Properties of some Hugoniot curves associated with shock instability

✍ Scribed by M. Cowperthwaite

• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Weight: 562 KB
• Volume: 285
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(68)90031-8

✦ Synopsis

Combining the Hugoniot equation e -ea = $(p + p,) (vo -v) un 'ti~ the (0-v) equation of state gives the Hugoniot mroe ph(pe, "0, v) centered at an initial condition (PO, uo) in the (p-v) plane. Since the Hugoniot equation satisfies the conservation laws of mass,momentum,and energy, only those IIugoniot curVes that are consistent with the second law of thermodynamics define the locus of states connected to (PO, ve) by a single cwrnpression shock. HugoGot cwues that tie in a domain Oj the (p-U) ph0 Where (a2p/av2), > 0 are consistent With the second law of thermodynamics; those that lie in a domain where (a2p/W)a > 0, as well as in a domain where (a2p/ao2). < 0, are inconsistent with the second law and are associated with shock instability. The first law oj thermodynamics gives properties of some Hugoniot EUTV~S associated witi shock instability. The second law of thermodynamics, together with conditions necessary for h~ydrodynamic stability, gives the locus of states connected to a g&en initial condition in the domain oj the (p-v) plane where a single compression shock is thermodynamically unstable.