پیش‌بینی ضریب دراگ برای حباب در حال صعود در یک سیال غیر نیوتونی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی شیمی، دانشگاه صنعتی جندی شاپور، دزفول، ایران

2 دانشکده مهندسی شیمی، دانشگاه صنعتی جندی شاپور، دزفول، ایـران

3 دانشکده مهندسی مکانیک، دانشگاه صنعتی جندی شاپور، دزفول، ایران

چکیده

در مطالعه‌ی حاضر به صورت آزمایشگاهی ضریب دراگ حباب تک در حال صعود در سیال غیرنیوتونی مورد مطالعه قرار گرفته است. برای این منظور محلول پلی آکریل آمید با غلظت‌های مختلف انتخاب شد. این محلول سیال غیرنیوتونی با خاصیت ویسکوالاستیک است. آزمایشات با قطر نازل‌های مختلف، برای حباب‌های گازی هوا، اکسیژن و دی‌اکسیدکربن و در دبی‌های تزریق مختلف انجام شده است. از این رو نتایج نسبت به مطالعات گذشته جامعیت بیشتری دارد. مقایسه‌ی بین نتایج به دست آمده با سایر معادلات نشان داد که هیچکدام از این روابط نمی‌توانند ضریب دراگ حباب در حال صعود درون سیال غیرنیوتونی با خاصیت ویسکوالاستیک را به خوبی پیش‌بینی کنند. از این رو به کمک تحلیل ابعادی، دو رابطه‌ی جدید برای پیش‌بینی ضریب دراگ برحسب اعداد بدون بعد رینولدز، ارشمیدس و اتوس ارائه شد. معادله‌ی اول که مستقیما از آنالیز ابعادی به دست آمده است نسبت به معادله‌ی دوم ساده‌تر بوده و متوسط درصد خطای پیش‌بینی آن 26 / 3 % است. این درحالی است که متوسط خطای پیش‌بینی معادله‌ی ارائه‌ی دوم که از لحاظ فرمولاسیون پیچیده‌تر می‌باشد در حدود 7/ 1 % به دست آمده است. علاوه بر آن معادلات جدیدی برای پیش بینی سرعت حد و همچنین بررسی رفتار حباب در حال صعود در سیال غیرنیوتونی ویسکوالاستیک ارائه شده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

The Drag Coefficient Prediction of a Rising Bubble through a Non-Newtonian Fluid

نویسندگان [English]

  • Safoora Karimi 1
  • Mojtaba Shafiee 2
  • Anna Abiri 1
  • Farzad Ghadam 3
1 Department of Chemical Engineering, Jundi-Shapur University of Technology, Dezful, Iran
2 Department of Chemical Engineering, Faculty of Chemical Engineering, Jundi-Shapur University of Technology, Dezful, Iran
3 Department of Mechanical Engineering, Jundi-Shapur University of Technology, Dezful, Iran
چکیده [English]

In the present research, the drag coefficient of a single bubble rising in the non-Newtonian fluid has been investigated. Polyacrylamide solutions were selected with different concentrations as a Non-Newtonian fluid. As known, these solutions have viscoelastic properties which strongly influence the drag coefficient. The experiments have been done with different nozzle diameters, for three types of gas (Air, and ) at different injection flow rates. Hence, the results are more comprehensive than in previous studies. A comparison between the obtained results and the equations in other studies showed that none of these relationships can predict the drag coefficient of a bubble rising in a non-Newtonian fluid with a viscoelastic property. Therefore, two new correlations have been presented to predict the drag coefficient based on Reynolds, Archimedes and Eötvös dimensionless number by dimensional analysis. The first equation which obtained directly from the dimensional analysis was simpler than the second equation. The average error of the first equation was 3.26%, while, the average prediction error of the second equation was about 1.7%, which is more complex in terms of formulation. In addition, new equations for predicting terminal velocities and the behavior of bubble rising in a non-Newtonian viscoelastic fluid are presented.

کلیدواژه‌ها [English]

  • Bubble motion
  • Dimensional analysis
  • Polyacrylamide
  • Terminal velocity
  • Viscoelastic fluid

مراجع

[1]  G. Bozzano, M. Dente, Shape and terminal velocity of single bubble motion: a novel approach, Computers & chemical engineering, 25(4-6) (2001) 571-576.
[2] H. Li, Z. Liu, J. Chen, B. Sun, Y. Guo, H. He, Correlation of aspect ratio and drag coefficient for hydrate-film- covered methane bubbles in water, Experimental Thermal and Fluid Science, 88 (2017) 554-565.
[3]  G. Kelbaliyev, K. Ceylan, Development of new empirical equations for estimation of drag coefficient, shape deformation, and rising velocity of gas bubbles or liquid drops, Chemical Engineering Communications, 194(12) (2007) 1623-1637.
[4]  A. Premlata, M.K. Tripathi, B. Karri, K.C. Sahu, Dynamics of an air bubble rising in a non-Newtonian liquid in the axisymmetric regime, Journal of Non- Newtonian Fluid Mechanics, 239 (2017) 53-61.
[5] B. Sun, Y. Guo, Z. Wang, X. Yang, P. Gong, J. Wang, N. Wang, Experimental study on  the  drag  coefficient of single bubbles rising  in  static  non-Newtonian  fluids in wellbore, Journal of Natural Gas Science and Engineering, 26 (2015) 867-872.
[6]    C.L. Henry, L. Parkinson, J.R. Ralston, V.S. Craig, A mobile gas− water interface in electrolyte solutions, The Journal of Physical Chemistry C, 112(39) (2008) 15094- 15097.
[7]  R. Chen, F.-M. Wang, T.-J. Lin, Bubble wake dynamics of a single bubble rising in the freeboard of     a two-dimensional liquid–solid fluidized bed, Chemical engineering science, 54(21) (1999) 4831-4838.
[8]  W. Nock, S. Heaven, C. Banks, Mass transfer and gas– liquid interface properties of single CO2 bubbles rising in tap water, Chemical engineering science, 140 (2016) 171-178.
[9]  Y. Zhang, Single bubble velocity profile: experiments and numerical simulation, McGill University, 2000.
[10]    Y. Fu, Y. Liu, 3D bubble reconstruction using multiple cameras and space carving method, Measurement Science and Technology, 29(7) (2018) 075206.
[11]  X. Yan, Y. Jia, L. Wang, Y. Cao, Drag coefficient fluctuation prediction of a single bubble rising in water, Chemical Engineering Journal, 316 (2017) 553-562.
 [12] X. Yan, K. Zheng, Y. Jia, Z. Miao, L. Wang, Y. Cao, J. Liu, Drag coefficient prediction of a single bubble rising in liquids, Industrial & Engineering Chemistry Research, 57(15) (2018) 5385-5393.
[13] R.P. Chhabra, Bubbles, drops, and particles in non- Newtonian fluids, CRC press, 2006.
[14] M. Kemiha, X. Frank, S. Poncin, H.Z. Li, Origin of the negative wake behind a bubble rising in non-Newtonian fluids, Chemical Engineering Science, 61(12) (2006) 4041-4047.
[15] L. Zhang, C. Yang, Z.-S. Mao, An empirical correlation of drag coefficient for a single bubble rising in non- Newtonian liquids, Industrial & Engineering Chemistry Research, 47(23) (2008) 9767-9772.
[16] X. Frank, J.-C. Charpentier, Y. Ma, N. Midoux, H.Z. Li, A multiscale approach for modeling bubbles rising  in non-Newtonian fluids, Industrial & Engineering Chemistry Research, 51(4) (2011) 2084-2093.
[17] W.Y. Fan, X.H. Yin, Fractal Approach to Bubble Rising Dynamics in Non-Newtonian Fluids, in: Advanced Materials Research, Trans Tech Publ 889-890, (2014) 559-562.
[18] X. Xu, J. Zhang, F. Liu, X. Wang, W. Wei, Z. Liu, Rising behavior of single bubble in infinite stagnant non- Newtonian liquids, International Journal of Multiphase Flow, 95 (2017) 84-90.
[19] M. Pang, M. Lu, Numerical study on dynamics of single bubble rising in shear-thinning power-law fluid in different gravity environment, Vacuum, 153 (2018) 101- 111.
[20] M. Dziubinski, M. Orczykowska, P. Budzynski, Comments on bubble rising velocity in non-Newtonian liquids, Chemical Engineering Science, 58(11) (2003) 2441-2443
[21] T.-J. Lin, G.-M. Lin, An experimental study on flow structures of a single bubble rising in a shear-thinning viscoelastic fluid with a new measurement technique, International journal of multiphase flow, 2(31) (2005) 239-252.
[22] M. Ohta, Y. Yoshida, M. Sussman, A computational study of the dynamic motion of a bubble rising in Carreau model fluids, Fluid dynamics research, 42(2) (2009) 025501.
[23] L. Zhang, C. Yang, Z.-S. Mao, Numerical simulation of a bubble rising in shear-thinning fluids, Journal of Non-Newtonian Fluid Mechanics, 165(11-12) (2010) 555-567.
[24] W. Fan, X. Yin, A laser imaging-LDV coupling measurement of single bubble forming and rising in shear-thinning fluid, Journal of Thermal Science, 23(3) (2014) 233-238.
[25] S.D. Dhole, R.P. Chhabra, V. Eswaran, Drag of a spherical bubble rising in power law fluids at intermediate Reynolds numbers, Industrial & engineering chemistry research, 46(3) (2007) 939-946.
[26] F. Wenyuan, M. Youguang, J. Shaokun, Y. Ke, L. Huaizhi, An experimental investigation for bubble rising in non-Newtonian fluids and empirical correlation of drag coefficient, Journal of Fluids Engineering, 132(2) (2010) 021305.
[27] S. Li, Y. Ma, S. Jiang, T. Fu, C. Zhu, H.Z. Li, The drag coefficient and the shape for a single bubble rising in non-Newtonian fluids, Journal of Fluids Engineering, 134(8) (2012) 084501.
[28]  W. Sun, C. Zhu, T. Fu, Y. Ma, H. Li, 3D Simulation of Interaction and Drag Coefficient of Bubbles Continuously Rising with Equilateral Triangle Arrangement in Shear- Thinning Fluids, International Journal of Multiphase Flow, (2018) In Press
[29] J. Araújo, J. Miranda, J. Campos, Taylor bubbles rising through flowing non-Newtonian inelastic fluids, Journal of Non-Newtonian Fluid Mechanics, 245 (2017) 49-66.
[30] C. Patrascu, I.L. Omocea, C. Balan, Experimental investigation of a liquid meniscus formed by close colliding viscous and viscoelastic jets, Proceeding  of the romanian academy series A-Mathematics physics technical sciences information sciences, 19(3) (2018) 483-488.
[31] W.L. Shew, J.-F. Pinton, Viscoelastic effects on the dynamics of a rising bubble, Journal of Statistical Mechanics: Theory and Experiment, 2006(01) (2006) P01009.
[32] R. Sousa, M. Riethmuller, A.M. Pinto, J. Campos, Flow around individual Taylor bubbles rising in stagnant polyacrylamide (PAA) solutions, Journal of non- newtonian fluid mechanics, 135(1) (2006) 16-31.
[33] J. Liu, C. Zhu, T. Fu, Y. Ma, H. Li, Numerical simulation of the interactions between three equal-interval parallel bubbles rising in non-Newtonian fluids, Chemical engineering science, 93 (2013) 55-66.
[34] M.K. Tripathi, K.C. Sahu, R. Govindarajan, Dynamics of an initially spherical bubble rising in quiescent liquid, Nature communications, 6 (2015) 6268
 [35] R. Clift, J.R. Grace, M.E. Weber, Bubbles, drops, and particles, Courier Corporation, 2005.
[36] H.D. Mendelson, The prediction of bubble terminal velocities from wave theory, AIChE Journal, 13(2) (1967) 250-253.
[37] M. Jamialahmadi,  H.  Müller-Steinhagen,  Effect  of alcohol, organic acid and potassium chloride concentration on bubble size, bubble rise velocity and gas hold-up in bubble columns, The Chemical Engineering Journal, 50(1) (1992) 47-56.
[38] D. Legendre, R. Zenit, J.R. Velez-Cordero, On the deformation of gas bubbles in liquids, Physics of Fluids, 24(4) (2012) 043303.
[39] L. Böhm, T. Kurita, K. Kimura, M. Kraume, Rising behaviour of single bubbles in narrow rectangular channels in Newtonian and non-Newtonian liquids, International Journal of Multiphase Flow, 65 (2014) 11-23. 
[40] R. Clift, W. Gauvin, Motion of entrained particles in gas streams, The Canadian Journal of Chemical Engineering, 49(4) (1971) 439-448.
[41] K. Dewsbury, D. Karamanev, A. Margaritis, Hydrodynamic characteristics of free rise of light solid particles and gas bubbles in non-Newtonian liquids, Chemical engineering science, 54(21) (1999) 4825-4830.
نشریه مهندسی مکانیک امیرکبیر
دوره 52، شماره 4
تیر 1399
صفحه 863-880

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