Skip to main content
SpringerLink
Log in

Boundary of Metastable Region within Equations of State by Nigmatulin–Bolotnova

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

The present paper considers the determination of the two-phase region boundary within a simplified version of the wide-range equations of state of water and steam by Nigmatulin–Bolotnova (EOS NB) in the case the determination is based on the temperature-dependence of the saturated vapor pressure. This version of EOS NB can be used when the temperature and pressure ranges under investigation do not include the area of abnormal features of water at temperatures close to freezing ones (lower than \(10^{o}C\)) and when some errors in adiabatic speed of sound in a nearly-critical zone are acceptable. In particular, it is applied to numerically simulating dynamics of cavitation bubbles under their strong collapse. It is shown that in determining the two-phase region boundary within the simplified version of EOS NB on the basis of the temperature-dependencies of the saturated vapor pressure, a number of problems can occur. A simple modification of one of the known temperature-dependencies of the saturated vapor pressure, free of such problems, is presented.

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

REFERENCES

  1. R. I. Nigmatulin and R. K. Bolotnova, ‘‘Wide-range equation of state for water and steam: Method of construction,’’ High Temp. 46, 182 (2008). https://doi.org/10.1134/s10740-008-2005-y

    Article  Google Scholar 

  2. R. I. Nigmatulin and R. K. Bolotnova, ‘‘Wide-range equation of state for water and steam: Calculation results,’’ High Temp. 46, 325–336 (2008). https://doi.org/10.1134/S0018151X08030061

    Article  Google Scholar 

  3. R. I. Nigmatulin and R. K. Bolotnova, ‘‘Wide-range equation of state of water and steam: Simplified form,’’ High Temp. 49, 303–306 (2011). https://doi.org/10.1134/S0018151X11020106

    Article  Google Scholar 

  4. R. I. Nigmatulin, Dynamics of Multiphase Media (Hemisphere, New York, 1991).

    Google Scholar 

  5. Ya. B. Zel’dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic, New York, 1968).

    Google Scholar 

  6. Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use (The Int. Assoc. Properties of Water and Steam, Frederica, Denmark, 1996).

  7. J. M. Walsh and M. H. Rice, ‘‘Dynamic compression of liquids from measurements on strong shock waves,’’ J. Chem. Phys. 26, 815 (1957).

    Article  Google Scholar 

  8. N. I. Sharipdzhanov, L. V. Altshuler, and S. E. Brusnikin, ‘‘Anomalies of shock and isentropic compressibility of water,’’ Fiz. Goreniya Vzryva 5, 149 (1983).

    Google Scholar 

  9. S. B. Kormer, ‘‘Optical study of the characteristics of shock-compressed condensed dielectrics,’’ Sov. Phys. Usp. 11, 229–254 (1968).

    Article  Google Scholar 

  10. G. A. Lyzenga, T. J. Ahrens, W. J. Nellis, and A. C. Mitchell, ‘‘The temperature of shock-compressed water,’’ J. Chem. Phys. 76, 6282 (1982).

    Article  Google Scholar 

  11. G. A. Gurtman, J. W. Kirsch, and C. R. Hasting, ‘‘Analitical equation of state for water compressed to 300 Kbar,’’ J. Appl. Phys. 42, 851 (1971).

    Article  Google Scholar 

  12. P. W. Bridgman, ‘‘Freezing parameters and compressions of twenty one substances to 50 000 kg/cm2,’’ Proc. Am. Acad. Arts Sci. 74, 399 (1942).

    Article  Google Scholar 

  13. R. C. Reid, J. M. Prausnitz, and T. K. Sherwood,The Properties of Gases and Liquids Properties of Gases and Liquids (McGraw-Hill, New York, 1977).

    Google Scholar 

  14. R. I. Nigmatulin, A. A. Aganin, D. Yu. Toporkov, and M. A. Il’gamov, ‘‘Formation of convergent shock waves in a bubble upon its collapse,’’ Dokl. Phys. 59 (9), 431–435 (2014). https://doi.org/10.1134/S1028335814090109

    Article  Google Scholar 

  15. A. A. Aganin, M. A. Il’gamov, and D. Yu. Toporkov, ‘‘Dependence of vapor compression in cavitation bubbles in water and benzol on liquid pressure,’’ Uch. Zap. Kazan. Univ., Ser. Fiz.-Mat. Nauki 158, 231–242 (2016).

    Google Scholar 

  16. A. A. Aganin and D. Yu. Toporkov, ‘‘Strong compression of bubbles in water, acetone and benzol,’’ J. Phys.: Conf. Ser. 1058, 012068 (2018).

  17. S. L. Rivkin and A. A. Aleksandrov,Thermodynamic Properties of Water and Water Vapor, The Handbook, 2nd ed. (Energoatomizdat, Moscow, 1984) [in Russian].

    Google Scholar 

  18. W. Wagner and A. Pruß, ‘‘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 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics and Engineering, Federal Research Center Kazan Scientific Center, Russian Academy of Sciences, 420111, Kazan, Tatarstan, Russia

    A. A. Aganin & I. N. Mustafin

Authors
  1. A. A. Aganin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. N. Mustafin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. A. Aganin or I. N. Mustafin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aganin, A.A., Mustafin, I.N. Boundary of Metastable Region within Equations of State by Nigmatulin–Bolotnova. Lobachevskii J Math 41, 1143–1147 (2020). https://doi.org/10.1134/S1995080220070045

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080220070045

Keywords:

Search

Navigation