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Hydrodynamic and thermal interactions of a cluster of solid particles in a pool of liquid of different Prandtl numbers using two-fluid model

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Abstract

The knowledge of thermal interaction between hot particles and liquid is essential for many engineering applications. The main focus of the present study is to understand the underlying phenomena of transient interaction between the hot particles and the liquid of varying Prandtl number under different parametric conditions. Analysis is carried out numerically using in-house multiphase code based on Eulerian two-fluid laminar model. The code is validated against existing results. The dispersion and penetration characteristics of the particles are observed to be a strong function of Prandtl number as well as volume fraction and particle diameter, with a stronger mushrooming observed for lower particle size or high Prandtl number liquid. The thermal interaction is observed to be between the particles and the narrow thermal envelope surrounding the particles. The particles cooling rate are observed to be several orders faster in a liquid with lower Prandtl number.

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Abbreviations

C>D :

Drag coefficient

C>L :

Lift coefficient

d :

Particle diameter (m)

g :

Gravitational acceleration (m/s2)

Pr :

Prandtl Number

P :

Pressure (Pa)

Re>D :

Reynolds number

t :

Time (s)

T :

Temperature (K)

T*:

Normalized temperature

u>r :

Radial velocity (m/s)

u>z :

Axial velocity (m/s)

\( \vec{v} \) :

Velocity vector (m/s)

V>rel :

Relative velocity (m/s)

ρ :

Density (kg/m3)

\( \mathop {Q_{pl} }\limits^{.} \) :

Heat transfer rate from particles to liquid (kg/s)

μ:

Viscosity (kg/m s)

α:

Volume fraction

amb :

Ambient

l :

Liquid

li :

Liquid initial

p :

Particle

pi :

Particle initial

References

  1. Hall RW, Fletcher DF (1995) Validation of CHYMES: simulant studies. Nucl Eng Des 155:97–114

    Article  Google Scholar 

  2. Fletcher DF, Witt PJ (1996) Numerical studies of multiphase mixing with application to small scale experiments. Nucl Eng Des 166:135–145

    Article  Google Scholar 

  3. Angelini S, Yuen WW, Theofanous TG (1995) Premixing-related behavior of steam explosions. Nucl Eng Des 155:115–157

    Article  Google Scholar 

  4. Angelini S, Theofanous TG, Yuen WW (1997) The mixing of particle clouds plunging into water. Nucl Eng Des 177:285–301

    Article  Google Scholar 

  5. Meyer L, Schumacher G (1996) Queos, a simulation-experiment of the premixing phase of a steam explosion with hot spheres in water base case experiments. FZKA Report 5612, Forschungszentrum Karlsruhe

  6. Annunziato A, Yerkess A, Addabbo C (1999) FARO and KROTOS Code simulation and analysis at JRC Ispra. Nucl Eng Des 189:359–378

    Article  Google Scholar 

  7. Berthoud G, Crecy Fd, Duplat F, Meignen R, Valette M Premixing of corium into water during a fuel–coolant interaction: the models used in the 3 fields version of the MC3D code and two examples of validation on BILLEAU and FARO experiments. In: JAERI-Conf 97-011, Tokai-mura, Japan, May 19–21 1997. Proceeding of the OECD/CSNI specialist meeting on fuel coolant interaction

  8. Pohlner G, Vujic Z, Bürger M, Lohnert G (2006) Simulation of melt jet breakup and debris bed formation in water pools with IKEJET/IKEMIX. Nucl Eng Des 206(19–21):2026–2048

    Article  Google Scholar 

  9. Melissari B, Argyropoulos SA (2005) Development of a heat transfer dimensionless correlation for spheres immersed in a wide range of Prandtl number fluids. Int J Heat Mass Transf 48:4333–4341

    Article  Google Scholar 

  10. Srinivasan V, Moon K-M, Greif D, Wang DM, M-h Kim (2010) Numerical simulation of immersion quench cooling process using an Eulerian multi-fluid approach. Appl Therm Eng 30:499–509

    Article  Google Scholar 

  11. Sahu AK, Chhabra RP, Eswaran V (2009) Effects of Reynolds and Prandtl numbers on heat transfer from a square cylinder in the unsteady flow regime. Int J Heat Mass Transf 52:839–850

    Article  Google Scholar 

  12. Wallis GB (1969) One-dimensional two-phase flow. McGraw- Hill, New York

    Google Scholar 

  13. Ishii M, Hibiki T (1975) Thermo fluid dynamics of two-phase flow. Eyrolles, Paris

    MATH  Google Scholar 

  14. Gidaspow D (1994) Multiphase flow and fluidization. Academic Press, New York

    MATH  Google Scholar 

  15. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39:201–225

    Article  Google Scholar 

  16. Peng D, Merriman B, Osher S, Zhao H, Kang M (1999) A PDE-based fast local level set method. J Comput Phys 155:410–438

    Article  MathSciNet  Google Scholar 

  17. Unverdi SO, Tryggvason G (1992) A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys 100:25–37

    Article  Google Scholar 

  18. Lakehal D (2002) On the modelling of multiphase turbulent flows for environmental and hydrodynamic applications. Int J Multiph Flow 28:823–863

    Article  Google Scholar 

  19. Chahed J, Roig V, Masbernat L (2003) Eulerian–Eulerian two-fluid model for turbulent gas–liquid bubbly flows. Int J Multiph Flow 29:23–49

    Article  Google Scholar 

  20. Yeoh GH, Tu JY (2006) Two-fluid and population balance models for subcooled boiling flow. Appl Math Model 30:1370–1391

    Article  Google Scholar 

  21. Hudson J, Harris D (2006) A high resolution scheme for Eulerian gas–solid two-phase isentropic flow. J Comput Phys 216:494–525

    Article  MathSciNet  Google Scholar 

  22. Antal SP Jr, Lahey RT, Flaherty JE (1991) Analysis of phase distribution in fully developed laminar bubbly two-phase flow. Int J Multiph Flow 17:635–652

    Article  Google Scholar 

  23. Yusuf R, Halvorsen B, Melaaen MC (2011) Eulerian–Eulerian simulation of heat transfer between a gas–solid fluidized bed and an immersed tube-bank with horizontal tubes. Chem Eng Sci 66:1550–1564

    Article  Google Scholar 

  24. Wachem BGMv, Almstedt AE (2003) Methods for multiphase computational fluid dynamics. Chem Eng J 96:81–98

    Article  Google Scholar 

  25. Kalteh M, Abbassi A, Saffar-Avval M, Harting J (2011) Eulerian–Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel. Int J Heat Fluid Flow 32:107–116

    Article  Google Scholar 

  26. Fard MH, Esfahany MN, Talaie MR (2010) Numerical study of convective heat transfer of nanofluids in a circular tube two-phase model versus single-phase model. Int Commun Heat Mass Transfer 37:91–97

    Article  Google Scholar 

  27. Clift R, Grace JR, Weber ME (1978) Bubbles, drops and particles. Academic press, New York

    Google Scholar 

  28. Ishii M, Chawla TC (1979) Local drag laws in dispersed two phase flow. NUREG/CR-1230:79–105

  29. Khan AR, Richardson JF (1987) The resistance to motion of a solid sphere in a fluid. Chem Eng Commun 62:135–150

    Article  Google Scholar 

  30. Wallis GB (1974) The terminal speed of single drops or bubbles in an infinite medium. Int J Multiph Flow 1:491–511

    Article  Google Scholar 

  31. Schiller L, Naumann Z (1935) A drag coefficient correlation. Z Ver Deutsch Ing 77:318–320

    Google Scholar 

  32. Drew D, Lahey RT (1979) Application of general constitutive principles to the derivation of multidimensional two phase flow equations. Int J Multiph Flow 5:243–264

    Article  Google Scholar 

  33. Leskovar M, Mavko B (2002) Simulation of the isothermal QUEOS steam explosion premixing experiment Q08. J Mech Eng 48:449–458

    Google Scholar 

  34. Ranz WE, Marshall WR (1952) Evaporation from drops: part I and II. Chem Eng Prog 48(141–146):173–180

    Google Scholar 

  35. Witte L (1968) An experimental investigation of forced convection heat transfer from a sphere to liquid sodium. ASME J Heat Transf 90:9–12

    Article  Google Scholar 

  36. Whitaker S (1972) Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles. AIChE J 18(2):361–371

    Article  Google Scholar 

  37. Argyropoulos SA, Mikrovas AC (1996) An experimental investigation on natural and forced convection in liquid metals. Int J Heat Mass Transf 39(3):547–561

    Article  Google Scholar 

  38. Patankar SV (1980) Numerical heat transfer and fluid flow. Taylor & Francis

  39. Mahapatra PS, Ghosh K, Manna NK, Mukhopadhyay A, Sen S (2011) Study of dispersion and cooling of a cluster of solid spherical particles in quiescent liquid of different Prandtl numbers. Paper presented at the 21st National & 10TH ISHMT-ASME heat and mass transfer conference, IIT Madras, India, December 27–30

  40. Leskovar M (2000) Comparison of multiphase mixing simulations performed on a staggered and collocated grid. Paper presented at the international conference nuclear energy in Central Europe 2000, Slovenia

  41. Theofanous TG, Yuen WW, Angelini S (1999) The verification basis of the PM-ALPHA code. Nucl Eng Des 189:59–102

    Article  Google Scholar 

  42. Ishii M, Zuber N (1979) Drag coefficient and relative velocity in bubbly, droplet or particulate flow. AIChE J 25:843–855

    Article  Google Scholar 

Download references

Acknowledgments

Authors gratefully acknowledge several constructive suggestions made by Prof. Achintya Mukhopadhyay (Now on lien to Indian Institute of Technology, Madras) and Prof. Swarnendu Sen of Department of Mechanical Engineering, Jadavpur University. The financial support for this work from Bhabha Atomic Research Centre (BARC), India, and Council of Science and Industrial Research (CSIR), India is gratefully acknowledged. The authors also acknowledge the encouragement and suggestions of Deb Mukhopadhyay of BARC for carrying out the research.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Jadavpur University, Kolkata, India

    Pallab S. Mahapatra, Nirmal K. Manna & Koushik Ghosh

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  1. Pallab S. Mahapatra
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  2. Nirmal K. Manna
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Correspondence to Nirmal K. Manna.

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Mahapatra, P.S., Manna, N.K. & Ghosh, K. Hydrodynamic and thermal interactions of a cluster of solid particles in a pool of liquid of different Prandtl numbers using two-fluid model. Heat Mass Transfer 49, 1659–1679 (2013). https://doi.org/10.1007/s00231-013-1206-z

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