نوع مقاله : علمی پژوهشی
نویسندگان
1 دانشجوی دکتری، دانشگاه آزاد اسلامی، واحد علوم و تحقیقات، دانشکده مهندسی مکانیک، برق و کامپیوتر، تهران، ایران.
2 استاد، دانشگاه صنعتی شریف، دانشکده هوافضا، تهران، ایران.
3 استادیار، دانشگاه آزاد اسلامی، واحد علوم و تحقیقات، دانشکده مهندسی مکانیک، برق و کامپیوتر، تهران، ایران.
چکیده
در این مقاله، معادله نیرو-جابجایی و نوسانات سه بعدی غیر خطی یک قطره آونگان به صورت عددی بررسی می‌شود. رشد و جدایش قطره، که به دلیل گرانش از انتهای لولة مویین آویزان است، (با فرض نسبت‌های چگالی و گرانروی بالا و جریانهای دو فازی غیرقابل اختلاط در نظر گرفته می‌شود. از روش شبکة بولتزمن با زمان آرامش سه بعدی برای شبیه‌سازی رشد، جدایش و نوسانات قطره استفاده شد. متوجه شدیم که قطره در حال رشد همزمان سه رفتار کششی مختلف را نشان می‌دهد. نشان داده شد که قطره دارای شتاب نوسانی است. حداکثر دامنه شتاب بدون بعد حدود 35 و فرکانس بدون بعد حدود 40 بود. نتیجه گیری شد که قطره هنگام رشد امواج صوتی را در بالادست تولید می‌کند. اگرچه جریان در جهت گرانش بود، نوسانات عرضی با دامنه کم و با فرکانس بدون بعد 500 تا 800 در طول رشد قطره تشخیص داده شد.
کلیدواژه‌ها
موضوعات
[1] Miller, R. and Liggieri, L., Bubble and Drop Interfaces. Sect. I., CRC Press, Boca Raton, Florida, USA, 2011.
[2] D’Innocenzo, A. and Renna, L., "Analytical Solution of the Dripping Faucet Dynamics", Phys. Lett. A, Vol. 220, pp. 75-80, 1996.
[3] Shaw, R., The Dripping Faucet as a Model Chaotic System, Aerial Press, Santa Cruz, CA, USA, 1984.
[4] DePaoli, D.W., Feng, J.Q., Basaran, O.A., and Scott, T.C., "Hysteresis in Forced Oscillations of Pendant Drops", Phys. Fluids, Vol. 7, pp. 1181-1183,1995.
[5] Zhang, D.F. and Stone, H.A., "Drop Formation in Viscous Flows at a Vertical Capillary Tube", Phys. Fluids, Vol. 9, pp. 2234-2242, 1997.
[6] Jones, L.A., Eagar, T.W., and Lang, JH., "A Dynamic Model of Drops Detaching from a Gas Metal Arc Welding Electrode", J. Phys. D. Appl. Phys., Vol. 31, pp. 107-123,1998.
[7] Miller, R., Bree, M., and Fainerman, V.B., "Hydrodynamic Effects in Measurements with the Drop Volume Technique at Small Drop Times-3. Surface Tensions of Viscous Liquids", Colloids Surfaces a Physicochem Eng. Asp., 142, pp. 237-242, 1998.
[8] Lau, B. and Mashayek, F., "Dynamics of Oscillating Drops with Thermocapillary Effects", Theor. Comput. Fluid Dyn., Vol. 14, pp. 203-222,2001.
[9] Davidson, M. and Copper-White, J., "Numerical Prediction of Shear-thinning Drop Formation", Third International Conference on CFD in the Minerals and Process Industries, Melborn, Australia, 2003.
[10] Cramer, C., "Continuous Drop Formation at a Capillary Tip and Drop deformation in a Flow Channel", Ph.D. Disertation, Swiss Federal Institute of Technology (ETH), Zürich, Swiss, 2004.
[11] Fainerman, V.B. and Miller, R., "Hydrodynamic Effects in Measurements with the Drop Volume Technique at Small Drop Times. 2. Drop Time and Drop Volume Bifurcations", Colloids Surfaces A Physicochem Eng. Asp., Vol. 97, pp. 255-262,1995.
[12] Fawehinmi, O.B., Gaskell, P.H., Jimack, P.K., Kapur, N., and Thompson, H.M., "A Combined Experimental and Computational Fluid Dynamics Analysis of the Dynamics of Drop Formation", Proc. Inst. Mech. Eng. Part C, J. Mech. Eng. Sci., Vol. 219, pp. 933-947,2005.
[13] Timgren, A., Trägårdh, G., and Trägårdh, C., "Effects of Cross-flow Velocity, Capillary Pressure and Oil Viscosity on Oil-in-water Drop Formation from a Capillary", Chem. Eng. Sci., Vol. 64, pp. 1111-1118, 2009.
[14] Bostwick, J.B. and Steen, PH., "Capillary Oscillations of a Constrained Liquid Drop", Phys. Fluids, Vol. 21, P. 032108, 2009.
[15] Bierbrauer, F., Kapur, N., Wilson, and M.C.T., "Drop Pinch-Off for Discrete Flows from a Capillary", ESAIM Proc., Vol. 40, pp. 16-33,2013.
[16] Karbaschi, M., Taeibi Rahni, M., Javadi, A., Cronan, C.L., Schano, K.H., and Faraji, S., "Dynamics of Drops — Formation, Growth, Oscillation, Detachment, and Coalescence", Adv. Colloid Interface, Vol. 222, pp. 413-424,2015.
[17] Nooranidoost, M., Izbassarov, D., and Muradoglu, M., "Droplet Formation in a Flow Focusing Configuration: Effects of Viscoelasticity", Phys. Fluids, Vol. 28, P. 123102, 2016.
[18] Taeibi Rahni, M., Karbaschi, M., and Miller, R., Computational Methods for Complex Liquid–Fluid Interfaces, CRC Press, Boca Raton, Florida, USA, 2015.
[19] Fakhari, A. and Rahimian, M.H., "Simulation of Falling Droplet by the Lattice Boltzmann Method", Commun Nonlinear Sci. Numer. Simul., Vol. 14, pp. 3046-3055, 2009.
[20] Fakhari, A. and Rahimian, M.H., "Phase-field Modeling by the Method of Lattice Boltzmann Equations", Phys. Rev. E - Stat Nonlinear, Soft Matter Phys., Vol. 81, P. 036707, 2010.
[21] Fakhari, A. and Rahimian, M.H., "Investigation of Deformation and Breakup of a Falling Droplet Using a Multiple-relaxation-time Lattice Boltzmann Method", Comput. Fluids, Vol. 40, pp. 156-171, 2011.
[22] Fakhari, A. and Lee, T., "Multiple-relaxation-time Lattice Boltzmann Method for Immiscible Fluids at High Reynolds Numbers", Phys. Rev. E - Stat Nonlinear, Soft Matter Phys., Vol. 87, P. 023304, 2013.
[23] Geier, M., Fakhari, A., and Lee, T., "Conservative Phase-field Lattice Boltzmann Model for Interface Tracking Equation", Phys. Rev. E - Stat Nonlinear, Soft Matter Phys., Vol. 91, P. 021108, 2015.
[24] Fakhari, A., Geier, M., and Lee, T., "A Mass-conserving Lattice Boltzmann Method with Dynamic Grid Refinement for Immiscible Two-phase Flows", J. Comput Phys., Vol. 315, pp. 434-457, 2016.
[25] Fakhari, A. and Bolster, D., "Diffuse Interface Modeling of Three-phase Contact Line Dynamics on Curved Boundaries: a Lattice Boltzmann Model for Large Density and Viscosity Ratios", J. Comput Phys., Vol. 334, pp. 620-638, 2017.
[26] Sheikholeslam Noori, S.M., Taeibi Rahni, M., and Shams Taleghani, S.A., "Numerical Analysis of Droplet Motion over a Flat Plate Due to Surface Acoustic Waves", Microgravity Sci. Technol., Vol. 32, No. 4, pp. 647-660, 2020.
[27] Sheikholeslam Noori, S.M., Taeibi Rahni, M., and Shams Taleghani, S.A., "Multiple-relaxation Time Color-gradient Lattice Boltzmann Model for Simulating Contact Angle in Two-phase Flows with High Density Ratio", Eur. Phys. J. Plus, Vol. 134, No. 8, P. 399, 2019.
[28] Sheikholeslam Noori, S.M., Taeibi Rahni, M., and Shams Taleghani, S.A., "Phenomenological Investigation of Drop Manipulation Using Surface Acoustic Waves", Microgravity Sci. Technol., Vol. 32, No. 6, pp. 1147-1158,2020.
[29] Sheikholeslam Noori, S.M., Taeibi Rahni, M., and Shams Taleghani, S.A., "Effects of Contact Angle Hysteresis on Drop Manipulation Using Surface Acoustic Waves", Theor. Comput. Fluid Dyn., Vol. 9, No's. 1-2, pp. 145-162,2020.
[30] Cahn, J.E. and Hilliard, J.W., "Free Energy of a Nonuniform System. II. Interfacial Free Energy Thermodynamic Basis", J. Chem. Phys., Vol. 28, pp. 258-267,1958.
[31] Allen, S.M. and Cahn, J.W., "A Microscopic Theory for Antiphase Boundary Motion and Its Application to Antiphase Domain Coarsening", Acta Metall., Vol. 27, pp. 1085-1095, 1979.
[32] Chiu, P-H. and Lin, Y-T., "A Conservative Phase Field Method for Solving Incompressible Two-phase Flows", J. Comput. Phys., Vol. 230, pp. 185-204, 2011.
[33] Lee, T., "Effects of Incompressibility on the Elimination of Parasitic Currents in the Lattice Boltzmann Equation Method for Binary Fluids", Comput. Math with Appl., Vol. 58, pp. 987-994, 2009.
[34] Jacqmin, D., "Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling", J. Comput. Phys., Vol. 155, pp. 96-127, 1999.
[35] Clift, R., Grace, J.R., and Weber, M.E., Bubbles, Drops, and Particles, Academic Press, New York, USA, 1978.
[36] Mitchell, T., Leonardi, C., and Fakhari, A., "Development of a Three-dimensional Phase-field Lattice Boltzmann Method for the Study of Immiscible Fluids at High Density Ratios", Int. J. Multiph. Flow, Vol. 107, pp. 1-15, 2018.
[37] Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G., and Viggen, E.M., The Lattice Boltzmann Method, Springer International Publishing, New York, USA, 2017.
[38] Fakhari, A., Mitchell, T., Leonardi, C., and Bolster, D., "Improved Locality of the Phase-field Lattice-boltzmann Model for Immiscible Fluids at High Density Ratios", Phys. Rev. E., Vol. 96, P. 201107, 2017.
[39] Fakhari, A., Bolster, D., and Luo, L-SS., "A Weighted Multiple-relaxation-time Lattice Boltzmann Method for Multiphase Flows and Its Application to Partial Coalescence Cascades", J. Comput. Phys., Vol. 341, pp. 22-43, 2017.
[40] Chen, S., Martínez, D., and Mei, R., "On Boundary Conditions in Lattice Boltzmann Methods", Phys. Fluids, Vol. 8, pp. 2527-2536, 1996.
[41] Zhang, X. and Basaran, O.A., "An Experimental Study of Dynamics of Drop Formation", Phys. Fluids, Vol. 7, pp. 1184-1203, 1995.
[42] Jones, L.A., "Dynamic Electrode Forces in Gas Metal Arc Welding", Ph.D. Disertation, Massachusetts Institute of Technology, Massachusetts, USA, 1996.
[43] de Gennes, P.G., "Wetting: Statics and Dynamics", Rev. Mod. Phys., Vol. 57, pp. 827-863, 1985.
[44] Nazari, A., Zadkazemi Derakhshi, A., Nazari, A., and Firoozabadi, B., "Drop Formation from a Capillary Tube: Comparison of Different Bulk Fluid on Newtonian Drops and Formation of Newtonian and Non-newtonian Drops in Air Using Image Processing", Int. J. Heat Mass Transf., Vol. 124, pp. 912-919, 2018.
[45] Moon, J.H., Kang, B.H., and Kim, H-Y. "The Lowest Oscillation Mode of a Pendant Drop", Phys. Fluids, Vol. 18, P. 21702, 2006.
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