ZND detonation model

The ZND detonation model is a one-dimensional model for the process of detonation of an explosive. It was proposed during World War II independently by Yakov Zeldovich,{{cite journal

|last= Zel’dovich

|first= Ya. B.

|title= On the theory of the propagation of detonation in gaseous systems

|script-title=ru:К теории распространения детонации в газообразных системах

|journal= Zhurnal Éksperimental'noĭ i Teoreticheskoĭ Fiziki

|volume=10

|pages=542–568|language=ru

|year= 1940

|hdl= 2060/19930093969

|trans-title=On the theory of the propagation of detonations on gaseous system|id=English translation }} John von Neumann,{{cite book

|last= von Neumann

|first= J.

|author-link= John von Neumann

|contribution= Theory of detonation waves. Progress Report to the National Defense Research Committee Div. B, OSRD-549 (PB 31090)

|date= 1963

|orig-year= 1942

|editor-last= Taub

|editor-first= A. H.

|title= John von Neumann: Collected Works, 1903–1957

|volume= 6

|pages= 178–218

|publisher= Pergamon Press

|location= New York

|isbn= 978-0-08-009566-0

}} and Werner Döring,{{cite journal

|last=Döring

|first= W.

|title= Über Detonationsvorgang in Gasen|language=de

|journal=Annalen der Physik

|volume= 43

|pages= 421–436

|year= 1943

|issn= 0003-4916

|doi=10.1002/andp.19434350605 |trans-title=On detonation processes in gases

|issue=6–7|bibcode = 1943AnP...435..421D }} hence the name.

This model admits finite-rate chemical reactions and thus the process of detonation consists of the following stages. First, an infinitesimally 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 condition. After that, the detonation products expand backward.

In the reference frame in which the shock is stationary, the flow following the shock is subsonic. 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.

However, in the 1960s, experiments revealed that gas-phase detonations were most often characterized by unsteady, three-dimensional structures, which can only in an averaged sense be predicted by one-dimensional steady theories. Indeed, such waves are quenched as their structure is destroyed.{{cite journal |last1=Edwards |first1= D. H. |last2=Thomas|first2= G. O. |last3=Nettleton |first3= M. A. |title=The Diffraction of a Planar Detonation Wave at an Abrupt Area Change |journal=Journal of Fluid Mechanics |volume= 95 |issue=1 |pages=79–96 |year= 1979 |doi=10.1017/S002211207900135X |bibcode = 1979JFM....95...79E |s2cid= 123018814 }}{{cite book |doi=10.2514/5.9781600865497.0341.0357 |volume=75 |series=Progress in Astronautics & Aeronautics |year=1981 |title=Diffraction of a Planar Detonation in Various Fuel-Oxygen Mixtures at an Area Change |isbn=978-0-915928-46-0 |pages=341 |editor1=A. K. Oppenheim |editor2= N. Manson |editor3= R. I. Soloukhin |editor4= J. R. Bowen |last1=Edwards |first1= D. H. |last2=Thomas |first2= G. O. |last3=Nettleton |first3= M. A. }} The Wood–Kirkwood detonation theory can correct for some of these limitations.{{cite journal | doi = 10.1007/s00214-007-0303-9 | title = Improved Wood–Kirkwood detonation chemical kinetics | year = 2007 | last1 = Glaesemann | first1 = Kurt R. | last2 = Fried | first2 = Laurence E. | journal = Theoretical Chemistry Accounts | volume = 120 | pages = 37–43 |issue=1–3 | s2cid = 95326309 | url = https://zenodo.org/record/1232641 }}