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Heat and mass transfer of countercurrent air-water flow in a vertical tube

Heat and Mass Transfer (2023)Cite this article

Abstract

The paper deals with the classification and the design features of direct contact heat exchangers used in various technological processes. It describes the existing two-phase flow regimes and the methods for heat and mass transfer prediction in heat exchangers with the direct contact of fluids in a vertical tube. The authors carried out the measurements of heat and mass transfer coefficients during the liquid film flow under the action of gravity towards the air flow in a vertical tube. The range of experimental variables is set to be the following: air mass flow rate is 1·10-3-4·10-3 kg/s, air inlet temperature is 26-28 °C, air inlet humidity is 38-50 %, water mass flow rate is 1.5·10-2 -4·10-2 kg/s, and water inlet temperature is 55-58 °C. It is shown that an increase in the fluid flow rate leads to the heat and mass transfer intensification due to an increase of waves on the film surface. The authors obtained new empirical correlations for calculating convective heat and mass transfer coefficients. These equations consider the influence of the water flow rate for the film Reynolds number. The described methods are recommended to be used in the range of air Reynolds numbers from 2300 to 6700 and film Reynolds numbers from 600 to 1300.

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Abbreviations

\(c_{p,air}\) :

specific heat capacity of air, J/(kgK)

d air :

humidity ratio of air, kg water/kg dry air

D :

diffusion coefficient of water vapour into air, m2/s

d:

inner diameter of flooding tube, m

F :

interphase surface area, m2

J :

diffusion flux, kg/(m2s)

h :

specific enthalpy, J/kg

h con :

convective heat transfer coefficient, W/(m2K)

h d :

mass transfer coefficient, m/s

\(h_{vl}\) :

latent heat of water, J/kg

m :

mass flow rate, kg/s

\(M_{{H_{2} O}}\) :

water molar mass (=18.02), g/mol

Nu :

Nusselt number (\(Nu = h_{con} \frac{d}{\lambda }\))

Pr :

Prandtl number

p par,air :

partial pressure of water vapour in moist air (\(p_{par,air} = 0.5\left[ {p_{par,in} + p_{par,out} } \right]\), Pa

p par,in :

partial pressure at the air inlet, Pa

p par,out :

partial pressure at the air outlet, Pa

Q :

heat transferred, W

R :

gas constant, (=8.314), J/(mol·K)

Re air :

Reynolds number of moist air (\({\text{Re}}_{air} = w_{air,in} d/v_{air}\))

Re film :

film Reynolds number (\({\text{Re}}_{film} = 4\Gamma /\mu_{air}\))

Sc air :

Schmidt number of moist air (\(Sc_{air} = v_{air} /D\))

Sh :

Sherwood number (\(Sh = h_{d} \frac{d}{D}\))

t :

temperature, °C

T db,aver :

average dry-bulb temperature of moist air (\(T_{db,aver}\)=\(0.5\left[ {T_{db,in} + T_{db,out} } \right]\)), K

w :

velocity, m/s

\(l\) :

height, m

Γ:

mass flow rate per unit perimeter, (\(\Gamma = m_{w} /\left[ {\pi d} \right]\)), kg/(m s)

\(\Delta G\) :

consumption of moisture absorbed by air, kg/s

\(\Delta T\) :

mean logarithmic temperature difference, (\(\Delta T = \frac{{\left( {t_{w,in} - t_{db,our} } \right) - \left( {t_{w,out} - t_{db,in} } \right)}}{{\ln \frac{{\left( {t_{w,in} - t_{db,our} } \right)}}{{\left( {t_{w,out} - t_{db,in} } \right)}}}}\)), K

\(\eta_{DHE}\) :

heat balance factor

λ :

thermal conductivity, W/(mK)

μ:

dynamic viscosity, [Pa·s]

ν :

kinematic viscosity, m2/s

ψ :

relative humidity of air

atm :

atmospheric

air :

moist air

aver :

average

con :

convective

db :

dry-bulb

evap :

evaporation

exp :

experimental

in :

tube inlet

out :

tube outlet

tot :

total

w :

water

wb :

wet-bulb

References

  1. Zhou X, Wang W, Chen L, Yang L, Du X(2021) Numerical investigation on novel water distribution for natural draft wet cooling tower. Int J Heat Mass Transf 181:121886. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121886

  2. Xu M, He S, Cheng J, Gao M, Lu Y, Hooman K, Xu Y, Geng Z, Zhang S(2021) Investigation on heat exchanger arrangement in solar enhanced natural draft dry cooling towers under various crosswind conditions. Case Stud Therm Eng 28:101505. https://doi.org/10.1016/j.csite.2021.101505

  3. Consuegro AJ, Kaiser AS, Zamora B, Sánchez F, Lucas M, Hernández M(2014) Numerical modeling of the drift and deposition of droplets emitted by mechanical cooling towers on buildings and its experimental validation. Build Environ 78:53–67. https://doi.org/10.1016/j.buildenv.2014.04.002

  4. Mohammed RH, El-Morsi M, Abdelaziz O(2022) Indirect evaporative cooling for buildings: A comprehensive patents review. J Build Eng 50(No 1):104158. https://doi.org/10.1016/j.jobe.2022.104158

  5. Abishek S, King Andrew JC, R Narayanaswamy (2017) Computational analysis of two-phase flow and heat transfer in parallel and counter flow double-pipe evaporators. Int J Heat Mass Transf 104:615–626. https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.089

    Article  Google Scholar 

  6. Bezrodny MK, Goliyad NN, Barabash PA, Kostyuk AP (2012) Interphase heat-and-mass transfer in a flowing bubbling layer. Therm Eng 59(6):479–484. https://doi.org/10.1134/S004060151206002X

    Article  Google Scholar 

  7. Rao RV, More KC(2017) Optimal Design and Analysis of Mechanical Draft Cooling Tower Using Improved Jaya Algorithm. Int J Ref 82:312–324. https://doi.org/10.1016/j.ijrefrig.2017.06.024

  8. Ami T, Umekawa H, Ozawa M(2014) Dryout of counter-current two-phase flow in a vertical tube. Int J Multiphase Flow 67:54–64. https://doi.org/10.1016/j.ijmultiphaseflow.2014.09.002

  9. Baqir ASh, Mahood HB, Sayer AH (2018) Temperature Distribution Measurements and Modelling of a Liquid-Liquid-Vapour Spray Column Direct Contact Heat Exchanger. Appl Therm Eng 139(5):542–551. https://doi.org/10.1016/j.applthermaleng.2018.04.128

    Article  Google Scholar 

  10. Wan J, Sun W, Deng J, Pan LM, Ding SH(2021) Experimental study on air-water countercurrent flow limitation in a vertical tube based on measurement of film thickness behavior. Nuclear Eng Technol 53(6):1821–1833. https://doi.org/10.1016/j.net.2020.12.019

  11. Li Cheng (2019) Characteristics of the high-temperature water film evaporation with countercurrent turbulent air flow in the duct. Ann Nucl Energy 130:1–7. https://doi.org/10.1016/j.anucene.2019.02.025

    Article  Google Scholar 

  12. Cherif AS, Kassim MA, Benhamou B, Harmand S, Corriou JP, Ben Jabrallah S (2011) Experimental and numerical study of mixed convection heat and mass transfer in a vertical channel with film evaporation. Int J Therm Sci 50(6):942–953. https://doi.org/10.1016/j.ijthermalsci.2011.01.002

    Article  Google Scholar 

  13. Rahmati M (2021) Effects of ZnO/water nanofluid on the thermal performance of wet cooling towers. Int J Refr 131:526–534. https://doi.org/10.1016/j.ijrefrig.2021.03.017

  14. Yu Z, Sun C, Zhang L, Bao B, Li Y, Bu S, Xu W(2021) Analysis of a novel combined heat exchange strategy applied for cooling towers. Int J Heat Mass Trans 169:120910. https://doi.org/10.1016/j.ijheatmasstransfer.2021.120910

  15. Milosavljevic Nenad, Heikkilä Pertti (2001) A comprehensive approach to cooling tower design. Appl Therm Eng 21(9):899–915. https://doi.org/10.1016/S1359-4311(00)00078-8

    Article  Google Scholar 

  16. Liu Q, Guo C, Ma X, You Y, Li Y(2020) Experimental study on total heat transfer efficiency evaluation of an indirect evaporative cooler. Appl Therm Eng 174(25):115287. https://doi.org/10.1016/j.applthermaleng.2020.115287

  17. Barabash P, Solomakha A, Sereda V(2020) Experimental investigation of heat and mass transfer characteristics in direct contact exchanger. Int J Heat Mass Trans 162:120359. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120359

  18. Lemouari M, Boumaza M, Kaabi A (2009) Experimental analysis of heat and mass transfer phenomena in a direct contact evaporative cooling tower. Energy Convers Manage 50(6):1610–1617. https://doi.org/10.1016/j.enconman.2009.02.002

    Article  Google Scholar 

  19. Fei Y, Xiao Q, Xu J, Pan J, Wang S, Wang H, Huang J(2015) A novel approach for measuring bubbles uniformity and mixing efficiency in a direct contact heat exchanger. Energy 93(2):2313–2320. https://doi.org/10.1016/j.energy.2015.10.126

  20. Barabash PA, Solomakha AS, Gurov AI, Panchenko OA (2020) Regimes of motion of water-air flow in a short vertical tube with the underfeed of phases. J Eng Phys Thermophys 93(2):443–451. https://doi.org/10.1007/s10891-020-02139-y

    Article  Google Scholar 

  21. Wu B, Firouzi M, Rufford TE, Towler B(2019) Characteristics of counter-current gas-liquid two-phase flow and its limitations in vertical annuli. Exp Therm Fluid Sci 109:109899. https://doi.org/10.1016/j.expthermflusci.2019.109899

  22. Ghosh S, Pratihar DK, Maiti B, Das PK (2012) Identification of flow regimes using conductivity probe signals and neural networks for counter-current gas-liquid two-phase flow. Chem Eng Sci 84:417–436. https://doi.org/10.1016/j.ces.2012.08.042

    Article  Google Scholar 

  23. Ghosh S, Pratihar DK, Maiti B, Das PK (2013) Automatic classification of vertical counter-current two-phase flow by capturing hydrodynamic characteristics through objective descriptions. Int J Multiph Flow 52:102–120. https://doi.org/10.1016/j.ijmultiphaseflow.2012.12.007

    Article  Google Scholar 

  24. Cengel YA, Ghajar AJ (2015) Heat and mass transfer. Fundamentals and applications, 5th edn

  25. Holman JP (2010) Heat transfer, 10th edn

  26. Cussler EL (2009) Diffusion: Mass transfer in fluid systems, 3rd edn. Cambridge University Press. https://doi.org/10.1017/CBO9780511805134.007

  27. Wongwises Somchai, Naphon Paisan (1998) Heat-mass transfer and flow characteristics of two-phase countercurrent annular flow in a vertical pipe. Int Commun Heat Mass Transfer 25(6):819–829. https://doi.org/10.1016/S0735-1933(98)00068-2

    Article  Google Scholar 

  28. Tsay YL (1994) Analysis of heat and mass transfer in a countercurrent-flow wet surface heat exchanger. Heat Fluid Flow 15(2):149–156

    Article  Google Scholar 

  29. Feddaoui M, Mir A, Belahmidi E (2003) Cocurrent turbulent mixed convection heat and mass transfer in falling film of water inside a vertical heated tube. Int J Heat Mass Transf 46(18):3497–3509. https://doi.org/10.1016/S0017-9310(03)00129-7

    Article  MATH  Google Scholar 

  30. Webb RL, Perez-Blanco H (1986) Enhancement of combined heat and mass transfer in a vertical-tube heat and mass exchanger. J Heat Trans 108(1):70–75. https://doi.org/10.1115/1.3246907

    Article  Google Scholar 

  31. http://www.coolprop.org/

  32. Hobler T (1986) Heat transfer and heat exchangers. WNT, Warsaw

  33. Isachenko V, Semyonov S (1980) Heat transfer, 3rd edn. Central Books Ltd, London

    Google Scholar 

  34. Lewis WK (1962) The evaporation of a liquid into a gas. Int J Heat Mass Transf 5(1–2):109–112

    Article  Google Scholar 

  35. Kreith F, Black WZ (1980) Basic heat transfer. Harper & Row, New York

    Google Scholar 

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Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Polytehnichna 6, Kyiv, 03056, Ukraine

    Peter Barabash, Andrii Solomakha, Volodymyr Sereda, Natalia Prytula, Peter Strynada & Yang Liu

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  1. Peter Barabash
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Contributions

Peter Barabash, Andrii Solomakha and Volodymyr Sereda contributed to the study conception and design. Material preparation, data collection and analysis were performed by Peter Strynada, Yang Liu, Andrii Solomakha, Volodymyr Sereda and Natalia Prytula. The first draft of the manuscript was written by Peter Barabash, Volodymyr Sereda, Natalia Prytula and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Volodymyr Sereda.

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Barabash, P., Solomakha, A., Sereda, V. et al. Heat and mass transfer of countercurrent air-water flow in a vertical tube. Heat Mass Transfer (2023). https://doi.org/10.1007/s00231-023-03342-2

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