Numerical investigation into the effect of viscosity on bubble dynamics in a narrow channel

Document Type : Article

Authors

1 Center for CFD Studies on Heat Engines, Cavitational Flows and Petroleum Industries, Department of Mechanical Engineering, University of Tabriz, Tabriz, P.O. Box 51666-14766, Iran.

2 Department of Mechanical Engineering, University of Tabriz, P. O. Box 51666-14766, Tabriz, Iran

Abstract

In this paper, dynamic behavior of a vapor bubble inside a narrow channel filled with a viscous liquid has been studied numerically. The boundary integral equation method (BIEM) and the procedure of viscous correction of viscous potential flow (VCVPF) have been employed for obtaining the vapor bubble profiles during its pulsations inside the narrow channel filled with a viscous liquid. In the present paper a new method has been proposed for considering the effects of viscosity in a viscous liquid flow in the framework of the Green's integral formula together with the modified form of unsteady Bernoulli equation. The reported experimental and numerical results of the problem under investigation have been used for verification of the results of the present work. Numerical results show that, by increasing the viscosity of liquid around the vapor bubble, the bubble lifetime increases. Numerical results also indicate that for Reynolds numbers with the order of , the viscosity effects are extremely reduced. Furthermore, the dynamic behavior of the bubble in water and oil is investigated at different Reynolds numbers and at different so-called dimensionless channel radii.

Keywords

Main Subjects


References:
[1] Guo, X., Du, Z., Li, G., et al. “High Frequency Vibration Recovery Enhancement Technology in the Heavy Oil Fields of China, SPE International Thermal Operations and Heavy Oil Symposium, Bakersfield, California, 16-18 March, SPE-86956, pp. 1-18 (2004).
[2] Xu, H., and Pu, C. “Removal of Near-wellbore Formation Damage by Ultrasonic Stimulation, Pet. Sci. Technol., 31, pp. 563-571 (2013).
[3] Jin, Y., Zheng, X., Chu, X., et al. “Oil Recovery from Oil Sludge through Combined Ultrasound and Thermochemical Cleaning Treatment, Ind. Eng. Chem. Res., 51, pp. 9213−9217 (2012).
[4] Massoud, E.Z., Xiao, Q., El-Gamal, H.A., et al. “Numerical study of an individual Taylor bubble rising through stagnant liquids under laminar flow regimeˮ, Ocean Eng., 162, pp. 117-137 (2018).
[5] Amani, E., Ahmadpour, A., Tohidi, M., “A numerical study of the rise of a Taylor bubble through a sudden/gradual expansion in Newtonian and shear-thinning liquids, Scientia Iranica, 152: pp. 236-246 (2019).
[6] Zhang, S., Wang, S.P., Zhang, A.M., et al. “Numerical study on motion of the air-gun bubble based on boundary integral methodˮ, Ocean Eng., 154, pp. 70-80 (2018).
[7] Ziolkowski, A. “Measurement of air-gun bubble oscillations, Geophys., 63, pp. 2009-2024 (1998).
[8] Chahine, G.L., Hsiao, Ch.T., Choi, J.K., et al. “Bubble Augmented Water jet Propulsion: Two-Phase Model Development and Experimental Validation, 27th Symposium on Naval Hydrodynamics, Seoul, Korea, 5-10 October, pp. 1-17 (2008).
[9] Wu, X., Choi, J.K., Singh, S., et al. “Experimental and numerical investigation of bubble augmented water jet propulsion, J. Hydraulics, 24, pp. 635-647 (2012).
[10] Hayati, A.N., Hashemi, S.M., Shams, M. “Design and analysis of bubble-injected water ramjets with discrete injection configurations by computational fluid dynamics method. Proc. IMechE Part C: J. Mechanical Engineering Science, 227, pp. 1945-1955 (2015).
[11] Makaloski, V., Rohlffs, F., Konstantinos, S., et al. “Bubble counter for measurement of air bubbles during thoracic stent-graft deployment in a flow model, J. Surg. Res., 232, pp. 121-127 (2018).
[12] Sánchez, R.M., Rivero, F., Bastante, T., et al. “Intracoronary Bubbles: Iatrogenic Air Embolism Assessed With Optical Coherence Tomography, JACC Cardiovascular Interventions, 10, pp. 153-154 (2017).
[13] Farhangmehr, V., Hajizadeh, A., Shervani-Tabar, M.T., et al. “Numerical investigation on the pulsating bubble dynamics in a narrow cylinder with a compliant coating. Fluid Dyn. Res., 46, 015513, pp. 1-27 (2014).
[14] Ni, B.Y., Zhang, A.M., Wang, Q.X., et al. “Experimental and numerical study on the growth and collapse of a bubble in a narrow tube. Acta Mech. Sin. 28, pp. 1248-1260 (2012).
[15] Baradaran-Fard, M. and Nikseresht, A.H. “Numerical simulation of unsteady 3D cavitating flows over axisymmetric cavitators, Scientia Iranica, 19, pp.1265-1278 (2012).
[16] Hanafizadeh, P., Saidi, M.H., Nouri Gheimasi, M.H., Ghanbarzadeh, S. “Experimental investigation of air–water, two-phase flow regimes in vertical mini pipe, Scientia Iranica, 18: pp.923-929 (2011).
[17] Shervani-Tabar, M.T., Rouhollahi, R.  “Numerical study on the effect of the concave rigid boundaries on the cavitation intensity, Scientia Iranica, 24: pp. 1958-1965 (2017).
[18] Fayzi, P., Bastani, D., Lotfi, M., Khararoodi, M.Gh. “The effects of bubble detachment shape on rising bubble hydrodynamics, Scientia Iranica, pp. -, (2018), doi: 10.24200/sci.2018.51823.2383.
[19] Ory, E., Yuan, H., Prosperetti, A., et al. “Growth and collapse of a vapor bubble in a narrow tube, Phys. Fluids, 12, pp. 1268-1277 (2000).
[20] Shervani-Tabar, M.T. and Eslamian, A. “Dynamics of a Vapour Bubble inside a Vertical Rigid Cylinder, 16th Australasian Fluid Mechanics Conference Crown Plaza, Gold Coast, Australia, 2-7 December, pp. 1420-1426 (2007).
[21] Miao, H., Gracewski, S.M., Dalecki, D. “Ultrasonic excitation of a bubble inside a deformable tube:Implications for ultrasonically induced hemorrhage, J. Acoust Soc. Am.,124, pp. 2374-2384 (2008).
[22] CLANET, Ch. and Heraud, P. “Starby G. On the motion of bubbles in vertical tubes of arbitrary cross-sections: some complements to the Dumitrescu–Taylor problem, J. Fluid Mech., 519, pp. 359-376 (2004). 
[23] Moore, D.W. “The boundary layer on a spherical gas bubble, J. Fluid Mech.,16, pp. 161-176 (1963).
[24] Kang,  I.S. and Leal, L.G. “The drag coefficient for a spherical bubble in a uniform streaming flow, Phys. Fluids, 31, pp. 233-237 (1988). 
[25] Joseph, D.D. “Potential Flow of Viscous Fluids: Historical Notes, Int. J. Multiphase Flow, 32, pp. 285-310 (2006).
[26] Klaseboer, E., Manica, R., Chan, D.Y.C., et al. “BEM simulations of potential flow with viscous effects as applied. Eng. Anal. Boundary Elem., 35, pp. 489-494 (2011).
[27] Joseph, D.D. and Wang H. “Dissipation approximation and viscous potential flow. J. Fluid Mech., 505, pp. 365-377 (2004).
[28] Manmi, K. and Wang, Q. “Acoustic microbubble dynamics with viscous effects, Ultrason. Sonochem., 36: pp. 427-436 (2016).
[29] Zhang, A.M. and Ni, B.Y. “Three-dimensional boundary integral simulations of motion and deformation of bubbles with viscous effects, Comput. Fluids, 92, pp. 22-33 (2014). 
[30] Wang, S.P., Wang, Q.X., Leppinen, D.M., et al. “Acoustic bubble dynamics in a microvessel surrounded by elastic material, Phys. Fluids, 30, 012104, pp. 1-10 (2018).
[31] Minsier, V., Wilde, J.D., Proost, J. “Simulation of the effect of viscosity on jet penetration into a single cavitating bubble, J. Appl. Phys., 106, 084906, pp. 1-10 (2009).
[32] Taib, B.B. “Boundary integral method applied to cavitation bubble dynamics, PhD Thesis, University of Wollongong, Australia (1985).
[33] Mehravarana, M., and Kazemzadeh, S. “Simulation of buoyant bubble motion in viscous flows employing lattice Boltzmann and level set methods, Scientia Iranica, 18: pp. 231-240 (2011).
[34] Lind, S.J. and Philips, T.N. “The effect of viscoelasticity on the dynamics of gas bubbles near free surfaces, Phys. Fluids, 25, 022104, pp. 1-32 (2013).
[35] Katsikadelis, J.T. “Preliminary Mathematical Concept, In Boundary Elements: Theory and Applications, 1th ed., UK, Elsevier Science, p. 16 (2002).
[36] Zhou, J., Hu, J., Yuan, Sh. “Modeling bubble evolution in air-oil mixture with a simplified method, Proc. IMechE Part C: J. Mechanical Engineering Science, 230, pp. 2865-2871 (2016). 
[37] White, F.M. “Fundamental Equations of Compressible Viscous Flow, In Viscous Fluid Flow, 2th ed., New York, McGraw-Hill, pp. 61-69 (1991).
 [38] Batchelor, G.K. “Flow at Large Reynolds Number: Effects of Viscosity, In An introduction to fluid dynamics,1th ed., UK, Cambridge University Press, pp. 264-377 (2000). 
 [39] Joseph, D.D., Funada, T., Wang, J. “Helmholtz decomposition coupling rotational to irrotational flow, In Potential flows of viscous and Viscoelastic fluids, 1th ed., UK, Cambridge University Press, pp. 15-18 (2007).
 [40] Shervani-Tabar, M.T. “Computer study of a cavity bubble near a rigid boundary, a free surface and a compliant wall, PhD Thesis, University of Wollongong, Australia (1995).
Volume 27, Issue 5 - Serial Number 5
Transactions on Mechanical Engineering (B)
September and October 2020
Pages 2419-2432
  • Receive Date: 16 November 2018
  • Revise Date: 04 March 2019
  • Accept Date: 02 July 2019