- Access by Xinjiang University
Normal shocks with high upstream pressure
Phys. Rev. Fluids 3, 093401 – Published 17 September, 2018
DOI: https://doi.org/10.1103/PhysRevFluids.3.093401
Abstract
A normal compressive shock wave with supercritical upstream thermodynamic conditions is analyzed using the Soave-Redlich-Kwong equation of state (EoS) relations for real-gas density, enthalpy, and entropy for argon, nitrogen, oxygen, and carbon dioxide. Upstream pressure and temperature vary from 10 to 500 bar and 160 to 800 K. At high pressures, the flow does not follow the calorically perfect-gas behavior. For the perfect gas, the enthalpy and ratio of pressure-to-density are directly proportional to the square of the sound speed, allowing direct substitution of the sound speed in the conservation equations. A thermodynamic function is identified for the real-gas sound speed which is shown to remain as the proper characteristic speed. Although the sound speed does not emerge directly from the conservation equations as it does for a perfect gas, the shock speed goes to this limiting value as shock strength goes to zero. For the real gas, modifications are obtained for Prandtl's relation and the Rankine-Hugoniot relation. The modified real-gas Riemann invariants are constructed and discussed for application to weak shocks. A foundation is presented for use with other cubic EoS, multicomponent flows, and/or for more complex flow configurations. Near-similar solutions are developed by normalization of the variables using critical values for pressure and temperature. These exact solutions are compared with approximate solutions obtained via a linearization of the cubic EoS for deviation from ideal-gas behavior.
Physics Subject Headings (PhySH)
Article Text
References (13)
- Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock waves and High-Temperature Hydrodynamic Phenomena, edited by W. D. Hayes and R. F. Probstein (Dover, Mineola, NY, 2002).
- R. Menikoff and B. J. Plohr, The Riemann problem for fluid flow of real materials, Rev. Mod. Phys. 61, 75 (1989).
- L. N. Tao, Gas dynamic behavior of real gases, J. Aeronaut. Sci. 22, 763 (1955).
- J. L. Wilson and J. D. Regan, A simple method for real gas flow calculations, Current Paper 772, UK Ministry of Aviation, Aeronautical Research Council, S. O. Code Number 23-9015-72 (1965), http://naca.central.cranfield.ac.uk/reports/arc/cp/0772.pdf.
- D. A. Kouremenos and K. A. Antonopoulos, Real gas normal shock waves with the Redlich-Kwong equation of state, Acta Mech. 76, 223 (1989).
- R. Arina, Numerical simulation of near-critical fluids, Appl. Numer. Math. 51, 409 (2004).
- E. Jassim, M. Abedinzadegan Abdi, and Y. Muzychka, Computational fluid dynamics study for flow of natural gas through high-pressure supersonic nozzles: Part 1. Real gas effects and shockwave, Pet. Sci. Technol. 26, 1757 (2008).
- W. A. Sirignano, Compressible flow at high upstream pressure with linear equation of state, J. Fluid Mech. 843, 244 (2018).
- A. Kluwick, Transonic nozzle flow of dense gases, J. Fluid Mech. 247, 661 (1993).
- B. E. Poling, J. M. Prausnitz, and J. P. O'Connell, The Properties of Gases and Liquids, 5th ed. (McGraw Hill, New York, 2001).
- H. W. Liepmann and A. Roshko, Elements of Gasdynamics (Wiley, London, 1957).
- J. Lighthill, Waves in Fluids (Cambridge University Press, Cambridge, 1978).
- D. M. Dattelbaum, P. M. Goodwin, D. B. Garcia, R. L. Gustavsen, J. M. Lang, T. D. Aslam, S. A. Sheffield, L. L. Gibson, and J. S. Morris, Shockwave compression of Ar gas at several initial densities, Shock Compression of Condensed Matter - 2015: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter, AIP Conf. Proc. 1793 (AIP, New York, 2017), p. 090004.
