzmann multiphase model, Computer Physics Communications, 129(1-3) (2000) 121-130.
[17] R. Zhang, X. He, G. Doolen, S. Chen, Surface tension effects on two-dimensional two-phase Kelvin–Helmholtz instabilities, Advances in Water Resources, 24(3-4) (2001) 461-478.
[18] Z. Guo, B. Shi, C. Zheng, Chequerboard effects on spurious currents in the lattice Boltzmann equation for two-phase flows, Philos Trans A Math Phys Eng Sci, 369(1944) (2011) 2283-2291.
[19] X. Shan, Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models, Phys Rev E Stat Nonlin Soft Matter Phys, 73(4 Pt 2) (2006) 047701.
[20] A. Kuzmin, A.A. Mohamad, S. Succi, Multi-Relaxation Time Lattice Boltzmann Model for Multiphase Flows, International Journal of Modern Physics C, 19(06) (2008) 875-902.
[21] D. Lycett-Brown, K.H. Luo, Multiphase cascaded lattice Boltzmann method, Computers & Mathematics with Applications, 67(2) (2014) 350-362.
[22] M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, K. Sugiyama, F. Toschi, Generalized lattice Boltzmann method with multirange pseudopotential, Phys Rev E Stat Nonlin Soft Matter Phys, 75(2 Pt 2) (2007) 026702.
[23] G.B. G. Falcucci, G. Chiatti, S. Chibbaro, M. Sbragaglia, and S. Succi, , Lattice Boltzmann Models with Mid-range Interactions, Commun. Comput. Phys, 1071(2) (2007).
[24] Q. Li, K.H. Luo, X.J. Li, Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows, Phys Rev E Stat Nonlin Soft Matter Phys, 86(1 Pt 2) (2012) 016709.
[25] C. Peng, S. Tian, G. Li, M.C. Sukop, Single-component multiphase lattice Boltzmann simulation of free bubble and crevice heterogeneous cavitation nucleation, Phys Rev E, 98(2-1) (2018) 023305.
[26] M.C. Sukop, D. Or, Lattice Boltzmann method for homogeneous and heterogeneous cavitation, Phys Rev E Stat Nonlin Soft Matter Phys, 71 (2005) 046703.
[27] E. Ezzatneshan, Study of surface wettability effect on cavitation inception by implementation of the lattice Boltzmann method, Physics of Fluids, 29(11) (2017) 113304.
[28] S.U. G. Falcucci, G. Bella, S. Palpacelli, and A. D. Maio, Lattice Boltzmann simulation of a cavitating diesel injector nozzle, SAE Technical Paper,  (2011).
[29] G. Falcucci, E. Jannelli, S. Ubertini, S. Succi, Direct numerical evidence of stress-induced cavitation, Journal of Fluid Mechanics, 728 (2013) 362-375.
[30] G. Falcucci, S. Ubertini, G. Bella, S. Succi, Lattice Boltzmann Simulation of Cavitating Flows, Communications in Computational Physics, 13(03) (2015) 685-695.
[31] G. Kähler, F. Bonelli, G. Gonnella, A. Lamura, Cavitation inception of a van der Waals fluid at a sack-wall obstacle, Physics of Fluids, 27(12) (2015) 123307.
[32] S.K. Mishra, P.A. Deymier, K. Muralidharan, G. Frantziskonis, S. Pannala, S. Simunovic, Modeling the coupling of reaction kinetics and hydrodynamics in a collapsing cavity, Ultrason Sonochem, 17(1) (2010) 258-265.
[33] J. Yang, Z. Shen, X. Zheng, L. Li, Simulation on Cavitation Bubble Collapsing with Lattice Boltzmann Method, Journal of Applied Mathematics and Physics, 03(08) (2015) 947-955.
[34] M.-L. Shan, C.-P. Zhu, C. Yao, C. Yin, X.-Y. Jiang, Pseudopotential multi-relaxation-time lattice Boltzmann model for cavitation bubble collapse with high density ratio, Chinese Physics B, 25(10) (2016) 104701.
[35] M.-l. Shan, C.-p. Zhu, X. Zhou, C. Yin, Q.-b. Han, Investigation of cavitation bubble collapse near rigid boundary by lattice Boltzmann method, Journal of Hydrodynamics, 28(3) (2016) 442-450.
[36] Y. Mao, Y. Peng, J. Zhang, Study of Cavitation Bubble Collapse near a Wall by the Modified Lattice Boltzmann Method, Water, 10(10) (2018) 1439.
[37] Y. Peng, B. Wang, Y. Mao, Study on Force Schemes in Pseudopotential Lattice Boltzmann Model for Two-Phase Flows, Mathematical Problems in Engineering, 2018 (2018) 1-9.
[38] C. Peng, S. Tian, G. Li, M.C. Sukop, Simulation of laser-produced single cavitation bubbles with hybrid thermal Lattice Boltzmann method, International Journal of Heat and Mass Transfer, 149 (2020) 119136.
[39] Timm Krüger, Halim Kusumaatmaja, Alexandr Kuzmin, Orest Shardt, Goncalo Silva, E.M. Viggen, The Lattice Boltzmann Method, 1 ed., Springer International Publishing, Switzerland, 2017.
[40] A.L. Kupershtokh, D.A. Medvedev, Lattice Boltzmann equation method in electrohydrodynamic problems, Journal of Electrostatics, 64(7-9) (2006) 581-585.
[41] Q. Zou, X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Physics of Fluids, 9(6) (1997) 1591-1598.
[42] D. Or, M. Tuller, Cavitation during desaturation of porous media under tension, Water Resources Research, 38(5) (2002) 19-11-19-14.
[43] M.S. Plesset, A. Prosperetti, Bubble Dynamics and Cavitation, Annual Review of Fluid Mechanics, 9(1) (1977) 145-185.
[44] L. Rayleigh, VIII. On the pressure developed in a liquid during the collapse of a spherical cavity, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 34(200) (2009) 94-98.
[45] V. Sofonea, T. Biciuşcă, S. Busuioc, V.E. Ambruş, G. Gonnella, A. Lamura, Corner-transport-upwind lattice Boltzmann model for bubble cavitation, Physical Review E, 97(2) (2018).
[46] J.J. Miau, H.W. Tsai, Y.J. Lin, J.K. Tu, C.H. Fang, M.C. Chen, Experiment on smooth, circular cylinders in cross-flow in the critical Reynolds number regime, Experiments in Fluids, 51(4) (2011) 949-967.
[47] D.D. Joseph, Cavitation in a flowing liquid, Physical Review E, 51(3) (1995) R1649-R1650.
نشریه مهندسی مکانیک امیرکبیر
دوره 53، شماره 5 (Special Issue)
مرداد 1400
صفحه 3151-3170

فایل ها

هم رسانی

ارجاع به این مقاله

آمار