Skip to main content
SpringerLink
Log in

On the numerical solution of non-equilibrium condensation of steam in nozzles

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

Recent benchmark test “International Wet Steam Modelling Project” promoted by Joerg Starzmann et al. (Proc. Inst. Mech. Eng. A: J. Power Energy 232, 550–570, 2018) pointed out limitations of current numerical simulations of non-equilibrium condensation of steam. Especially, nucleation and droplet growth models as well as experiments still need some evolution. This paper is focused on the implementation of non-equilibrium condensation model intended for the wider range of pressures covering the typical expansion in steam turbine from high- to low-pressure parts. Due to the wide pressure range, a special attention has been also paid to the implementation of real thermodynamics. The properties of steam are implemented in the form of the spline-based table look-up method (SBTL) approximating the set of IAPWS-95/97 thermodynamics equations for water and steam.

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

Similar content being viewed by others

References

  1. Ahmadpour, A., Noori Rahim Abadi, S.M.A., Meyer, J.P.: On the performance enhancement of thermo-compressor and steam turbine blade cascade in the presence of spontaneous nucleation. Energy 119, 675–693 (2017)

    Article  Google Scholar 

  2. Aldridge, C.J., Fowler, A.C.: Stability and instability in evaporating two-phase flows. Surv. Math. Ind. 6, 75–107 (1996)

    MathSciNet  MATH  Google Scholar 

  3. Azzini, L., Pini, M.: Numerical investigation of high pressure condensing flows in supersonic nozzles. J. Phys. Conf. Ser. 823, 012008 (2017)

    Article  Google Scholar 

  4. Bagheri Esfe, H., Kermani, M.J., Saffar Avval, M.: Effects of non-equilibrium condensation on deviation angle and performance losses in wet steam turbines. J. Appl. Fluid Mech. 9, 1627–1639 (2016)

    Article  Google Scholar 

  5. Bakhtar, F., et al.: Classical nucleation theory and its application to condensing steam flow calculations. J. Mech. Eng. Sci. 219, 1315–1333 (2005)

    Article  Google Scholar 

  6. Barschdorff, D.: Verlauf der Zustandsgrossen und gasdynamische Zusammenhange bei der spontanen Kondensation reinen Wasserdampfes in Lavaldusen. Forsch. Ing.-Wes. 37, 146–157 (1971)

    Article  Google Scholar 

  7. Dykas, S., Wroblewski, W.: Numerical modelling of steam condensing flow in low and high-pressure nozzles. Int. J. Heat Mass Transf. 55, 6191–6199 (2012)

    Article  Google Scholar 

  8. Dykas, S., Wróblewski, W.: Two-fluid model for prediction of wet steam transonic flow. Int. J. Heat Mass Transf. 60, 88–94 (2013)

    Article  Google Scholar 

  9. Dykas, S., Majkut, M., Strozik, M., Smolka, K.: Losses estimation in transonic wet steam flow through linear blade cascade. J. Therm. Sci. 24, 109–116 (2015)

    Article  Google Scholar 

  10. Dykas, S., Majkut, M., Smolka, K., Strozik, M.: An attempt to make a reliable assessment of the wet steam flow field in the de Laval nozzle. Heat Mass Transf. 54, 2675–2681 (2018)

    Article  Google Scholar 

  11. Fransen, M.A.L.J.: On the growth of homogeneously nucleated water droplets in nitrogen: an experimental study. Exp. Fluids 55, 1780 (2014)

    Article  Google Scholar 

  12. Grübel, M., Starzmann, J., Schatz, M., Eberle, T., Vogt, D.M., Sieverding, F.: Two-phase flow modeling and measurements in low-pressure turbines—part 1: numerical validation of wet steam models and turbine modeling. ASME Paper GT2014-25244 (2014)

  13. Gyarmathy, G.: Nucleation of steam in high-pressure nozzle experiments. Proc. Inst. Mech. Eng. 219(6), 511 (2005)

    Article  Google Scholar 

  14. Hale, B.N.: Temperature dependence of homogeneous nucleation rates for water: near equivalence of the empirical fit of Wölk and Strey, and the scaled nucleation model. J. Chem. Phys. 122, 122–620 (2005)

    Google Scholar 

  15. Hill, P.G.: Condensation of water vapor during supersonic expansion in nozzles. J. Fluid Mech. 3, 593–620 (1966)

    Article  Google Scholar 

  16. Hrubý, J., Duška, M.: Analytical description of thermodynamic properties of steam, water and the phase interface for use in CFD. In: EPJ Web of Conferences, p 67 (2014)

  17. IAPWS: Guideline on the fast calculation of steam and water properties with the spline-based table look-up method (SBTL) (2015)

  18. Moore, M.J., Sieverding, C.H.: Two-Phase Steam Flow in Turbines and Separators, A von Karman Institute Book. Hemisphere Publishing, London (1976)

    Google Scholar 

  19. Noori Rahim Abadi, S.M.A., Kouhikamali, R., Atashkari, K.: Non-equilibrium condensation of wet steam flow within high-pressure thermo-compressor. Appl. Therm. Eng. 81, 74–82 (2015)

    Article  Google Scholar 

  20. Noori Rahim Abadi, S.M.A., Kouhikamali, R., Atashkari, K.: Two-fluid model for simulation of supersonic flow of wet steam within high-pressure nozzles. Int J. Therm. Sci. 96, 173–182 (2015)

    Article  Google Scholar 

  21. Sidin, R.S.R.: Droplet size distribution in condensing flow. Doctoral Thesis, University of Twente Enschede (2009)

  22. Starzmann, J., Hughes, F.R., White, A.J., Grubel, M., Vogt, D.M.: Numerical investigation of boundary layers in wet steam nozzles. ASME Paper GT2016-57598 (2016)

  23. Starzmann, J., et al.: Results of the International Wet Steam Modeling Project. Proc. Inst. Mech. Eng. A: J. Power Energy 232, 550–570 (2018)

    Article  Google Scholar 

  24. Wagner, W., Pruss, A.: The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387–535 (2002)

    Article  Google Scholar 

  25. White, A.J.: A comparison of modelling methods for polydispersed wet-steam flow. Int. J. Numer. Methods Eng. 57, 819–834 (2003)

    Article  MATH  Google Scholar 

  26. Xiaofei, L., Bofeng, B.: A multi-fluid model for non-equilibrium condensation in gaseous carrier flows. Appl. Therm. Eng. 65, 24–33 (2014)

    Article  Google Scholar 

  27. Zha, G.-C., Bilgen, E.: Numerical solutions of Euler equations by using a new flux vector splitting scheme. Int. J. Numer. Methods Fluids 17, 115–144 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhu, X., Lin, Z., Yuan, X., Tejima, T., Niizeki, Y., Shibukawa, N.: Non-equilibrium condensing flow modeling in nozzle and turbine cascade. Int. J. Gas Turb. Propuls. Power Syst. 4, 9–16 (2012)

    Google Scholar 

Download references

Funding

This study was supported by the ESIF, EU Operational Programme Research, Development and Education and by the Center of Advanced Aerospace Technology (CZ.02.1.01/0.0/0.0/16_019/0000826), Faculty of Mechanical Engineering, Czech Technical University in Prague. We appreciate also the additional support of CTU Grant No. SGS16/206/OHK2/3T/12.

Author information

Authors and Affiliations

  1. Department of Technical Mathematics, Faculty of Mechanical Engineering, Center of Advanced Aerospace Technology, Czech Technical University in Prague, Technicka Street 4, 16607, Prague 6, Czech Republic

    Vladimír Hric & Jan Halama

Authors
  1. Vladimír Hric
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan Halama
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimír Hric.

Additional information

Communicated by: Pavel Solin

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

Hric, V., Halama, J. On the numerical solution of non-equilibrium condensation of steam in nozzles. Adv Comput Math 45, 2147–2162 (2019). https://doi.org/10.1007/s10444-019-09700-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10444-019-09700-1

Keywords

Mathematics Subject Classification (2010)

Search

Navigation