Heat and Mass Transfer

, Volume 51, Issue 12, pp 1655–1667 | Cite as

Partially-averaged Navier–Stokes method for turbulent thermal plume

  • Rajesh Kumar
  • Anupam DewanEmail author


In this paper, the partially-averaged Navier–Stokes (PANS) simulation is performed for a turbulent thermal plume. The aim of the paper is to assess the PANS method for modeling buoyancy-driven flows at a reasonable computational cost. PANS is a turbulence closure model which is developed to be used as a bridging model ranging from the direct numerical simulation to the Reynolds-averaged Navier–Stokes simulation by varying the level of resolution. The PANS computations are performed for various values of the filter-width to evaluate the sensitivity of the filter-widths to the computed flow statistics. The present simulations have been carried out employing a source code buoyantPimpleFOAM based on the OpenFOAM platform. In order to capture the effect of buoyancy on turbulence, the generalized gradient diffusion hypothesis is employed to model the production of turbulence due to buoyancy. A detailed comparison of the time-averaged and turbulent statistics obtained from the PANS simulations with the experimental data and LES results reported in the literature has been presented. The present results have also been compared with the results of the unsteady Reynolds-averaged Navier–Stokes solutions. The PANS model is shown to enhance the computing capability significantly in predicting buoyancy-driven flows compared with those of URANS model. Finally, various important unsteady flow structures of turbulent thermal plume have been visualized from the instantaneous flow statistics obtained using the PANS simulations.


Large Eddy Simulation Direct Numerical Simulation RANS Filter Parameter Thermal Plume 
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


Production of turbulence due to buoyancy (kg/ms3)


Acceleration due to gravity (m/s2)


Specific enthalpy (J/kg)


Turbulent kinetic energy (m2/s2)


Unresolved turbulent kinetic energy (m2/s2)


Total pressure (N/m2)


Component of total pressure, \(p_{d} = p - \rho \varvec{g} \cdot \varvec{X}\) (N/m2)


Production of turbulence due to shear (kg/ms3)


Radius (m)


Strain rate (s−1)


Strain rate tensor (s−1)


Temperature (K)


Velocity component in the ith direction (m/s)


Time-averaged velocity in the axial direction (m/s)


Vertical distance (m)


Kronecker delta (dimensionless)


Unresolved turbulent viscosity (kg/ms)


Turbulent Prandtl number (dimensionless)


Shear stress tensor (N/m2)


Turbulent dissipation rate (m2/s3)


Unresolved turbulent dissipation rate (m2/s3)


Molecular viscosity (kg/ms)


Density (kg/m3)


Properties of the ambient


Vector direction


Quantities at the centerline


\(\bar{\varphi }\)

Partially-averaged quantity


Unresolved fluctuation

\(\tilde{\varphi }\)

Favre-averaged quantity


Fluctuation (Favre statistics)


  1. 1.
    Shabbir A, George WK (1994) Experiments on a round turbulent buoyant plume. J Fluid Mech 275:1–32CrossRefGoogle Scholar
  2. 2.
    Dewan A (2011) Tackling turbulent flows in engineering, 1st edn. Springer, BerlinCrossRefzbMATHGoogle Scholar
  3. 3.
    Jiang X, Luo KH (2001) Spatial DNS of flow transition of a rectangular buoyant reacting free-jet. J Turbul 2(5):1–18MathSciNetGoogle Scholar
  4. 4.
    George WK, Alpert RL, Tamanini F (1977) Turbulence measurement in an axisymmetric buoyant plume. Int J Heat Mass Transf 20:1145–1153CrossRefGoogle Scholar
  5. 5.
    Papanicolaou PN, List EJ (1988) Investigation of round vertical turbulent buoyant jets. J Fluid Mech 195:341–391CrossRefGoogle Scholar
  6. 6.
    Sreenivas KR, Prasad AK (2000) Vortex-dynamics model for entrainment in jets and plumes. Phys Fluids 12:1–7CrossRefGoogle Scholar
  7. 7.
    Morton BR, Taylor G, Turner JS (1956) Turbulent gravitational convection from maintained and instantaneous sources. Proc R Soc Lond Ser A 234:1–23MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Agrawal A, Prasad AK (2003) Integral solution for the mean flow profiles of turbulent jets, plumes and wakes. J Fluids Eng 125:813–822CrossRefGoogle Scholar
  9. 9.
    Hunt GR, Kaye NG (2001) Virtual origin correction for lazy turbulent plumes. J Fluid Mech 435:377–396zbMATHGoogle Scholar
  10. 10.
    Nam S, Bill JRG (1993) Numerical simulation of thermal plumes. Fire Saf J 21:231–256CrossRefGoogle Scholar
  11. 11.
    Zhou X, Luo KH, Williams JJR (2001) Large eddy simulation of a turbulent forced plume. Eur J Mech B Fluids 20:233–254CrossRefzbMATHGoogle Scholar
  12. 12.
    Pham MV, Plourde F, Doan KS (2007) Direct and large-eddy simulations of a pure thermal plume. Phys Fluids 19:1–13CrossRefGoogle Scholar
  13. 13.
    Dewan A, Arakeri JH, Srinivasan J (1997) A new turbulence model for the axisymmetric plume. Appl Math Model 21:709–719CrossRefzbMATHGoogle Scholar
  14. 14.
    List EJ (1982) Turbulent jet and plumes. Annu Rev Fluid Mech 14:189–212CrossRefGoogle Scholar
  15. 15.
    Dai Z, Tseng LK, Faeth GM (1995) Velocity statistics of round, fully-developed buoyant turbulent plume. J Heat Transf 117:138–145CrossRefGoogle Scholar
  16. 16.
    Rooney GG, Linden PF (1996) Similarity considerations for non-Boussinesq plumes in an unstratified environment. J Fluid Mech 318:237–250CrossRefzbMATHGoogle Scholar
  17. 17.
    Van Maele K, Merci B (2006) Application of two buoyancy-modified kε turbulence models to different types of buoyant plumes. Fire Saf J 41:122–318CrossRefGoogle Scholar
  18. 18.
    Kumar R, Dewan A (2013) Assessment of buoyancy-corrected turbulence models for thermal plumes. Eng Appl Comput Fluid Mech 7:239–249Google Scholar
  19. 19.
    Bastiaans JM, Rindt CCM, Nieuwstadt FTM, van Steenhoven AA (2000) Direct and large-eddy simulation of the transition of two and three-dimensional plane plumes in a confined enclosure. Int J Heat Mass Transf 43:2375–2393CrossRefzbMATHGoogle Scholar
  20. 20.
    Kumar R, Dewan A (2014) Computational models for turbulent thermal plumes: recent advances and challenges. Heat Transf Eng 35(4):367–383CrossRefGoogle Scholar
  21. 21.
    Girimaji SS, Abdol-Hamid KS (2005) Partially-averaged Navier–Stokes model for turbulence: implementation and validation. In: 43rd AIAA aerospace sciences meeting and exhibit, Reno, NV, AIAA 2005, vol 502, pp 1–14Google Scholar
  22. 22.
    Girimaji SS (2006) Partially averaged Navier–Stokes model for turbulence: a Reynolds-averaged Navier–Stokes to direct numerical simulation bridging method. J Appl Mech 73:413–421CrossRefzbMATHGoogle Scholar
  23. 23.
    Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys 12:620–631CrossRefGoogle Scholar
  24. 24.
    Daly BJ, Harlow FH (1970) Transport equations in turbulence. Phys Fluids 13:2634–2649CrossRefGoogle Scholar
  25. 25.
    Markatos NC, Malin MR (1982) Mathematical modeling of buoyancy-induced smoke flow in enclosures. Int J Heat Mass Transf 25:63–75CrossRefzbMATHGoogle Scholar
  26. 26.
    Worthy J, Sanderson V, Rubini P (2001) Comparison of modified kε turbulence models for buoyant plumes. Numer Heat Transf Part A 39:151–165 CrossRefGoogle Scholar
  27. 27.
    Frendi A, Tosh A, Girimaji SS (2007) Flow past a backward-facing step: comparison of PANS, DES and URANS results with experiments. Int J Comput Methods Eng Sci Mech 8:23–38CrossRefzbMATHGoogle Scholar
  28. 28.
    Lakshmipathy S, Girimaji SS (2010) Partially averaged Navier–Stokes (PANS) method for turbulence simulations: flow past a circular cylinder. J Fluids Eng 132:121–129CrossRefGoogle Scholar
  29. 29.
    Girimaji SS, Lavin TA (2006) Investigation of turbulent square jet using PANS Method. In: 44th AIAA aerospace sciences meeting and exhibit, Reno, NV, AIAA 2006, vol 488, pp 1–11Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Applied MechanicsIndian Institute of Technology DelhiNew DelhiIndia

Personalised recommendations