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General correlation of two-phase frictional pressure drop inside smooth tubes

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Abstract

Calculating a two-phase pressure drop is required in many fields. A general and accurate correlation is still needed, although numerous studies of frictional pressure drop correlations have been conducted. Therefore, a wide range of experimental data points were collected on the two-phase pressure drop of smooth tubes, 2012 points, covering 16 refrigerants with tube diameters ranging from 1.88 to 12 mm. The experimental data points were compared and evaluated with nine widely used correlations and models. The results show that the (Kim and Mudawar in Journal of Int J Heat Mass Transf 55:3246-3261, 2012) correlation gives the best prediction, followed by the Wang et al. (Exp Therm Fluid Sci 15:395–405, 1997) correlation and Friedel (European Two-Phase Flow Group Meeting, Ispra, Italy, 1979) correlation with mean deviations of 26.94%, 27.26% and 29.76%, respectively. A general two-phase frictional pressure drop correlation is proposed. The proposed correlation is validated against the database and compared with other correlations. The proposed correlation agrees better with the database than the others, with an absolute mean deviation of 19.84%.

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Data availability

No datasets were generated or analysed during the current study.

Abbreviations

A D :

average deviation [%]

Bo :

Bond number [-]

C :

Chisholm parameter [-]

d :

diameter [m]

dp/dz :

pressure gradient [kPa m−1]

f :

friction factor [-]

F r :

Froude number [-]

g :

gravitational acceleration [m s−2]

G :

mass flux [kg m−2 s−1]

L a :

Laplace constant [-]

M D :

absolute mean deviation [%]

n :

number of data points [-]

p :

pressure [kPa]

R e :

Reynolds number [-]

S u :

Suratman number [-]

T :

temperature [°C]

W e :

Weber number [-]

X :

Lockhart - Martinelli parameter [-]

x :

vapor quality [-]

z :

channel length [m]

\(\mu\) :

dynamic viscosity [Pa s]

\(\rho\) :

density [kg m−3]

\(\sigma\) :

surface tension [N m−1]

\({\varnothing }^{2}\) :

two-phase multiplier

exp :

experimental

f :

frictional

l :

liquid

lo :

liquid only

pre :

predicted

sat :

saturation

tp :

two-phase

tt :

turbulent liquid-turbulent vapor

tv :

turbulent liquid-viscous vapor

v :

vapor

vo :

vapor only

vt :

viscous liquid-turbulent vapor

vv :

viscous liquid-viscous vapor

References

  1. Xu Y, Fang X (2012) A new correlation of two-phase frictional pressure drop for evaporating flow in pipes. Int J Refrigeration 35:2039–2050. https://doi.org/10.1016/J.IJREFRIG.2012.06.011

    Article  Google Scholar 

  2. Xu Y, Fang X, Su X, Zhou Z, Chen W (2012) Evaluation of frictional pressure drop correlations for two-phase flow in pipes. Nucl Eng Des 253:86–97. https://doi.org/10.1016/j.nucengdes.2012.08.007

    Article  Google Scholar 

  3. Xu Y, Fang X (2013) A new correlation of two-phase frictional pressure drop for condensing flow in pipes. Nucl Eng Des 263:87–96. https://doi.org/10.1016/J.NUCENGDES.2013.04.017

    Article  Google Scholar 

  4. Chisholm D (1967) A theoretical basis for the Lockhart-Martinelli correlation for two-phase flow. Int J Heat Mass Transf 10:1767–1778. https://doi.org/10.1016/0017-9310(67)90047-6

    Article  Google Scholar 

  5. Idsinga W, Todreas N, Bowring R (1977) An assessment of two-phase pressure drop correlations for steam-water systems. Int J Multiph Flow 3:401–413. https://doi.org/10.1016/0301-9322(77)90019-2

    Article  Google Scholar 

  6. Sun L, Mishima K (2009) Evaluation analysis of prediction methods for two-phase flow pressure drop in mini-channels. Int J Multiph Flow 35:47–54. https://doi.org/10.1016/J.IJMULTIPHASEFLOW.2008.08.003

    Article  Google Scholar 

  7. Khairul Bashar M, Nakamura K, Kariya K, Miyara A (2020) Development of a correlation for pressure drop of two-phase flow inside horizontal small diameter smooth and microfin tubes. Int J Refrigeration 119:80–91. https://doi.org/10.1016/j.ijrefrig.2020.08.013

    Article  Google Scholar 

  8. Hirose M, Ichinose J, Inoue N (2018) Development of the general correlation for condensation heat transfer and pressure drop inside horizontal 4 mm small-diameter smooth and microfin tubes. Int J Refrigeration 90:238–248. https://doi.org/10.1016/J.IJREFRIG.2018.04.014

    Article  Google Scholar 

  9. Beattie DRH, Whalley PB (1982) A simple two-phase frictional pressure drop calculation method. 8:83–87. https://doi.org/10.1016/0301-9322(82)90009-X

    Article  Google Scholar 

  10. Dukler AE, Wicks M, Cleveland RG (1964) Frictional pressure drop in two-phase flow: B. An approach through similarity analysis. AIChE J 10:44–51. https://doi.org/10.1002/aic.690100118

    Article  Google Scholar 

  11. Andrzejczyk R, Muszynski T, Dorao CA (2017) Experimental investigations on adiabatic frictional pressure drops of R134a during flow in 5 mm diameter channel. Exp Therm Fluid Sci 83:78–87. https://doi.org/10.1016/J.EXPTHERMFLUSCI.2016.12.016

    Article  Google Scholar 

  12. Wang L, Dang C, Hihara E (2012) Experimental study on condensation heat transfer and pressure drop of low GWP refrigerant HFO1234yf in a horizontal tube. Int J Refrigeration 35:1418–1429. https://doi.org/10.1016/J.IJREFRIG.2012.04.006

    Article  Google Scholar 

  13. Haraguchi H, Koyama S, Tetsu F (1994) Condensation of rerigerant HCF C22, HFC 134a and HCFC 123 in a horizontal smooth tube. Trans Japan Soc Mech Eng Ser B 60:2117–2124

    Article  Google Scholar 

  14. Lockhart RW, Martinelli RC (1949) Proposed correlation of data for isothermal two-phase two component flow in pipes. Chem Eng Prog 45:39–48

    Google Scholar 

  15. Ding XHG, Deng HHYZYG (2010) Two-phase frictional pressure Drop characteristics of R410A-Oil mixture Flow Condensation inside 4.18 mm and 1.6 mm I.D. horizontal smooth tubes. HVAC&R Res 16:453–470. https://doi.org/10.1080/10789669.2010.10390915

    Article  Google Scholar 

  16. Yang C-Y, Nalbandian H, Lin F-C (2018) Flow boiling heat transfer and pressure drop of refrigerants HFO-1234yf and HFC-134a in small circular tube. Int J Heat Mass Transf 121:726–735. https://doi.org/10.1016/j.ijheatmasstransfer.2017.12.161

    Article  Google Scholar 

  17. Zhang M, Webb RL (2001) Correlation of two-phase friction for refrigerants in small-diameter tubes. Exp Therm Fluid Sci 25:131–139. https://doi.org/10.1016/S0894-1777(01)00066-8

    Article  Google Scholar 

  18. Friedel L (1979) Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. ROHRE - ROHRELEITUNGSBAU - ROHRELEITUNGSTRANSPORT, pp 485–491. Retrieved from https://api.semanticscholar.org/CorpusID:133284728

  19. Mauro AW, Napoli G, Pelella F, Viscito L (2020) Flow boiling heat transfer and pressure drop data of non-azeotropic mixture R455A in a horizontal 6.0 mm stainless-steel tube. Int J Refrigeration 119:195–205. https://doi.org/10.1016/j.ijrefrig.2020.07.017

    Article  Google Scholar 

  20. Müller-Steinhagen H, Heck K (1986) A simple friction pressure drop correlation for two-phase flow in pipes. Chem Eng Process Process Intensif 20:297–308. https://doi.org/10.1016/0255-2701(86)80008-3

    Article  Google Scholar 

  21. Asadi M, Xie G, Sunden B (2014) A review of heat transfer and pressure drop characteristics of single and two-phase microchannels. Int J Heat Mass Transf 79:34–53. https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2014.07.090

    Article  Google Scholar 

  22. Liu N, Li JM, Sun J, Wang HS (2013) Heat transfer and pressure drop during condensation of R152a in circular and square microchannels. Exp Therm Fluid Sci 47:60–67. https://doi.org/10.1016/J.EXPTHERMFLUSCI.2013.01.002

    Article  Google Scholar 

  23. Mishima K, Hibiki T (1996) Some characteristics of air-water two-phase flow in small diameter vertical tubes. Int J Multiph Flow 22:703–712. https://doi.org/10.1016/0301-9322(96)00010-9

    Article  Google Scholar 

  24. Wang CC, Chiang CS, Lu DC (1997) Visual observation of two-phase flow pattern of R-22, R-134a, and R-407 C in a 6.5-mm smooth tube. Exp Therm Fluid Sci 15:395–405. https://doi.org/10.1016/S0894-1777(97)00007-1

    Article  Google Scholar 

  25. Zhang W, Hibiki T, Mishima K (2010) Correlations of two-phase frictional pressure drop and void fraction in mini-channel. Int J Heat Mass Transf 53:453–465. https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2009.09.011

    Article  Google Scholar 

  26. Kim SM, Mudawar I (2012) Universal approach to predicting two-phase frictional pressure drop for adiabatic and condensing mini/micro-channel flows. Int J Heat Mass Transf 55:3246–3261. https://doi.org/10.1016/j.ijheatmasstransfer.2012.02.047

    Article  Google Scholar 

  27. Lu MC, Tong JR, Wang CC (2013) Investigation of the two-phase convective boiling of HFO-1234yf in a 3.9 mm diameter tube. Int J Heat Mass Transf 65:545–551. https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2013.06.004

    Article  Google Scholar 

  28. Grauso S, Mastrullo R, Mauro AW, Thome JR, Vanoli GP (2013) Flow pattern map, heat transfer and pressure drops during evaporation of R-1234ze(E) and R134a in a horizontal, circular smooth tube: experiments and assessment of predictive methods. Int J Refrigeration 36:478–491. https://doi.org/10.1016/J.IJREFRIG.2012.07.016

    Article  Google Scholar 

  29. Xu Y, Yan Z, Li L (2022) Flow boiling heat transfer, pressure drop and flow patterns of the environmentally friendly refrigerant R1234yf for cooling avionics. Appl Therm Eng 209:118301. https://doi.org/10.1016/J.APPLTHERMALENG.2022.118301

    Article  Google Scholar 

  30. Diani A, Rossetto L (2020) Characteristics of R513A evaporation heat transfer inside small-diameter smooth and microfin tubes. International Journal of Heat and Mass Transfer 162. https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2020.120402

    Article  Google Scholar 

  31. Lee BM, Gook HH, Lee SB, Lee YW, Park DH, Kim NH (2021) Condensation heat transfer and pressure drop of low GWP R-404A alternative refrigerants (R-448A, R-449A, R-455A, R-454 C) in a 5.6 mm inner diameter horizontal smooth tube. Int J Refrigeration 128:71–82. https://doi.org/10.1016/J.IJREFRIG.2020.12.025

    Article  Google Scholar 

  32. Garcia Pabon J, Khosravi A, Nunes R, Machado L (2019) Experimental investigation of pressure drop during two-phase flow of R1234yf in smooth horizontal tubes with internal diameters of 3.2 mm to 8.0 mm. Int J Refrigeration 104:426–436. https://doi.org/10.1016/J.IJREFRIG.2019.05.019

    Article  Google Scholar 

  33. Lillo G, Mastrullo R, Mauro AW, Viscito L (2019) Flow boiling of R32 in a horizontal stainless steel tube with 6.00 Mm ID. Experiments, assessment of correlations and comparison with refrigerant R410A. Int J Refrigeration 97:143–156. https://doi.org/10.1016/J.IJREFRIG.2018.09.024

    Article  Google Scholar 

  34. Ould Didi MB, Kattan N, Thome JR (2002) Prediction of two-phase pressure gradients of refrigerants in horizontal tubes. Int J Refrigeration 25:935–947. https://doi.org/10.1016/S0140-7007(01)00099-8

    Article  Google Scholar 

  35. Bandarra Filho EP, Saiz Jabardo JM, Barbieri PEL (2004) Convective boiling pressure drop of refrigerant R-134a in horizontal smooth and microfin tubes. Int J Refrigeration 27:895–903. https://doi.org/10.1016/J.IJREFRIG.2004.04.014

    Article  Google Scholar 

  36. Wang CC, Chiang SK, Chang YJ, Chung TW (2001) Two-phase Flow Resistance of refrigerants R-22, R-410A and R-407 C in small diameter tubes. Chem Eng Res Des 79:553–560. https://doi.org/10.1205/02638760152424325

    Article  Google Scholar 

  37. Miyara A, Higashi Y, Akasaka R, Kamei A (2023) Development of heat transfer database for boiling and condensation. ICBCHT11: 11th International Conference Boiling & Condensation Heat Transfer (2023), p ES4

  38. Ghajar AJ, Ghajar, (2022) Single-and two-phase flow pressure drop and heat transfer in tubes, 1st edn. Springer International Publishing. https://doi.org/10.1007/978-3-030-87281-6

    Book  Google Scholar 

  39. ASHRAE S (2019) Standard 34–2019 designation and safety classification of refrigerants. American Society of Heating, Refrigerating and Air-Conditioning Engineers Inc, Atlanta, GA, USA

    Google Scholar 

  40. Lemmon EW, Bell IH, Huber ML, McLinden MO (2018) NIST standard reference database 23: reference fluid thermodynamic and transport properties-REFPROP, Version 10.0. National Institute of Standards and Technology. https://doi.org/10.18434/T4/1502528

    Book  Google Scholar 

  41. Miyara A, Kuwahara K, Shigeru K (2004) Correlation of frictional pressure loss of two-phase flow including effects of tube diameter and mass velocity. The Proceedings of Conference of Kyushu Branch. 57, pp 117–118. https://doi.org/10.1299/jsmekyushu.2004.57.117

    Book  Google Scholar 

  42. Mainil AK, Sakamoto N, Ubudiyah H, Kariya K, Miyara A (2022) Experimental study and general correlation for frictional pressure drop of two-phase flow inside microfin tubes. Int J Refrigeration 144:342–353. https://doi.org/10.1016/J.IJREFRIG.2022.07.017

    Article  Google Scholar 

  43. Afroz HMM, Miyara A (2011) Prediction of condensation pressure drop inside herringbone microfin tubes. Int J Refrigeration 34:1057–1065. https://doi.org/10.1016/j.ijrefrig.2011.02.005

    Article  Google Scholar 

  44. Hossain MA, Onaka Y, Miyara A (2012) Experimental study on condensation heat transfer and pressure drop in horizontal smooth tube for R1234ze(E), R32 and R410A. Int J Refrigeration 35:927–938. https://doi.org/10.1016/J.IJREFRIG.2012.01.002

    Article  Google Scholar 

  45. Park CY, Hrnjak P (2008) NH3 in-tube condensation heat transfer and pressure drop in a smooth tube. Int J Refrigeration 31:643–651. https://doi.org/10.1016/J.IJREFRIG.2008.01.005

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Japan Copper Development Association for financial support, and one of the authors was supported by the State University of Jakarta-Saudi Fund for Development Scholarship Project (Phase-2) No. 105/PIU-SFD/UNJ/VII/2021.

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Authors and Affiliations

  1. Graduate School of Science and Engineering, Saga University, 1 Honjo-machi, Saga-shi, 840-8502, Japan

    I Wayan Sugita

  2. Department of Mechanical Engineering, Universitas Negeri Jakarta, Jakarta, 13220, Indonesia

    I Wayan Sugita

  3. Department of Mechanical Engineering, Universitas Bengkulu, Bengkulu, 38371A, Indonesia

    Afdhal Kurniawan Mainil

  4. Department of Mechanical Engineering, Saga University, 1 Honjo-machi, Saga-shi, 840-8502, Japan

    Akio Miyara

  5. International Institute for Carbon-Neutral Energy Research, Kyushu University, Fukuoka-shi, 819-0395, Japan

    Akio Miyara

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  1. I Wayan Sugita
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Contributions

I.W.S: Conceptualization, Methodology, Software, Formal analysis, Investigation, Data Curation, Writing - Original Draft, Writing - Review and editing, Visualization. A.K.M: Conceptualization, Methodology, Validation, Investigation, Supervision. A.M: Conceptualization, Methodology, Validation, Resources, Writing - Review & Editing, Supervision, Project administration, Funding acquisition.

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Correspondence to I Wayan Sugita.

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Sugita, I.W., Mainil, A.K. & Miyara, A. General correlation of two-phase frictional pressure drop inside smooth tubes. Heat Mass Transfer (2024). https://doi.org/10.1007/s00231-024-03470-3

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