Skip to main content

Advertisement

SpringerLink
Log in

Viscosities of Liquid Refrigerants from a Rough Hard-Sphere Theory-Based Semi-Empirical Model

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

A Correction to this article was published on 21 January 2022

This article has been updated

Abstract

In this study, the application of a semi-empirical model for the prediction of dynamic viscosities of liquid refrigerants has been explored for both saturated and compressed states. The model used rough hard-sphere (RHS) theory in the model development; a smooth hard-sphere expression and a coupling parameter of translational–rotational motions were employed. Also, the model used the three inputs, the critical temperature, critical density, as well as the liquid densities, for which the values were taken from Carnahan-Starling-vdW-β equation of state (EoS). Most of the refrigerants investigated herein are those based on methane, ethane, and propane. The ability of the RHS-based model been checked by the calculation of dynamic viscosities of 26 liquid refrigerants at compressed states in the 200 K to 420 K range and pressures up to 50 MPa. The average absolute deviation of 4.47 % (for 1539 data points) and 5.22 % (for 121 data points), respectively, were obtained for the cases of compressed and saturated liquid refrigerants studied. The degree of accuracy of the present semi-empirical model has also been compared with the literature RHS-based models as well as other approach based on the viscosity EoS.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Change history

Abbreviations

b :

Van der Waals co-volume, m3

P :

Pressure, Pa

R :

Gas constant, J·mol−1·K−1

T :

Absolute temperature, K

k B :

Boltzmann constant, J·K−1

\( g\left( {\sigma^{ + } } \right) \) :

Pair radial distribution function of hard-spheres at contact

w :

Adjustable parameter used in Eq. (11)

ρ :

Molar density, mol·m−3

η :

Dynamic viscosity, Pa·s

σ :

Hard-sphere dimeter, nm

C:

Critical

Lit:

Literature value

Calc:

Calculated value

SHS:

Smooth hard-sphere

RHS:

Rough hard-sphere

MET:

Modified Enskog’s theory

*:

Reduced

References

  1. K.N. Marsh, M.E. Kandil, Fluid Phase Equilib. 199, 319 (2002)

    Article  Google Scholar 

  2. A. Laesecke, S. Bair, Int. J. Thermophys. 32, 925 (2011)

    Article  ADS  Google Scholar 

  3. E. Lemmon, M. McLinden, D. Friend, webbook. nist. gov. Accessed 28 Oct 2012, (2011)

  4. S.A. Klein, M.O. McLinden, A. Laesecke, Int. J. Refrig. 20, 208 (1997)

    Article  Google Scholar 

  5. Bell, A. Laesecke, In 16th international refrigeration and air conditioning conference, (Indiana, USA., 2016)

  6. F. Ghaderi, A.H. Ghaderi, B. Najafi, N. Ghaderi, J. Supercrit. Fluids 81, 67. https://doi.org/10.1016/j.supflu.2013.04.017

    Article  Google Scholar 

  7. L.H. Zhi, P. Hu, L.X. Chen, G. Zhao, Int. J. Refrig 88, 432. https://doi.org/10.1016/j.ijrefrig.2018.02.011

    Article  Google Scholar 

  8. J. Dymond, Chem. Soc. Rev. 14, 317 (1985)

    Article  Google Scholar 

  9. D. Chandler, J. Chem. Phys. 62, 1358 (1975)

    Article  ADS  Google Scholar 

  10. S.E. Quiñones-Cisneros, C.K. Zéberg-Mikkelsen, E.H. Stenby, Fluid Phase Equilib. 169, 249 (2000)

    Article  Google Scholar 

  11. W.A. Burgess, D. Tapriyal, I.K. Gamwo, B.D. Morreale, M.A. McHugh, R.M. Enick, Ind. Eng. Chem. Res. 51, 16721 (2012)

    Article  Google Scholar 

  12. I. Polishuk, Ind. Eng. Chem. Res. 51, 13527 (2012)

    Article  Google Scholar 

  13. A. Kumagai, H. Miura-Mochida, C. Yokoyama, Int. J. Thermophys. 15, 567 (1994). https://doi.org/10.1007/BF01563714

    Article  ADS  Google Scholar 

  14. J.H. Dymond, Physica B+C 144, 267 (1987). https://doi.org/10.1016/0378-4363(87)90009-X

    Article  ADS  Google Scholar 

  15. J. Dymond, B. Alder, J. Chem. Phys. 45, 2061 (1966)

    Article  ADS  Google Scholar 

  16. M. Assael, J. Dymond, S. Polimatidou, Int. J. Thermophys. 16, 761 (1995)

    Article  ADS  Google Scholar 

  17. A.S. Teja, R.L. Smith Jr., R.K. King, T.F. Sun, Int. J. Thermophys. 20, 149 (1999). https://doi.org/10.1023/A:1021438516081

    Article  Google Scholar 

  18. M. Assael, N. Dalaouti, J. Dymond, E. Feleki, Int. J. Thermophys. 21, 367 (2000)

    Article  Google Scholar 

  19. T. Sun, A.S. Teja, J. Chem. Eng. Data 54, 2527 (2009)

    Article  Google Scholar 

  20. D.D. Royal, V. Vesovic, J.P.M. Trusler, W.A. Wakeham, Int. J. Refrig 28, 311 (2005). https://doi.org/10.1016/j.ijrefrig.2004.09.007

    Article  Google Scholar 

  21. T.-B. Fan, L.-S. Wang, Fluid Phase Equilib. 247, 59 (2006)

    Article  Google Scholar 

  22. X.-Q. Guo, C.-Y. Sun, S.-X. Rong, G.-J. Chen, T.-M. Guo, J. Petrol. Sci. Eng. 30, 15 (2001)

    Article  Google Scholar 

  23. S. Khosharay, M. Pierantozzi, G. Di Nicola, Int. J. Refrig 85, 255 (2018)

    Article  Google Scholar 

  24. X. Wang, J. Wu, Z. Liu, Fluid Phase Equilib. 262, 251 (2007)

    Article  Google Scholar 

  25. Q.X.-T. HE Mao-Gang, LIU Xiang-Yang, SU Chao, J Eng Thermophy 36, 1186 (2015)

  26. M. He, X. Qi, X. Liu, C. Su, N. Lv, Int. J. Refrig 54, 55 (2015)

    Article  Google Scholar 

  27. F. Llovell, R. Marcos, L. Vega, J. Phys. Chem. B 117, 8159 (2013)

    Article  Google Scholar 

  28. M. Assael, J. Dymond, M. Papadaki, P. Patterson, Int. J. Thermophys. 13, 269 (1992)

    Article  ADS  Google Scholar 

  29. M. Assael, J. Dymond, M. Papadaki, P. Patterson, Fluid Phase Equilib. 75, 245 (1992)

    Article  Google Scholar 

  30. S.M. Hosseini, Fluid Phase Equilib. 458, 300 (2018)

    Article  Google Scholar 

  31. S.M. Hosseini, M.M. Alavianmehr, J. Moghadasi, Fluid Phase Equilib. 429, 266 (2016)

    Article  Google Scholar 

  32. S.M. Hosseini, M.M. Alavianmehr, J. Moghadasi, Fluid Phase Equilib. 458, 186 (2018). https://doi.org/10.1016/j.fluid.2017.11.019

    Article  Google Scholar 

  33. S.M. Hosseini, M. Pierantozzi, J. Moghadasi, Fuel 235, 1083 (2019). https://doi.org/10.1016/j.fuel.2018.08.088

    Article  Google Scholar 

  34. M.M. Papari, J. Moghadasi, S.M. Hosseini, F. Akbari, J. Mol. Liq. 158, 57 (2011)

    Article  Google Scholar 

  35. S.M. Hosseini, Physical Chemistry Research 6, 447 (2018)

    Google Scholar 

  36. D.I.f.P. Properties, (Design Institute for Physical Property Data/AIChE, 2005)

  37. J. Dymond, Chem. Phys. 17, 101 (1976)

    Article  Google Scholar 

  38. J. Dymond, Physica A 85, 175 (1976)

    Article  ADS  Google Scholar 

  39. H. Gürbüz Yücel, S. Özdoǧan, Can. J. Chem. Eng. 76, 148 (1998)

    Article  Google Scholar 

  40. J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, M.G. Mayer, Molecular theory of gases and liquids (Wiley, New York, 1954)

    MATH  Google Scholar 

  41. P.R. Bienkowski, K.C. Chao, J. Chem. Phys. 63, 4217 (1975)

    Article  ADS  Google Scholar 

  42. D. McQuarrie, Happer and Row, New York

  43. N. Carnahan, K. Starling, J. Chem. Phys 51, 635 (1969)

    Article  ADS  Google Scholar 

  44. N.F. Carnahan, K.E. Starling, J. Chem. Phys. 51, 635 (1969)

    Article  ADS  Google Scholar 

  45. M. Assael, S. Polimatidou, Int. J. Thermophys. 15, 779 (1994)

    Article  ADS  Google Scholar 

  46. M. Assael, J. Dymond, S. Polimatidou, Int. J. Thermophys. 15, 591 (1994)

    Article  ADS  Google Scholar 

  47. C. Oliveira, W.A. Wakeham, Int. J. Thermophys. 14, 33 (1993)

    Article  ADS  Google Scholar 

  48. T. Okubo, T. Hasuo, A. Nagashima, Int. J. Thermophys. 13, 931 (1992)

    Article  ADS  Google Scholar 

  49. D.E. Diller, A.S. Aragon, A. Laesecke, Fluid Phase Equilib. 88, 251 (1993)

    Article  Google Scholar 

  50. M. Assael, S. Polimatidou, E. Vogel, W. Wakeham, Int. J. Thermophys. 15, 575 (1994)

    Article  ADS  Google Scholar 

  51. D. Diller, S. Peterson, Int. J. Thermophys. 14, 55 (1993)

    Article  ADS  Google Scholar 

  52. M. Assael, E. Karagiannidis, W. Wakeham, Int. J. Thermophys. 13, 735 (1992)

    Article  ADS  Google Scholar 

  53. H.M. Avelino, J.M. Fareleira, C.M. Oliveira, J. Chem. Eng. Data 51, 1672 (2006)

    Article  Google Scholar 

  54. T. Sun, A.S. Teja, J. Phys. Chem. 100, 17365 (1996)

    Article  Google Scholar 

  55. K.D. Hammonds, D.M. Heyes, J Chem Soc Faraday Trans 2 Mol Chem Phys 84, 705 (1988). https://doi.org/10.1039/f29888400705

    Article  Google Scholar 

  56. D. DIADEM, (DIADEM Professional–Version 8.0.2-Database Date, 2016)

Download references

Acknowledgment

The University of Hormozgan is acknowledged for supporting this work.

Author information

Authors and Affiliations

  1. Department of Chemistry, Yasouj University, Yasouj, 75914-353, Iran

    F. Yousefi & K. Hamidi

  2. Departments of Chemistry, Faculty of Sciences, University of Hormozgan, Bandar Abbas, 71961, Iran

    S. M. Hosseini

  3. SAAD, Università degli Studi di Camerino, 63100, Ascoli Piceno, Italy

    M. Pierantozzi

Authors
  1. F. Yousefi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. M. Hosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Hamidi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Pierantozzi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to F. Yousefi or S. M. Hosseini.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yousefi, F., Hosseini, S.M., Hamidi, K. et al. Viscosities of Liquid Refrigerants from a Rough Hard-Sphere Theory-Based Semi-Empirical Model. Int J Thermophys 40, 74 (2019). https://doi.org/10.1007/s10765-019-2541-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10765-019-2541-1

Keywords

Search

Navigation