# Experimental investigation of head resistance reduction in bubbly Couette–Taylor flow

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## Abstract

Small bubble experiments are carried out in a circulating vertical Couette–Taylor flow system to investigate the effect of air bubbles on head resistance. In the system with inner rotating cylinder and circulating flow, flow is combined with circumferential and axial flow. Moreover, the variation range of rotational Reynolds number is \(7 \times 10^{3} \le {Re}_{\omega } \le 70 \times 10^{3}\) and small bubbles are dispersed into fully turbulent flow which consists of Taylor vortices. The modification of head resistance is examined by measuring the pressure difference between two certain holes along the cylinders axis. The results show that head resistance is decreased in the presence of small bubbles and a head resistance reduction greater than 60 % is achieved in low \({Re}_{\omega }\) s and in all \({Re}_{ax}\) s changing from 299.15 to 396.27. The effect of air bubbles on vortices could be possible reason for head resistance reduction. Since Taylor vortices are stable in this regime, bubbles decrease the momentum transfer by elongating vortices along the axis of cylinders and decreasing their numbers. The positive effect of air bubbles on head resistance reduction is diminished when \({Re}_{\omega }\) is increased. Moreover, in certain ranges of \({Re}_{\omega }\), small bubbles enhance head resistance when \({Re}_{ax}\) is increased. It is predicted that negative effect of small bubbles on head resistance reduction is due to flow turbulence enhancement when \({Re}_{\omega }\) and \({Re}_{ax}\) are increased.

## Keywords

Void Fraction Drag Reduction Axial Flow Small Bubble Fluid Element## List of symbols

*r*Cylinder radius (m)

*l*Distance between pressure holes (m)

*h*Head loss (m)

*v*_{m}Mean velocity of axial flow (m/s)

*Q*Volume flow rate (m

^{3}/s)*g*Gravity (m/s

^{2})- \(\Delta P = P_{2} - P_{1}\)
Pressure difference between pressure holes (N/m

^{2})*Re*Reynolds number (−)

*Ta*Taylor number (−)

## Greek symbols

*λ*Head resistance coefficient (−)

*ν*Kinematic viscosity (m

^{2}/s)*ω*Angular velocity (rpm)

- \(\delta = r_{2} - r_{1}\)
Gap width (m)

*ξ*Head resistance coefficient ratio (−)

*γ*Specific weight (N/m

^{3})*ρ*Density (kg/m

^{3})

## Subscripts

- 1
Inner cylinder

- 2
Outer cylinder

*ax*Axial

*ω*Rotational

*w*Water

*a*Air

## References

- 1.Saeki T, De Guzman MR, Morishima H, Usui H, Nishimura T (2000) A flow visualization study of the mechanism of turbulent drag reduction by surfactants. Nihon Reoroji Gakkaishi 20:35–40Google Scholar
- 2.Drappier J, Divoux T, Amarouchene Y, Bertrand F, Rodts S, Cadot O, Meunier J, Bonn D (2006) Turbulent drag reduction by surfactants. Europhys Lett 74:362CrossRefGoogle Scholar
- 3.Virk PS (1975) Drag reduction fundamentals. AIChE J 21:625–656CrossRefGoogle Scholar
- 4.Berman NS (1978) Drag reduction by polymers. Annu Rev Fluid Dyn 10:47–64CrossRefzbMATHGoogle Scholar
- 5.Benzi R, Ching ESC, Horesh N, Procaccia I (2004) Theory of concentration dependence in drag reduction by polymers and of the maximum drag reduction asymptote. Phys Rev Lett 92:78302CrossRefGoogle Scholar
- 6.Bonn D, Amarouchene Y, Wagner C, Douady S, Cadot O (2005) Turbulent drag reduction by polymers. J Phys Condens Matter 17:1195CrossRefGoogle Scholar
- 7.White CM, Mungal MG (2008) Mechanics and prediction of turbulent drag reduction with polymer additives. Annu Rev Fluid Mech 40:235–256MathSciNetCrossRefzbMATHGoogle Scholar
- 8.Procaccia I, Lvov VS, Benzi R (2008) Colloquium: theory of drag reduction by polymers in wall-bounded turbulence. Rev Mod Phys 80:225–247CrossRefGoogle Scholar
- 9.McCormick ME, Bhattacharyya R (1973) Drag reduction of a submersible hull by electrolysis. Nav Eng J 85:11–16CrossRefGoogle Scholar
- 10.Bogdevich VG, Evseev AR, Mayyuga AG, Migirenko GS (1977) Gas saturation effect on near-wall turbulence characteristics. In: Proceedings of the second international conference on drag reduction. BHRA, Cambridge, pp 25–37 Google Scholar
- 11.Madavan NK, Deutsch S, Merkle CL (1984) Reduction of turbulent skin friction by micro bubbles. Phys Fluids 27:356–363CrossRefGoogle Scholar
- 12.Madavan NK, Deutsch S, Merkle CL (1985) Measurements of local skin frictions in a microbubble modified turbulent boundary layer. J Fluid Mech 156:237–256CrossRefGoogle Scholar
- 13.Deutsch S, Castano J (1986) Micro bubble skin friction on an axisymmetric body. Phys Fluids 29:3590–3597CrossRefGoogle Scholar
- 14.Kato H, Miyanaga M, Haramoto Y, Guin MM (1994) Frictional drag reduction by injecting bubbly water into turbulent boundary layer. In: Proceedings of the cavitation and gas–liquid flow in fluid machinery and devices ASME, pp 185–194Google Scholar
- 15.Guin MM, Kato H, Yamaguchi H, Maeda M, Miyanaga M (1996) Reduction of skin friction by micro bubbles and its relation with near wall concentration in a channel. J Mar Sci Technol 1:241–254CrossRefGoogle Scholar
- 16.Kanai A, Miyata H (2001) Direct numerical simulation of wall turbulent flows with micro bubbles. Int J Numer Methods Fluids 35:593–615CrossRefzbMATHGoogle Scholar
- 17.Xu J, Maxey MR, Karniadakis GE (2002) Numerical simulation of turbulent drag reduction using micro-bubbles. J Fluid Mech 468:271–281CrossRefzbMATHGoogle Scholar
- 18.Ferrante A, Elghobashi S (2004) On the physical mechanisms of drag reduction in a spatially developing turbulent boundary layer laden with microbubbles. J Fluid Mech 503:345–355CrossRefzbMATHGoogle Scholar
- 19.Lu J, Fernandez A, Tryggvason G (2005) The effect of bubbles on the wall drag in a turbulent channel flow. Phys Fluids 17:095102CrossRefzbMATHGoogle Scholar
- 20.Takahashi T, Kakugawa A, Makino M, Yanagihara T, Kodama Y (2000) A brief report on microbubble experiments using 50-m long at plate ship. In: 74th General meeting of SRIGoogle Scholar
- 21.van der Berg TH, Luther S, Lathrop D, Lohse D (2005) Drag reduction in bubbly Taylor–Couette turbulence. Phys Rev Lett 94:044501CrossRefGoogle Scholar
- 22.van der Berg TH, van Gils DPM, Lathrop DP, Lohse D (2007) Bubbly turbulent drag reduction is a boundary layer effect. Phys Rev Lett 98:084501CrossRefGoogle Scholar
- 23.Murai Y, Oiwa H, Takeda Y (2005) Bubble behavior in a vertical Taylor–Couette flow. J Phys Conf Ser 14:143–156CrossRefGoogle Scholar
- 24.Murai Y, Oiwa H, Takeda Y (2008) Frictional drag reduction in bubbly Couette–Taylor flow. Phys Fluids 20:034101CrossRefzbMATHGoogle Scholar
- 25.Deutsch S, Fontaine AA, Moeny MJ, Petrie H (2006) Combined polymer and microbubble drag reduction on a large at plate. J Fluid Mech 556:309–327CrossRefzbMATHGoogle Scholar
- 26.Sanders WC, Winkel ES, Dowling DR, Perlin M, Ceccio SL (2006) Bubble friction drag reduction in a high-Reynolds-number at-plate turbulent boundary layer. J Fluid Mech 552:353–380CrossRefzbMATHGoogle Scholar
- 27.Elbing BR, Winkel ES, Lay KA, Ceccio SL, Dowling DR, Perlin M (2008) Bubble induced skin-friction drag reduction and the abrupt transition to air-layer drag reduction. J Fluid Mech 612:201–236CrossRefzbMATHGoogle Scholar
- 28.Gutierrez-Torres CC, Hassan YA, Jimenez-Bernal JA (2008) Turbulence structure modification and drag reduction by microbubble injections in a boundary layer channel flow. J Fluids Eng 130:111–304CrossRefGoogle Scholar
- 29.Sugiyama K, Calzavarini E, Lohse D (2008) Microbubble drag reduction in Taylor–Couette flow in the wavy vortex regime. J Fluid Mech 601:21–41zbMATHGoogle Scholar
- 30.Jacob B, Olivieri A, Miozzi M, Campana EF, Piva R (2010) Drag reduction by microbubbles in a turbulent boundary layer. Phys Fluids 22:115104CrossRefGoogle Scholar
- 31.Kodama Y, Kakugawa A, Takahashi T, Kawashima H (2000) Experimental studies on microbubbles and their applicability to ships for skin friction reduction. Int J Heat Fluid Flow 21:582–588CrossRefGoogle Scholar
- 32.Merkle C, Deutsch S (1989) Microbubble drag reduction. In: Gad-el-Hak M (ed) Frontiers in experimental fluid mechanics—lecture notes in engineering, vol 46. Springer, Berlin, p 291CrossRefGoogle Scholar
- 33.Latorre R, Miller A, Philips R (2003) Micro-bubble resistance reduction on a model SES catamaran. Ocean Eng 30:2297–2309CrossRefGoogle Scholar
- 34.Ceccio SL (2010) Friction drag reduction of external ows with bubble and gas injection. Annu Rev Fluid Mech 42:183–203CrossRefGoogle Scholar
- 35.Djeridi H, Gabillet C, Billard JY (2004) Two-phase Couette–Taylor ow: arrangement of the dispersed phase and effects on the flow structures. Phys Fluids 16:128–139CrossRefzbMATHGoogle Scholar
- 36.Mehel A, Gabillet C, Djeridi H (2007) Analysis of the flow patterns modifications in a bubbly Couette–Taylor flow. Phys Fluids 19:118101CrossRefzbMATHGoogle Scholar
- 37.Lathrop DP, Fineberg J, Swinney HL (1992) Transition to shear-driven turbulence in Couette–Taylor flow. Phys Rev A 46:6390–6405CrossRefGoogle Scholar
- 38.Eckhardt B, Grossmann S, Lohse D (2007) Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J Fluid Mech 581:221–250MathSciNetCrossRefzbMATHGoogle Scholar
- 39.Ahlers G, Grossmann S, Lohse D (2009) Heat transfer and large scale dynamics in turbulent Rayleigh–Benard convection. Rev Mod Phys 51:503CrossRefGoogle Scholar
- 40.Lord R (1916) On the dynamics of revolving fluids. Proc R Sac Lond 93:148–154zbMATHGoogle Scholar
- 41.Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Philos Trans R Soc Lond 1923(223):289–343CrossRefzbMATHGoogle Scholar
- 42.Cornish JA (1933) Flow of water through fine clearances with relative motion of the boundaries. Proc R Soc Lond A 140:227–240CrossRefGoogle Scholar
- 43.Goldstein S (1937) The stability of viscous fluid flow between rotating cylinders. Proc Camb Philos Soc 33:41–61CrossRefzbMATHGoogle Scholar
- 44.Chandrasekhar S (1960) The hydrodynamic stability of viscous flow between coaxial cylinders. Proc Natl Acad Sci USA 46:141–143MathSciNetCrossRefzbMATHGoogle Scholar
- 45.Di Prima RC (1960) The stability of a viscous fluid between rotating cylinders with an axial flow. J Fluid Mech 9:621–631MathSciNetCrossRefGoogle Scholar
- 46.Donnelly RJ, Fultz D (1960) Experiments on the stability of spiral flow between rotating cylinders. Proc Natl Acad Sci USA 46:1150–1154CrossRefzbMATHGoogle Scholar
- 47.Yamada Y (1960) Resistance of a flow through an annulus with an inner rotating cylinder. Bull JSME 5:302–310CrossRefGoogle Scholar
- 48.Chung KC, Astill KN (1977) Hydrodynamic instability of viscous flow between rotating coaxial cylinders with fully developed axial flow. J Fluid Mech 81:641–655CrossRefzbMATHGoogle Scholar
- 49.Takeuchi DI, Jankowski DF (1981) A numerical and experimental investigation of the stability of spiral Poiseuille flow. J Fluid Mech 102:101–126CrossRefGoogle Scholar
- 50.Lueptow RM, Docter A, Kyungyoon M (1992) Stability of axial flow in an annulus with a rotating inner cylinder. Phys Fluids A 4:2446–2455CrossRefGoogle Scholar
- 51.Shiomi Y, Kutsuna H, Akagawa K, Ozawa M (1993) Two-phase flow in an annulus with a rotating inner cylinder (flow pattern in bubbly flow region). Nucl Eng Des 141:27–34CrossRefGoogle Scholar
- 52.Atkhen K, Fontaine J, Wesfreid JE (2000) Highly turbulent Couette–Taylor bubbly flow patterns. J Fluid Mech 422:55–68CrossRefzbMATHGoogle Scholar
- 53.Hubacz R, Wronski S (2004) Horizontal Couette–Taylor flow in a two phase gas-liquid system: flow patterns. Exp Therm Fluid Sci 28:457–466CrossRefGoogle Scholar
- 54.van Gilsz DPM, Guzman DN, Suny C, Lohsey D (2013) The importance of bubble deformability for strong drag reduction in bubbly turbulent Taylor–Couette flow. J Fluid Mech 722:317–347CrossRefGoogle Scholar
- 55.Maryami R, Farahat S, Javad Poor M, Shafiei Mayam MH (2014) Bubbly drag reduction in a vertical Couette–Taylor system with superimposed axial flow. Fluid Dyn Res 46:055504CrossRefGoogle Scholar
- 56.Maryami R, Farahat S, Javad Poor M, Shafiei Mayam MH (2015) Frictional drag reduction using small bubbles in a Couette-Taylor flow. J Mar Sci Technol 20:1–20CrossRefGoogle Scholar
- 57.Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge, pp 289–306 (The original paper by Einstein A 1904 Ann Phys)Google Scholar
- 58.Rust AC, Manga M (2002) Effects of bubble deformation on the viscosity of dilute suspensions. J Non-Newton Fluid Mech 104:53–63CrossRefzbMATHGoogle Scholar
- 59.Dorfman LA (1963) Hydrodynamic resistance and the heat loss of rotating solid, vol 214. Oliver & Boy, EdinburghzbMATHGoogle Scholar
- 60.Sugiyama K, Kawamura T, Takagi S, Matsumoto Y (2004) The Reynolds number effect on micro bubble drag reduction. In: Proceedings of the 5th symposium on smart control of turbulence. The University of Tokyo, Tokyo, Japan, pp 31–43Google Scholar