 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 44, Issue 4 / 2009 | Next article >> |
| K. Yu. Osipenko and I. V. Simonov, "On the Jet Collision: General Model and Reduction to the Mie-Grüneisen State Equation," Mech. Solids. 44 (4), 639-648 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
4 |
Pages |
639-648 |
| DOI |
10.3103/S0025654409040141 |
| Title |
On the Jet Collision: General Model and Reduction to the Mie-Grüneisen State Equation |
| Author(s) |
K. Yu. Osipenko (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, osipenko@ipmnet.ru)
I. V. Simonov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, simonov@ipmnet.ru) |
| Abstract |
We study the stationary direct supersonic collision of jets of condensed materials. We determine the basic flow characteristics: the maximum values of pressure, temperature, and densities on outgoing shock wave fronts and at the wave stagnation and penetration points. To this end, just as in the Lavrentiev problem about the jet collision in the framework of an incompressible fluid model, it suffices to consider the flow only along the central streamline, i.e., the symmetry axis. We consider the general caloric (incomplete) equation of state and, to close the thermodynamic construction and determine the temperature dependence on the state parameters, supplement them with thermodynamic identities. We also consider the conditions on discontinuities, the Bernoulli integrals, i.e., the conservation laws, to relate the states behind the wave front and the stagnation point, and the continuity conditions at this point. Just as in the collision problem for jets of incompressible fluid, we neglect the strength, viscosity, and heat conduction. As a result, we construct a mathematical model, i.e., a system of 12 integro-algebraic equations, and propose a semi-inverse solution method, in which the system splits into separate equations. In the special case of the Mie-Grüneisen state equation, the system becomes much simpler. We perform computations and construct the dependence of maximal pressures and temperatures on the impact velocity in the range 1-20 km/s for many pairs of materials of the colliding jets. We also compare the results with the solution obtained according to the incompressible fluid model. |
| Keywords |
jet, supersonic collision, state equation, thermodynamics |
| References |
| 1. | G. Birkhoff, D. P. MacDougall, E. M. Pugh, and G. Taylor,
"Explosives with Lined Cavities,"
J. Appl. Phys.
19 (6), 563-582 (1948). |
| 2. | J. M. Walsh, R. G. Shreffler, and F. J. Willig,
"Limiting Conditions for Jet Formation in High Velocity Collisions,"
J. Appl. Phys.
24 (3), 349-359 (1953). |
| 3. | R. J. Eichelberger,
"Experimental Test of the Theory of Penetration by Metallic Jets,"
J. Appl. Phys.
27 (1), 63-68 (1956). |
| 4. | A. Tate,
"A Theory for the Deceleration of Long Rods after Impact,"
J. Mech. Phys. Solids
15 (6), 387-399 (1967). |
| 5. | M. A. Lavrent'ev,
"Cumulative Charge and Principles of Its Operation,"
Uspekhi Mat. Nauk
12 (4), 41-56 (1957)
[Russ. Math. Surv. (Engl. Transl.)]. |
| 6. | F. H. Harlow and F. E. Pracht,
"Formation and Penetration of High-Speed Collapse Jets,"
Phys. Fluids
9 (10), 1951-1959 (1966). |
| 7. | H. J. Melosh,
Impact Cratering: A Geologic Process
(Clarendon Press, Oxford Univ. Press, New York, Oxford, 1989; Mir, Moscow, 1994). |
| 8. | R. N. Keeler and E. G. Royce,
"Shock Waves in Condensed Media,"
in Physics Of High Energy Density,
Ed. by P. Caldirola and H. Knoepfel
(Academic Press, New York, 1971; Mir, Moscow, 1974)
pp. 51-150
[pp. 60-170]. |
| 9. | Ya. B. Zel'dovich and Yu. P. Raizer,
Physics of Shock Waves and High Temperature Hydrodynamical Phenomena
(Nauka, Moscow, 1966)
[in Russian]. |
| 10. | F. E. Prieto and C. Renero,
"The Equation of State of Solids,"
J. Phys. Chem. Solids
37 (2), 151-160 (1976). |
| 11. | A. Ya. Sagomonyan,
"To the Problem of Jet Interaction with Unbounded Flow
at Large Velocities at Infinity,"
Vestnik Moskov. Univ. Ser. I Mat. Mekh., No. 4, 99-104 (1967)
[Moscow Univ. Math. Bull. (Engl. Transl.)]. |
| 12. | I. V. Simonov,
"Maximum Pressure, Temperature and Resistance at Supersonic Flow of a Body by Condensed Medium,"
Intern. J. Impact Engng
20 (6-10), 743-751 (1997). |
| 13. | R. Kinslow,
High Velocity Impact Phenomena,
(Academic Press, New York, 1970; Mir, Moscow, 1973). |
| 14. | I. V. Simonov,
"On Supersonic Jet Collision,"
Dokl. Ross. Akad. Nauk
376 (1), 48-52 (2001)
[Dokl. Phys. (Engl. Transl.)
46 (1), 45-49 (2001)]. |
|
| Received |
22 September 2006 |
| Link to Fulltext |
|
| << Previous article | Volume 44, Issue 4 / 2009 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English