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Transverse ionizing MHD detonation waves. Part 1. Structure, Hugoniot curves and Chapman–Jouguet limit

Published online by Cambridge University Press:  13 March 2009

Shimshon Frankenthal ,
Allan B. Friedland  and
Saul Abarbanel
Shimshon Frankenthal
Affiliation:
American Science and Engineering, Cambridge, Massachusetts
Allan B. Friedland
Affiliation:
American Science and Engineering, Cambridge, Massachusetts
Saul Abarbanel
Affiliation:
University of Tel Aviv
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Abstract

The structure and jump relations across a one-dimensional ionizing magnetohydrodynamic detonation wave with transverse electromagnetic fields are studied. It is shown that the downstream point in a three-dimensional phase space, constructed from the gas velocity, magnetic field and burned fraction of gas, is of a singular nature and leads to a unique solution. In the zero viscosity, infinite transitional electrical conductivity limit, the ‘fast wave’ degenerates into a pre-compression ionizing shock followed by a perfectly-conducting deflagration zone, and the ‘slow wave’ degenerates into an ordinary gas dynamic pre-compression shock followed by a deflagration zone in which the transition to perfect conductivity occurs. In both cases, a relationship is derived connecting the electric field (which cannot be arbitrarily imposed) and both the upstream variables and parameters describing the ionization transition point. This relationship must be appended to the Rankine–Hugoniot jump relations and a Chapman-Jouguet condition (or its equivalent) to provide a unique relationship between the assumed unknown shock-speed and the downstream state as a function of the assumed known upstream state.

The ionization temperature is found to affect the jump and determines the electric field developed upstream. It is found that the Hugoniot consists of two branches: a ‘normal’ one which retains the character of an ordinary detonation Hugoniot, and an ‘anomalous’ one which does not. Although both branches represent detonations endowed with a transition structure, it is suggested that ‘anomalous’ detonations are either unstable or non-evolutionary. The evolution of the topology of the Hugoniot, as a function of the upstream magnetic field and ionizing temperature, is studied and correlated with Chapman-Jouguet propagations. Results are presented for the Chapman-Jouguet jump values and detonation speeds, as functions of dimensionless parameters that represent the upstream magnetic and electric field. Relationships between this upstream electric field and ionization temperature is derived and found to differ according as ionization precedes or follows ignition.

Type
Research Article
Information
Journal of Plasma Physics , Volume 10 , Issue 1 , August 1973 , pp. 53 - 87
Copyright
Copyright © Cambridge University Press 1973

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References

REFERENCES

Abarbanel, S. & Frankenthal, S. 1969 Israel J. Tech. 7, 465.Google Scholar
Chu, C. K. 1964 Phys. Fluids, 7, 1349.CrossRefGoogle Scholar
Courant, R. & Fredricks, K. O. 1956 Supersonic Flow and Shock Waves. Interscience.Google Scholar
Cowley, M. D. 1967 J. Plasma Phys. 1, 37.CrossRefGoogle Scholar
Gordon, A. R. & Helliwell, J. B. 1967 J. Plasma Phys. 1, 219.CrossRefGoogle Scholar
Gross, R. A. 1965 Rev. Mod. Phys. 37, 724.CrossRefGoogle Scholar
Hartman, P. 1964 Ordinary Differential Equations. Wiley.Google Scholar
Helliwell, J. B. 1962 J. Fluid Mech. 14, 405.CrossRefGoogle Scholar
Helliwell, J. B. 1963 J. Fluid Mech. 16, 243.CrossRefGoogle Scholar
Helliwell, J. B. & Pack, D. C. 1962 Phys. Fluids, 5, 738.CrossRefGoogle Scholar
Jameson, R. L., Lukasik, S. J. & Pernick, B. J. 1964 J. Appl. Phys. 35, 714.CrossRefGoogle Scholar
Kulikoviskii, A. G. & Lyubimov, G. A. 1960 a Soviet Phys. Doklady, 4, 1185.Google Scholar
Kulikoviskii, A. G. & Lyubimov, G. A. 1960 b Soviet Phys. Doklady, 4, 1195.Google Scholar
Ludford, G. S. S. 1959 J. Fluid Mech. 5, 67.CrossRefGoogle Scholar
Lyubimov, G. A. 1959 Soviet Phys. Doklady, 4, 510.Google Scholar
Marshall, W. 1955 Proc. Roy. Soc. A 233, 367.Google Scholar
McKinnon, C. N. 1967 Pulsed electrical power from magnetically loaded explosives. 8th Symp. on Engineering Aspects of MHD.Google Scholar
Stebbins, C. F. & Vlases, G. C. 1968 J. Plasma Phys. 2, 633.CrossRefGoogle Scholar
Taylor, G. 1950 Proc. Roy. Soc. A200, 235.Google Scholar
Tendys, J. 1969 Plasma Phys. 11, 223.CrossRefGoogle Scholar
Zeldovich, I. B. & Kompaneets, A. S. 1960 Theory of Detonation. Academic.Google Scholar
Zhilin, I. L. 1960 Prikl. Mat. Mekh. 24, 543.Google Scholar