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Three-dimensional shock tube flows for dense gases

Published online by Cambridge University Press:  04 July 2007

ALBERTO GUARDONE
ALBERTO GUARDONE*
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy
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Abstract

The formation process of a non-classical rarefaction shock wave in dense gas shock tubes is investigated by means of numerical simulations. To this purpose, a novel numerical scheme for the solution of the Euler equations under non-ideal thermodynamics is presented, and applied for the first time to the simulation of non-classical fully three-dimensional flows. Numerical simulations are carried out to study the complex flow field resulting from the partial burst of the shock tube diaphragm, a situation that has been observed in preliminary trials of a dense gas shock tube experiment. Beyond the many similarities with the corresponding classical flow, the non-classical wave field is characterized by the occurrence of anomalous compression isentropic waves and rarefaction shocks propagating past the leading rarefaction shock front. Negative mass flow through the rarefaction shock wave results in a limited interaction with the contact surface close to the diaphragm, a peculiarity of the non-classical regime. The geometrical asymmetry does not prevent the formation of a single rarefaction shock front, though the pressure difference across the rarefaction wave is predicted to be weaker than the one which would be obtained by the complete burst of the diaphragm.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 423 - 442
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Argrow, B. M. 1996 Computational analysis of dense gas shock tube flow. Shock Waves 6, 241–248.Google Scholar
Bethe, H. A. 1942 The theory of shock waves for an arbitrary equation of state. Tech. Rep. 545. Office of Scientific Research and Development.Google Scholar
Blumen, W., Drazin, P. G. & Billings, D. F. 1975 Shear layer instability of an inviscid compressible fluid. Part 2. J. Fluid Mech. 71, 305–316.CrossRefGoogle Scholar
Borisov, A. A., Borisov, A normalfont, l. A., Kutateladze, S. S. & Nakoryakov, V. E. 1983 Rarefaction shock waves near the critical liquid–vapour 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.CrossRefGoogle Scholar
Callen, H. B. 1985 Thermodynamics and an Introduction to Thermostatistics, 2nd edn. Wiley.Google Scholar
Chang, K.-S. & Kim, J.-K. 1995 Numerical investigation of inviscid shock wave dynamics in an expansion tube. Shock Waves 5, 33–45.Google Scholar
Chatterjee, A. 1999 Shock wave deformation in shock–vortex interactions. Shock Waves 9, 95–105.Google Scholar
Colonna, P. & Silva, P. 2003 Dense gas thermodynamic properties of single and multicomponent fluids for fluid dynamics simulations. Trans. A SME I: J. Fluids Engng 125, 414–427.Google Scholar
Cramer, M. S. 1989 Negative nonlinearity in selected fluorocarbons. Phys. Fluids 1 (11), 1894–1897.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
Drazin, P. G. & Davey, A. 1977 Shear layer instability of an inviscid compressible fluid. Part 3. J. Fluid Mech. 82, 255–260.Google Scholar
Emanuel, G. 1994 Assessment of the Martin–Hou equation for modelling a nonclassical fluid. Trans. ASME I: J. Fluids Engng 116, 883–884.Google Scholar
Fergason, S. H. 2001 Dense gas shock tube: design and analysis. PhD thesis, University of Colorado, Boulder.Google Scholar
Fergason, S. H., Ho, T. L., Argrow, B. M. & Emanuel, G. 2001 Theory for producing a single-phase rarefaction shock wave in a shock tube. J. Fluid Mech. 445, 37–54.CrossRefGoogle Scholar
Fergason, S. H., Guardone, A. & Argrow, B. M. 2003 Construction and validation of a dense gas shock tube. J. Thermophys. Heat Tr 17, 326–333.Google Scholar
Glass, I. I. & Sislian, J. P. 1994 Nonstationary Flows and Shock Waves. Clarendon.Google Scholar
Godlewski, E. & Raviart, P. A. 1994 Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer.Google Scholar
Guardone, A. 2001 Nonclassical gasdynamics: thermodynamic modeling and numerical simulation of multidimensional flows of BZT fluids. PhD thesis, Politecnico di Milano, Italy.Google Scholar
Guardone, A. & Argrow, B. M. 2005 Nonclassical gasdynamic region of selected fluorocarbons. Phys. Fluids 17 (11), 116102–1–17.Google Scholar
Guardone, A. & Vigevano, L. 2002 Roe linearization for the van der Waals gas. J. Comput. Phys. 175, 50–78.Google 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
Harten, A. & Hyman, J. M. 1983 Self adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comput. Phys. 50, 253–269.Google Scholar
Hayes, W. 1960 The basic theory of gasdynamic discontinuities. In Fundamentals of Gasdynamics (ed. Emmons, H. W.), High Speed Aerodynamics and Jet Propulsion, vol. 3, pp. 416–481. Princeton University Press.Google Scholar
Ivanov, A. & Novikov, S. 1961 Rarefaction shock waves in iron and steel. Sov. Phys. J. Exp. Theor. Phys. 40, 1880–1882.Google Scholar
Jiang, Z., Takayama, K., Babinsky, H. & Meguro, T. 1997 Transient shock-wave flows in tubes with a sudden change in cross-section. Shock Waves 7, 151–162.Google Scholar
Lambrakis, K. C. & Thompson, P. A. 1972 Existence of real fluids with a negative fundamental derivative. Phys. Fluids 15 (5), 933–935.Google Scholar
vanLeer, B. Leer, B. 1974 Towards the ultimate conservative difference scheme II. Monotoniticy and conservation combined in a second order scheme. J. Comput. Phys. 14, 361–370.Google Scholar
Lu, F. & Kim, C. H. 2000 Detection of wave propagation by cross correlation, In 38th Aerospace Sciences Meeting and Exhibit, Reno, NV, paper 2000–0676.Google Scholar
Martin, J. J. & Hou, Y. 1955 Development of an equation of state for gases. AIChE J. 1, 142–151.Google Scholar
Martin, J. J., Kapoor, R. M. & DeNevers, N. Nevers, N. 1958 An improved equation of state. AIChE J. 5, 159–160.Google Scholar
Menikoff, R. & Plohr, B. J. 1989 The Riemann problem for fluid flow of real material. Rev. Mod. Phys. 61, 75–130.Google Scholar
Perry, R. H. & Green, D. 1984 Perry's Chemical Engineers' Handbook, 6th edn. McGraw–Hill.Google Scholar
Persico, G., Gaetani, P. & Guardone, A. 2005 Dynamic calibration of fast-response probes in low-pressure shock tubes. Meas. Sci. Technol. 16, 1751–1759.Google Scholar
Petrie-Repar, P. & Jacobs, P. A. 1998 A computational study of shock speeds in high-performance shock tubes. Shock Waves 8, 79–91.Google Scholar
Rider, W. J. & Bates, J. W. 2001 A high-resolution Godunov method for modeling anomalous fluid behaviour. In Godunov Methods: Theory and Application. (ed. Toro, E. F.). Kluwer/Plenum Academic.Google Scholar
Roe, P. L. 1981 Approximate R iemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43, 357–372.Google Scholar
Selmin, V. 1993 The node-centred finite volume approach: bridge between finite differences and finite elements. Comput. Meths. Appl. Mech. Engng 102, 107–138.Google Scholar
Shu, C.-W. 1988 Total-variation-diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9, 1073–1084.Google Scholar
Skews, B. 1967 The shape of a diffracting shock wave. J. Fluid Mech. 29, 297–304.Google Scholar
Sun, M. & Takayama, K. 2003 Vorticity production in shock diffraction. J. Fluid Mech. 478, 237–256.Google Scholar
Thompson, P. A. 1971 A fundamental derivative in gas dynamics. Phys. Fluids 14, 1843–1849.Google Scholar
Thompson, P. A. & Lambrakis, K. C. 1973 Negative shock waves. J. Fluid Mech. 60, 187–208.Google Scholar
Thompson, P. A. & Loutrel, W. F. 1973 Opening time of brittle shock-tube diaphragms for dense fluids. Rev. Sci. Instrum. 44, 1436–1437.Google Scholar
Thompson, P. A., Carofano, G. A. & Kim, Y. 1986 Shock waves and phase changes in a large heat capacity fluid emerging from a tube. J. Fluid Mech. 166, 57–96.Google Scholar
Weyl, H. 1949 Shock waves in arbitrary fluids. Commun. Pure Appl. Maths. 2, 102–122.CrossRefGoogle Scholar
Zamfirescu, C., Guardone, A. & Colonna, P. 2006 Preliminary design of the FAST dense gas Ludwieg tube. AIAA Paper. 2006–3249.Google Scholar
Zel'dovich, Y. B. 1946 On the possibility of rarefaction shock waves. Sov. Phys., J. Exp. Theor. 4, 363–364.Google Scholar