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Open AccessOpen Access JUSTC Engineering & Materials 05 July 2022

Comparison between homogeneous and separated flow models of isobutane flowing through adiabatic capillary tubes

  • Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230027, China

Cite this:
https://doi.org/10.52396/JUSTC-2021-0130
More Information
  • Author Bio:

    Yonghui Shu is currently a Master’s student under the tutelage of Prof. Peng Hu at the University of Science and Technology of China. His research interests include refrigeration and cryogenics

    Peng Hu received his Ph.D. degree in Engineering Thermophysics from the University of Science and Technology of China (USTC). He is currently a professor at USTC. His research interests include thermophysical properties, refrigeration, heat and mass transfer, and solar energy

  • Corresponding author: E-mail: hupeng@ustc.edu.cn
  • Received Date: 12 May 2021
  • Accepted Date: 26 November 2021
    • Available Online: 05 July 2022
    Abstract

  • Abstract

    Capillary tubes have been widely used as expansion devices in small-scale refrigeration and heat-pump systems. However, adiabatic flow through a capillary tube is extremely complicated, despite its simple geometry. This work presents a comparative study on the homogenous flow model and separated flow model, which were used to simulate the flow of isobutene (R600a) through adiabatic capillary tubes. The influence of different combinations of friction factor and two-phase viscosity correlations, and the effect of metastable flow on the flow characteristics were investigated. The predicted mass flow rate was lower when the separated flow model was used. The separated flow model performed better in predicting a mass flow rate over 2 kg·h−1. The Colebrook friction factor correlation combined with the Dukler or McAdams viscosity correlation yielded smaller deviations of 5.43%, 5.49% and 5.44%, 5.43% when ignoring and considering the metastable flow, respectively. Additionally, the homogenous flow model adopting the Bittle and Pate friction factor and Dukler viscosity correlations achieved the highest accuracy with a mass flow rate under 2 kg·h−1. The mean error was 4.12% in the case without metastable flow, and 3.37% in the case with metastable flow.

    Graphical abstract

    Simulation on the throttling process of refrigerant flowing through adiabatic capillary tubes.

    Abstract

    Capillary tubes have been widely used as expansion devices in small-scale refrigeration and heat-pump systems. However, adiabatic flow through a capillary tube is extremely complicated, despite its simple geometry. This work presents a comparative study on the homogenous flow model and separated flow model, which were used to simulate the flow of isobutene (R600a) through adiabatic capillary tubes. The influence of different combinations of friction factor and two-phase viscosity correlations, and the effect of metastable flow on the flow characteristics were investigated. The predicted mass flow rate was lower when the separated flow model was used. The separated flow model performed better in predicting a mass flow rate over 2 kg·h−1. The Colebrook friction factor correlation combined with the Dukler or McAdams viscosity correlation yielded smaller deviations of 5.43%, 5.49% and 5.44%, 5.43% when ignoring and considering the metastable flow, respectively. Additionally, the homogenous flow model adopting the Bittle and Pate friction factor and Dukler viscosity correlations achieved the highest accuracy with a mass flow rate under 2 kg·h−1. The mean error was 4.12% in the case without metastable flow, and 3.37% in the case with metastable flow.

    • Public Summary

    • Homogeneous flow models and separated flow models with and without metastable flow are compared in detail.
    • The optimal hypothesis models for different R600a mass flow rate ranges are investigated.
    • The optimal combinations of friction factor and two-phase viscosity correlations for each model are recommended.

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    • References(44)
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    Ali M S, Anwar Z, Mujtaba M A, et al. Two-phase frictional pressure drop with pure refrigerants in vertical mini/micro-channels. Case Studies in Thermal Engineering, 2021, 23: 100824. doi: https://doi.org/10.1016/j.csite.2020.100824
    [2]
    Zhang N C, Li B, Feng L H, et al. Research on the thermophysical properties and cycle performances of R1234yf/R290 and R1234yf/R600a. International Journal of Thermophysics, 2021, 42: 123. doi: 10.1007/s10765-021-02875-0
    [3]
    Zhang N, Hu P, Chen L X, et al. Measurements of critical properties of the binary mixture of 1,1,1-trifluoroethane (HFC-143a)+ trans-1,3,3,3-Tetrafluoropropene (HFO-1234ze (E)). Journal of Chemical & Engineering Data, 2021, 66: 2717–2722. doi: https://doi.org/10.1021/acs.jced.1c00065
    [4]
    Bagherzadeh S A, D'Orazio A, Karimipour A, et al. A novel sensitivity analysis model of EANN for F-MWCNTs-Fe3O4/EG nanofluid thermal conductivity: Outputs predicted analytically instead of numerically to more accuracy and less costs. Physica A: Statistical Mechanics and its Applications, 2019, 521: 406–415. doi: 10.1016/j.physa.2019.01.048
    [5]
    Giwa S O, Sharifpur M, Goodarzi M, et al. Influence of base fluid, temperature, and concentration on the thermophysical properties of hybrid nanofluids of alumina–ferrofluid: Experimental data, modeling through enhanced ANN, ANFIS, and curve fitting. Journal of Thermal Analysis and Calorimetry, 2021, 143: 4149–4167. doi: 10.1007/s10973-020-09372-w
    [6]
    Sánchez D, Cabello R, Llopis R, et al. Energy performance evaluation of R1234yf, R1234ze(E), R600a, R290 and R152a as low-GWP R134a alternatives. International Journal of Refrigeration, 2017, 74: 269–282. doi: https://doi.org/10.1016/j.ijrefrig.2016.09.020
    [7]
    Hwang S, Jeong J H. The effects of the parameters of a refrigeration system working with R600a on the non-equilibrium subcooled two-phase flow of the refrigerant. International Journal of Refrigeration, 2020, 118: 462–469. doi: 10.1016/j.ijrefrig.2020.06.026
    [8]
    Bahmani M H, Sheikhzadeh G, Zarringhalam M, et al. Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger. Advanced Powder Technology, 2018, 29 (2): 273–282. doi: 10.1016/j.apt.2017.11.013
    [9]
    Sarafraz M M, Tian Z, Tlili I, et al. Thermal evaluation of a heat pipe working with n-pentane-acetone and n-pentane-methanol binary mixtures. Journal of Thermal Analysis and Calorimetry, 2020, 139: 2435–2445. doi: 10.1007/s10973-019-08414-2
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    Heimel M, Lang W, Berger E, et al. A homogeneous capillary tube model - comprehensive parameter studies using isobutane as refrigerant. In: International Refrigeration and Air Conditioning Conference. West Lafayette: Purdue University, 2012: Paper 1233.
    [11]
    de Lara J F, Melo C, Boeng J, et al. Experimental analysis of HFC-134a expansion through small-bore adiabatic capillary tubes. International Journal of Refrigeration, 2020, 112: 37–43. doi: 10.1016/j.ijrefrig.2019.12.015
    [12]
    Ardhapurkar P M, Sridharan A, Atrey M D. Investigation of pressure drop in capillary tube for mixed refrigerant Joule-Thomson cryocooler. AIP Conference Proceedings, 2014, 1573: 155. doi: https://doi.org/10.1063/1.4860696
    [13]
    Kruthiventi S S H, Venkatarathnam G. Studies on capillary tube expansion device used in J-T refrigerators operating with nitrogen-hydrocarbon mixtures. Cryogenics, 2017, 87: 76–84. doi: 10.1016/j.cryogenics.2017.09.002
    [14]
    Parmar D, Atrey M D. Experimental and numerical investigation on the flow of mixed refrigerants through capillary tubes at cryogenic temperatures. Applied Thermal Engineering, 2020, 175: 115339. doi: 10.1016/j.applthermaleng.2020.115339
    [15]
    Rocha T T M, de Paula C H, Cangussu V M, et al. Effect of surface roughness on the mass flow rate predictions for adiabatic capillary tubes. International Journal of Refrigeration, 2020, 118: 269–278. doi: 10.1016/j.ijrefrig.2020.05.020
    [16]
    Khan M K, Kumar R, Sahoo P K. Flow characteristics of refrigerants flowing through capillary tubes-A review. Applied Thermal Engineering, 2009, 29: 1426–1439. doi: 10.1016/j.applthermaleng.2008.08.020
    [17]
    García-Valladares O. Numerical simulation and experimental validation of coiled adiabatic capillary tubes. Applied Thermal Engineering, 2007, 27: 1062–1071. doi: 10.1016/j.applthermaleng.2006.07.034
    [18]
    Schenk M, Oellrich L R. Experimental investigation of the refrigerant flow of isobutane (R600a) through adiabatic capillary tubes. International Journal of Refrigeration, 2014, 38: 275–280. doi: 10.1016/j.ijrefrig.2013.08.024
    [19]
    Chingulpitak S, Wongwises S. Two-phase flow model of refrigerants flowing through helically coiled capillary tubes. Applied Thermal Engineering, 2010, 30: 1927–1936. doi: 10.1016/j.applthermaleng.2010.04.026
    [20]
    Vinš V, Hrubý J, Vacek V. Numerical simulation of gas-contaminated refrigerant two-phase flow through adiabatic capillary tubes. International Journal of Heat and Mass Transfer, 2010, 53: 5430–5439. doi: 10.1016/j.ijheatmasstransfer.2010.07.013
    [21]
    Rasti M, Jeong J H. A generalized continuous empirical correlation for the refrigerant mass flow rate through adiabatic straight and helically coiled capillary tubes. Applied Thermal Engineering, 2018, 143: 450–460. doi: 10.1016/j.applthermaleng.2018.07.124
    [22]
    Hermes C J L, Melo C, Knabben F T. Algebraic solution of capillary tube flows Part I: Adiabatic capillary tubes. Applied Thermal Engineering, 2010, 30: 449–457. doi: 10.1016/j.applthermaleng.2009.10.005
    [23]
    Dubba S K, Kumar R. Flow of refrigerants through capillary tubes: A state-of-the-art. Experimental Thermal and Fluid Science, 2017, 81: 370–381. doi: 10.1016/j.expthermflusci.2016.09.012
    [24]
    Jadhav P, Agrawal N. A comparative study in the straight and a spiral adiabatic capillary tube. International Journal of Ambient Energy, 2019, 40: 693–698. doi: 10.1080/01430750.2017.1422146
    [25]
    Alok P, Sahu D. Numerical simulation of capillary tube for selected refrigerants using homogeneous equilibrium model. International Journal of Air-Conditioning and Refrigeration, 2019, 27: 1950001. doi: 10.1142/S2010132519500019
    [26]
    Jadhav P, Agrawal N. A comparative study of flow characteristics of adiabatic spiral and helical capillary tube in a CO2 transcritical system. International Journal of Ambient Energy, 2021: 1–8. doi: 10.1080/01430750.2021.1913645
    [27]
    Zareh M, Heidari M G, Javidmand P. Numerical simulation and experimental comparison of the R12, R22 and R134a flow inside straight and coiled helical capillary tubes. Journal of Mechanical Science and Technology, 2016, 30: 1421–1430. doi: 10.1007/s12206-016-0250-2
    [28]
    Wang J, Cao F, Wang Z Z, et al. Numerical simulation of coiled adiabatic capillary tubes in CO2 transcritical systems with separated flow model including metastable flow. International Journal of Refrigeration, 2012, 35 (8): 2188–2198. doi: 10.1016/j.ijrefrig.2012.07.012
    [29]
    Agrawal N, Bhattacharyya S. Homogeneous versus separated two phase flow models: Adiabatic capillary tube flow in a transcritical CO2 heat pump. International Journal of Thermal Sciences, 2008, 47 (11): 1555–1562. doi: 10.1016/j.ijthermalsci.2007.12.008
    [30]
    Furlong T W, Schmidt D P. A comparison of homogenous and separated flow assumptions for adiabatic capillary flow. Applied Thermal Engineering, 2012, 48: 186–193. doi: 10.1016/j.applthermaleng.2012.05.007
    [31]
    Lorbek L, Kuhelj A, Dular M, et al. Two-phase flow patterns in adiabatic refrigerant flow through capillary tubes. International Journal of Refrigeration, 2020, 115: 107–116. doi: 10.1016/j.ijrefrig.2020.02.030
    [32]
    Melo C, Ferreira R T S, Neto C B, et al. An experimental analysis of adiabatic capillary tubes. Applied Thermal Engineering, 1999, 19: 669–684. doi: 10.1016/S1359-4311(98)00062-3
    [33]
    Collier J G, Thome J R. Convective Boiling and Condensation. 3rd ed. New York: Clarendon Press, 1994.
    [34]
    Chen Z H, Li R Y, Lin S, et al. A correlation for metastable flow of R-12 through capillary tubes. ASHRAE Transactions, 1990, 96: 550–554.
    [35]
    Feburie V, Giot M, Granger S, et al. A model for choked flow through cracks with inlet subcooling. International Journal of Multiphase Flow, 1993, 19: 541–562. doi: 10.1016/0301-9322(93)90087-B
    [36]
    Premoli A, Francesco D, Prina A. An empirical correlation for evaluating two-phase mixture density under adiabatic conditions. In: European Two-Phase Flow Group Meeting, Milan, Italy, 1970.
    [37]
    Chisholm D. Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels. International Journal of Heat and Mass Transfer, 1973, 16: 347–358. doi: 10.1016/0017-9310(73)90063-X
    [38]
    Deodhar S D, Kothadia H B, Iyer K N, et al. Experimental and numerical studies of choked flow through adiabatic and diabatic capillary tubes. Applied Thermal Engineering, 2015, 90: 879–894. doi: 10.1016/j.applthermaleng.2015.07.073
    [39]
    Chung M. A numerical procedure for simulation of Fanno flows of refrigerants or refrigerant mixtures in capillary tubes. 1998 ASHRAE Summer Annual Meeting, 1998 [2021-04-10]. https://www.osti.gov/biblio/687663-numerical-procedure-simulation-fanno-flows-refrigerants-refrigerant-mixtures-capillary-tubes.
    [40]
    Zhang Y F, Zhou G B, Xie H, et al. An assessment of friction factor and viscosity correlations for model prediction of refrigerant flow in capillary tubes. International Journal of Energy Research, 2005, 29 (3): 233–248. doi: 10.1002/er.1050
    [41]
    Ahmadi M H, Mohseni-Gharyehsafa B, Ghazvini M, et al. Comparing various machine learning approaches in modeling the dynamic viscosity of CuO/water nanofluid. Journal of Thermal Analysis and Calorimetry, 2020, 139: 2585–2599. doi: 10.1007/s10973-019-08762-z
    [42]
    Zhou G B, Zhang Y F. Numerical and experimental investigations on the performance of coiled adiabatic capillary tubes. Applied Thermal Engineering, 2006, 26: 1106–1114. doi: 10.1016/j.applthermaleng.2005.11.003
    [43]
    Bansal P K, Wang G. Numerical analysis of choked refrigerant flow in adiabatic capillary tubes. Applied Thermal Engineering, 2004, 24: 851–863. doi: 10.1016/j.applthermaleng.2003.10.010
    [44]
    Lemmon E, Huber M, McLinden M. NIST Standard Reference Database 23: NIST thermodynamic and transport properties of refrigerants and refrigerant mixtures-REFPROP, version 9.1. Gaithersburg, MD: National Institute of Standards and Technology, 2013.
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    Figure  1.  Schematic diagram of adiabatic capillary tube. (a) Case with metastable flow. (b) Case without metastable flow.

    Figure  2.  Control volume of adiabatic capillary tube.

    Figure  3.  Flowcharts of mass flow rate algorithm in case without metastable flow. (a) Algorithm for data of Melo et al.[32]. (b) Algorithm for data of Schenk and Oellrich[18].

    4.  Flowcharts of mass flow rate algorithm in case with metastable flow. (a) Algorithm for data of Melo et al.[32]. (b) Algorithm for data of Schenk and Oellrich[18].

    Figure  5.  Comparison of different viscosity correlations.

    Figure  6.  Comparison of different friction factor correlations.

    Figure  7.  Comparison of mass flow rates predicted by homogenous flow model and separated flow model to experimental data. (a) Case without metastable flow. (b) Case with metastable flow.

    Figure  8.  Comparison of pressure distributions along tube.

    Figure  9.  Comparison of temperature distributions along tube.

    Figure  10.  Comparison of vapor phase mass fraction distributions along two-phase region.

    Figure  11.  Comparison of velocity distributions along two-phase region.

    [1]
    Ali M S, Anwar Z, Mujtaba M A, et al. Two-phase frictional pressure drop with pure refrigerants in vertical mini/micro-channels. Case Studies in Thermal Engineering, 2021, 23: 100824. doi: https://doi.org/10.1016/j.csite.2020.100824
    [2]
    Zhang N C, Li B, Feng L H, et al. Research on the thermophysical properties and cycle performances of R1234yf/R290 and R1234yf/R600a. International Journal of Thermophysics, 2021, 42: 123. doi: 10.1007/s10765-021-02875-0
    [3]
    Zhang N, Hu P, Chen L X, et al. Measurements of critical properties of the binary mixture of 1,1,1-trifluoroethane (HFC-143a)+ trans-1,3,3,3-Tetrafluoropropene (HFO-1234ze (E)). Journal of Chemical & Engineering Data, 2021, 66: 2717–2722. doi: https://doi.org/10.1021/acs.jced.1c00065
    [4]
    Bagherzadeh S A, D'Orazio A, Karimipour A, et al. A novel sensitivity analysis model of EANN for F-MWCNTs-Fe3O4/EG nanofluid thermal conductivity: Outputs predicted analytically instead of numerically to more accuracy and less costs. Physica A: Statistical Mechanics and its Applications, 2019, 521: 406–415. doi: 10.1016/j.physa.2019.01.048
    [5]
    Giwa S O, Sharifpur M, Goodarzi M, et al. Influence of base fluid, temperature, and concentration on the thermophysical properties of hybrid nanofluids of alumina–ferrofluid: Experimental data, modeling through enhanced ANN, ANFIS, and curve fitting. Journal of Thermal Analysis and Calorimetry, 2021, 143: 4149–4167. doi: 10.1007/s10973-020-09372-w
    [6]
    Sánchez D, Cabello R, Llopis R, et al. Energy performance evaluation of R1234yf, R1234ze(E), R600a, R290 and R152a as low-GWP R134a alternatives. International Journal of Refrigeration, 2017, 74: 269–282. doi: https://doi.org/10.1016/j.ijrefrig.2016.09.020
    [7]
    Hwang S, Jeong J H. The effects of the parameters of a refrigeration system working with R600a on the non-equilibrium subcooled two-phase flow of the refrigerant. International Journal of Refrigeration, 2020, 118: 462–469. doi: 10.1016/j.ijrefrig.2020.06.026
    [8]
    Bahmani M H, Sheikhzadeh G, Zarringhalam M, et al. Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger. Advanced Powder Technology, 2018, 29 (2): 273–282. doi: 10.1016/j.apt.2017.11.013
    [9]
    Sarafraz M M, Tian Z, Tlili I, et al. Thermal evaluation of a heat pipe working with n-pentane-acetone and n-pentane-methanol binary mixtures. Journal of Thermal Analysis and Calorimetry, 2020, 139: 2435–2445. doi: 10.1007/s10973-019-08414-2
    [10]
    Heimel M, Lang W, Berger E, et al. A homogeneous capillary tube model - comprehensive parameter studies using isobutane as refrigerant. In: International Refrigeration and Air Conditioning Conference. West Lafayette: Purdue University, 2012: Paper 1233.
    [11]
    de Lara J F, Melo C, Boeng J, et al. Experimental analysis of HFC-134a expansion through small-bore adiabatic capillary tubes. International Journal of Refrigeration, 2020, 112: 37–43. doi: 10.1016/j.ijrefrig.2019.12.015
    [12]
    Ardhapurkar P M, Sridharan A, Atrey M D. Investigation of pressure drop in capillary tube for mixed refrigerant Joule-Thomson cryocooler. AIP Conference Proceedings, 2014, 1573: 155. doi: https://doi.org/10.1063/1.4860696
    [13]
    Kruthiventi S S H, Venkatarathnam G. Studies on capillary tube expansion device used in J-T refrigerators operating with nitrogen-hydrocarbon mixtures. Cryogenics, 2017, 87: 76–84. doi: 10.1016/j.cryogenics.2017.09.002
    [14]
    Parmar D, Atrey M D. Experimental and numerical investigation on the flow of mixed refrigerants through capillary tubes at cryogenic temperatures. Applied Thermal Engineering, 2020, 175: 115339. doi: 10.1016/j.applthermaleng.2020.115339
    [15]
    Rocha T T M, de Paula C H, Cangussu V M, et al. Effect of surface roughness on the mass flow rate predictions for adiabatic capillary tubes. International Journal of Refrigeration, 2020, 118: 269–278. doi: 10.1016/j.ijrefrig.2020.05.020
    [16]
    Khan M K, Kumar R, Sahoo P K. Flow characteristics of refrigerants flowing through capillary tubes-A review. Applied Thermal Engineering, 2009, 29: 1426–1439. doi: 10.1016/j.applthermaleng.2008.08.020
    [17]
    García-Valladares O. Numerical simulation and experimental validation of coiled adiabatic capillary tubes. Applied Thermal Engineering, 2007, 27: 1062–1071. doi: 10.1016/j.applthermaleng.2006.07.034
    [18]
    Schenk M, Oellrich L R. Experimental investigation of the refrigerant flow of isobutane (R600a) through adiabatic capillary tubes. International Journal of Refrigeration, 2014, 38: 275–280. doi: 10.1016/j.ijrefrig.2013.08.024
    [19]
    Chingulpitak S, Wongwises S. Two-phase flow model of refrigerants flowing through helically coiled capillary tubes. Applied Thermal Engineering, 2010, 30: 1927–1936. doi: 10.1016/j.applthermaleng.2010.04.026
    [20]
    Vinš V, Hrubý J, Vacek V. Numerical simulation of gas-contaminated refrigerant two-phase flow through adiabatic capillary tubes. International Journal of Heat and Mass Transfer, 2010, 53: 5430–5439. doi: 10.1016/j.ijheatmasstransfer.2010.07.013
    [21]
    Rasti M, Jeong J H. A generalized continuous empirical correlation for the refrigerant mass flow rate through adiabatic straight and helically coiled capillary tubes. Applied Thermal Engineering, 2018, 143: 450–460. doi: 10.1016/j.applthermaleng.2018.07.124
    [22]
    Hermes C J L, Melo C, Knabben F T. Algebraic solution of capillary tube flows Part I: Adiabatic capillary tubes. Applied Thermal Engineering, 2010, 30: 449–457. doi: 10.1016/j.applthermaleng.2009.10.005
    [23]
    Dubba S K, Kumar R. Flow of refrigerants through capillary tubes: A state-of-the-art. Experimental Thermal and Fluid Science, 2017, 81: 370–381. doi: 10.1016/j.expthermflusci.2016.09.012
    [24]
    Jadhav P, Agrawal N. A comparative study in the straight and a spiral adiabatic capillary tube. International Journal of Ambient Energy, 2019, 40: 693–698. doi: 10.1080/01430750.2017.1422146
    [25]
    Alok P, Sahu D. Numerical simulation of capillary tube for selected refrigerants using homogeneous equilibrium model. International Journal of Air-Conditioning and Refrigeration, 2019, 27: 1950001. doi: 10.1142/S2010132519500019
    [26]
    Jadhav P, Agrawal N. A comparative study of flow characteristics of adiabatic spiral and helical capillary tube in a CO2 transcritical system. International Journal of Ambient Energy, 2021: 1–8. doi: 10.1080/01430750.2021.1913645
    [27]
    Zareh M, Heidari M G, Javidmand P. Numerical simulation and experimental comparison of the R12, R22 and R134a flow inside straight and coiled helical capillary tubes. Journal of Mechanical Science and Technology, 2016, 30: 1421–1430. doi: 10.1007/s12206-016-0250-2
    [28]
    Wang J, Cao F, Wang Z Z, et al. Numerical simulation of coiled adiabatic capillary tubes in CO2 transcritical systems with separated flow model including metastable flow. International Journal of Refrigeration, 2012, 35 (8): 2188–2198. doi: 10.1016/j.ijrefrig.2012.07.012
    [29]
    Agrawal N, Bhattacharyya S. Homogeneous versus separated two phase flow models: Adiabatic capillary tube flow in a transcritical CO2 heat pump. International Journal of Thermal Sciences, 2008, 47 (11): 1555–1562. doi: 10.1016/j.ijthermalsci.2007.12.008
    [30]
    Furlong T W, Schmidt D P. A comparison of homogenous and separated flow assumptions for adiabatic capillary flow. Applied Thermal Engineering, 2012, 48: 186–193. doi: 10.1016/j.applthermaleng.2012.05.007
    [31]
    Lorbek L, Kuhelj A, Dular M, et al. Two-phase flow patterns in adiabatic refrigerant flow through capillary tubes. International Journal of Refrigeration, 2020, 115: 107–116. doi: 10.1016/j.ijrefrig.2020.02.030
    [32]
    Melo C, Ferreira R T S, Neto C B, et al. An experimental analysis of adiabatic capillary tubes. Applied Thermal Engineering, 1999, 19: 669–684. doi: 10.1016/S1359-4311(98)00062-3
    [33]
    Collier J G, Thome J R. Convective Boiling and Condensation. 3rd ed. New York: Clarendon Press, 1994.
    [34]
    Chen Z H, Li R Y, Lin S, et al. A correlation for metastable flow of R-12 through capillary tubes. ASHRAE Transactions, 1990, 96: 550–554.
    [35]
    Feburie V, Giot M, Granger S, et al. A model for choked flow through cracks with inlet subcooling. International Journal of Multiphase Flow, 1993, 19: 541–562. doi: 10.1016/0301-9322(93)90087-B
    [36]
    Premoli A, Francesco D, Prina A. An empirical correlation for evaluating two-phase mixture density under adiabatic conditions. In: European Two-Phase Flow Group Meeting, Milan, Italy, 1970.
    [37]
    Chisholm D. Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels. International Journal of Heat and Mass Transfer, 1973, 16: 347–358. doi: 10.1016/0017-9310(73)90063-X
    [38]
    Deodhar S D, Kothadia H B, Iyer K N, et al. Experimental and numerical studies of choked flow through adiabatic and diabatic capillary tubes. Applied Thermal Engineering, 2015, 90: 879–894. doi: 10.1016/j.applthermaleng.2015.07.073
    [39]
    Chung M. A numerical procedure for simulation of Fanno flows of refrigerants or refrigerant mixtures in capillary tubes. 1998 ASHRAE Summer Annual Meeting, 1998 [2021-04-10]. https://www.osti.gov/biblio/687663-numerical-procedure-simulation-fanno-flows-refrigerants-refrigerant-mixtures-capillary-tubes.
    [40]
    Zhang Y F, Zhou G B, Xie H, et al. An assessment of friction factor and viscosity correlations for model prediction of refrigerant flow in capillary tubes. International Journal of Energy Research, 2005, 29 (3): 233–248. doi: 10.1002/er.1050
    [41]
    Ahmadi M H, Mohseni-Gharyehsafa B, Ghazvini M, et al. Comparing various machine learning approaches in modeling the dynamic viscosity of CuO/water nanofluid. Journal of Thermal Analysis and Calorimetry, 2020, 139: 2585–2599. doi: 10.1007/s10973-019-08762-z
    [42]
    Zhou G B, Zhang Y F. Numerical and experimental investigations on the performance of coiled adiabatic capillary tubes. Applied Thermal Engineering, 2006, 26: 1106–1114. doi: 10.1016/j.applthermaleng.2005.11.003
    [43]
    Bansal P K, Wang G. Numerical analysis of choked refrigerant flow in adiabatic capillary tubes. Applied Thermal Engineering, 2004, 24: 851–863. doi: 10.1016/j.applthermaleng.2003.10.010
    [44]
    Lemmon E, Huber M, McLinden M. NIST Standard Reference Database 23: NIST thermodynamic and transport properties of refrigerants and refrigerant mixtures-REFPROP, version 9.1. Gaithersburg, MD: National Institute of Standards and Technology, 2013.
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