Advertisement

Sādhanā

, 44:37 | Cite as

A numerical study of natural convection properties of supercritical water (H2O) using Redlich–Kwong equation of state

  • Hussain Basha
  • G Janardhana ReddyEmail author
  • N S Venkata Narayanan
Article
  • 16 Downloads

Abstract

In this article, the Crank-Nicolson implicit finite difference method is utilized to obtain the numerical solutions of highly nonlinear coupled partial differential equations (PDEs) for the flow of supercritical fluid (SCF) over a vertical flat plate. Based on the equation of state (EOS) approach, suitable equations are derived to calculate the thermal expansion coefficient (\( \beta \)) values. Redlich–Kwong equation of state (RK-EOS), Peng-Robinson equation of state (PR-EOS), Van der Waals equation of state (VW-EOS) and Virial equation of state (Virial-EOS) are used in this study to evaluate \( \beta \) values. The calculated values of \( \beta \) based on RK-EOS is closer to the experimental values, which shows the greater accuracy of the RK-EOS over PR-EOS, VW-EOS and Virial-EOS models. Numerical simulations are performed for \( {\text{H}}_{2} {\text{O}} \) in three regions namely subcritical, supercritical and near critical regions. The unsteady velocity, temperature, average heat and momentum transport coefficients for different values of reduced pressure and reduced temperature are discussed based on the numerical results and are shown graphically across the boundary layer.

Keywords

Supercritical water Crank-Nicolson scheme RK-EOS PR-EOS virial-EOS VW-EOS correlation 

Notes

Acknowledgements

The first author Hussain Basha would like to thank Maulana Azad National Fellowship programme, University Grants Commission, Government of India, Ministry of Minority Affairs, MANF (F1-17.1/2017-18/MANF-2017-18-KAR-81943) for the Grant of research fellowship and to the Central University of Karnataka for providing the research facilities. NSV Narayanan thanks DST-SERB for the partial financial support through the research Grant (EMR/2016/000236). The authors wish to express their gratitude to the reviewers who highlighted important areas for improvement in this article. Their suggestions have served specifically to enhance the clarity and depth of the interpretation in the manuscript.

References

  1. 1.
    Oka Y, Jevremovic T and Koshizuka S 1994 A direct-cycle, supercritical-water-cooled fast breeder reactor. J. Nucl. Sci. Technol. 31: 83–85CrossRefGoogle Scholar
  2. 2.
    Hui J, Xiao Z, Su X, Zhu C, Cao C and Guo L 2017 Supercritical water synthesis of bimetallic catalyst and its application in hydrogen production by furfural gasification in supercritical water. Int. J. Hydrog. Energy 42: 4943–4950CrossRefGoogle Scholar
  3. 3.
    Schulenberg T, Laurence K H L and Oka Y 2014 Review of R&D for supercritical water cooled reactors. Prog. Nuclear Energy 77: 282–299CrossRefGoogle Scholar
  4. 4.
    Guzonas D, Edwards M, and Zheng W 2016 Assessment of candidate fuel cladding alloys for the Canadian supercritical water-cooled reactor concept. J. Nuclear Eng. Rad. Sci. 2: 011016–8CrossRefGoogle Scholar
  5. 5.
    Kiran E, Debenedetti P G and Peters C J 2000 Supercritical Fluids: Fundamentals and Applications, NATO Science Series, Netherlands: SpringerCrossRefGoogle Scholar
  6. 6.
    Maitri V R, Zhang C and Jiang J 2017 Computational fluid dynamic assisted control system design methodology using system identification technique for CANDU supercritical water cooled reactor (SCWR). Appl. Therm. Eng. 118: 17–22CrossRefGoogle Scholar
  7. 7.
    Hosseinpour M, Fatemi S and Javad S 2016 Deuterium tracing study of unsaturated aliphatics hydrogenation by supercritical water during upgrading of petroleum heavy oil. Part I: Non-catalytic cracking. J. Supercrit. Fluids 107: 278–285CrossRefGoogle Scholar
  8. 8.
    Gaudet M, Yetisir M and Sartipi A 2016 Conceptual plant layout of the Canadian generation IV supercritical water-cooled reactor. CNL Nuclear Rev. 5: 203–219Google Scholar
  9. 9.
    Alshammari Y M and Hellgardt K 2016 Sub and supercritical water reforming of n hexadecane in a tubular flow reactor. J. Supercrit. Fluids 107: 723–732CrossRefGoogle Scholar
  10. 10.
    Kiss A, Balasko M, Horvath L, Kis Z and Aszodi A 2017 Experimental investigation of the thermal hydraulics of supercritical water under natural circulation in a closed loop. Ann. Nucl. Energy 100: 178–203CrossRefGoogle Scholar
  11. 11.
    Liu Q, Ding X, Du B and Fang T (2017) Multi-phase equilibrium and solubilities of aromatic compounds and inorganic compounds in sub and supercritical water: a review. Crit. Rev. Anal. Chem. 0: 1–11Google Scholar
  12. 12.
    Caputo G, Rubio P, Scargiali F, Marotta G and Brucato A 2016 Experimental and fluid dynamic study of continuous supercritical water gasification of glucose. J. Supercrit. Fluids 107: 450–451CrossRefGoogle Scholar
  13. 13.
    Savage P E 2000 Heterogeneous catalysis in supercritical water. Catal. Today 62: 167–173CrossRefGoogle Scholar
  14. 14.
    Toyama S, Hayashi H, Takesue M, Watanabe M, and Smith R L 2016 Synthesis of alkali niobate \( {\text{K}}_{{1 - {{\rm x}}}} {\text{Na}}_{{\rm x}} {\text{NbO}}_{3} \) nanoparticles using supercritical water flow system. J. Supercrit. Fluids 107: 1–8CrossRefGoogle Scholar
  15. 15.
    Forooghi P and Hooman K 2014 Experimental analysis of heat transfer of supercritical fluids in plate heat exchangers. Int. J. Heat Mass Transf. 74: 48–459CrossRefGoogle Scholar
  16. 16.
    Lei X, Li H, Zhang Y and Zhang W 2013 Effect of buoyancy on the mechanism of heat transfer deterioration of supercritical water in horizontal tubes. ASME J. Heat Transf. 135: 071703–9Google Scholar
  17. 17.
    Long Z Q and Zhang P 2014 Natural convection heat transfer of supercritical helium in a closed vertical cylinder. Cryogenics 61: 120–126CrossRefGoogle Scholar
  18. 18.
    Long Z Q, Zhang P, Shen B and Li T 2015 Experimental investigation of natural convection in a supercritical binary fluid. Int. J. Heat Mass Transf. 90: 922–930CrossRefGoogle Scholar
  19. 19.
    Lu Y, Zhang T and Dong X 2016 Numerical analysis of heat transfer and solid volume fraction profiles around a horizontal tube immersed in a supercritical water fluidized bed. Appl. Therm. Eng. 93: 200–213CrossRefGoogle Scholar
  20. 20.
    Zhang T and Che D 2016 Numerical investigation on heat transfer of supercritical water in a roughened tube. Numer. Heat Transf. A 69: 558–573CrossRefGoogle Scholar
  21. 21.
    Zhang L, Caia B, Wenga Y, Gua H, Wanga H, Li H and Chatoorgoon V 2016 Experimental investigations on flow characteristics of two parallel channels in a forced circulation loop with supercritical water. Appl. Therm. Eng. 106: 98–108CrossRefGoogle Scholar
  22. 22.
    Arai Y, Sako T and Takebayashi Y 2002 Supercritical Fluids. Springer, BerlinCrossRefGoogle Scholar
  23. 23.
    Brunner G 1994 Topics in Physical Chemistry: Gas Extraction. Springer, BerlinCrossRefGoogle Scholar
  24. 24.
    Domingo C and Peternault P S 2016 Supercritical Fluid Nanotechnology: Advances and Applications in Composites and Hybrid Nanomaterial’s. Pan Stanford Publishing CRC press Taylor and Francis Group, Boca Raton, USAGoogle Scholar
  25. 25.
    McHugh M A and Krukonis V J 1994 Supercritical Fluid Extraction, Principles and Practice, 2nd edition. Butterworth-Heinemann, Boston, USAGoogle Scholar
  26. 26.
    Sparrow E M and Gregg J L 1958 Similar solutions for free convection from a non-isothermal vertical plate. ASME J. Heat Transf. 80: 379–386Google Scholar
  27. 27.
    Takhar H S, Ganesan P, Ekambavanan P and Soundalgekar V M 1997 Transient free convection past a semi-infinite vertical plate with variable surface temperature. Int. J. Numer. Methods Heat Fluid Flow 7: 280–296CrossRefGoogle Scholar
  28. 28.
    Onbasioglu S U and Onbastoglu H 2004 On enhancement of heat transfer with ribs. Appl. Therm. Eng. 24: 43–57CrossRefGoogle Scholar
  29. 29.
    Bhavnani S H and Bergles A E 1990 Effect of surface geometry and orientation on laminar natural convection heat transfer from a vertical flat plate with transverse roughness elements. Int. J. Heat Mass Transf. 33: 965- 981CrossRefGoogle Scholar
  30. 30.
    Teymourtash A R, Khonakdar D R and Raveshi M R 2013 Natural convection on a vertical plate with variable heat flux in supercritical fluids. J. Supercrit. Fluids 74: 115–127CrossRefGoogle Scholar
  31. 31.
    Khonakdar D R and Raveshi M R 2016 Mixed convection on a vertical plate in supercritical fluids by selecting the best equation of state. J. Supercrit. Fluids 107: 549–559CrossRefGoogle Scholar
  32. 32.
    Soave G 1993 20 years of Redlich–Kwong equation of state. Fluid Phase Equilib. 82: 345–359CrossRefGoogle Scholar
  33. 33.
    Muller E A and Estevez L A 1990 Mixing expansivities and Grashof number in supercritical fluids using cubic equations of state. J. Supercrit. Fluids 3: 136–142CrossRefGoogle Scholar
  34. 34.
    Echeverry J S L, Acherman S R and Lopez E A 2017 Peng-Robinson equation of state: 40 years through cubics. Fluid Phase Equilib. 447: 39–71CrossRefGoogle Scholar
  35. 35.
    Blundell S J and Blundell K M 2006 Concepts in Thermal Physics. Oxford University Press, UKzbMATHGoogle Scholar
  36. 36.
    Annamalai K and Puri I K, 2002 Advanced Thermodynamics Engineering. CRC Press, Boca Raton, New YorkzbMATHGoogle Scholar
  37. 37.
    Kundu P K, Cohen I M and Dowling D R 2012 Fluid Mechanics, 5th edition. Academic Press, USAzbMATHGoogle Scholar
  38. 38.
    Rani H P, Reddy G J and Kim C N 2013 Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder. Appl. Math. Mech. Engl. Ed. 34: 985–1000Google Scholar
  39. 39.
    NIST (National Institute of Standards and Technology) Chemistry Web Book, 2017, U.S. Secretary of Commerce on behalf of the United States of America, USA.Google Scholar
  40. 40.
    Poling B E, Prausnitz J M and O’Connell J P 2001 The Properties of Gases and Liquids, 5th edition. USA: McGraw-HillsGoogle Scholar
  41. 41.
    Churchill S W and Chu H H S 1975 Correlating equations for laminar and turbulent free convection from a vertical plate. Int. J. Heat Mass Transf. 18: 1323–1329CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  • Hussain Basha
    • 1
  • G Janardhana Reddy
    • 1
    Email author
  • N S Venkata Narayanan
    • 2
  1. 1.Department of MathematicsCentral University of KarnatakaKalaburagiIndia
  2. 2.Department of ChemistryCentral University of KarnatakaKalaburagiIndia

Personalised recommendations