Advertisement

Heat and Mass Transfer

, Volume 54, Issue 10, pp 3035–3045 | Cite as

Pseudo-potential MRT - thermal LB simulation of flow boiling in vertical tubes

  • Tingzhen Sun
  • Nan Gui
  • Xingtuan Yang
  • Jiyuan Tu
  • Shengyao Jiang
Original
  • 93 Downloads

Abstract

The flow boiling in vertical tubes is simulated by the MRT pseudo-potential - thermal LB model to study the effect of contact angle. No empirical correlations are given in this simulation. To validate the model, the relationship between the acceleration of gravity and the departure velocity of bubble in the departure period is compared with the empirical formula. The effect of dynamic contact angle on boiling is investigated. The simulation results of the dynamic contact angle and the static contact angle show that the dynamic contact angle has great influence on the bubble behavior. The key features of dynamic contact angle, i.e. the advancing contact angle, receding contact angle and contact angle hysteresis, are investigated. The mechanisms of differences of entire bubble period and bubble departure diameter under various contact angles are discussed. The heat transfer coefficient, the critical heat flux and the flow pattern of different surfaces are investigated. The results suggest that the critical heat flux of hydrophilic surface are higher than that of hydrophobic surface.

Nomenclature

Physical meaning

fi

Density distribution function

e

Lattice velocity vector

δt

Time step

τ

Dimensionless velocity relaxation time

F

Resultant force

Cv

Constant-volume specific heat

g

Acceleration of gravity

gi

Temperature distribution function

fieq

Equilibrium density distribution function

Ts

Saturation temperature

Step

Calculation steps

D

Bubble departure diameter

ɛ

A factor related with temperature

Q

Heat flux

θa

Advancing contact angle

p

Pressures

ν

Kinematic viscosity

ρ

Fluid density

u

Macroscopic velocity

ueq

Equilibrium velocity

Fint

Interparticle contact force

Cs

Sound speed of lattice

ψ

Potential function

τT

Dimensionless temperature relaxation time

gieq

Equilibrium temperature distribution function

σ

Surface tension

f

Bubble departure frequency

h

Heat transfer coefficient

Tc

Critical temperature

Tr

Equal to T/Tc

θr

Receding contact angle

Vmax

Interface velocity

Notes

Acknowledgements

The authors are grateful for the support of this research by the National Natural Science Foundations of China (Grant No. 51576211), the Science Fund for Creative Research Groups of National Natural Science Foundation of China (Grant No. 51621062), the National High Technology Research and Development Program of China (863)(2014AA052701), and the Foundation for the Author of National Excellent Doctoral Dissertation of P.R. China (FANEDD, Grant No. 201438).

References

  1. 1.
    Niknam PH, Haghighi M, Kasiri N, Khanof MH (2015) Numerical study of low concentration nanofluids pool boiling, investigating of boiling parameters introducing nucleation site density ratio. Heat Mass Transf 51(5):601–609CrossRefGoogle Scholar
  2. 2.
    Wu Z, Wadekar V, Wang C et al (2018) Dryout-type critical heat flux in vertical upward annular flow: effects of entrainment rate, initial entrained fraction and diameter. Heat Mass Transf 54(1):81–90CrossRefGoogle Scholar
  3. 3.
    Dong L, Quan X, Cheng P (2014) An experimental investigation of enhanced pool boiling heat transfer from surfaces with micro/nano-structures. Int J Heat Mass Transf 71:189–196CrossRefGoogle Scholar
  4. 4.
    Hegde RN, Rao SS, Reddy RP (2012) Boiling induced nanoparticle coating and its effect on pool boiling heat transfer on a vertical cylindrical surface using CuO nanofluids. Heat Mass Transf 48(9):1549–1557CrossRefGoogle Scholar
  5. 5.
    Acharya A, Pise A (2017) A review on augmentation of heat transfer in boiling using surfactants/additives. Heat Mass Transf 53(4):1457–1477CrossRefGoogle Scholar
  6. 6.
    Ramanujapu N, Dhir VK (1999) Dynamics of contact angle during growth and detachment of a vapor bubble at a single nucleation site. Univ. of California, Los AngelesGoogle Scholar
  7. 7.
    Kurul N, Podowski MZ. (1990) Multidimensional effects in forced convection subcooled boiling. In: Proceedings of the Ninth International Heat Transfer Conference, Hemisphere Publishing New YorkGoogle Scholar
  8. 8.
    Tu JY, Yeoh GH (2002) On numerical modelling of low-pressure subcooled boiling flows. Int J Heat Mass Transf 45(6):1197–1209CrossRefzbMATHGoogle Scholar
  9. 9.
    Gunstensen AK, Rothman DH, Zaleski S et al (1991) Lattice Boltzmann model of immiscible fluids. Phys Rev A 43(8):4320CrossRefGoogle Scholar
  10. 10.
    Shan X, Chen H (1993) Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 47(3):1815CrossRefGoogle Scholar
  11. 11.
    Swift MR, Osborn WR, Yeomans JM (1995) Lattice Boltzmann simulation of nonideal fluids. Phys Rev Lett 75(5):830CrossRefGoogle Scholar
  12. 12.
    Shan X, Chen H (1994) Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. Phys Rev E 49(4):2941CrossRefGoogle Scholar
  13. 13.
    Gong S, Cheng P (2012) Numerical investigation of droplet motion and coalescence by an improved lattice Boltzmann model for phase transitions and multiphase flows. Comput Fluids 53:93–104MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Gong S, Cheng P (2012) A lattice Boltzmann method for simulation of liquid–vapor phase-change heat transfer. Int J Heat Mass Transf 55(17):4923–4927CrossRefGoogle Scholar
  15. 15.
    Gong S, Cheng P (2013) Lattice Boltzmann simulation of periodic bubble nucleation, growth and departure from a heated surface in pool boiling. Int J Heat Mass Transf 64:122–132CrossRefGoogle Scholar
  16. 16.
    Mu Y, Chen L, He YL et al (2017) Nucleate boiling performance evaluation of cavities at mesoscale level. Int J Heat Mass Transf 106:708–719CrossRefGoogle Scholar
  17. 17.
    Fang W, Chen L, Kang QJ et al (2017) Lattice Boltzmann modeling of pool boiling with large liquid-gas density ratio. Int J Therm Sci 114:172–183CrossRefGoogle Scholar
  18. 18.
    Song JH, Lee J, Chang SH et al (2017) Onset of nucleate boiling in narrow, rectangular channel for downward flow under low pressure. Ann Nucl Energy 109:498–506CrossRefGoogle Scholar
  19. 19.
    Moufekkir F, Moussaoui MA, Mezrhab A et al (2015) Study of coupled double diffusive convection–radiation in a tilted cavity via a hybrid multi-relaxation time-lattice Boltzmann-finite difference and discrete ordinate methods. Heat Mass Transf 51(4):567–586CrossRefGoogle Scholar
  20. 20.
    Li Q, Luo KH, Li XJ (2013) Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model. Phys Rev E 87(5):053301CrossRefGoogle Scholar
  21. 21.
    Lallemand P, Luo L (2000) Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys Rev E 61(6):6546MathSciNetCrossRefGoogle Scholar
  22. 22.
    Shan X (2006) Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models. Phys Rev E 73(4):047701MathSciNetCrossRefGoogle Scholar
  23. 23.
    Yuan P, Schaefer L (2006) Equations of state in a lattice Boltzmann model. Phys Fluids 18(4):042101MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Li Q, Kang QJ, Francois MM et al (2015) Lattice Boltzmann modeling of boiling heat transfer: the boiling curve and the effects of wettability. Int J Heat Mass Transf 85:787–796CrossRefGoogle Scholar
  25. 25.
    Zou Q, He X (1997) On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids 9(6):1591–1598MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Lou Q, Guo Z, Shi B (2013) Evaluation of outflow boundary conditions for two-phase lattice Boltzmann equation. Phys Rev E 87(6):063301CrossRefGoogle Scholar
  27. 27.
    He YL, Wang Y, Li Q (2009) Lattice Boltzmann method: theory and applications. Science, BeijingGoogle Scholar
  28. 28.
    Peebles FN (1953) Studies on the motion of gas bubbles in liquids. Chem Eng Prog 49:88–97Google Scholar
  29. 29.
    Kutsteladze SS, Styrikovich MA (1960) Hydraulics of gas-liquid systems. Foreign Technology Div Wright-Patterson AFB OhioGoogle Scholar
  30. 30.
    Mukherjee A, Kandlikar SG (2007) Numerical study of single bubbles with dynamic contact angle during nucleate pool boiling. Int J Heat Mass Transf 50(1):127–138CrossRefzbMATHGoogle Scholar
  31. 31.
    Lam C, Wu R, Li D et al (2002) Study of the advancing and receding contact angles: liquid sorption as a cause of contact angle hysteresis. Adv Colloid Interf Sci 96(1):169–191CrossRefGoogle Scholar
  32. 32.
    Kocamustafaogullari G, Ishii M (1995) Foundation of the interfacial area transport equation and its closure relations. Int J Heat Mass Transf 38(3):481–493CrossRefzbMATHGoogle Scholar
  33. 33.
    Basu N, Warrier GR, Dhir VK (2005) Wall heat flux partitioning during subcooled flow boiling: part 1-model development. Trans ASME C J Heat Transfer 127(2):131–140CrossRefGoogle Scholar
  34. 34.
    Cole R (1960) A photographic study of pool boiling in the region of the critical heat flux. AICHE J 6(4):533–538CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of EducationTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.School of EngineeringRMIT UniversityMelbourneAustralia

Personalised recommendations