Skip to main content

Nonclassical Dynamics of Classical Gases

  • Chapter

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 315))

Abstract

In the present article we examine the dynamics of single-phase, equilibrium, i.e., classical, fluids in the dense gas regime. The behavior of fluids of moderately large molecular weight is seen to differ significantly from that of air and water under normal conditions. New phenomena include the formation and propagation of expansion shocks, sonic shocks, double sonic shocks, and shock-splitting. The more complicated existence conditions for shock waves are described and related to the dissipative structure. We also give a brief description of transonic flows and show that the critical Mach number for conventional blade shapes can be increased by a factor of 30–50% for these fluids.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Thompson, P. A.: A fundamental derivative in gasdynamics, Phys. Fluids, 14 (1971), 1843–1849.

    Article  MATH  Google Scholar 

  2. Borisov, A. A., AL. A. Borisov, S. S. Kutateladze and V. E. Nakorykov: Rarefaction shock wave near the critical-liquidvapour point, J. Fluid Mech., 126 (1983), 59–73.

    Article  Google Scholar 

  3. Novikov, I. I.: Existence of shock waves rarefaction, Dokl. Akad. Nauk SSSR, 59 (1948), 1545–1546.

    MATH  Google Scholar 

  4. Kahl, G. D. and D. C. Mylin: Rarefaction shock possibility in a van der Waals-Maxwell fluid, Phys. Fluids, 12 (1969), 2283–2291.

    Article  Google Scholar 

  5. Temperley, H. N. V.: The theory of propagation in liquid helium II of ‘temperature waves’ of finite amplitude, Proc. Phys. Soc. Lond., A 64 (1951), 105–114.

    Article  MATH  Google Scholar 

  6. Osborne, D. V.: Second sound in liquid helium II, Proc. Phys. Soc. Lond, A 64 (1951), 114–123.

    Article  Google Scholar 

  7. Dessler, A. J. and W. M. Fairbank: Amplitude dependence of the velocity of second sound, Phys. Rev., 104 (1956), 6–10.

    Article  Google Scholar 

  8. Turner, T. N. Second-sound shock waves and critical velocities in liquid helium II, Ph.D. Dissertation, California Institute of Technology, Pasadena, CA 1979.

    Google Scholar 

  9. Turner, T. N.: New experimental results obtained with second-sound shock waves, Physica, 107B (1981), 701–702.

    Google Scholar 

  10. Atkin, R. J., and N. Fox: The dependence of thermal shock wave velocity on heat flux in Helium II, J. Phys. C: Solid State Phys., 17 (1984), 1191–1198.

    Article  Google Scholar 

  11. Torczynski, J. R. Nonlinear fourth sound, Wave Motion, 7 (1985), 487–501.

    Article  MATH  Google Scholar 

  12. Garrett, S. Nonlinear distortion of 4th sound in superfluid 3He-B, J. Acoust. Am., 60 (1981), 139–144.

    Article  Google Scholar 

  13. Bezzerides, B., D. W. Forslund, and E. L. Lindman: Existence of rarefaction shocks in a laser-plasma corona, Phys. Fluids, 21 (1978), 2179–2185.

    Article  MATH  MathSciNet  Google Scholar 

  14. Nariboli, G. A. and W. C. Lin: A new type of Burgers’ equation, ZAMM, 53 (1973), 505–510.

    Article  MATH  Google Scholar 

  15. Kynch, G. J.: A theory of sedimentation, Trans. Faraday Soc., 48 (1952), 166–176.

    Article  Google Scholar 

  16. Shannon, P. T. and E. M. Tory: Settling of slurries, Ind. Engng Chem, 57 (1965), 18–25.

    Google Scholar 

  17. Amberg, G., A. A. Dahlkild, F. H. Bark, and D. S. Henningson: On time-dependent settling of a dilute suspension in a rotating conical channel, J. Fluid Mech., 166 (1986), 473–502.

    Article  MATH  Google Scholar 

  18. Auzerais, F. M., R. Jackson,and W. B. R.ssel: The resolution of shocks and the effects of compressible sediments in transient settling, J. Fluid Mech., 195 (1988), 437–462.

    Google Scholar 

  19. Thompson, P. A., G. C. Carafano, and Y. G. Kim: Shock waves and phase changes in a large-heat-capacity fluid emerging from a tube, J. Fluid Mech., 166 (1986), 57–92.

    Article  MATH  Google Scholar 

  20. Dettleff, G., G. E. A. Meier, H. D. Speckmann, P. A. Thompson, and C. Yoon: Experiments in shock liquefaction, In Proc. 13th Intl. Symp. on Shock Tubes and Waves (ed. C. E. Trainor zhaohuan J. G. Hall ), (1982), 716–723.

    Google Scholar 

  21. Thompson, P. A. and Y. G. Kim: Direct observation of shock splitting in a vapor-liquid system, Phys. Fluids, 26 (1986), 3211–3215.

    Article  Google Scholar 

  22. Thompson, P. A., H. Chaves, G. E. A. Meier, Y. G. Kim, and H. D. Speckmann: Wave splitting in a fluid of large heat capacity, J. Fluid Mech, 185 (1987), 385–414.

    Article  Google Scholar 

  23. Zel’dovich, Ya. B. and Yu. P. Raizer: Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, Vol. 2, Academic 1967.

    Google Scholar 

  24. McQueen, R. G. and S. P. Marsh: Hugoniots of graphites of various initial densitites and the equation of state of carbon, in: Behavior of Dense Media Under High Dynamic Pressures, Gordon and Breach 1968, 207–216.

    Google Scholar 

  25. Gust, W. H. and D. A. Young: High Pressure Science and Technology, Vol. I, Plenum 1979.

    Google Scholar 

  26. Ivanov, A. G. and S. A. Novikov: Shock rarefaction waves in iron and steel, Zh. Eksp. Teor. Fiz, 40 (1961), 1880–1882.

    Google Scholar 

  27. Erkman, J. 0. Smooth spalls and the polymorphism in iron, J. Appl. Phys, 32 (1961), 939–944.

    Article  Google Scholar 

  28. Kolsky, H. Production of tensile shock waves in stretched natural rubber, Nature, 224 (1969), 1301.

    Google Scholar 

  29. Barker, L. M. and R. E. Hollenbach: Shock wave studies of PMMA, fused silica, and sapphire, J. Appl. Phys, 42 (1970), 42084226.

    Google Scholar 

  30. Bains, J. A. and M. A. Breazeale: Nonlinear distortion of ultrasonic waves in solids: approach of a stable backward sawtooth, J. Acoustic Soc. Amer., 57 (1975), 745–746.

    Article  Google Scholar 

  31. Conner, M. P. Shear Wave Measurements to Determine Nonlinear Elastic Response of Fused Silica Under Shock Loading, MS Thesis, Washington State University, Pullman, Washington.

    Google Scholar 

  32. Lee-Bapty, I. P. Nonlinear wave propagation in stratified and viscoelastic media, Ph.D. dissertation, Leeds University, England, 1981.

    Google Scholar 

  33. Morris, F. E. and G. A. Nariboli: Photoelastic waves, Int. J. Engng. Sci., 10 (1972), 765–774.

    Article  MATH  MathSciNet  Google Scholar 

  34. Kakutani, T. and N. Yamasaki: Solitary waves on a two-layer fluid, J. Phys. Soc. Japan, 45 (1978), 674–679.

    Article  Google Scholar 

  35. Helfrich, K. R., W. K. Melville, and J. W. Miles: On interfacial waves over slowly varying topography, J. Fluid Mech., 149 (1984), 305–317.

    Article  MATH  MathSciNet  Google Scholar 

  36. Bethe, H. A. The theory of shock waves for an arbitrary equation of state, Office Sci. Res. zhaohuan Dev. Rep. 545, Washington, D.C. 1942.

    Google Scholar 

  37. Hayes, W. D.: Gasdynamic discontinuities, in: Princeton Series on High Speed Aerodyanmics and Jet Propulsion, Princeton University Press 1960.

    Google Scholar 

  38. Beyer, R. T.: Nonlinear Acoustics, Naval Ship Systems Command, Dept. of the Navy, Washington, D. C. 1974.

    Google Scholar 

  39. Thompson, P. A.: Compressible Fluid Dynamics, McGraw-Hill, New York 1972.

    MATH  Google Scholar 

  40. Zel’dovich, Ya. B.: On the possibility of rarefaction shock waves, Zh. Eksp. Teor. Fiz., 4 (1946), 363–364.

    Google Scholar 

  41. Thompson, P. A. and K. Lambrakis: Negative shock waves, J. Fluid Mech., 60 (1973), 187–208.

    Article  MATH  Google Scholar 

  42. Lambrakis, K. and P. A. Thompson: Existence of real fluids with a negative fundamental derivative r, Phys. Fluids, 5 (1972), 933–935.

    Article  Google Scholar 

  43. Cramer, M. S.: Negative nonlinearity in selected fluorocarbons, Phys. Fluids, A. 1 (1989), 1894–1897.

    Article  Google Scholar 

  44. Martin, J. J. and Y. C. Hou: Development of an equation of state for gases, AIChE J., 1 (1955), 142–151.

    Article  Google Scholar 

  45. Rihani, D. N. and L. K. Doraiswany: Estimation of heat capacity of organic compounds from group contributions, Ind. Engr. Chem. Fund., 4 (1965), 17–21.

    Article  Google Scholar 

  46. Burnside, B. M.: Thermodynamic properties of five halogenated hydrocarbon vapour power cycle working fluids, J. Mechanical Engineering Science, 15 (1973), 132–143.

    Article  Google Scholar 

  47. Richter, H. R. D. and B. M. Burnside: A general programme for producing pressure-enthalpy diagram, J. Mechanical Engineering Science, 17 (1975), 31–39.

    Article  Google Scholar 

  48. Cramer, M. S. and R. Sen: Shock formation in fluids having embedded regions of negative nonlinearity, Phys. Fluids, 29 (1986), 2181–2191.

    Article  MATH  Google Scholar 

  49. Cramer, M. S. and A. Kluwick: On the propagation of waves exhibiting both positive and negative nonlinearity, J. Fluid Mech., 142 (1984), 9–37.

    Article  MATH  MathSciNet  Google Scholar 

  50. Cramer, M. S. and R. Sen: Exact solutions for sonic shocks in van der Waals gases, Phys. Fluids, 30 (1987), 377–385.

    Article  MATH  Google Scholar 

  51. Gilbarg, D.: The existence and limit behavior of the one-dimensional shock layer, Am. J. Maths, 73 (1951), 256–274.

    Article  MATH  MathSciNet  Google Scholar 

  52. Cramer, M. S.: Shock splitting in single-phase gases, J. Fluid Mech., 199 (1989), 281–296.

    Article  MATH  MathSciNet  Google Scholar 

  53. Menikoff, R. and B. Plohr: Riemann problem for fluid flow of real materials, Reviews of Modern Physics, 61 (1989), 75–130.

    Article  MATH  MathSciNet  Google Scholar 

  54. Lax, P. D.: Shock waves and entropy, in: Contributions to Nonlinear Functional Analysis (ed. E. H. Zarantonello ), Academic 1971.

    Google Scholar 

  55. Cramer, M. S., A. Kluwick, L. T. Watson, and W. Pelz: Dissipative waves in fluids having both positive and negative nonlinearity, J. Fluid Mech., 169 (1986), 323–336.

    Article  MATH  Google Scholar 

  56. Cramer, M. S.: Structure of weak shocks in fluids having embedded regions of negative nonlinearity, Phys. Fluids, 30 (1987), 3034–3044.

    Article  Google Scholar 

  57. Taylor, G. I.: The conditions necessary for discontinuous motion in gases, Proc. R. Soc. Lond., A 84 (1910), 371–377.

    Article  MATH  Google Scholar 

  58. Lee-Bapty, I. P. and D. G. Crighton: Nonlinear wave motion governed by the modified Burger’s equation, Phil. Trans. R. Soc. Lond., A 323 (1987), 173–209.

    Article  MATH  MathSciNet  Google Scholar 

  59. Reid, R. C. J. M. Prausnitz, and B. E. Poling: The Properties of Gases and Liquids, 4th Edition, Wiley 1987.

    Google Scholar 

  60. Landau, L. D. and E. M. Lifshitz: Fluid Mechanics, Addison-Wesley 1959.

    Google Scholar 

  61. Cramer, M. S. Nonclassical Dynamics of Classical Gases, Virginia Polytechnic Institute and State University Engineering Report #VPI-E-89–20, Blacksburg, VA 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Wien

About this chapter

Cite this chapter

Cramer, M.S. (1991). Nonclassical Dynamics of Classical Gases. In: Kluwick, A. (eds) Nonlinear Waves in Real Fluids. International Centre for Mechanical Sciences, vol 315. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2608-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2608-0_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82277-7

  • Online ISBN: 978-3-7091-2608-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics