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Numerical investigation and deep learning-based prediction of heat transfer characteristics and bubble dynamics of subcooled flow boiling in a vertical tube

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Abstract

Subcooled flow boiling presents an enormous ability of heat transfer rate, which is extremely important in the heat-dissipating systems of many industrial applications, such as power plants and internal combustion engines. Using an Euler-Euler-based three-dimensional numerical simulation of subcooled flow boiling in a vertical tube, we investigated different heat transfer quantities (average and local heat transfer coefficient, average and local vapor volume fraction, average and local wall temperature) and bubble dynamics quantities (bubble departure diameter, bubble detachment frequency, bubble detachment waiting time, and nucleation site density) under various boundary conditions (pressure, subcooled temperature, mass flux, heat flux). Numerical results show that an increase in heat flux leads to the increase in all of the physical quantities of interest but the bubble detachment frequency. An entirely opposite behavior is observed when we change the mass flux and inlet subcooled temperature. Furthermore, a rise in pressure reduces all of the target quantities but the wall temperature and bubble detachment frequency. Since numerical simulation of such multiphase flow requires significant computational resources, we also present a deep learning approach, based on artificial neural networks (ANN), to predicting the physical quantities of interest. Prediction results demonstrate that the ANN model is capable of accurately predicting the target quantities with mean absolute errors less than 2.5% and R-squared more than 0.93.

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Abbreviations

Ac :

area of fraction of the heater surface subjected to convection [m2]

Aq :

area of fraction of the heater surface subjected to quenching [m2]

Cp :

specific heat of the fluid [J kg−1 K−1]

dw :

bubble departure diameter on the wall [m]

Flg :

action of interfacial forces from vapor on liquid [N]

Fgl :

action of interfacial forces from liquid on vapor [N]

f:

bubble departure frequency [Hz]

α :

volume fraction

Si :

additional source terms due to coalescence and breakage [kg m−3 s−1]

fi :

scalar fraction related to the number density of the discrete bubble classes

G:

mass flux [kg nf−2 s−1]

g:

gravitational constant [m s−2]

H:

specific enthalpy [J kg−1]

h:

interfacial heat transfer coefficient [J kg−1]

hfg :

specific latent heat of vaporization [J kg−1]

k:

conductivity [W m−2 K−1]

m:

mass [kg]

ṁ:

mass flux [kg m−2 s−1]

na :

active nucleation site density [m2]

n:

number of data points

P:

pressure [N m−2]

qc :

heat transfer due to forced convective [W m−2]

qe :

heat transfer due to evaporation [W m−2]

q q :

heat transfer due to quenching [W m−2]

q:

heat flux [W m−2]

R2 :

R_squared

St:

stanton number [St=h/ρucp]

T:

temperature [K]

Tsup :

wall superheat temperature [K]=Tw−Tsat

Tsub :

subcooled temperature [K]

Tw :

wall temperature [K]

tw :

bubble detachment waiting time [s]

t:

time [s]

u:

velocity [m s−1]

Xin :

entrance length [m]

Yi :

real value of the target quantity

Ŷi :

predicted value of the target quantity by the ANN

Ȳ:

mean of the data

μ :

viscosity [Pa·s]

ρ :

density [kg m−3]

σ :

surface tension [N m−1]

Γ lg :

interfacial mass transfer from vapor to liquid [kg m−3 s−1]

Γ gl :

interfacial mass transfer from liquid to vapor [kg m−3 s−1]

g:

vapor

l :

liquid

w:

wall

e:

Euler’s number

ANN:

artificial neural network

HTC:

heat transfer coefficient

References

  1. Y. Qiu, D. Garg, L. Zhou, C. R. Kharangate, S.-M. Kim and I. Mudawar, Int. J. Heat Mass Transfer, 149, 119211 (2020).

    Article  Google Scholar 

  2. G. P. Celata, M. Cumo, A. Mariani and G. Zummo, Int. J. Therm. Sci., 39(9–11), 896 (2000).

    Article  CAS  Google Scholar 

  3. Z. Guo, J. Yang, Z. Tan, X. Tian and Q. Wang, Int. J. Heat Mass Transfer, 174, 121296 (2021).

    Article  Google Scholar 

  4. J. Zhou, J. Bai and Y. Liu, Micromachines, 13(5), 781 (2022).

    Article  Google Scholar 

  5. J. Lee, D. Jo, H. Chae, S. H. Chang, Y. H. Jeong and J. J. Jeong, Exp. Therm. Fluid Sci., 69, 86 (2015).

    Article  Google Scholar 

  6. Q. Fan, Z. Zhang and X. Huang, Adv. Theory Simulations, 2200047 (2022).

  7. G. Zhang, J. Chen, Z. Zhang, M. Sun, Y. Yu, J. Wang and S. Cai, Smart Mater. Struct., 31(7), 075008 (2022).

    Article  Google Scholar 

  8. M. E. Steinke and S. G. Kandlikar, J. Heat Transfer, 126(4), 518 (2004).

    Article  CAS  Google Scholar 

  9. D. Jige and N. Inoue, Int. J. Heat Fluid Flow, 78, 108433 (2019).

    Article  Google Scholar 

  10. V. Schrock and L. Grossman, Forced convection boiling studies. final report on forced convection vaporization project, California. Univ., Berkeley. Inst. of Engineering Research (1959).

  11. J. Bennett, Trans. Inst. Chem. Eng., 39, 113 (1961).

    CAS  Google Scholar 

  12. J. C. Chen, Ind. Eng. Chem. Process Des. Dev., 5(3), 322 (1966).

    Article  CAS  Google Scholar 

  13. M. M. Shah, ASHRAE Trans.; (United States), 88, 185 (1982).

    Google Scholar 

  14. D. L. Bennett and J. C. Chen, AIChE J., 26(3), 454 (1980).

    Article  CAS  Google Scholar 

  15. S. G. Kandlikar, J. Heat Transfer, 112(1), 219 (1990).

    Article  CAS  Google Scholar 

  16. H. J. Lee and S. Y. Lee, Int. J. Multiphase Flow, 27(12), 2043 (2001).

    Article  CAS  Google Scholar 

  17. H. Alimoradi, S. Zaboli and M. Shams, Korean J. Chem. Eng., 39(1), 69 (2022).

    Article  CAS  Google Scholar 

  18. S. Zaboli, H. Alimoradi and M. Shams, J. Therm. Anal. Calorim., 147, 10659 (2022).

    Article  CAS  Google Scholar 

  19. S. S. Bertsch, E. A. Groll and S. V. Garimella, Int. J. Heat Mass Transfer, 52(7–8), 2110 (2009).

    Article  CAS  Google Scholar 

  20. D. L. Bennett, M. W. Davies and B. L. Hertzler, Am. Inst. Chem. Eng. Symposium Ser., 76, 91 (1980).

    CAS  Google Scholar 

  21. S. Edelstein, A. Perez and J. Chen, AIChE J., 30(5), 840 (1984).

    Article  CAS  Google Scholar 

  22. X. Fang, Q. Wu and Y. Yuan, Int. J. Heat Mass Transfer, 107, 972 (2017).

    Article  CAS  Google Scholar 

  23. M. Piasecka, Int. J. Heat Mass Transfer, 81, 114 (2015).

    Article  Google Scholar 

  24. K. Strąk and M. Piasecka, Int. J. Heat Mass Transfer, 158, 119933 (2020).

    Article  Google Scholar 

  25. S. Paul, M. Fernandino and C. A. Dorao, Int. J. Heat Mass Transfer, 164, 120589 (2021).

    Article  CAS  Google Scholar 

  26. G. Zhang, Z. Zhang, M. Sun, Y. Yu, J. Wang and S. Cai, Adv. Eng. Mater., 2101680 (2022).

  27. B. Chen, Y. Lu, W. Li, X. Dai, X. Hua, J. Xu, Z. Wang, C. Zhang, D. Gao and Y. Li, Int. J. Heat Mass Transfer, 192, 122927 (2022).

    Article  Google Scholar 

  28. M. Ahmadlou, M. R. Delavar, A. Basiri and M. Karimi, J. Indian Soc. Remote Sensing, 47(1), 53 (2019).

    Article  Google Scholar 

  29. H. A. Amirkolaee, H. Arefi, M. Ahmadlou and V. Raikwar, Remote Sensing Environ., 274, 113014 (2022).

    Article  Google Scholar 

  30. A. Azadeh, M. Saberi, A. Kazem, V. Ebrahimipour, A. Nourmohammadzadeh and Z. Saberi, Appl. Soft Comput., 13(3), 1478 (2013).

    Article  Google Scholar 

  31. L. Zhou, Q. Fan, X. Huang and Y. Liu, Optimization, In press (2022).

  32. H. Alimoradi and M. Shams, Appl. Therm. Eng., 111, 1039 (2017).

    Article  Google Scholar 

  33. Y. Seong, C. Park, J. Choi and I. Jang, Energies, 13(4), 968 (2020).

    Article  Google Scholar 

  34. X. Wang and X. Lyu, Ocean Eng., 221, 108508 (2021).

    Article  Google Scholar 

  35. Y. Wang, H. Wang, B. Zhou and H. Fu, Ocean Eng., 242, 110106 (2021).

    Article  Google Scholar 

  36. S. Cheung, S. Vahaji, G. Yeoh and J. Tu, Int. J. Heat Mass Transfer, 75, 736 (2014).

    Article  Google Scholar 

  37. B. E. Launder and D. B. Spalding, Comput. Meth. Appl. Mech. Eng., 3, 269 (1974).

    Article  Google Scholar 

  38. W. E Ranz and W. R. Marshall, Chem. Eng. Prog., 48(3), 141 (1952).

    Google Scholar 

  39. M. Ishii and N. Zuber, AIChE J., 25(5), 843 (1979).

    Article  CAS  Google Scholar 

  40. N. Kurul and M. Z. Podowski, Multidimensional effects in forced convection subcooled boiling, In: Proceedings of the 9th Heat Transfer Conference, 19–24 (1990).

  41. M. Lemmert and J. M. Chawla, Influence of flow velocity on surface boiling heat transfer coefficient, In: Boiling, Hahne, E., Grigull, U. (Eds.), Heat Transfer. Academic Press and Hemisphere, ISBN 0-12-314450-7, pp. 237–247 (1977).

  42. V. I. Tolubinsky and D. M. Kostanchuk, Vapour bubbles groth rate and heat transfer intensity at subcooled water boiling; Heat Transfer 1970, Preprints of papers presented at the 4th International Heat Transfer Conference, vol. 5, Paris (Paper No. B-2.8) (1970).

  43. R. Cole, AIChE J., 6(4), 533 (1960).

    Article  CAS  Google Scholar 

  44. G. Bartolomei, V. Brantov, Y. S. Molochnikov, Y. V. Kharitonov, V. Solodkii, G. Batashova and V. Mikhailov, Therm. Eng., 29(3), 132 (1982).

    Google Scholar 

  45. S. Z. Rouhani and E. Axelsson, Int. J. Heat Mass Transfer, 13(2), 383 (1970).

    Article  CAS  Google Scholar 

  46. A. Krizhevsky, I. Sutskever and G. E. Hinton, Commun. ACM, 60(6), 84 (2017).

    Article  Google Scholar 

  47. D. Svozil, V. Kvasnicka and J. Pospichal, Chemom. Intell. Lab. Syst., 39(1), 43 (1997).

    Article  CAS  Google Scholar 

  48. D. P. Kingma and B. Jimmy, Adam: A method for stochastic optimization, arXiv preprint arXiv:1412.6980 (2014).

  49. A. E. Bergles and W. M. Rohsenow, ASME J. Heat Transfer, 1, 365 (1964).

    Article  Google Scholar 

  50. D. Liu, P.-S. Lee and S. V. Garimella, Int. J. Heat Mass Transfer, 48(25–26), 5134 (2005).

    Article  CAS  Google Scholar 

  51. N. Basu, G. R. Warrier and V. K. Dhir, J. Heat Transfer, 124(4), 717 (2002).

    Article  CAS  Google Scholar 

  52. G. Costigan and P. Whalley, Int. J. Multiphase Flow, 23(2), 263 (1997).

    Article  CAS  Google Scholar 

  53. N. Basu, G. R. Warrier and V. K. Dhir, J. Heat Transfer, 127(2), 131 (2005).

    Article  CAS  Google Scholar 

  54. W. Friz, Physic. Zeitschz., 36, 379 (1935).

    Google Scholar 

  55. L. Yang, A. Guo and D. Liu, Exp. Heat Transfer, 29(2), 221 (2016).

    Article  CAS  Google Scholar 

  56. R. Sugrue, J. Buongiorno and T. McKrell, Nucl. Eng. Des., 279, 182 (2014).

    Article  CAS  Google Scholar 

  57. J. Yoo, C. E. Estrada-Perez and Y. A. Hassan, Int. J. Multiphase Flow, 84, 292 (2016).

    Article  CAS  Google Scholar 

  58. C.-Y. Han and P. Griffith, Int. J. Heat Mass Transfer, 8, 905 (1965).

    Article  CAS  Google Scholar 

  59. L. Z. Zeng and J. F. Klausner, J. Heat Transfer, 115, 215 (1993).

    Article  Google Scholar 

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Authors and Affiliations

  1. Computational and Data-Driven Multiphysics Laboratory, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

    Erfan Eskandari & Mahdi Pourbagian

  2. Multiphase Flow Lab, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

    Hasan Alimoradi & Mehrzad Shams

Authors
  1. Erfan Eskandari
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  2. Hasan Alimoradi
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  3. Mahdi Pourbagian
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  4. Mehrzad Shams
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Correspondence to Mahdi Pourbagian.

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Eskandari, E., Alimoradi, H., Pourbagian, M. et al. Numerical investigation and deep learning-based prediction of heat transfer characteristics and bubble dynamics of subcooled flow boiling in a vertical tube. Korean J. Chem. Eng. 39, 3227–3245 (2022). https://doi.org/10.1007/s11814-022-1267-0

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  • DOI: https://doi.org/10.1007/s11814-022-1267-0

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