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Numerical study of turbulent bubbly upflow: effect of density ratio

Published online by Cambridge University Press:  17 March 2025

Min Lu ,
Zixuan Yang Open the ORCID record for Zixuan Yang [Opens in a new window]  and
Bingqing Deng Open the ORCID record for Bingqing Deng [Opens in a new window]
Min Lu
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 101408, PR China
Zixuan Yang*
Affiliation:
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 101408, PR China
Bingqing Deng
Affiliation:
School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 101408, PR China
*
Corresponding author: Zixuan Yang, [email protected]
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Abstract

In this study, we conducted interface-capturing high-resolution simulations of a bubbly upflow in a vertical channel to investigate the bubble distribution and its interaction with surrounding turbulence, focusing on the effects of the density ratio. A bulk Reynolds number $Re_b=2300$ was used for all simulations. The influence of density ratio on vortex structures and turbulence statistics differed between the near-wall and core regions of the channel. Adding 5.43 $\%$ gas caused an increase in wall friction. By applying a generalised FIK identity to analyse wall friction, it was determined that the drag rise in the bubbly channel was mostly due to the near-wall region. Visualisation of the bubble and vortex structures showed that small bubbles near the wall induced larger magnitude of Reynolds shear stress and increased wall friction. Bubble behaviour near the wall region was similar for density ratios above 30, leading to wall friction saturation. In the core region, large deformable bubbles created wake vortices due to slip velocity between liquid and gas phases. Wake vortices help large bubbles absorb smaller bubbles and maintain their sizes. As the density ratio increased, the slip velocity increased owing to greater difference in the gravitational acceleration between liquid and gas phases, resulting in corresponding increase in wake intensity and velocity fluctuations. However, quadrant analysis showed that Q1 and Q3 events increased together with Q2 and Q4 events in the core region, cancelling out any net effect of wake vortices on Reynolds shear stress or wall friction.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1007 , 25 March 2025 , A63
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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References

Bazesefidpar, K., Brandt, L. & Tammisola, O. 2022 A dual resolution phase-field solver for wetting of viscoelastic droplets. Intl J. Numer. Methods Fluids 94 (9), 1517–1541.CrossRefGoogle ScholarPubMed
Bolotnov, I.A., Jansen, K.E., Drew, D.A., Oberai, A.A., Lahey, R.T. Jr & Podowski, M.Z. 2011 Detached direct numerical simulations of turbulent two-phase bubbly channel flow. Intl J. Multiphase Flow 37 (6), 647–659.CrossRefGoogle Scholar
Bullee, P.A., Verschoof, R.A., Bakhuis, D., Huisman, S.G., Sun, C., Lammertink, R.G.H. & Lohse, D. 2020 Bubbly drag reduction using a hydrophobic inner cylinder in Taylor–Couette turbulence. J. Fluid Mech. 883, A61.CrossRefGoogle Scholar
Cannon, I., Izbassarov, D., Tammisola, O., Brandt, L. & Rosti, M.E. 2021 The effect of droplet coalescence on drag in turbulent channel flows. Phys. Fluids 33 (8), 085112.CrossRefGoogle Scholar
Cannon, I., Soligo, G. & Rosti, M.E. 2024 Morphology of clean and surfactant-laden droplets in homogeneous isotropic turbulence. J. Fluid Mech. 987, A31.CrossRefGoogle Scholar
Chong, K.L., Ding, G. & Xia, K.-Q. 2018 Multiple-resolution scheme in finite-volume code for active or passive scalar turbulence. J. Comput. Phys. 375, 1045–1058.CrossRefGoogle Scholar
Cifani, P., Kuerten, J.G.M. & Geurts, B.J. 2018 Highly scalable DNS solver for turbulent bubble-laden channel flow. Comput. Fluids 172, 67–83.CrossRefGoogle Scholar
Crialesi-Esposito, M., Rosti, M.E., Chibbaro, S. & Brandt, L. 2022 Modulation of homogeneous and isotropic turbulence in emulsions. J. Fluid Mech. 940, A19.CrossRefGoogle Scholar
Dabiri, S., Lu, J. & Tryggvason, G. 2013 Transition between regimes of a vertical channel bubbly upflow due to bubble deformability. Phys. Fluids 25 (10), 102110.CrossRefGoogle Scholar
De Vita, F., Rosti, M.E., Caserta, S. & Brandt, L. 2019 On the effect of coalescence on the rheology of emulsions. J. Fluid Mech. 880, 969–991.CrossRefGoogle Scholar
Ding, H. & Yuan, C.-J. 2014 On the diffuse interface method using a dual-resolution cartesian grid. J. Comput. Phys. 273, 243–254.CrossRefGoogle Scholar
du Cluzeau, A., Bois, G. & Toutant, A. 2019 Analysis and modelling of Reynolds stresses in turbulent bubbly up-flows from direct numerical simulations. J. Fluid Mech. 866, 132–168.CrossRefGoogle Scholar
du Cluzeau, A., Bois, G., Toutant, A. & Martinez, J.-M. 2020 On bubble forces in turbulent channel flows from direct numerical simulations. J. Fluid Mech. 882, A27.CrossRefGoogle Scholar
Elghobashi, S. 2019 Direct numerical simulation of turbulent flows laden with droplets or bubbles. Annu. Rev. Fluid Mech 51 (1), 217–244.CrossRefGoogle Scholar
Ervin, E.A. & Tryggvason, G. 1997 The rise of bubbles in a vertical shear flow. J. Fluids Engng 119 (2), 443–449.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73–L76.CrossRefGoogle Scholar
Garrett, C., Li, M. & Farmer, D. 2000 The connection between bubble size spectra and energy dissipation rates in the upper ocean. J. Phys. Oceanogr. 30 (9), 2163–2171.2.0.CO;2>CrossRefGoogle Scholar
Hajisharifi, A., Marchioli, C. & Soldati, A. 2022 Interface topology and evolution of particle patterns on deformable drops in turbulence. J. Fluid Mech. 933, A41.CrossRefGoogle Scholar
Hasslberger, J., Cifani, P., Chakraborty, N. & Klein, M. 2020 A direct numerical simulation analysis of coherent structures in bubble-laden channel flows. J. Fluid Mech. 905, A37.CrossRefGoogle Scholar
Hendrickson, K., Weymouth, G.D., Yu, X. & Yue, D.K. 2019 Wake behind a three-dimensional dry transom stern. Part 1. Flow structure and large-scale air entrainment. J. Fluid Mech. 875, 854–883.CrossRefGoogle Scholar
Herrmann, M. 2010 A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure. J. Comput. Phys. 229 (3), 745–759.CrossRefGoogle Scholar
Lee, I., Chang, J., Kim, K. & Choi, H. 2024 A numerical study on the turbulence characteristics in an air–water upward bubbly pipe flow. J. Fluid Mech. 994, A10.CrossRefGoogle Scholar
Li, R., Yang, Z. & Zhang, W. 2024 Numerical investigation of mixed-phase turbulence induced by a plunging jet. J. Fluid Mech. 979, A27.CrossRefGoogle Scholar
Liu, H.-R., Ng, C.S., Chong, K.L., Lohse, D. & Verzicco, R. 2021 An efficient phase-field method for turbulent multiphase flows. J. Comput. Phys. 446, 110659.CrossRefGoogle Scholar
Lu, J. & Tryggvason, G. 2008 Effect of bubble deformability in turbulent bubbly upflow in a vertical channel. Phys. Fluids 20 (4), 040701.CrossRefGoogle Scholar
Lu, J. & Tryggvason, G. 2013 Dynamics of nearly spherical bubbles in a turbulent channel upflow. J. Fluid Mech. 732, 166–189.CrossRefGoogle Scholar
Lu, J. & Tryggvason, G. 2018 Direct numerical simulations of multifluid flows in a vertical channel undergoing topology changes. Phys. Rev. Fluids 3 (8), 084401.CrossRefGoogle Scholar
Lu, J. & Tryggvason, G. 2019 Multifluid flows in a vertical channel undergoing topology changes: effect of void fraction. Phys. Rev. Fluids 4 (8), 084301.CrossRefGoogle Scholar
Lu, M., Lu, J., Zhang, Y. & Tryggvason, G. 2019 Effect of electrostatic forces on the distribution of drops in turbulent channel flows. Phys. Fluids 31 (10), 105104.CrossRefGoogle Scholar
Lu, M., Yang, Z., He, G. & Shen, L. 2024 Numerical investigation on the heat transfer in wind turbulence over breaking waves. Phys. Rev. Fluids 9 (8), 084606.CrossRefGoogle Scholar
Mangani, F., Soligo, G., Roccon, A. & Soldati, A. 2022 Influence of density and viscosity on deformation, breakage, and coalescence of bubbles in turbulence. Phys. Rev. Fluids 7 (5), 053601.CrossRefGoogle Scholar
Mathai, V., Lohse, D. & Sun, C. 2020 Bubbly and buoyant particle–laden turbulent flows. Annu. Rev. Condens. Matt. Phys. 11 (1), 529–559.CrossRefGoogle Scholar
Mostert, W. & Deike, L. 2020 Inertial energy dissipation in shallow-water breaking waves. J. Fluid Mech. 890, A12.CrossRefGoogle Scholar
Ni, R. 2024 Deformation and breakup of bubbles and drops in turbulence. Annu. Rev. Fluid Mech. 56 (1), 319–347.CrossRefGoogle Scholar
Ostilla-Mónico, R., Yang, Y., Van Der Poel, E.P., Lohse, D. & Verzicco, R. 2015 A multiple-resolution strategy for direct numerical simulation of scalar turbulence. J. Comput. Phys. 301, 308–321.CrossRefGoogle Scholar
Park, H., Choi, C.-H. & Kim, C.-J. 2021 Superhydrophobic drag reduction in turbulent flows: a critical review. Exp. Fluids 62 (11), 1–29.CrossRefGoogle Scholar
Patel, J.K. & Natarajan, G. 2015 A generic framework for design of interface capturing schemes for multi-fluid flows. Comput. Fluids 106, 108–118.CrossRefGoogle Scholar
Santarelli, C. & Fröhlich, J. 2015 Direct numerical simulations of spherical bubbles in vertical turbulent channel flow. Intl J. Multiphase Flow 75, 174–193.CrossRefGoogle Scholar
Schenk, M., Giamagas, G., Roccon, A., Soldati, A. & Zonta, F. 2024 Computationally efficient and interface accurate dual-grid phase-field simulation of turbulent drop-laden flows. J. Fluids. Engng 146 (12), 121401.CrossRefGoogle Scholar
So, S., Morikita, H., Takagi, S. & Matsumoto, Y. 2002 Laser Doppler velocimetry measurement of turbulent bubbly channel flow. Exp. Fluids 33 (1), 135–142.CrossRefGoogle Scholar
Soligo, G., Roccon, A. & Soldati, A. 2019 Breakage, coalescence and size distribution of surfactant-laden droplets in turbulent flow. J. Fluid Mech. 881, 244–282.CrossRefGoogle Scholar
Soligo, G., Roccon, A. & Soldati, A. 2021 Turbulent flows with drops and bubbles: what numerical simulations can tell us–freeman scholar lecture. J. Fluids. Engng 143 (8), 080801.CrossRefGoogle Scholar
Su, J., Yi, L., Zhao, B., Wang, C., Xu, F., Wang, J. & Sun, C. 2024 Numerical study on the mechanism of drag modulation by dispersed drops in two-phase Taylor–Couette turbulence. J. Fluid Mech. 984, R3.CrossRefGoogle Scholar
Sui, Y., Ding, H. & Spelt, P.D.M. 2014 Numerical simulations of flows with moving contact lines. Annu. Rev. Fluid Mech. 46 (2014), 97–119.CrossRefGoogle Scholar
Sussman, M. & Puckett, E.-G. 2000 A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. J. Comput. Phys. 162 (2), 301–337.CrossRefGoogle Scholar
Takagi, S. & Matsumoto, Y. 2011 Surfactant effects on bubble motion and bubbly flows. Annu. Rev. Fluid Mech. 43 (1), 615–636.CrossRefGoogle Scholar
Tryggvason, G. & Lu, J. 2015 Direct numerical simulations of bubbly flows. Mech. Engng Rev. 2 (2), 15–00220.Google Scholar
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–liquid Multiphase Flows. Cambridge University Press.Google Scholar
Tsukahara, T., Seki, Y., Kawamura, H. & Tochio, D. 2005 DNS of turbulent channel flow at very low Reynolds numbers. In Fourth International Symposium on Turbulence and Shear Flow Phenomena, 935–940. Begell House.CrossRefGoogle Scholar
Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20 (5), 053305.CrossRefGoogle Scholar
Yang, Z., Deng, B.-Q. & Shen, L. 2018 Direct numerical simulation of wind turbulence over breaking waves. J. Fluid Mech. 850, 120–155.CrossRefGoogle Scholar
Yang, Z., Lu, M. & Wang, S. 2021 A robust solver for incompressible high-Reynolds-number two-fluid flows with high density contrast. J. Comput. Phys. 441, 110474.5CrossRefGoogle Scholar
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