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.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
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
Y. Qiu, D. Garg, L. Zhou, C. R. Kharangate, S.-M. Kim and I. Mudawar, Int. J. Heat Mass Transfer, 149, 119211 (2020).
G. P. Celata, M. Cumo, A. Mariani and G. Zummo, Int. J. Therm. Sci., 39(9–11), 896 (2000).
Z. Guo, J. Yang, Z. Tan, X. Tian and Q. Wang, Int. J. Heat Mass Transfer, 174, 121296 (2021).
J. Zhou, J. Bai and Y. Liu, Micromachines, 13(5), 781 (2022).
J. Lee, D. Jo, H. Chae, S. H. Chang, Y. H. Jeong and J. J. Jeong, Exp. Therm. Fluid Sci., 69, 86 (2015).
Q. Fan, Z. Zhang and X. Huang, Adv. Theory Simulations, 2200047 (2022).
G. Zhang, J. Chen, Z. Zhang, M. Sun, Y. Yu, J. Wang and S. Cai, Smart Mater. Struct., 31(7), 075008 (2022).
M. E. Steinke and S. G. Kandlikar, J. Heat Transfer, 126(4), 518 (2004).
D. Jige and N. Inoue, Int. J. Heat Fluid Flow, 78, 108433 (2019).
V. Schrock and L. Grossman, Forced convection boiling studies. final report on forced convection vaporization project, California. Univ., Berkeley. Inst. of Engineering Research (1959).
J. Bennett, Trans. Inst. Chem. Eng., 39, 113 (1961).
J. C. Chen, Ind. Eng. Chem. Process Des. Dev., 5(3), 322 (1966).
M. M. Shah, ASHRAE Trans.; (United States), 88, 185 (1982).
D. L. Bennett and J. C. Chen, AIChE J., 26(3), 454 (1980).
S. G. Kandlikar, J. Heat Transfer, 112(1), 219 (1990).
H. J. Lee and S. Y. Lee, Int. J. Multiphase Flow, 27(12), 2043 (2001).
H. Alimoradi, S. Zaboli and M. Shams, Korean J. Chem. Eng., 39(1), 69 (2022).
S. Zaboli, H. Alimoradi and M. Shams, J. Therm. Anal. Calorim., 147, 10659 (2022).
S. S. Bertsch, E. A. Groll and S. V. Garimella, Int. J. Heat Mass Transfer, 52(7–8), 2110 (2009).
D. L. Bennett, M. W. Davies and B. L. Hertzler, Am. Inst. Chem. Eng. Symposium Ser., 76, 91 (1980).
S. Edelstein, A. Perez and J. Chen, AIChE J., 30(5), 840 (1984).
X. Fang, Q. Wu and Y. Yuan, Int. J. Heat Mass Transfer, 107, 972 (2017).
M. Piasecka, Int. J. Heat Mass Transfer, 81, 114 (2015).
K. Strąk and M. Piasecka, Int. J. Heat Mass Transfer, 158, 119933 (2020).
S. Paul, M. Fernandino and C. A. Dorao, Int. J. Heat Mass Transfer, 164, 120589 (2021).
G. Zhang, Z. Zhang, M. Sun, Y. Yu, J. Wang and S. Cai, Adv. Eng. Mater., 2101680 (2022).
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).
M. Ahmadlou, M. R. Delavar, A. Basiri and M. Karimi, J. Indian Soc. Remote Sensing, 47(1), 53 (2019).
H. A. Amirkolaee, H. Arefi, M. Ahmadlou and V. Raikwar, Remote Sensing Environ., 274, 113014 (2022).
A. Azadeh, M. Saberi, A. Kazem, V. Ebrahimipour, A. Nourmohammadzadeh and Z. Saberi, Appl. Soft Comput., 13(3), 1478 (2013).
L. Zhou, Q. Fan, X. Huang and Y. Liu, Optimization, In press (2022).
H. Alimoradi and M. Shams, Appl. Therm. Eng., 111, 1039 (2017).
Y. Seong, C. Park, J. Choi and I. Jang, Energies, 13(4), 968 (2020).
X. Wang and X. Lyu, Ocean Eng., 221, 108508 (2021).
Y. Wang, H. Wang, B. Zhou and H. Fu, Ocean Eng., 242, 110106 (2021).
S. Cheung, S. Vahaji, G. Yeoh and J. Tu, Int. J. Heat Mass Transfer, 75, 736 (2014).
B. E. Launder and D. B. Spalding, Comput. Meth. Appl. Mech. Eng., 3, 269 (1974).
W. E Ranz and W. R. Marshall, Chem. Eng. Prog., 48(3), 141 (1952).
M. Ishii and N. Zuber, AIChE J., 25(5), 843 (1979).
N. Kurul and M. Z. Podowski, Multidimensional effects in forced convection subcooled boiling, In: Proceedings of the 9th Heat Transfer Conference, 19–24 (1990).
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).
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).
R. Cole, AIChE J., 6(4), 533 (1960).
G. Bartolomei, V. Brantov, Y. S. Molochnikov, Y. V. Kharitonov, V. Solodkii, G. Batashova and V. Mikhailov, Therm. Eng., 29(3), 132 (1982).
S. Z. Rouhani and E. Axelsson, Int. J. Heat Mass Transfer, 13(2), 383 (1970).
A. Krizhevsky, I. Sutskever and G. E. Hinton, Commun. ACM, 60(6), 84 (2017).
D. Svozil, V. Kvasnicka and J. Pospichal, Chemom. Intell. Lab. Syst., 39(1), 43 (1997).
D. P. Kingma and B. Jimmy, Adam: A method for stochastic optimization, arXiv preprint arXiv:1412.6980 (2014).
A. E. Bergles and W. M. Rohsenow, ASME J. Heat Transfer, 1, 365 (1964).
D. Liu, P.-S. Lee and S. V. Garimella, Int. J. Heat Mass Transfer, 48(25–26), 5134 (2005).
N. Basu, G. R. Warrier and V. K. Dhir, J. Heat Transfer, 124(4), 717 (2002).
G. Costigan and P. Whalley, Int. J. Multiphase Flow, 23(2), 263 (1997).
N. Basu, G. R. Warrier and V. K. Dhir, J. Heat Transfer, 127(2), 131 (2005).
W. Friz, Physic. Zeitschz., 36, 379 (1935).
L. Yang, A. Guo and D. Liu, Exp. Heat Transfer, 29(2), 221 (2016).
R. Sugrue, J. Buongiorno and T. McKrell, Nucl. Eng. Des., 279, 182 (2014).
J. Yoo, C. E. Estrada-Perez and Y. A. Hassan, Int. J. Multiphase Flow, 84, 292 (2016).
C.-Y. Han and P. Griffith, Int. J. Heat Mass Transfer, 8, 905 (1965).
L. Z. Zeng and J. F. Klausner, J. Heat Transfer, 115, 215 (1993).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11814-022-1267-0