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The admissibility domain of rarefaction shock waves in the near-critical vapour–liquid equilibrium region of pure typical fluids

Published online by Cambridge University Press:  14 April 2016

Nawin R. Nannan ,
Corrado Sirianni ,
Tiemo Mathijssen ,
Alberto Guardone  and
Piero Colonna
Nawin R. Nannan
Affiliation:
Mechanical Engineering Discipline, Anton de Kom University of Suriname, Leysweg 86, PO Box 9212, Paramaribo, Suriname
Corrado Sirianni
Affiliation:
Mechanical Engineering Discipline, Anton de Kom University of Suriname, Leysweg 86, PO Box 9212, Paramaribo, Suriname
Tiemo Mathijssen
Affiliation:
Propulsion and Power, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands
Alberto Guardone
Affiliation:
Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy
Piero Colonna*
Affiliation:
Propulsion and Power, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

Application of the scaled fundamental equation of state of Balfour et al. (Phys. Lett. A, vol. 65, 1978, pp. 223–225) based upon universal critical exponents, demonstrates that there exists a bounded thermodynamic domain, located within the vapour–liquid equilibrium region and close to the critical point, featuring so-called negative nonlinearity. As a consequence, rarefaction shock waves with phase transition are physically admissible in a limited two-phase region in the close proximity of the liquid–vapour critical point. The boundaries of the admissibility region of rarefaction shock waves are identified from first-principle conservation laws governing compressible flows, complemented with the scaled fundamental equations. The exemplary substances considered here are methane, ethylene and carbon dioxide. Nonetheless, the results are arguably valid in the near-critical state of any common fluid, namely any fluid whose molecular interactions are governed by short-range forces conforming to three-dimensional Ising-like systems, including, e.g. water. Computed results yield experimentally feasible admissible rarefaction shock waves generating a drop in pressure from 1 to 6 bar and pre-shock Mach numbers exceeding 1.5.

JFM classification

Phase change: Condensation/evaporation Compressible Flows: Gas dynamics Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 795 , 25 May 2016 , pp. 241 - 261
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Copyright
© 2016 Cambridge University Press 

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References

Albright, P. C., Edwards, T. J., Chen, Z. Y. & Sengers, J. V. 1987 A scaled fundamental equation for the thermodynamic properties of carbon dioxide in the critical region. J. Chem. Phys. 87 (3), 1717–1725.CrossRefGoogle Scholar
Anisimov, M. A., Kiselev, S. B., Sengers, J. V. & Tang, S. 1992 Crossover approach to global critical phenomena in fluids. Physica A 188, 487–525.CrossRefGoogle Scholar
Argrow, B. M. 1996 Computational analysis of dense gas shock tube flow. Shock Waves 6, 241–248.Google Scholar
Balfour, F. W., Sengers, J. V., Moldover, M. R. & Levelt-Sengers, J. M. H. 1978 Universality, revisions and corrections to scaling in fluids. Phys. Lett. A 65, 223–225.CrossRefGoogle Scholar
Borisov, A. A., Kutateladze, S. S. & Nakoryakov, V. E. 1983 Rarefaction shock wave near the critical liquid–vapor point. J. Fluid Mech. 126, 59–73.Google Scholar
Brown, B. P. & Argrow, B. M. 1997 Two-dimensional shock tube flow for dense gases. J. Fluid Mech. 349, 95–115.Google Scholar
Brown, B. P. & Argrow, B. M. 2000 Application of Bethe–Zel’dovich–Thompson fluids in organic Rankine cycle engines. J. Propul. Power 16 (6), 1118–1123.Google Scholar
Callen, H. B. 1985 Thermodynamics and an Introduction to Thermostatistics, 2nd edn. Wiley.Google Scholar
Colonna, P. & Guardone, A. 2006 Molecular interpretation of nonclassical gas dynamics of dense vapors under the Van der Waals model. Phys. Fluids 18, 056101,1–14.CrossRefGoogle Scholar
Colonna, P., Guardone, A. & Nannan, N. 2006 The thermodynamic region of negative nonlinearity in selected siloxanes predicted by modern thermodynamic models. In Proceedings of the 15th U.S. National Congress on Theoretical and Applied Mechanics, University of Colorado.Google Scholar
Colonna, P., Guardone, A. & Nannan, N. R. 2007 Siloxanes: a new class of candidate Bethe–Zel’dovich–Thompson fluids. Phys 19, 086102,1–12.Google Scholar
Colonna, P., Harinck, J., Rebay, S. & Guardone, A. 2008 Real-gas effects in organic Rankine cycle turbine nozzles. J. Propul. Power 24 (2), 282–294.Google Scholar
Colonna, P., Nannan, N. R., Guardone, A. & van der Stelt, T. P. 2009 On the computation of the fundamental derivative of gas dynamics using equations of state. Fluid Phase Equilib. 286 (1), 43–54.Google Scholar
Cramer, M. & Fry, N. 1993 Nozzle flows of dense gases. Phys. Fluids A 5 (5), 1246–1259.Google Scholar
Cramer, M. & Sen, R. 1986 Shock formation in fluids having embedded regions of negative nonlinearity. Phys. Fluids 29, 2181–2191.CrossRefGoogle Scholar
Cramer, M. S. 1987 Structure of weak shocks in fluids having embedded regions of negative nonlinearity. Phys. Fluids 30 (10), 3034–3044.CrossRefGoogle Scholar
Cramer, M. S. 1989 Negative nonlinearity in selected fluorocarbons. Phys. Fluids A 11 (1), 1894–1897.CrossRefGoogle Scholar
Cramer, M. S. 1991 Nonclassical dynamics of classical gases. In Nonlinear Waves in Real Fluids (ed. Kluwick, A.), pp. 91–145. Springer.Google Scholar
Cramer, M. S. & Kluwick, A. 1984 On the propagation of waves exhibiting both positive and negative nonlinearity. J. Fluid Mech. 142, 9–37.Google Scholar
Cramer, M. S., Kluwick, A., Watson, L. T. & Pelz, W. 1986 Dissipative waves in fluids having both positive and negative nonlinearity. J. Fluid Mech. 169, 323–336.Google Scholar
Cramer, M. S. & Sen, R. 1987 Exact solutions for sonic shocks in van der Waals gases. Phys. Fluids 30, 377.Google Scholar
Cramer, M. S., Tarkenton, L. M. & Tarkenton, G. M. 1992 Critical Mach number estimates for dense gases. Phys. Fluids A 4 (8), 1840.CrossRefGoogle Scholar
Duschek, W., Kleinrahm, R. & Wagner, W. 1990 Measurement and correlation of the (pressure, density, temperature) relation of carbon dioxide. I: the homogeneous gas and liquid regions in the temperature range from 217 to 340 K at pressures up to 9 MPa. J. Chem. Thermodyn. 22 (9), 827–840.Google Scholar
Emanuel, G.1996 The fundamental derivative of gas dynamics in the vicinity of the critical point. Tech. Rep. AME Report 96-1. University of Oklahoma.Google Scholar
Fergason, B., Ho, T., Argrow, B. & Emanuel, G. 2001 Theory for producing a single-phase rarefaction shock wave in a shock tube. J. Fluid Mech. 445, 37–54.Google Scholar
Fergason, S. H. & Argrow, B. M. 2001 Simulations of nonclassical dense gas dynamics. In 35th AIAA Thermophysics Conference, Anaheim, CO.Google Scholar
Fergason, S., Guardone, A. & Argrow, B. 2003 Construction and validation of a dense gas shock tube. J. Thermophys. Heat Transfer 17 (3), 326–333.CrossRefGoogle Scholar
Guardone, A., Vigevano, L. & Argrow, B. M. 2004 Assessment of thermodynamic models for dense gas dynamics. Phys. Fluids 16 (11), 3878–3887.Google Scholar
Guardone, A., Zamfirescu, C. & Colonna, P. 2009 Maximum intensity of rarefaction shock waves for dense gases. J. Fluid Mech. 642, 127.Google Scholar
Gulen, S. C., Thompson, P. A. & Cho, H. J. 1989 Rarefaction and liquefaction shock waves in regular and retrograde fluidswith near-critical end states. In IUTAM Symposium: Adiabatic Waves in Liquid–Vapor Systems (ed. Meier, G. E. A. & Thompson, P. A.), pp. 281–290. Springer.Google Scholar
Hayes, W. D. 1958 The basic theory of gas dynamic discontinuities. In Fundamentals of Gas Dynamics, vol. 3, chap., p. 426. Princeton University Press.Google Scholar
Kluwick, A. 1993 Transonic nozzle flow of dense gases. J. Fluid Mech. 247, 661–688.Google Scholar
Kluwick, A. 1995 Adiabatic waves in the neighbourhood of the critical point. In UITAM Symposium: Waves in Liquid/Gas and Liquid/Vapour Two-Phase Systems (ed. Morioka, S. & van Wijngaarden, L.), vol. 31, pp. 387–404. Kluwer.Google Scholar
Kluwick, A. 2001 Rarefaction shocks. In Handbook of Shock Waves, chap. 3.4, pp. 339–411. Academic.Google Scholar
Kurumov, D. S., Olchowy, G. A. & Sengers, J. V. 1988 Thermodynamic properties of methane in the critical region. Intl J. Thermophys. 9 (1), 73–84.Google Scholar
Kutateladze, S. S., Nakoryakov, V. E. & Borisov, A. A. 1987 Rarefaction waves in liquid and gas-liquid media. Annu. Rev. Fluid Mech. 19, 577–600.Google Scholar
Lambrakis, K. C. & Thompson, P. A. 1972 Existence of real fluids with a negative fundamental derivative 𝛤. Phys. Fluids 15 (5), 933–935.CrossRefGoogle Scholar
Lax, P. D. 1957 Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10, 537–566.Google Scholar
Lemmon, E. W., Huber, M. & McLinden, M. O.2007 REFPROP – Reference Fluid Thermodynamic and Transport Properties. Software, Version 8.Google Scholar
Levelt-Sengers, J. M. H. 1970 Scaling predictions for thermodynamic anomalies near the gas-liquid critical point. Ind. Engng Chem. Fundam. 9 (3), 470–480.Google Scholar
Levelt-Sengers, J. M. H., Kamgar-Parsi, B. & Sengers, J. V. 1983a Thermodynamic properties of isobutane in the critical region. J. Chem. Engng Data 28 (4), 354–362.Google Scholar
Levelt-Sengers, J. M. H., Morrison, G. & Chang, R. F. 1983b Critical behavior in fluids and fluid mixtures. Fluid Phase Equilib. 14, 19–44.Google Scholar
Menikoff, R. & Plohr, B. J. 1989 The Riemann problem for fluid flow of real material. Rev. Mod. Phys. 61 (1), 75–130.Google Scholar
Michels, A., Sengers, J. V. & van der Gulik, P. S. 1962 The thermal conductivity of carbon dioxide in the critical region II. Measurements and conclusions. Physica 28 (12), 1216–1237.Google Scholar
Nannan, N., Guardone, A. & Colonna, P. 2013 On the fundamental derivative of gas dynamics in the vapor–liquid critical region of single-component typical fluids. Fluid Phase Equilib. 337 (0), 259–273.Google Scholar
Nannan, N. R., Guardone, A. & Colonna, P. 2014 Critical point anomalies include expansion shock waves. Phys. Fluids 26 (2), 021701.Google Scholar
Nehzat, M. S., Hall, K. R. & Eubank, P. T. 1983 Thermophysical properties of ethylene in the critical region. J. Chem. Engng Data 28 (2), 205–210.Google Scholar
Nowak, P., Kleinrahm, R. & Wagner, W. 1996 Measurement and correlation of the (P, 𝜌, T) relation of ethylene ii. Saturated-liquid and saturated-vapour densities and vapour pressures along the entire coexistence curve. J. Chem. Thermodyn. 28 (12), 1441–1460.Google Scholar
Oleinik, O. 1959 Uniqueness and stability of the generalized solution of the Cauchy problemfora quasi-linear problem. Usp. Mat. Nauk 14, 165–170.Google Scholar
Schofield, P., Litster, J. & Ho, J. T. 1969 Correlation between critical coefficients and critical exponents. Phys. Rev. Lett. 23 (19), 1098.Google Scholar
Sengers, J. L., Greer, W. & Sengers, J. 1976 Scaled equation of state parameters for gases in the critical region. J. Phys. Chem. Ref. Data 5 (1), 1–52.Google Scholar
Sengers, J. V. & Levelt-Sengers, J. M. H. 1984 A universal representation of the thermodynamic properties of fluids in the critical region. Intl J. Thermophys. 5 (2), 195–208.Google Scholar
Setzmann, U. & Wagner, W. 1991 A new equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 1000 MPa. J. Phys. Chem. Ref. Data 20 (6), 1061–1151.Google Scholar
Smukala, J., Span, R. & Wagner, W. 2000 New equation of state for ethylene covering the fluid region for temperatures from the melting line to 450 K at pressures up to 300 mPa. J. Phys. Chem. Ref. Data 29 (5), 1053–1121.Google Scholar
Span, R. & Wagner, W. 1996 A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 {K} at pressures up to 800 {MPa}. J. Phys. Chem. Ref. Data 25 (6), 1509–1596.Google Scholar
Thompson, P. A. 1971 A fundamental derivative in gasdynamics. Phys. Fluids 14 (9), 1843–1849.CrossRefGoogle Scholar
Thompson, P. A. 1988 Compressible Fluid Dynamics. McGraw-Hill.Google Scholar
Thompson, P. A., Carofano, G. C. & Kim, Y. 1986 Shock waves and phase changes in a large-heat-capacity fluid emerging from a tube. J. Fluid Mech. 166, 57–92.CrossRefGoogle Scholar
Thompson, P. A. & Lambrakis, K. C. 1973 Negative shock waves. J. Fluid Mech. 60, 187–208.CrossRefGoogle Scholar
Wegner, F. J. 1972 Corrections to scaling laws. Phys. Rev. B 5 (11), 4529.Google Scholar
Wyczalkowska, A. K. & Sengers, J. V. 1999 Thermodynamic properties of sulfurhexafluoride in the critical region. J. Chem. Phys. 111 (4), 1551–1560.CrossRefGoogle Scholar
Zamfirescu, C., Guardone, A. & Colonna, P. 2008 Admissibility region for rarefaction shock waves in dense gases. J. Fluid Mech. 599, 363–381.Google Scholar