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Partially-averaged Navier–Stokes method for turbulent thermal plume

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Abstract

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.

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Abbreviations

Bu :

Production of turbulence due to buoyancy (kg/ms3)

g:

Acceleration due to gravity (m/s2)

h:

Specific enthalpy (J/kg)

k:

Turbulent kinetic energy (m2/s2)

ku :

Unresolved turbulent kinetic energy (m2/s2)

p:

Total pressure (N/m2)

p d :

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

Pu :

Production of turbulence due to shear (kg/ms3)

r:

Radius (m)

S:

Strain rate (s−1)

Sij :

Strain rate tensor (s−1)

T:

Temperature (K)

u i :

Velocity component in the ith direction (m/s)

W:

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

z:

Vertical distance (m)

δ ij :

Kronecker delta (dimensionless)

μ u :

Unresolved turbulent viscosity (kg/ms)

σ t :

Turbulent Prandtl number (dimensionless)

τ ij :

Shear stress tensor (N/m2)

ɛ :

Turbulent dissipation rate (m2/s3)

ɛ u :

Unresolved turbulent dissipation rate (m2/s3)

μ :

Molecular viscosity (kg/ms)

ρ :

Density (kg/m3)

∞:

Properties of the ambient

i:

Vector direction

c:

Quantities at the centerline

\(\bar{\varphi }\) :

Partially-averaged quantity

φ′:

Unresolved fluctuation

\(\tilde{\varphi }\) :

Favre-averaged quantity

φ″:

Fluctuation (Favre statistics)

References

  1. Shabbir A, George WK (1994) Experiments on a round turbulent buoyant plume. J Fluid Mech 275:1–32

    Article  Google Scholar 

  2. Dewan A (2011) Tackling turbulent flows in engineering, 1st edn. Springer, Berlin

    Book  MATH  Google Scholar 

  3. Jiang X, Luo KH (2001) Spatial DNS of flow transition of a rectangular buoyant reacting free-jet. J Turbul 2(5):1–18

    MathSciNet  Google Scholar 

  4. George WK, Alpert RL, Tamanini F (1977) Turbulence measurement in an axisymmetric buoyant plume. Int J Heat Mass Transf 20:1145–1153

    Article  Google Scholar 

  5. Papanicolaou PN, List EJ (1988) Investigation of round vertical turbulent buoyant jets. J Fluid Mech 195:341–391

    Article  Google Scholar 

  6. Sreenivas KR, Prasad AK (2000) Vortex-dynamics model for entrainment in jets and plumes. Phys Fluids 12:1–7

    Article  Google Scholar 

  7. Morton BR, Taylor G, Turner JS (1956) Turbulent gravitational convection from maintained and instantaneous sources. Proc R Soc Lond Ser A 234:1–23

    Article  MathSciNet  MATH  Google Scholar 

  8. Agrawal A, Prasad AK (2003) Integral solution for the mean flow profiles of turbulent jets, plumes and wakes. J Fluids Eng 125:813–822

    Article  Google Scholar 

  9. Hunt GR, Kaye NG (2001) Virtual origin correction for lazy turbulent plumes. J Fluid Mech 435:377–396

    MATH  Google Scholar 

  10. Nam S, Bill JRG (1993) Numerical simulation of thermal plumes. Fire Saf J 21:231–256

    Article  Google Scholar 

  11. Zhou X, Luo KH, Williams JJR (2001) Large eddy simulation of a turbulent forced plume. Eur J Mech B Fluids 20:233–254

    Article  MATH  Google Scholar 

  12. Pham MV, Plourde F, Doan KS (2007) Direct and large-eddy simulations of a pure thermal plume. Phys Fluids 19:1–13

    Article  Google Scholar 

  13. Dewan A, Arakeri JH, Srinivasan J (1997) A new turbulence model for the axisymmetric plume. Appl Math Model 21:709–719

    Article  MATH  Google Scholar 

  14. List EJ (1982) Turbulent jet and plumes. Annu Rev Fluid Mech 14:189–212

    Article  Google Scholar 

  15. Dai Z, Tseng LK, Faeth GM (1995) Velocity statistics of round, fully-developed buoyant turbulent plume. J Heat Transf 117:138–145

    Article  Google Scholar 

  16. Rooney GG, Linden PF (1996) Similarity considerations for non-Boussinesq plumes in an unstratified environment. J Fluid Mech 318:237–250

    Article  MATH  Google Scholar 

  17. Van Maele K, Merci B (2006) Application of two buoyancy-modified k–ε turbulence models to different types of buoyant plumes. Fire Saf J 41:122–318

    Article  Google Scholar 

  18. Kumar R, Dewan A (2013) Assessment of buoyancy-corrected turbulence models for thermal plumes. Eng Appl Comput Fluid Mech 7:239–249

    Google Scholar 

  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 43:2375–2393

    Article  MATH  Google Scholar 

  20. Kumar R, Dewan A (2014) Computational models for turbulent thermal plumes: recent advances and challenges. Heat Transf Eng 35(4):367–383

    Article  Google Scholar 

  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 1–14

  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 73:413–421

    Article  MATH  Google Scholar 

  23. Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys 12:620–631

    Article  Google Scholar 

  24. Daly BJ, Harlow FH (1970) Transport equations in turbulence. Phys Fluids 13:2634–2649

    Article  Google Scholar 

  25. Markatos NC, Malin MR (1982) Mathematical modeling of buoyancy-induced smoke flow in enclosures. Int J Heat Mass Transf 25:63–75

    Article  MATH  Google Scholar 

  26. Worthy J, Sanderson V, Rubini P (2001) Comparison of modified k–ε turbulence models for buoyant plumes. Numer Heat Transf Part A 39:151–165

    Article  Google Scholar 

  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 8:23–38

    Article  MATH  Google Scholar 

  28. Lakshmipathy S, Girimaji SS (2010) Partially averaged Navier–Stokes (PANS) method for turbulence simulations: flow past a circular cylinder. J Fluids Eng 132:121–129

    Article  Google Scholar 

  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 1–11

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Authors and Affiliations

  1. Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi, 110016, India

    Rajesh Kumar & Anupam Dewan

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  1. Rajesh Kumar
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  2. Anupam Dewan
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Correspondence to Anupam Dewan.

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Kumar, R., Dewan, A. Partially-averaged Navier–Stokes method for turbulent thermal plume. Heat Mass Transfer 51, 1655–1667 (2015). https://doi.org/10.1007/s00231-015-1527-1

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