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Three Equations of State of Near-critical Fluids and Numerical Simulation of the Piston Effect

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Abstract

Analysis of three different equations of state suitable for describing fluids near the thermodynamic critical point is performed. Numerical simulation of the piston effect (adiabatic heating) with the use of the equations of state is carried out. The range of temperature distances to the critical point in which the calculated time of the piston effect is equal to the analytical time is defined. The reasons of discrepancy between the calculated and analytical times of the piston effect beyond the range defined is discussed.

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References

  • Arina, R.: Numerical simulation of near-critical fluids. Appl. Numer. Math. 51, 409–426 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Bailly, D., Zappoli, B.: Hydrodynamic theory of density relaxation in near-critical fluids. Phys. Rev. E 62 (2), 2353–2368 (2000)

    Article  Google Scholar 

  • Barmatz, M., Hahn, I., Lipa, J.A., Duncan, R.V.: Critical phenomena in microgravity: Past, present and future. Rev. Mod. Phys. 79(1), 1–52 (2007)

    Article  Google Scholar 

  • Beysens, D.: Critical point in space: a quest for universality. Microgravity Sci. Technol. 26, 201–218 (2014)

    Article  Google Scholar 

  • Beysens, D.A., et al.: Thermal effects in near-critical fluids: piston effect and related phenomena. In: Chen, L., Iwamoto, Y (eds.) Advanced Applications of Supercritical Fluids in Energy Systems. Chapter 1. IGI Global Online. https://doi.org/10.4018/978-1-5225-2047-4 (2017)

  • Boukari, H., Shaumeyer, J.N., Briggs, M.E., Gammon, R.W.: Critical speeding up in pure fluids. Phys. Rev. A 41, 2260–2263 (1990)

    Article  Google Scholar 

  • Deng, B.L., Kanda, Y., Chen, L., Okajima, J., Komiya, A., Maruyama, S h: Visualization study of supercritical fluid convection and heat transfer in weightlessness by interferometry: a brief review. Microgravity Sci. Technol. 29, 275–295 (2017)

    Article  Google Scholar 

  • Emelianov, V.M., Lednev, A.K., Polezhaev, V.I., Ivanov, A.I., Putin, G.F., Zyuzgin, A.V., Beysens, D., Garrabos, Y.: Convection and heat transfer experiments in supercritical fluid under microgravity: from MIR to ISS. Micrograv. Sci. Tech. 16, 164–169 (2005)

    Article  Google Scholar 

  • Garrabos, Y., Beysens, D., Lecoutre, C., Dejoan, A., Polezhaev, V., Emelianov, V.: Thermoconvectional phenomena induced by vibrations in supercritical SF6 under weightlessness. Phys. Rev. E 75, 056317 (2007)

    Article  Google Scholar 

  • Gorbunov, A., Emelyanov, V., Lednev, A., Soboleva, E.: Dynamic and thermal effects in supercritical fluids under various gravity conditions. Microgravity Sci. Technol. 30(1-2), 53–62 (2018)

    Article  Google Scholar 

  • Ivanov, D.Y.: Critical Behavior of Non-Ideal Systems. Wiley Online Library (2009)

  • Ivanov, D. Y. u., Makarevich, L.A., Sokolova, O.N.: Shape of coexistence curve of pure matter near critical point. JETP Lett. 20(4), 121–125 (1974)

    Google Scholar 

  • Kogan, A.B., Meyer, H.: Heat transfer and convection onset in a compressible fluid: 3He near the critical point. Phys. Rev. E 63, 056310 (2001)

    Article  Google Scholar 

  • Landau, L.D., Lifshitz, E.M.: Course of Theoretical Physics. Vol. 5. Statistical Physics. Part 1. Pergamon Press, Oxford (1980)

    Google Scholar 

  • Landau, L.D., Lifshitz, E.M.: Course of Theoretical Physics, vol. 6. Fluid Mechanics. Pergamon Press, Oxford (1987)

    Google Scholar 

  • Lyubimov, D., Lyubimova, T., Vorobev, A., Mojtabi, A., Zappoli, B.: Thermal vibrational convection in near-critical fluids. Part. 1. Non-uniform heating. J. Fluid Mech. 564, 159–183 (2006a)

    Article  MathSciNet  MATH  Google Scholar 

  • Lyubimov, D., Lyubimova, T., Vorobev, A., Mojtabi, A., Zappoli, B.: Thermal vibrational convection in near-critical fluids. Part. 2. Weakly non-uniform heating. J. Fluid Mech. 564, 185–196 (2006b)

    Article  MathSciNet  MATH  Google Scholar 

  • Lyubimova, T., Ivantsov, A., Garrabos, Y., Lecourte, C., Gandikova, G., Beysens, D.: Band instability in near-critical fluids subjected to vibration under weightlessness. Phys. Rev. E 95(1), 013105 (2017)

    Article  Google Scholar 

  • Migdal, A.A.: Equation of state near a critical point. Sov. Phys. JETP 35(4), 816–822 (1972)

    Google Scholar 

  • Onishi, M., Yoshihara, S.h., Sakurai, M., Miura, Y.u., Ishikawa, M., Kobayashi, H., Takenouchi, T., Kawai, J. u., Honda, K., Matsumoto, M.: Ultra-sensitive high-speed density measurement of the “piston effect” in a critical fluid. Micrograv. Sci. Tech. 16, 306–310 (2005)

    Article  Google Scholar 

  • Onuki, A.: Phase Transition Dynamics. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  • Onuki, A., Ferrell, R.A.: Adiabatic heating effect near the gas-liquid critical point. Physica A 164, 245–264 (1990)

    Article  Google Scholar 

  • Onuki, A., Hao, H., Ferrell, R.A.: Fast adiabatic equilibration in a single-component fluid near the liquid-vapor critical point. Phys. Rev. A 41(4), 2256–2259 (1990)

    Article  Google Scholar 

  • Polezhaev, V.I.: Modeling convective and wave processes and heat transfer in near-critical media. An overview. Unsteady thermo-gravitational convection effects in a side-heated or cooled near-critical fluid. Fluid Dyn. 46(2), 175–195 (2011)

    Article  MathSciNet  Google Scholar 

  • Polezhaev, V.I., Gorbunov, A.A., Soboleva, E.B.: Classical Problems of Convection near Critical Point. Ground-based and Microgravity Applications. Advances in Space Research (includes Cospar Information Bulletin) 29(4), 581–588 (2002)

    Google Scholar 

  • Polezhaev, V.I., Gorbunov, A.A., Soboleva, E.B.: Unsteady near critical flows in microgravity environment. Ann. N. Y. Acad. Sci. 1027, 286–302 (2004)

    Article  Google Scholar 

  • Polezhaev, V.I., Gorbunov, A.A., Nikitin, S.A., Soboleva, E.B.: Hydrostatic Compressibility phenomena: New Opportunity for Near-critical Research in Microgravity. Ann. N. Y. Acad. Sci. 1077, 304–327 (2006)

    Article  Google Scholar 

  • Rabinovich, V.A., Sheludyak, Y.E.: The values of critical exponents of individual substances. High Temp. 34(6), 874–881 (1996)

    Google Scholar 

  • Rutin, S.B., Volosnikov, D.V., Skripov, P.V.: Heat transfer under high-power heating of liquids. 3. Threshold decrease of heat conduction in supercritical region. Int. J. Heat Mass Transf. 91, 1–6 (2015)

    Article  Google Scholar 

  • Schofield, P.: Parametric representation of the equation of state near a critical point. Phys. Rev. Lett. 22, 606–608 (1969)

    Article  Google Scholar 

  • Shen, B., Zhang, P.: Raylegh-benard convection in a supercritical fluid along its critical isochore in a shallow cavity. Int. J. Heat Mass Transf.s 55, 7151–7165 (2012)

    Article  Google Scholar 

  • Soboleva, E.B.: The effect of equations of state on simulation of convective flow and heat transfer in Near-Critical liquids. High Temp. 38(6), 893–899 (2000)

    Article  Google Scholar 

  • Soboleva, E.B.: Adiabatic heating and convection caused by a Fixed-Heat-Flux source in a Near-Critical fluid. Phys. Rev. E 68, 042201 (2003)

    Article  Google Scholar 

  • Soboleva, E.B.: Thermal gravitational convection of a side-heated supercritical fluid with variable physical properties. Fluid Dyn. 48(5), 648–657 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Soboleva, E.B.: Adiabatic heating (cooling) of a supercritical fluid with variation in its physical properties. Fluid Dyn. 52(1), 25–36 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Soboleva, E.B., Nikitin, S.A.: Benchmark data on laminar rayleigh-benard convection in a stratified supercritical fluis: a case of two-dimensional flow in a square cell. Int. J. Heat Mass Transf. 69, 6–16 (2014)

    Article  Google Scholar 

  • Walas, S.M.: Phase Equilibria in Chemical Engineering, vol. 1. Butterworth Publishers, Boston (1985)

    Google Scholar 

  • Yamamoto, S., Furusawa, T., Matsuzawa, R.: Numerical simulation of supercritical carbon dioxide flows across critical point. Int. J. Heat Mass Transf. 54, 774–782 (2011)

    Article  MATH  Google Scholar 

  • Zappoli, B., Bailly, D., Garrabos, Y., Le Neindre, B., Guenoun, P., Beysens, D.: Anomalous heat transport by the piston effect in supercritical fluids under zero gravity. Phys. Rev. A 41, 2264–2267 (1990)

    Article  Google Scholar 

  • Zappoli, B., Beysens, D.Y., Garrabos, Y.: Heat transfers and related effects in supercritical fluids. Fluid mechanics and its applications. v. 108 springer (2015)

  • Zyuzgin, A.B., Putin, G.F., Ivanov, A.I., Polezhaev, V.I., Soboleva, E.B.: Convective motions in near-critical fluids under real zero-gravity conditions. Cosm. Res. 39(2), 175–186 (2001)

    Article  Google Scholar 

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Acknowledgements

The work was financially supported by the Government program of the Russian Federation (contract AAAA-A17-117021310375-7).

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  1. Ishlinsky Institute for Problems in Mechanics RAS, Pr. Vernadskogo, 101, b. 1, 119526, Moscow, Russia

    Alexander Gorbunov & Elena Soboleva

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  1. Alexander Gorbunov
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  2. Elena Soboleva
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Correspondence to Elena Soboleva.

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Gorbunov, A., Soboleva, E. Three Equations of State of Near-critical Fluids and Numerical Simulation of the Piston Effect. Microgravity Sci. Technol. 32, 47–57 (2020). https://doi.org/10.1007/s12217-019-09735-5

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  • DOI: https://doi.org/10.1007/s12217-019-09735-5

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