# Turbulent shear stress profiles in a bubbly channel flow assessed by particle tracking velocimetry

## Abstract

Particle tracking velocimetry (PTV) is applied to a bubbly two-phase turbulent flow in a horizontal channel at *Re* = 2 × 10^{4} to investigate the turbulent shear stress profile which had been altered by the presence of bubbles. Streamwise and vertical velocity components of liquid phase are obtained using a shallow focus imaging method under backlight photography. The size of bubbles injected through a porous plate in the channel ranged from 0.3 to 1.5 mm diameter, and the bubbles show a significant backward slip velocity relative to liquid flow. After bubbles and tracer particles are identified by binarizing the image, velocity of each phase and void fraction are profiled in a downstream region. The turbulent shear stress, which consists of three components in the bubbly two-phase flow, is computed by analysis of PTV data. The result shows that the fluctuation correlation between local void fraction and vertical liquid velocity provides a negative shear stress component which promotes frictional drag reduction in the bubbly two-phase layer. The paper also deals with the source of the negative shear stress considering bubble’s relative motion to liquid.

### References

- Dominguez-Lerma MA, Ahlers G, Channell DS (1985) Effects of Kalliroscope flow visualization particles on rotating Couette-Taylor flow. Phys Fluids 28:1204–1206CrossRefGoogle Scholar
- Felton K, Loth E (2002) Diffusion of spherical bubbles in a turbulent boundary layer. Int J Multiphase Flow 28:69–92MATHCrossRefGoogle Scholar
- Ferrante A, Elghobashi S (2004) On the physical mechanism of drag reduction in a spatially developing turbulent boundary layer laden with microbubbles. J Fluid Mech 503:345–355MATHCrossRefGoogle Scholar
- Fukagata K, Iwamoto K, Kasagi N (2002) Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys Fluids 14:L73–L76CrossRefGoogle Scholar
- Fukuda K, Tokunaga J, Nobunaga T, Nakatani T, Iwasaki T (2000) Frictional drag reduction with air lubricant over a super-water-repellent surface. J Mar Sci Tech 5:123–130CrossRefGoogle Scholar
- Fukuda H, Oishi Y, Murai Y, Kodama Y, Yamamoto F (2005) Modification of skin frictional drag of gas-liquid two-phase flow in a horizontal channel. In: Proceedings of the 2nd international symposium on seawater drag reduction, pp 125–133Google Scholar
- Gabillet C, Colin C, Fabre J (2002) Experimental study of bubble injection in a turbulent boundary layer. Int J Multiphase Flow 28:553–578MATHCrossRefGoogle Scholar
- Kato H, Iwashina T, Miyanaga M, Yamaguchi H (1999) Effect of microbubbles on the structure of turbulence in a turbulent boundary layer. J Mar Sci Tech 4:115–162Google Scholar
- Kawamura T, Kodama Y (2002) Numerical simulation method to resolve interactions between bubbles and turbulence. Int J Heat Fluid Flow 23:627–638CrossRefGoogle Scholar
- Kitagawa A, Murai Y, Yamamoto F (2001) Two-way coupling of Eulerian-Lagrangian model for dispersed multiphase flows using filtering functions. Int J Multiphase Flow 27:2129–2153MATHCrossRefGoogle Scholar
- Kitagawa A, Hishida K, Kodama Y (2005) Flow structure of microbubble-laden turbulent channel flow measured by PIV combined with the shadow image technique. Exp Fluids 38:466–475CrossRefGoogle Scholar
- Kodama Y, Kakugawa A, Takahashi T, Kawashima H (2000) Experimental study on microbubbles and their applicability to ships for skin friction reduction. Int J Heat Fluid Flow 21:582–588CrossRefGoogle Scholar
- Latorre R, Miller A, Philips R (2003) Micro-bubble resistance reduction on a model SES catamaran. Ocean Eng 30:2297–2309CrossRefGoogle Scholar
- Legner HH (1984) Simple model for gas bubble drag reduction. Phys Fluids 27:2788–2790CrossRefGoogle Scholar
- Li FC, Kawaguchi Y, Segawa T (2005) Reynolds-number dependence of turbulence structures in a drag-reducing surfactant solution channel flow investigated by particle image velocimetry. Phys Fluids 17:1–13MATHGoogle Scholar
- Lu J, Fernandez A, Tryggvason G (2005) The effect of bubbles on the wall drag in a turbulent channel flow. Phys Fluids 17:1–12Google Scholar
- Madavan NK, Deutsch S, Merkle CL (1985) Measurements of local skin friction in microbubble-modified turbulent boundary layer. J Fluid Mech 156:237–256CrossRefGoogle Scholar
- Marie JL (1987) A simple analytical formulation for microbubble drag reduction. J Phys Chem Hydro 13:213–220Google Scholar
- Masliyah J, Jauhari R, Gray M (1994) Drag coefficient for air bubbles rising along an inclined surface. Chem Eng Sci 49:1905–1911CrossRefGoogle Scholar
- Mazzetelli IM, Lohse D, Toschi F (2003) On the relevance of the lift force in bubbly turbulence. J Fluid Mech 488:283–313CrossRefGoogle Scholar
- McCormick M, Bhattacharyya R (1973) Drag reduction of a submersible hull by electrolysis. Nav Eng J 85:11–16CrossRefGoogle Scholar
- Merkle CL, Deutsch S (1992) Microbubble drag reduction in liquid turbulent boundary layers. ASME Appl Mech Rev 45:103–127CrossRefGoogle Scholar
- Moctezuma MF, Lima-Ochoterena R, Zenit R (2005) Velocity fluctuations resulting from the interaction of a bubble with vertical wall. Phys Fluids 17:1–4CrossRefGoogle Scholar
- Moriguchi Y, Kato H (2002) Influence of microbubble diameter and distribution on frictional resistance reduction. J Mar Sci Tech 7:79–85CrossRefGoogle Scholar
- Murai Y, Matsumoto Y (2000) Numerical study of the three-dimensional structure of a bubble plume. J Fluids Eng Trans ASME 122:754–760CrossRefGoogle Scholar
- Nishino K, Kasagi N, Hirata M (1989) Three dimensional particle tracking velocimetry based on automatic digital image processing. J Fluids Eng ASME 111:384–391CrossRefGoogle Scholar
- Takahashi T, Kakugawa A, Makino M., Kodama Y (2003) Experimental study on scale effect of drag reduction by microbubbles using very large flat plate ships. J Kansai Soc N A Japan 239:11–20Google Scholar
- Xu J, Maxey ML, Karniadakis GE (2002) Numerical simulation of turbulent drag reduction using micro-bubbles. J Fluid Mech 468:271–281MATHCrossRefGoogle Scholar