Investigation of the effect of small bubbles on energy dissipation in a vertical Couette–Taylor system

  • Mohammad Hossein Shafiei Mayam
  • Reza Maryami
  • Mohammad Mustafa Ghafurian
Technical Paper


The effect of small bubbles on reduction of energy dissipation has been numerically investigated in a vertical Couette–Taylor system. Flow is in the annular space between two concentric cylinders as the internal cylinder is rotating while the outer cylinder is stationary. Main fluid between cylinders is silicone, while air bubbles are constantly injected into the main flow at the bottom of cylinders’ gap. The air bubbles rise through the flow when they are injected into the silicone flow. The flow is fully turbulence and Taylor vortices have appeared in the annulus gap. The rotational Reynolds number (Reω) varies from 700 to 3000. The fully two-phase turbulent flow has been studied using a discrete phase model and Euler–Lagrange approach. Air bubbles distribution or bubbles pattern through the main flow, which is acquired using numerical method, shows a good agreement to those acquired via experimental data in all Reynolds numbers. To investigate the changes of skin friction drag, the rate of energy dissipation in the system is calculated. The effect of injected air with constant flow rate on the total energy dissipation rate and the drag coefficient is also investigated. The results confirmed reduction of energy dissipation and about 25% of drag reduction when small bubbles were injected in the system. This reduction was the effect of the bubbles on the density of fluid and transformed momentum. Moreover, the acquired numerical results were in good agreement with those found in the previous experimental works, in which maximum Reω is up to 3000.


Bubbly flow Taylor coquette system Energy loss 

List of symbols


Drag force


Froude number


Gravity (m/s2)


Turbulence intensity


Mach number


Volume rate (m3/s)


Reynolds number




Taylor number


The average velocity




Velocity in Reynolds stress (m/s)


The kinematic viscosity of the pure water


Dissipation term


Weber number







Power gain factor


X direction


Y direction


Z direction



Greek symbols


Volume fraction (closure coefficient in the dissipation rate equation)


Closure coefficient in the turbulent-kenetic energy equation


Radial gap


Surface tension




Turbulence viscosity


Energy dissipation rate


Density (kg/m3)




  1. 1.
    McCormick ME, Bhattacharyya R (1973) Drag reduction of a submersible hull by electrolysis. Naval Eng J 85(2):11–16CrossRefGoogle Scholar
  2. 2.
    Bodgevich VG, Evseev AR (1976) The distribution of skin friction in a turbulent boundary layer of water beyond the location of gas injection. Investigations of boundary layer control. Thermophysics Institute Publishing, p 62 (in Russian) Google Scholar
  3. 3.
    Bogdevich VG, Evseev AR, Mayyuga AG, Migirenko GS (1977) Gas-saturation effect on near-wall turbulence characteristics. In: Stephens HS, Clark JA (eds) Proc second international conference on drag reduction. Cambridge, England. BHRA Fluid Engineering pp D2–D25Google Scholar
  4. 4.
    Madavan NK, Deutsch S, Merkle CL (1984) Reduction of turbulent skin friction by micro bubbles. Phys Fluids 27:356–363CrossRefGoogle Scholar
  5. 5.
    Madavan NK, Merkle CL, Deutsch S (1985) Numerical investigations into the mechanisms of microbubble drag reduction. J Fluids Eng 107(3):370–377CrossRefGoogle Scholar
  6. 6.
    Kim SY, Cleaver JW (1995) The persistence of drag reduction following the injection of microbubbles into a turbulent boundary layer. Int Commun Heat Mass Transf 22(3):353–357CrossRefGoogle Scholar
  7. 7.
    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(5):582–588CrossRefGoogle Scholar
  8. 8.
    Deutsch S, Castano J (1986) Microbubble skin friction on an axisymmetric body. Phys Fluids 29(11):3590–3597. CrossRefGoogle Scholar
  9. 9.
    Lance M, Bataille J (1991) Turbulence in the liquid phase of a uniform bubbly air–water flow 222:95–118. Google Scholar
  10. 10.
    Deutsch S, Fontaine AA (1992) The influence of the type of gas on the reduction of skin friction drag by microbubble injection. Exp Fluids 13(2):128–136. Google Scholar
  11. 11.
    Pal S (1989) Turbulence characteristics and bubble dynamics of a microbubble modified boundary layer. Ph.D. thesis the Pennsylvania State UniversityGoogle Scholar
  12. 12.
    Kato H, Miyanaga M, Haramoto Y, Guin MM (1994) Frictional drag reduction by injecting bubbly water into turbulent boundary layer. In: Proc. 1994 cavitation and gas-liquid flow in fluid machinery and devices ASME 190, pp 185–194Google Scholar
  13. 13.
    Kanai A, Miyata H (2001) Direct numerical simulation of wall turbulent flows with microbubbles. Int J Numer Meth Fluids 35(5):593–615CrossRefzbMATHGoogle Scholar
  14. 14.
    Xu J, Maxey MR, Karniadakis GE (2002) Numerical simulation of turbulent drag reduction using micro-bubbles. J Fluid Mech 468:271–281. CrossRefzbMATHGoogle Scholar
  15. 15.
    Kitagawa A, Sugiyama K, Ashihara M, Hishida K, Kodama Y (2003) Measurement of turbulence modification by microbubbles causing frictional drag reduction. Proc ASME 1:675–681. Google Scholar
  16. 16.
    Couette M (1890) Etudes sur le frottement des liquides. Ann Chim Phys 21:433–510zbMATHGoogle Scholar
  17. 17.
    Mallock A (1896) Experiments on fluid viscosity. Philos Trans R Soc Lond Ser A 187:41–56CrossRefzbMATHGoogle Scholar
  18. 18.
    Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Philos Trans R Soc Lond Ser A 223:289–343CrossRefzbMATHGoogle Scholar
  19. 19.
    Van den Berg TH, Luther S, Lathrop D, Lohse D (2005) Drag reduction in bubbly Taylor–Couette turbulence. Phys Rev Lett 94(4):044501. CrossRefGoogle Scholar
  20. 20.
    Van den Berg TH, van Gils DPM, Lathrop DP, Lohse D (2007) Bubbly turbulent drag reduction is a boundary layer effect. Phys Rev Lett 98(8):08450. Google Scholar
  21. 21.
    Murai Y, Oiwa H, Takeda Y (2008) Frictional drag reduction in bubbly Couette-Taylor flow. Phys Fluids 20(3):034101. CrossRefzbMATHGoogle Scholar
  22. 22.
    Cazley C Jr (1985) Heat transfer characteristics of the rotational and axial flow between cocentric cylinders. Trans ASME 80:77–90Google Scholar
  23. 23.
    Lu J, Fernadez A, Tryggvason G (2005) The effect of bubbles on the wall drag in a turbulent channel flow. Phys Fluids 17(9):1–12. CrossRefGoogle Scholar
  24. 24.
    Legner HH (1984) A simple model for gas bubble drag reduction. Phys Fluids 27(12):2788–2790. CrossRefGoogle Scholar
  25. 25.
    Lewis GS, Swinney HL (1999) Velocity structure functions, scaling, and transitions in high-Reynolds-number Couette–Taylor flow. Phys Rev E 59(5):5457–5467. CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • Mohammad Hossein Shafiei Mayam
    • 1
  • Reza Maryami
    • 2
  • Mohammad Mustafa Ghafurian
    • 3
  1. 1.Department of Mechanical EngineeringBozorgmehr University of QaenatQaenIran
  2. 2.Department of Mechanical EngineeringUniversity of Sistan and BaluchestanZahedanIran
  3. 3.Department of Mechanical EngineeringFerdowsi University of MashhadMashhadIran

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