ZND detonation model
Encyclopedia
The ZND detonation model is a one-dimensional model for the process of detonation
Detonation
Detonation involves a supersonic exothermic front accelerating through a medium that eventually drives a shock front propagating directly in front of it. Detonations are observed in both conventional solid and liquid explosives, as well as in reactive gases...

 of an explosive. It was proposed during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

 independently by Y. B. Zel'dovich, John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...

, and Werner Döring
Werner Döring
Werner Döring was a German theoretical physicist. From 1963 until his retirement in 1977, he was ordinary professor at the University of Hamburg. His main interest was the theory of magnetism...

, hence the name.

This model admits finite-rate chemical reactions and thus the process of detonation consists of the following stages. First, an infinitely thin shock wave compresses the explosive to a high pressure called the von Neumann spike. At the von Neumann spike point the explosive still remains unreacted. The spike marks the onset of the zone of exothermic chemical reaction, which finishes at the Chapman-Jouguet state. After that, the detonation products expand backward.

In the reference frame in which the shock is stationary, the flow following the shock is subsonic
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....

. Because of this, energy release behind the shock is able to be transported acoustically to the shock for its support. For a self-propagating detonation, the shock relaxes to a speed given by the Chapman–Jouguet condition, which induces the material at the end of the reaction zone to have a locally sonic speed in the reference frame in which the shock is stationary. In effect, all of the chemical energy is harnessed to propagate the shock wave forward.
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