Heat and Mass Transfer

, Volume 53, Issue 9, pp 2885–2899 | Cite as

Numerical simulation of superheated vapor bubble rising in stagnant liquid

  • N. Samkhaniani
  • M. R. AnsariEmail author


In present study, the rising of superheated vapor bubble in saturated liquid is simulated using volume of fluid method in OpenFOAM cfd package. The surface tension between vapor–liquid phases is considered using continuous surface force method. In order to reduce spurious current near interface, Lafaurie smoothing filter is applied to improve curvature calculation. Phase change is considered using Tanasawa mass transfer model. The variation of saturation temperature in vapor bubble with local pressure is considered with simplified Clausius–Clapeyron relation. The couple velocity–pressure equation is solved using PISO algorithm. The numerical model is validated with: (1) isothermal bubble rising and (2) one-dimensional horizontal film condensation. Then, the shape and life time history of single superheated vapor bubble are investigated. The present numerical study shows vapor bubble in saturated liquid undergoes boiling and condensation. It indicates bubble life time is nearly linear proportional with bubble size and superheat temperature.


Bubble Size Viscosity Ratio Vapor Bubble Saturated Liquid Bubble Shape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Bubble area (m2)


Bond number (\(\frac{{g(\rho_{L} - \rho_{g} )D_{0}^{2} }}{\sigma }\)) (–)

\(C_{\alpha }\)

Compression factor (–)


Specific heat (J/kg K)


Drag coefficient (–)


Equivalent diameter (M)


Bubble initial diameter (M)


Numerical error

\(\overrightarrow {g}\)

Gravity acceleration (m/s2)


Latent heat (J/kg)


Thermal conductivity (W/m K)


Molar mass (kg/K mol)


Condensate mass flow rate per unit volume (kg/m3 s)


Morton number (\(\frac{{g(\rho_{L} - \rho_{g} )\mu_{L}^{4} }}{{\rho_{L}^{2} \sigma^{3} }}\)) (–)


Pressure (Pa)


Specific gas constant (\(\frac{{R_{universal} }}{M}\)) (J/kg K)


Reynolds number (\(\frac{{\rho_{L} U_{t} D_{0} }}{{\mu_{L} }}\)) (–)


Temperature (K)

\(\overrightarrow {U}\)

Velocity (m/s)

\(\overrightarrow {{U_{b} }}\)

Bubble velocity (m/s)

\(\overrightarrow {{U_{c} }}\)

Compressive velocity (m/s)

\(\overrightarrow {{U_{rel} }}\)

Relative velocity (m/s)


Terminal velocity (m/s)


Bubble volume (m3)

Greek symbols


Volume fraction factor (–)


Film thickness (m)


Interface curvature (m−1)


Dynamic viscosity (Pa s)


Kinematic viscosity (m2/s)


Density (kg/m3)



Gas (vapor) phase


Liquid phase


Saturation condition


Superheated condition


  1. 1.
    Albadawi A, Donoghue D, Robinson A, Murray D, Delauré Y (2014) On the assessment of a VOF based compressive interface capturing scheme for the analysis of bubble impact on and bounce from a flat horizontal surface. Int J Multiph Flow 65:82–97CrossRefGoogle Scholar
  2. 2.
    Alhendal Y, Turan A (2015) Thermocapillary bubble dynamics in a 2D axis swirl domain. Heat Mass Transf 51:529–542CrossRefGoogle Scholar
  3. 3.
    Alhendal Y, Turan A, Hollingsworth P (2013) Thermocapillary simulation of single bubble dynamics in zero gravity. Acta Astronaut 88:108–115CrossRefGoogle Scholar
  4. 4.
    Alke A, Bothe D, Kröger M, Warnecke H (2009) VOF-based simulation of conjugate mass transfer from freely moving fluid particles. Comput Methods Multiph Flow V 63:157–168CrossRefGoogle Scholar
  5. 5.
    Amaya-Bower L, Lee T (2010) Single bubble rising dynamics for moderate Reynolds number using lattice Boltzmann method. Comput Fluids 39:1191–1207CrossRefzbMATHGoogle Scholar
  6. 6.
    Ansari M, Nimvari M (2011) Bubble viscosity effect on internal circulation within the bubble rising due to buoyancy using the level set method. Ann Nucl Energy 38:2770–2778CrossRefGoogle Scholar
  7. 7.
    Ansari MR, Azadi R, Salimi E (2016) Capturing of interface topological changes in two-phase gas–liquid flows using a coupled volume-of-fluid and level-set method (VOSET). Comput Fluids 125:82–100MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bahreini M, Ramiar A, Ranjbar AA (2015) Numerical simulation of bubble behavior in subcooled flow boiling under velocity and temperature gradient. Nucl Eng Des 293:238–248CrossRefGoogle Scholar
  9. 9.
    Beard K, Pruppacher H (1969) A determination of the terminal velocity and drag of small water drops by means of a wind tunnel. J Atmos Sci 26:1066–1072CrossRefGoogle Scholar
  10. 10.
    Berberović E, van Hinsberg NP, Jakirlić S, Roisman IV, Tropea C (2009) Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution. Am Phys Soc 79:036306 (036315)Google Scholar
  11. 11.
    Bhaga D, Weber M (1981) Bubbles in viscous liquids: shapes, wakes and velocities. J Fluid Mech 105:61–85CrossRefGoogle Scholar
  12. 12.
    Bothe D, Fleckenstein S (2013) A volume-of-fluid-based method for mass transfer processes at fluid particles. Chem Eng Sci 101:283–302CrossRefGoogle Scholar
  13. 13.
    Brackbill JU, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100:335–354MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Chakraborty I, Biswas G, Ghoshdastidar P (2013) A coupled level-set and volume-of-fluid method for the buoyant rise of gas bubbles in liquids. Int J Heat Mass Transf 58:240–259CrossRefGoogle Scholar
  15. 15.
    Chen Y, Mayinger F (1992) Measurement of heat transfer at the phase interface of condensing bubbles. Int J Multiph Flow 18:877–890CrossRefzbMATHGoogle Scholar
  16. 16.
    Clift R, Grace JR, Weber ME (1978) Bubbles, drops and particles. Academic Press, New YorkGoogle Scholar
  17. 17.
    Ellingsen K, Risso F (2001) On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid-induced velocity. J Fluid Mech 440:235–268CrossRefzbMATHGoogle Scholar
  18. 18.
    Gumulya M, Joshi JB, Utikar RP, Evans GM, Pareek V (2016) Bubbles in viscous liquids: time dependent behaviour and wake characteristics. Chem Eng Sci 144:298–309CrossRefGoogle Scholar
  19. 19.
    Harada T, Nagakura H, Okawa T (2010) Dependence of bubble behavior in subcooled boiling on surface wettability. Nucl Eng Des 240:3949–3955CrossRefGoogle Scholar
  20. 20.
    Hoang DA, van Steijn V, Portela LM, Kreutzer MT, Kleijn CR (2013) Benchmark numerical simulations of segmented two-phase flows in microchannels using the volume of fluid method. Comput Fluids 86:28–36CrossRefzbMATHGoogle Scholar
  21. 21.
    Hua J, Lou J (2007) Numerical simulation of bubble rising in viscous liquid. J Comput Phys 222:769–795CrossRefzbMATHGoogle Scholar
  22. 22.
    Hua J, Stene JF, Lin P (2008) Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method. J Comput Phys 227:3358–3382MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Issa RI (1986) Solution of the implicitly discretised fluid flow equations by operator-splitting. J Comput Phys 62:40–65MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Jasak H (1996) Error analysis and estimation for the finite volume method with applications to fluid flows. Imperial College. University of LondonGoogle Scholar
  25. 25.
    Kulkarni AA, Joshi B (2005) Bubble formation and bubble rise velocity in gas–liquid systems: a review. Ind Eng Chem Res 44:5873–5931CrossRefGoogle Scholar
  26. 26.
    Lafaurie B, Nardone C, Scardovelli R, Zaleski S, Zanetti G (1994) Modelling merging and fragmentation in multiphase flows with SURFER. J Comput Phys 113:134–147MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Legendre D, Zenit R, Velez-Cordero JR (2012) On the deformation of gas bubbles in liquids. Phys Fluids (1994-present) 24:043303CrossRefGoogle Scholar
  28. 28.
    Lemmon EW, McLinden MO, Friend DG (2016) Thermophysical properties of fluid systems.
  29. 29.
    Maldonado M, Quinn J, Gomez C, Finch J (2013) An experimental study examining the relationship between bubble shape and rise velocity. Chem Eng Sci 98:7–11CrossRefGoogle Scholar
  30. 30.
    Marek R, Straub J (2001) Analysis of the evaporation coefficient and the condensation coefficient of water. Int J Heat Mass Transf 44:39–53CrossRefzbMATHGoogle Scholar
  31. 31.
    Marschall H, Hinterberger K, Schuler C, Habla F, Hinrichsen O (2012) Numerical simulation of species transfer across fluid interfaces in free-surface flows using OpenFOAM. Chem Eng Sci 78:111–127CrossRefGoogle Scholar
  32. 32.
    Mukundakrishnan K, Quan S, Eckmann DM, Ayyaswamy PS (2007) Numerical study of wall effects on buoyant gas-bubble rise in a liquid-filled finite cylinder. Phys Rev E 76:036308CrossRefGoogle Scholar
  33. 33.
    Ohta M, Imura T, Yoshida Y, Sussman M (2005) A computational study of the effect of initial bubble conditions on the motion of a gas bubble rising in viscous liquids. Int J Multiph Flow 31:223–237CrossRefzbMATHGoogle Scholar
  34. 34.
    Ohta M, Sussman M (2012) The buoyancy-driven motion of a single skirted bubble or drop rising through a viscous liquid. Phys Fluids (1994-present) 24:112101CrossRefGoogle Scholar
  35. 35.
    Pan L-M, Tan Z-W, Chen D-Q, Xue L-C (2012) Numerical investigation of vapor bubble condensation characteristics of subcooled flow boiling in vertical rectangular channel. Nucl Eng Des 248:126–136CrossRefGoogle Scholar
  36. 36.
    Pivello MR, Villar M, Serfaty R, Roma A, Silveira-Neto A (2014) A fully adaptive front tracking method for the simulation of two phase flows. Int J Multiph Flow 58:72–82MathSciNetCrossRefGoogle Scholar
  37. 37.
    Rattner AS, Garimella S (2014) Simple mechanistically consistent formulation for volume-of-fluid based computations of condensing flows. J Heat Transf 136:071501CrossRefGoogle Scholar
  38. 38.
    Rhie C, Chow W (1983) Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J 21:1525–1532CrossRefzbMATHGoogle Scholar
  39. 39.
    Samkhaniani N, Ajami A, Kayhani MH, Dari AS (2012) Direct numerical simulation of single bubble rising in viscous stagnant liquid. In: International conference on mechanical, automobile and robotics engineering (ICMAR’2012)Google Scholar
  40. 40.
    Samkhaniani N, Ansari M (2016) Numerical simulation of bubble condensation using CF-VOF. Prog Nucl Energy 89:120–131CrossRefGoogle Scholar
  41. 41.
    Samkhaniani N, Gharehbaghi A, Ahmadi Z (2013) Numerical simulation of reaction injection molding with polyurethane foam. J Cell Plast 49:405–421CrossRefGoogle Scholar
  42. 42.
    Shew WL, Poncet S, Pinton J-F (2006) Force measurements on rising bubbles. J Fluid Mech 569:51–60CrossRefzbMATHGoogle Scholar
  43. 43.
    Sideman S, Hirsch G (1965) Direct contact heat transfer with change of phase: condensation of single vapor bubbles in an immiscible liquid medium. Preliminary studies. AIChE J 11:1019–1025CrossRefGoogle Scholar
  44. 44.
    Tanasawa I (1991) Advances in condensation heat transfer. Adv Heat Transf 21:55–139CrossRefGoogle Scholar
  45. 45.
    Tian W, Ishiwatari Y, Ikejiri S, Yamakawa M, Oka Y (2010) Numerical computation of thermally controlled steam bubble condensation using moving particle semi-implicit (MPS) method. Ann Nucl Energy 37:5–15CrossRefGoogle Scholar
  46. 46.
    Tripathi MK, Sahu KC, Govindarajan R (2015) Dynamics of an initially spherical bubble rising in quiescent liquid. Nat Commun 6:6268. doi: 10.1038/ncomms7268 CrossRefGoogle Scholar
  47. 47.
    Van Leer B (1974) Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme. J Comput Phys 14:361–370CrossRefzbMATHGoogle Scholar
  48. 48.
    van Sint Annaland M, Deen N, Kuipers J (2005) Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method. Chem Eng Sci 60:2999–3011CrossRefGoogle Scholar
  49. 49.
    Weller H (2008) A new approach to VOF-based interface capturing methods for incompressible and compressible flow. OpenCFD Ltd., Report TR/HGW/04Google Scholar
  50. 50.
    Weller HG, TaboraI G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys 12:620–632CrossRefGoogle Scholar
  51. 51.
    Zeng Q, Cai J, Yin H, Yang X, Watanabe T (2015) Numerical simulation of single bubble condensation in subcooled flow using OpenFOAM. Prog Nucl Energy 83:336–346CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringTarbiat Modares UniversityTehranIslamic Republic of Iran

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