Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T09:51:16.914Z Has data issue: false hasContentIssue false
  • English
  • Français

Computational analysis of experiments on shock detachment in hypersonic flow of nitrogen and carbon dioxide over a wedge

Published online by Cambridge University Press:  08 November 2022

H.G. Hornung Open the ORCID record for H.G. Hornung [Opens in a new window] ,
R.J. Gollan Open the ORCID record for R.J. Gollan [Opens in a new window]  and
P.A. Jacobs
H.G. Hornung*
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
R.J. Gollan
Affiliation:
Centre for Hypersonics, School of Mechanical and Mining Engineering, The University of Queensland, St. Lucia, Queensland 4067, Australia
P.A. Jacobs
Affiliation:
Centre for Hypersonics, School of Mechanical and Mining Engineering, The University of Queensland, St. Lucia, Queensland 4067, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

One of the most dramatic effects of vibrational and chemical non-equilibrium in hypersonic flows occurs in the bow-shock detachment process in flow over a wedge. This was shown theoretically and in reflected shock tunnel experiments by Hornung & Smith (J. Fluid Mech., vol. 93, 1979, pp. 225–239). In the present work, the effect is first demonstrated by computation of two-dimensional non-equilibrium flows. The effect of the finite transverse extent of the wedge is then studied by three-dimensional computations of non-relaxing flows. An analytical formula is obtained that gives the shock detachment distance of a finite wedge for ideal-gas and equilibrium flows. In the experiment, the finite transverse extent of the wedge competes with the non-equilibrium effects, as each introduces a new length scale. The carbon dioxide and nitrogen flows of the experiment are therefore computed in three dimensions and with two-temperature chemistry accounting for vibrational and chemical non-equilibrium. In the case of nitrogen flow, the agreement between experiment and computation is not good, the experimental detachment distance being larger. A number of possible reasons are quantitatively examined. A conclusive resolution of the discrepancy is considered to require a repeat of the experiment with more accurately characterized conditions. In the case of the carbon dioxide experiments, the computed results agree remarkably well with experiment. This is partially due to the fact that the condition is very close to equilibrium, where the sensitivity of the detachment process to relaxation effects is small. The analytical expression for the dimensionless detachment distance agrees very well with all the three-dimensional computations of non-relaxing flows.

JFM classification

Compressible Flows: Hypersonic Flow Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 951 , 25 November 2022 , A6
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

van Albada, G.D., van Leer, B. & Roberts, W.W. 1981 A comparative study of computational methods in cosmic gas dynamics. ICASE Report 81-24. NASA.Google Scholar
Belouaggadia, N., Olivier, H. & Brun, R. 2008 Numerical and theoretical study of shock stand-off distance in non-equilibrium flows. J. Fluid Mech. 607, 167–197.CrossRefGoogle Scholar
Bondar, Y.A., Markelov, G.N., Gimelshein, S.F. & Ivanov, M.S. 2005 DSMC study of shock-detachment process in hypersonic chemically reacting flow. Tech. Rep. Institute of Theoretical and Applied Mechanics, Novosibirsk.CrossRefGoogle Scholar
Candler, G.V. 2010 Comparison of CFD and theoretical post-shock gradients in hypersonic flow. Prog. Aerosp. Sci. 46, 81–88.Google Scholar
Chapman, C.J. 2000 High Speed Flow. Cambridge Texts in Applied Mathematics. Cambridge University Press.Google Scholar
Chaudry, R.S., Boyd, I.D., Torres, E., Schwartzentruber, T.E. & Candler, G.V. 2020 Implementation of a chemical kinetics model for hypersonic flows in air for high-performance CFD. AIAA Paper 2020-2191.Google Scholar
Ebrahim, N.A. & Hornung, H.G. 1973 Nonequilibrium nozzle expansions of carbon dioxide from a high-enthalpy reservoir. AIAA J. 11 (10), 1369–1370.CrossRefGoogle Scholar
Gibbons, N.N., Damm, K.A., Gollan, R.J. & Jacobs, P.A. 2022 Eilmer: an open-source multi-physics hypersonic flow solver. Comput. Phys. Commun. 282, 108551.CrossRefGoogle Scholar
Girard, J.J., Finch, P.M., Strand, C.L., Hanson, R.K., Yu, W.M., Austin, J.M. & Hornung, H.G. 2021 Measurements of reflected shock tunnel freestream nitric oxide temperatures and partial pressure. AIAA J. 59, 5266–5275.CrossRefGoogle Scholar
Gnoffo, P.A., Gupta, R.N. & Shinn, J.L. 1989 Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium. NASA Tech. Paper 2867.Google Scholar
Gollan, R.J. & Jacobs, P.A. 2013 About the formulation, verification and validation of the hypersonic flow solver Eilmer. Intl J. Numer. Meth. Fluids 73, 19–57.CrossRefGoogle Scholar
Gordon, S. & McBride, B.J. 1994 Computer program for calulation of complex chemical equilibrium and applications. NASA Tech. Rep. 1311.Google Scholar
Hanson, R.K. & Baganoff, D. 1972 Shock tube study of nitrogen dissociation rates using pressure measurements. AIAA J. 10, 211–216.CrossRefGoogle Scholar
Hayes, W.D. & Probstein, R.F. 1959 Hypersonic Flow Theory. Academic Press.Google Scholar
Hornung, H.G. 1972 Non-equilibrium flow of nitrogen over spheres and circular cylinders. J. Fluid Mech. 53, 149–176.CrossRefGoogle Scholar
Hornung, H.G. 2010 Deriving features of reacting hypersonic flow from gradients at a curved shock. AIAA J. 48, 287–296.CrossRefGoogle Scholar
Hornung, H.G. 2021 Shock detachment and drag in hypersonic flow over wedges and circular cylinders. J. Fluid Mech. 915, A100.CrossRefGoogle Scholar
Hornung, H.G. & Schoeler, H. 1985 Three-dimensional effects in shock detachment from a wedge. AIAA J. 23, 1121–1122.CrossRefGoogle Scholar
Hornung, H.G. & Smith, G.H. 1979 The influence of relaxation on shock detachment. J. Fluid Mech. 93, 225–239.Google Scholar
Jacobs, P.A. 1991 Single-block Navier–Stokes integrator. ICASE Interim Report 18. NASA.Google Scholar
Kewley, D.J. & Hornung, H.G. 1974 Free-piston shock-tube study of nitrogen dissociation. Chem. Phys. Lett. 25, 531–539.CrossRefGoogle Scholar
Knab, O., Frühauf, H.-H. & Messerschmid, E.W. 1995 Theory and validation of the physically consistent coupled vibration-chemistry-vibration model. J. Thermophys. Heat Transfer 9 (2), 219–226.CrossRefGoogle Scholar
Macdonald, R.L., Torres, E., Schwartzentruber, T.E. & Panesi, M. 2020 State-to-state master equation and direct molecular simulation study of energy transfer and dissociation for the n2-N system. J. Phys. Chem. A 124, 6986–7000.CrossRefGoogle ScholarPubMed
Maus, J.R., Griffith, B.J., Szema, K.Y. & Best, J.T. 1984 Hypersonic mach number and real gas effects on space shuttle orbiter aerodynamics. J. Spacecr. Rockets 21 (2), 136–141.CrossRefGoogle Scholar
Millikan, R.C. & White, D.R. 1963 Systematics of vibrational relaxation. J. Chem. Phys. 39 (12), 3209–3213.CrossRefGoogle Scholar
Park, C. 1988 Assessment of a two-temperature kinetic model for dissociating and weakly ionizing nitrogen. J. Thermophys. Heat Transfer 2 (1), 8–16.CrossRefGoogle Scholar
Park, C. 1993 Review of chemical-kinetic problems of future NASA missions, I: Earth entries. J. Thermophys. Heat Transfer 7, 385–429.CrossRefGoogle Scholar
Park, C. 2010 The limits of two-temperature model. AIAA Paper 2010-911.Google Scholar
Park, C., Howe, J.T., Jaffe, R.L. & Candler, G.V. 1994 Review of chemical-kinetic problems of future NASA missions, II: Mars entries. J. Thermophys. Heat Transfer 8 (1), 9–23.CrossRefGoogle Scholar
Stulov, V.P. 1969 Similarity law for supersonic flow past blunt bodies. Izv. AN SSSR, Mechanika Zhidkosti i Gaza 4, 142–146.Google Scholar
Sudani, N. & Hornung, H.G. 1998 Gasdynamical detectors of driver-gas contamination in a high-enthalpy shock tunnel. AIAA J. 36, 313–319.CrossRefGoogle Scholar
Wada, Y. & Liou, M.S. 1994 A flux splitting scheme with high-resolution and robustness for discontinuities. AIAA Paper 94-0083.Google Scholar
Wada, Y. & Liou, M.S. 1997 An accurate and robust flux splitting scheme for shock and contact discontinuities. SIAM J. Sci. Comput. 18, 633–657.CrossRefGoogle Scholar
Wen, C.-Y. & Hornung, H.G. 1995 Non-equilibrium dissociating flow over spheres. J. Fluid Mech. 299, 389–405.Google Scholar