Abstract
The two-phase micro-bubble flow over an axisymmetric body is investigated using the OpenFOAM framework. The numerical model consists of an Eulerian-Eulerian two-fluid model with closure relationships for the interfacial momentum transfer to capture the multiphase flow, a standard k – ε model for the continuous phase and one turbulence model inside the OpenFOAM for the dispersed phase. The bubble sizes are calculated based on the solution of the transport equation of the interfacial area density. The simulations in this work are carried out with different air injection rates and different flow velocities. The effects of bubble size on drag reduction are analyzed. The numerical results are compared against some available experiments and other numerical simulations. The numerical results indicate that the airflow rate and air volume fraction within the boundary layer near the body play important roles in micro-bubble drag reduction. The frictional drag reduction effect by micro bubbles is larger for lower water speed, and the presence of the micro bubbles can increase the pressure resistance of the body. Drag reduction rates are generally higher when the bubble diameter is smaller.
Similar content being viewed by others
References
Murai Y. Frictional drag reduction by bubble injection [J]. Experiments in Fluids, 2014, 55(7): 1773.
Song W., Wang C., Wei Y. et al. Experimental study of microbubble drag reduction on an axisymmetric body [J]. Modern Physics Letters B, 2018, 32(3): 1850035.
Wang S. P., Zhang A. M., Liu Y. L. et al. Bubble dynamics and its applications [J]. Journal of Hydrodynamics, 2018, 30(6): 975–991.
Modama Y., Kakugawa A., Takahashi T. et al. Experimental study on microbubbles and their applicability to ships for skin friction reduction [J]. International Journal of Heat and Fluid Flow, 2000, 21(5): 582–588.
Sanders W. C., Winkel E. S., Dowling D. R. et al. Bubble friction drag reduction in a high-Reynolds-number flatplate turbulent boundary layer [J]. Journal of Fluid Mechanics, 2006, 552: 353–380.
Paik B. G., Yim G. T., Kim K. Y. et al. The effects of microbubbles on skin friction in a turbulent boundary layer flow [J]. International Journal of Multiphase Flow, 2016, 80: 164–175.
Marié J L. A simple analytical formulation for microbubble drag reduction [J]. Hot Working Technology, 1987, 92(2): 168–174.
Wu C. S., He S. L., Zhu D. X. et al. Numerical simulation of microbubble flow around an axisymmetric body [J]. Journal of Hydrodynamics, 2006, 18(3): 217–222.
Kunz R. F., Gibeling H. J., Maxey M. R. et al. Validation of two-fluid Eulerian CFD modeling for microbubble drag reduction across a wide range of Reynolds numbers [J]. Journal of Fluids Engineering, 2007, 129(1): 66–79.
Mohanarangam K., Cheung S. C. P., Tu J. Y. et al. Numerical simulation of micro-bubble drag reduction using population balance model [J]. Ocean Engineering, 2009, 36(11): 863–872.
Marschall H., Mornhinweg R., Kossmann A. et al. Numerical simulation of dispersed gas/liquid flows in bubble columns at high phase fractions using OpenFOAM®. Part I-Modeling basics [J]. Chemical Engineering and Technology, 2011, 34(8): 1321–1327.
Xu L., Yuan B., Ni H. et al. Numerical simulation of bubble column flows in churn-turbulent regime: Comparison of bubble size models [J]. Industrial and Engineering Chemistry Research, 2013, 52(20): 6794–6802.
Qin S., Chu N., Yao Y. et al. Stream-wise distribution of skin-friction drag reduction on a flat plate with bubble injection [J]. Physics of Fluids, 2017, 29(3): 1–15.
Drew D. A., Lahey Jr. R. T. Application of general constitutive principles to the derivation of multidimensional two-phase flow equation [J]. International Journal of Multiphase Flow, 1979, 5(4): 243–264.
Bertodano M. A. L. D. Two fluid model for two-phase turbulent jets [J]. Nuclear Engineering and Design, 1998, 179(1): 65–74.
Ishii M., Kim S., Uhle J. Interfacial area transport equation: Model development and benchmark experiments [J]. International Journal of Heat and Mass Transfer, 2002, 45(15): 3111–3123.
Ishii M., Kim S., Kelly J. Development of interfacial area transport equation [J]. Nuclear Engineering and Technology, 2005, 37: 13–29.
Pollard A, Martinuzzi R. Comparative study of turbulence models in predicting turbulent pipe flow. II-Reynolds stress and k-epsilon models [J]. AIAA Journal, 2015, 27(1): 29–36.
Lyu X., Tang H., Sun J. et al. Simulation of microbubble resistance reduction on a suboff model [J]. Brodogradnja, 2014, 65(2): 23–32.
Liu H. L., Huang T. T. Summary of DARPA suboff experimental program data [R]. West Bethesda, MD, USA: Naval Surface Warfare Center Carderock Division (NSWCCD), Report CRDKNSWC/HD-1298-11, 1998.
Madavan N. K., Deutsch S., Merkle C. L. Measurements of local skin friction in a microbubble-modified turbulent boundary layer [J]. Journal of Fluid Mechanics, 2006, 156: 237–256.
Marusic I., Monty J. P., Hultmark M. et al. On the logarithmic region in wall turbulence [J]. Journal of Fluid Mechanics, 2013, 716: R3.
Sayyaadi H., Nematollahi M. Determination of optimum injection flow rate to achieve maximum micro bubble drag reduction in ships; an experimental approach [J]. ScientiaIranica, 2013, 20(3): 535–541.
Winkel E. S., Ceccio S. L., Dowling D. R. et al. Bubble-size distributions produced by wall injection of air into flowing freshwater, saltwater and surfactant solutions [J]. Experiments in Fluids, 2004, 37(6): 802–810.
Xu J., Maxey M. R., Karniadakis G. E. Numerical simulation of turbulent drag reduction using microbubbles [J]. Journal of Fluid Mechanics, 2002, 468: 271–281.
Kawamura T., Moriguchi Y., Kato H. et al. Effect of bubble size on the microbubble drag reduction of a turbulent boundary layer [C]. ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. American Society of Mechanical Engineers Digital Collection, Honolulu, Hawaii, USA, 2009, 647–654.
Hashim A., Yaakob O.B., Koh K. K. et al. Review of micro-bubble ship resistance reduction methods and the mechanisms that affect the skin friction on drag reduction from 1999 to 2015 [J]. Jurnal Teknologi, 2015, 74(5): 105–114.
Mingjun P., Zhan Z. Numerical investigation on turbulence drag reduction by small bubbles in horizontal channel with mixture model combined with population balance model [J]. Ocean Engineering, 2018, 162: 80–97.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Grant Nos. 51679037, 51639003), the National Basic Research Development Program of China (973 Program, Grant No. 2013CB036101).
Biography: Xiao-jie Zhao (1992-), Male, Ph. D. Candidate
Rights and permissions
About this article
Cite this article
Zhao, Xj., Zong, Z., Jiang, Yc. et al. Numerical simulation of micro-bubble drag reduction of an axisymmetric body using OpenFOAM. J Hydrodyn 31, 900–910 (2019). https://doi.org/10.1007/s42241-018-0118-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42241-018-0118-2