 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| A.N. Kraiko and N.I. Tillyayeva, "The flow of a combustible mixture with a Chapman-Jouguet detonation wave around a cone," J. Appl. Math. Mech. 77 (1), 1-8 (2013) |
| Year |
2013 |
Volume |
77 |
Issue |
1 |
Pages |
1-8 |
| Title |
The flow of a combustible mixture with a Chapman-Jouguet detonation wave around a cone |
| Author(s) |
A.N. Kraiko (Moscow, Russia, akraiko@ciam.ru)
N.I. Tillyayeva (Moscow, Russia) |
| Abstract |
The flow around a circular cone under conditions of Chapman-Jouguet (CJ) self-sustaining detonation is investigated in the classical formulation of an infinitely thin detonation wave (DW) in an inviscid and non-heat conducting combustible mixture. Such conditions for flow around a cone are remarkable in several respects. In 1959, Chernyi and Kvashnina had already shown that, for supersonic flows of a combustible mixture around a cone, CJ detonation, as in the case of a wedge, is not only possible for a strictly fixed cone angle (the "CJ" angle) but also for angles smaller than this (including a zero angle, that is, when there is no cone). In the case of flow around a wedge with an angle that is less than the corresponding CJ angle, a centred rarefaction wave that turns the supersonic flow in the required direction borders on the CJ DW. In the case of a cone, a conical rarefaction flow also borders on the CJ DW. However, if, in the plane case, a uniform supersonic flow adjoins the centred rarefaction wave along its boundary C+-characteristic then the conical rarefaction flow is bounded by a conical shock wave (SW), bordered up to the surface of the cone by a conical compression flow. Only for a zero cone angle does the SW degenerate into the C+-characteristic and the conical compression flow degenerates into a uniform supersonic flow. The configuration obtained in the general case became the first example of a self-similar solution with two SW of "one family" (the first of them is the DW) diverging from a single point. The results of calculations carried out in this paper with the construction of streamlines and the characteristics of the two families give a fairly complete representation of the above mentioned features of the flows considered. |
| Received |
30 August 2012 |
| Link to Fulltext |
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