Numerical Simulation of Single Bubble Deformation in Straight Duct and 90° Bend Using Lattice Boltzmann Method

Affiliation(s)

School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.

School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.

ABSTRACT

The paper aims to give a comprehensive investigation of the two dimensional deformation of a single bubble in a straight duct and a 90° bend under the zero gravity condition. For this, the two phase flow lattice Boltzmann equation (LBE) model is used. An averaging scheme of boundary condition implementation has been applied and validated. A generalized deformation benchmark has been introduced. By presenting and analyzing the shape of the bubbles moving through the channels, the effects of the all important nondimensional numbers on the bubble deformation are examined thoroughly. It is seen that by increasing the Weber number the rate of the deformation enhances. Besides, because of the velocity dissimilarity between the particles constructing the bubble, the initial coordinates and the diameter of the bubble play a great role in the future behavior of the bubble. The density ratio has a little effect on the shape of the bubble within the assumed range of the density ratio. Moreover, as the Reynolds number or the viscosity ratio is decreased, higher rate of deformation is exhibited. Finally it is found that there is an inverse proportionality between the amplitude and frequency of the bubble deformation.

The paper aims to give a comprehensive investigation of the two dimensional deformation of a single bubble in a straight duct and a 90° bend under the zero gravity condition. For this, the two phase flow lattice Boltzmann equation (LBE) model is used. An averaging scheme of boundary condition implementation has been applied and validated. A generalized deformation benchmark has been introduced. By presenting and analyzing the shape of the bubbles moving through the channels, the effects of the all important nondimensional numbers on the bubble deformation are examined thoroughly. It is seen that by increasing the Weber number the rate of the deformation enhances. Besides, because of the velocity dissimilarity between the particles constructing the bubble, the initial coordinates and the diameter of the bubble play a great role in the future behavior of the bubble. The density ratio has a little effect on the shape of the bubble within the assumed range of the density ratio. Moreover, as the Reynolds number or the viscosity ratio is decreased, higher rate of deformation is exhibited. Finally it is found that there is an inverse proportionality between the amplitude and frequency of the bubble deformation.

KEYWORDS

Bubble Deformation, Straight Duct, 90° Bend, Lattice Boltzmann Method, Curved Wall Boundary Condition, Deformation Benchmark

Bubble Deformation, Straight Duct, 90° Bend, Lattice Boltzmann Method, Curved Wall Boundary Condition, Deformation Benchmark

Cite this paper

Daryan, H. and Rahimian, M. (2015) Numerical Simulation of Single Bubble Deformation in Straight Duct and 90° Bend Using Lattice Boltzmann Method.*Journal of Electronics Cooling and Thermal Control*, **5**, 89-118. doi: 10.4236/jectc.2015.54007.

Daryan, H. and Rahimian, M. (2015) Numerical Simulation of Single Bubble Deformation in Straight Duct and 90° Bend Using Lattice Boltzmann Method.

References

[1] Grace, J.R. (1973) Shapes and Velocities of Bubbles Rising in Infinite Liquids. Transactions of the Institution of Chemical Engineers, 51, 116-120.

[2] Bhaga, D. and Weber, M.E. (1981) Bubbles in Viscous Liquids: Shapes, Wakes and Velocities. Journal of Fluid Mechanics, 105, 61-85.

http://dx.doi.org/10.1017/S002211208100311X

[3] Fan, L. and Tsuchiya, K. (1990) Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions. Butterworth-Heinemann, Oxford.

[4] Clift, R., Grace, J.R. and Weber, M.E. (1978) Bubbles, Drops and Particles. Academic Press, New York.

[5] Prosperetti, A. and Tryggvason, G. (2007) Computational Methods for Multiphase Flow. Cambridge University Press, Cambridge.

[6] Chen, L., Garimella, S.V., Reizes, J.A. and Leonardi, E. (1999) The Development of a Bubble Rising in a Viscous Liquid. Journal of Fluid Mechanics, 387, 61-96.

http://dx.doi.org/10.1017/S0022112099004449

[7] van Sint Annaland, M., Deen, N.G. and Kuipers, J.A.M. (2005) Numerical Simulation of Gas Bubbles Behaviour Using a Three-Dimensional Volume of Fluid Method. Chemical Engineering Science, 60, 2999-3011.

http://dx.doi.org/10.1016/j.ces.2005.01.031

[8] Ohta, M., Imura, T., Yoshida, Y. and Sussman, M. (2005) A Computational Study of the Effect of Initial Bubble Conditions on the Motion of a Gas Bubble Rising in Viscous Liquids. International Journal of Multiphase Flow, 31, 223-237.

http://dx.doi.org/10.1016/j.ijmultiphaseflow.2004.12.001

[9] Bonometti, T. and Magnaudet, J. (2006) Transition from Spherical Cap to Toroidal Bubbles. Physics of Fluids, 18, Article ID: 052102.

http://dx.doi.org/10.1063/1.2196451

[10] Feng, J. Q. (2007) A Spherical-Cap Bubble Moving at Terminal Velocity in a Viscous Liquid. Journal of Fluid Mechanics, 579, 347-371.

http://dx.doi.org/10.1017/S0022112007005319

[11] Hua, J., Stene, J.F. and Lin, P. (2008) Numerical Simulation of 3D Bubbles Rising in Viscous Liquids Using a Front Tracking Method. Journal of Computational Physics, 227, 3358-3382.

http://dx.doi.org/10.1016/j.jcp.2007.12.002

[12] Sukop M.C. and Thorne, D.T. (2006) Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. Springer, Berlin Heidelberg.

[13] Yu, D., Mei, R., Luo, L.S. and Shyy, W. (2003) Viscous Flow Computations with the Method of Lattice Boltzmann Equation. Progress in Aerospace Sciences, 39, 329-367.

http://dx.doi.org/10.1016/S0376-0421(03)00003-4

[14] Succi, S. (2001) The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Oxford University Press, Oxford.

[15] He, X., Chen, S. and Zhang, R. (1999) A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and its Application in Simulation of Rayleigh-Taylor Instability. Journal of Computational Physics, 152, 642-663.

http://dx.doi.org/10.1006/jcph.1999.6257

[16] He, X., Zhang, R., Chen, S. and Doolen, G.D. (1999) On the Three-Dimensional Rayleigh-Taylor Instability. Physics of Fluids, 11, 1143-1152.

http://dx.doi.org/10.1063/1.869984

[17] Jacqmin, D. (1999) Calculation of Two-Phase Navier-Stokes Flows Using Phase-Field Modeling. Journal of Computational Physics, 155, 96-127.

http://dx.doi.org/10.1006/jcph.1999.6332

[18] Lee, T. and Lin, C.L. (2005) A Stable Discretization of the Lattice Boltzmann Equation for Simulation of Incompressible Two-Phase Flows at High Density Ratio. Journal of Computational Physics, 206, 16-47.

http://dx.doi.org/10.1016/j.jcp.2004.12.001

[19] Lee, T. (2009) Effects of Incompressibility on the Elimination of Parasitic Currents in the Lattice Boltzmann Equation Method for Binary Fluids. Computers & Mathematics with Applications, 58, 987-994.

http://dx.doi.org/10.1016/j.camwa.2009.02.017

[20] Gupta, A. and Kumar, R. (2008) Lattice Boltzmann Simulation to Study Multiple Bubble Dynamics. International Journal of Heat and Mass Transfer, 51, 5192-5203.

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2008.02.050

[21] Fakhari, A. and Rahimian, M.H. (2009) Simulation of an Axisymmetric Rising Bubble by a Multiple Relaxation Time Lattice Boltzmann Method. International Journal of Modern Physics B, 23, 4907-4932.

http://dx.doi.org/10.1142/S0217979209053965

[22] Amaya-Bower, L. and Lee, T. (2010) Single Bubble Rising Dynamics for Moderate Reynolds Number Using Lattice Boltzmann Method. Computers & Fluids, 39, 1191-1207.

http://dx.doi.org/10.1016/j.compfluid.2010.03.003

[23] Amaya-Bower, L. and Lee, T. (2011) Numerical Simulation of Single Bubble Rising in Vertical and Inclined Square Channel Using Lattice Boltzmann Method. Chemical Engineering Science, 66, 935-952.

http://dx.doi.org/10.1016/j.ces.2010.11.043

[24] Tölke, J., Freudiger, S. and Krafczyk, M. (2006) An Adaptive Scheme Using Hierarchical Grids for Lattice Boltzmann Multi-Phase Flow Simulations. Computers & Fluids, 35, 820-830.

http://dx.doi.org/10.1016/j.compfluid.2005.08.010

[25] Yu, Z., Yang, H. and Fan, L.S. (2011) Numerical Simulation of Bubble Interactions Using an Adaptive Lattice Boltzmann Method. Chemical Engineering Science, 66, 3441-3451.

http://dx.doi.org/10.1016/j.ces.2011.01.019

[26] Qian, Y.H. and Chen, S.Y. (2000) Dissipative and Dispersive Behaviors of Lattice-Based Models for Hydrodynamics. Physical Review E, 61, 2712.

http://dx.doi.org/10.1103/PhysRevE.61.2712

[27] Lee, T., Lin, C.L. and Chen, L.D. (2006) A Lattice Boltzmann Algorithm for Calculation of the Laminar Jet Diffusion Flame. Journal of Computational Physics, 215, 133-152.

http://dx.doi.org/10.1016/j.jcp.2005.10.021

[28] Lee, T. and Liu, L. (2010) Lattice Boltzmann Simulations of Micron-Scale Drop Impact on Dry Surfaces. Journal of Computational Physics, 229, 8045-8063.

http://dx.doi.org/10.1016/j.jcp.2010.07.007

[29] Zou, Q. and He, X. (1997) On Pressure and Velocity Boundary Conditions for the Lattice Boltzmann BGK Model. Physics of Fluids, 9, 1591-1598.

http://dx.doi.org/10.1063/1.869307

[30] Hua, J. and Lou, J. (2007) Numerical Simulation of Bubble Rising in Viscous Liquid. Journal of Computational Physics, 222, 769-795.

http://dx.doi.org/10.1016/j.jcp.2006.08.008

[1] Grace, J.R. (1973) Shapes and Velocities of Bubbles Rising in Infinite Liquids. Transactions of the Institution of Chemical Engineers, 51, 116-120.

[2] Bhaga, D. and Weber, M.E. (1981) Bubbles in Viscous Liquids: Shapes, Wakes and Velocities. Journal of Fluid Mechanics, 105, 61-85.

http://dx.doi.org/10.1017/S002211208100311X

[3] Fan, L. and Tsuchiya, K. (1990) Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions. Butterworth-Heinemann, Oxford.

[4] Clift, R., Grace, J.R. and Weber, M.E. (1978) Bubbles, Drops and Particles. Academic Press, New York.

[5] Prosperetti, A. and Tryggvason, G. (2007) Computational Methods for Multiphase Flow. Cambridge University Press, Cambridge.

[6] Chen, L., Garimella, S.V., Reizes, J.A. and Leonardi, E. (1999) The Development of a Bubble Rising in a Viscous Liquid. Journal of Fluid Mechanics, 387, 61-96.

http://dx.doi.org/10.1017/S0022112099004449

[7] van Sint Annaland, M., Deen, N.G. and Kuipers, J.A.M. (2005) Numerical Simulation of Gas Bubbles Behaviour Using a Three-Dimensional Volume of Fluid Method. Chemical Engineering Science, 60, 2999-3011.

http://dx.doi.org/10.1016/j.ces.2005.01.031

[8] Ohta, M., Imura, T., Yoshida, Y. and Sussman, M. (2005) A Computational Study of the Effect of Initial Bubble Conditions on the Motion of a Gas Bubble Rising in Viscous Liquids. International Journal of Multiphase Flow, 31, 223-237.

http://dx.doi.org/10.1016/j.ijmultiphaseflow.2004.12.001

[9] Bonometti, T. and Magnaudet, J. (2006) Transition from Spherical Cap to Toroidal Bubbles. Physics of Fluids, 18, Article ID: 052102.

http://dx.doi.org/10.1063/1.2196451

[10] Feng, J. Q. (2007) A Spherical-Cap Bubble Moving at Terminal Velocity in a Viscous Liquid. Journal of Fluid Mechanics, 579, 347-371.

http://dx.doi.org/10.1017/S0022112007005319

[11] Hua, J., Stene, J.F. and Lin, P. (2008) Numerical Simulation of 3D Bubbles Rising in Viscous Liquids Using a Front Tracking Method. Journal of Computational Physics, 227, 3358-3382.

http://dx.doi.org/10.1016/j.jcp.2007.12.002

[12] Sukop M.C. and Thorne, D.T. (2006) Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. Springer, Berlin Heidelberg.

[13] Yu, D., Mei, R., Luo, L.S. and Shyy, W. (2003) Viscous Flow Computations with the Method of Lattice Boltzmann Equation. Progress in Aerospace Sciences, 39, 329-367.

http://dx.doi.org/10.1016/S0376-0421(03)00003-4

[14] Succi, S. (2001) The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Oxford University Press, Oxford.

[15] He, X., Chen, S. and Zhang, R. (1999) A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and its Application in Simulation of Rayleigh-Taylor Instability. Journal of Computational Physics, 152, 642-663.

http://dx.doi.org/10.1006/jcph.1999.6257

[16] He, X., Zhang, R., Chen, S. and Doolen, G.D. (1999) On the Three-Dimensional Rayleigh-Taylor Instability. Physics of Fluids, 11, 1143-1152.

http://dx.doi.org/10.1063/1.869984

[17] Jacqmin, D. (1999) Calculation of Two-Phase Navier-Stokes Flows Using Phase-Field Modeling. Journal of Computational Physics, 155, 96-127.

http://dx.doi.org/10.1006/jcph.1999.6332

[18] Lee, T. and Lin, C.L. (2005) A Stable Discretization of the Lattice Boltzmann Equation for Simulation of Incompressible Two-Phase Flows at High Density Ratio. Journal of Computational Physics, 206, 16-47.

http://dx.doi.org/10.1016/j.jcp.2004.12.001

[19] Lee, T. (2009) Effects of Incompressibility on the Elimination of Parasitic Currents in the Lattice Boltzmann Equation Method for Binary Fluids. Computers & Mathematics with Applications, 58, 987-994.

http://dx.doi.org/10.1016/j.camwa.2009.02.017

[20] Gupta, A. and Kumar, R. (2008) Lattice Boltzmann Simulation to Study Multiple Bubble Dynamics. International Journal of Heat and Mass Transfer, 51, 5192-5203.

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2008.02.050

[21] Fakhari, A. and Rahimian, M.H. (2009) Simulation of an Axisymmetric Rising Bubble by a Multiple Relaxation Time Lattice Boltzmann Method. International Journal of Modern Physics B, 23, 4907-4932.

http://dx.doi.org/10.1142/S0217979209053965

[22] Amaya-Bower, L. and Lee, T. (2010) Single Bubble Rising Dynamics for Moderate Reynolds Number Using Lattice Boltzmann Method. Computers & Fluids, 39, 1191-1207.

http://dx.doi.org/10.1016/j.compfluid.2010.03.003

[23] Amaya-Bower, L. and Lee, T. (2011) Numerical Simulation of Single Bubble Rising in Vertical and Inclined Square Channel Using Lattice Boltzmann Method. Chemical Engineering Science, 66, 935-952.

http://dx.doi.org/10.1016/j.ces.2010.11.043

[24] Tölke, J., Freudiger, S. and Krafczyk, M. (2006) An Adaptive Scheme Using Hierarchical Grids for Lattice Boltzmann Multi-Phase Flow Simulations. Computers & Fluids, 35, 820-830.

http://dx.doi.org/10.1016/j.compfluid.2005.08.010

[25] Yu, Z., Yang, H. and Fan, L.S. (2011) Numerical Simulation of Bubble Interactions Using an Adaptive Lattice Boltzmann Method. Chemical Engineering Science, 66, 3441-3451.

http://dx.doi.org/10.1016/j.ces.2011.01.019

[26] Qian, Y.H. and Chen, S.Y. (2000) Dissipative and Dispersive Behaviors of Lattice-Based Models for Hydrodynamics. Physical Review E, 61, 2712.

http://dx.doi.org/10.1103/PhysRevE.61.2712

[27] Lee, T., Lin, C.L. and Chen, L.D. (2006) A Lattice Boltzmann Algorithm for Calculation of the Laminar Jet Diffusion Flame. Journal of Computational Physics, 215, 133-152.

http://dx.doi.org/10.1016/j.jcp.2005.10.021

[28] Lee, T. and Liu, L. (2010) Lattice Boltzmann Simulations of Micron-Scale Drop Impact on Dry Surfaces. Journal of Computational Physics, 229, 8045-8063.

http://dx.doi.org/10.1016/j.jcp.2010.07.007

[29] Zou, Q. and He, X. (1997) On Pressure and Velocity Boundary Conditions for the Lattice Boltzmann BGK Model. Physics of Fluids, 9, 1591-1598.

http://dx.doi.org/10.1063/1.869307

[30] Hua, J. and Lou, J. (2007) Numerical Simulation of Bubble Rising in Viscous Liquid. Journal of Computational Physics, 222, 769-795.

http://dx.doi.org/10.1016/j.jcp.2006.08.008