Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30840
A Wall Law for Two-Phase Turbulent Boundary Layers

Authors: Dhahri Maher, Aouinet Hana


The presence of bubbles in the boundary layer introduces corrections into the log law, which must be taken into account. In this work, a logarithmic wall law was presented for bubbly two phase flows. The wall law presented in this work was based on the postulation of additional turbulent viscosity associated with bubble wakes in the boundary layer. The presented wall law contained empirical constant accounting both for shear induced turbulence interaction and for non-linearity of bubble. This constant was deduced from experimental data. The wall friction prediction achieved with the wall law was compared to the experimental data, in the case of a turbulent boundary layer developing on a vertical flat plate in the presence of millimetric bubbles. A very good agreement between experimental and numerical wall friction prediction was verified. The agreement was especially noticeable for the low void fraction when bubble induced turbulence plays a significant role.

Keywords: boundary layer, bubbly flows, log law

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 740


[1] Moursali E., Marié J.L., Bataille J., "An upward turbulent bubbly layer along a vertical flat plate", Int. J. of Multiphase flow. VoL 21 N°1, pp 107-117.1995.
[2] Marie, J., Moursali, E, Tang-Cong, S., “Similarity law and turbulence intensity profiles in a bubbly boundary layer at low void fraction” International journal of multiphase flow, 23(2), pp.227-247, 1997.
[3] Mikielewicz, D. “Hydrodynamics and heat transfer in bubbly flow in the turbulent boundary layer”. International journal of heat and mass transfer 46(2), pp.207-220, 2003.
[4] Hideki Murakawa, Hiroshige Kikura, Masanori Aritomi. “Measurement of Liquid Turbulent Structure in Bubbly Flow at Low Void Fraction Using Ultrasonic Doppler Method”, Journal of Nuclear Science and Technology, 40:9, 644-654, 2003.
[5] Yassin A. Hassan, “Full-field measurements of turbulent bubbly flow using innovative experimental techniques”. Texas A&M University. CASL-8-2014-0209-000, 2014.
[6] Avinash Vaidheeswaran, Deoras Prabhudharwadkar, Paul Guilbert, John R. Buchanan, Jr., Martin Lopez de Bertodano, “New Two-Fluid Model Near-Wall Averaging and Consistent Matching for Turbulent Bubbly Flows”, ASME Journal of Fluids Engineering.2016.
[7] Lance M., Bataille J., "Turbulence in the liquid phase of a uniform bubbly air water flow", J. Fluid Mech., vol. 222, pp. 95-118.1991.
[8] Dhahri Maher, Bellakhel Ghazi, and Chahed Jamel, “A Two Time Scales Turbulence Model of Turbulent Bubbly Flows” International Journal of Fluid Mechanics Research. v40.i3.10, pages 185-203, 2013.
[9] M. Ishii and N. Zuber, "Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows," AIChE, vol. 25, pp. 843-855, 1979.
[10] A. Tomiyama, "Struggle with Computational Bubble Dynamics," Multiphase Science and Technology, vol. 10, pp. 369-405, 1998.
[11] M. Lopez de Bertodano, R. T. LaheyJr and O. C. Jones, "Phase Distribution in Bubbly Two-Phase Flow in Vertical Ducts," International Journal of Multiphase Flow, vol. 20, pp. 805-818, 1994.
[12] S. P. Antal, R. T. Lahey and J. E. Flaherty, "Analysis of Phase distribution in Fully Developed Laminar Bubbly Two-phase Flow," International Journal of Multiphae Flow, vol. 17, pp. 635-652, 1991.
[13] Sato, Y., Sadatomi, M. and Sekoguchi, K. “Momentum and heat Transfer in Two-phase Bubble Flow”, Int. J. Multiphase Flow, Vol. 7, pp. 179-190, 1981.
[14] Clark, N.N. and R.L. Flemmer. ‘’ Predicting the Holdup in Two Phase Bubble Upflow and Downflow Using the Zuber and Findlay Drift-Flux Model’’. AIChE Journal 31, 500-503.1985.