Editing Detonation (section)

== Theories ==
The simplest theory to predict the behaviour of detonations in gases is known as the [[Chapman–Jouguet condition|Chapman–Jouguet]] (CJ) condition, developed around the turn of the 20th century. This theory, described by a relatively simple set of algebraic equations, models the detonation as a propagating shock wave accompanied by exothermic heat release. Such a theory describes the chemistry and diffusive transport processes as occurring abruptly as the shock passes.

A more complex theory was advanced during World War II independently by [[Yakov B. Zel'dovich|Zel'dovich]], [[John von Neumann|von Neumann]], and [[Werner Döring|Döring]].<ref name="Zel'dovichKompaneets">{{cite book |last1=Zel'dovich |first1=Yakov B. |last2=Kompaneets |first2=Aleksandr Solomonovich |title=Theory of Detonation |publisher=Academic Press |location=New York |year=1960 |asin=B000WB4XGE |oclc=974679 }}</ref><ref name="vonNeumann">{{cite report |year=1942 |last=von Neumann |first=John |title=Progress report on "Theory of Detonation Waves" |id=OSRD Report No. 549. Ascension number ADB967734 |url=http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADB967734 |access-date=2017-12-22 |archive-date=2011-07-17 |archive-url=https://web.archive.org/web/20110717145048/http://oai.dtic.mil/oai/oai?verb=getRecord |url-status=dead }}</ref><ref name="Döring">{{cite journal |last1=Döring |first1=Werner |journal=Annalen der Physik |volume=43 |pages=421–436 |year=1943 |doi=10.1002/andp.19434350605 |title="Über den Detonationsvorgang in Gasen" |trans-title="On the detonation process in gases" |issue=6–7 |bibcode=1943AnP...435..421D }}</ref> This theory, now known as [[ZND theory]], admits finite-rate chemical reactions and thus describes a detonation as an infinitesimally thin shock wave, followed by a zone of exothermic chemical reaction. With a reference frame of a stationary shock, the following flow is subsonic, so that an acoustic reaction zone follows immediately behind the lead front, the [[Chapman–Jouguet condition]].<ref>{{cite journal |last=Chapman |first=David Leonard |title=On the rate of explosion in gases |journal=Philosophical Magazine |location=London |series=Series 5 |volume=47 |issue=284 |pages=90–104 |date=January 1899 |url=https://books.google.com/books?id=N4u8y0Kf8NQC&pg=PA90 |issn=1941-5982 |lccn=sn86025845 |doi=10.1080/14786449908621243 |url-access=subscription }}</ref><ref name="Jouguet1905">{{cite journal |last=Jouguet |first=Jacques Charles Émile |url=http://math-doc.ujf-grenoble.fr/JMPA/PDF/JMPA_1905_6_1_A9_0.pdf |title=Sur la propagation des réactions chimiques dans les gaz |journal=Journal de mathématiques pures et appliquées |series=6 |volume=1 |pages=347–425 |year=1905 |trans-title="On the propagation of chemical reactions in gases" |url-status=dead |archive-url=https://web.archive.org/web/20131019171453/http://math-doc.ujf-grenoble.fr/JMPA/PDF/JMPA_1905_6_1_A9_0.pdf |archive-date=2013-10-19 |access-date=2013-10-19 }} Continued in {{cite journal |last=Jouguet |first=Jacques Charles Émile |journal=Journal de mathématiques pures et appliquées |series=6 |volume=2 |pages=5–85 |year=1906 |url=http://sites.mathdoc.fr/JMPA/PDF/JMPA_1906_6_2_A1_0.pdf |title=Sur la propagation des réactions chimiques dans les gaz |trans-title="On the propagation of chemical reactions in gases" |url-status=dead |archive-url=https://web.archive.org/web/20151016140100/http://sites.mathdoc.fr/JMPA/PDF/JMPA_1906_6_2_A1_0.pdf |archive-date=2015-10-16 }}</ref>

There is also some evidence that the reaction zone is [[Semimetal|semi-metallic]] in some explosives.<ref>{{cite journal |doi=10.1038/nphys806 |title=A transient semimetallic layer in detonating nitromethane |year=2007 |last1=Reed |first1=Evan J. |last2=Riad Manaa |first2=M. |last3=Fried |first3=Laurence E. |last4=Glaesemann |first4=Kurt R. |last5=Joannopoulos |first5=J. D. |journal=Nature Physics |volume=4 |pages=72–76 |issue=1 |bibcode=2008NatPh...4...72R }}</ref>

Both theories describe one-dimensional and steady wavefronts. 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.<ref>{{cite journal |last1=Edwards |first1=D. H. |last2=Thomas |first2=G. O. |last3=Nettleton |first3=M. A. |name-list-style=amp |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 }}</ref><ref>{{cite journal |doi=10.2514/5.9781600865497.0341.0357 |volume=75 |journal=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=341–357 |editor=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. }}</ref> The Wood-Kirkwood detonation theory can correct some of these limitations.<ref>{{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 }}</ref>

Experimental studies have revealed some of the conditions needed for the propagation of such fronts. In confinement, the range of composition of mixes of fuel and oxidant and self-decomposing substances with inerts are slightly below the flammability limits and, for spherically expanding fronts, well below them.<ref>{{cite journal |last=Nettleton |first=M. A. |title=Detonation and flammability limits of gases in confined and unconfined situations |journal=Fire Prevention Science and Technology |issn=0305-7844 |pages=29 |year=1980 |issue=23 }}</ref> The influence of increasing the concentration of diluent on expanding individual detonation cells has been elegantly demonstrated.<ref>{{cite journal |last1=Munday |first1=G. |last2=Ubbelohde |first2=A. R. |last3=Wood |first3=I. F. |name-list-style=amp |title=Fluctuating Detonation in Gases |journal=Proceedings of the Royal Society A |volume=306 |pages=171–178 |year=1968 |doi=10.1098/rspa.1968.0143 |issue=1485 |bibcode=1968RSPSA.306..171M |s2cid=93720416 }}</ref> Similarly, their size grows as the initial pressure falls.<ref>{{cite journal |last=Barthel |first=H. O. |title=Predicted Spacings in Hydrogen-Oxygen-Argon Detonations |journal=Physics of Fluids |volume=17 |issue=8 |pages=1547–1553 |year=1974 |doi=10.1063/1.1694932 |bibcode=1974PhFl...17.1547B }}</ref> Since cell widths must be matched with minimum dimension of containment, any wave overdriven by the initiator will be quenched.

Mathematical modeling has steadily advanced to predicting the complex flow fields behind shocks inducing reactions.<ref>{{cite book |last1=Oran |last2=Boris |title=Numerical Simulation of Reactive Flows |publisher=Elsevier Publishers |year=1987 }}</ref><ref>{{cite journal |last1=Sharpe |first1=G. J. |last2=Quirk |first2=J. J. |title=Nonlinear cellular dynamics of the idealized detonation model: Regular cells |journal=Combustion Theory and Modelling |volume=12 |issue=1 |pages=1–21 |year=2008 |doi=10.1080/13647830701335749
 |bibcode=2008CTM....12....1S |s2cid=73601951 |url=http://eprints.whiterose.ac.uk/7931/1/cells_revised.pdf |url-status=live |archive-url=https://web.archive.org/web/20170705073324/http://eprints.whiterose.ac.uk/7931/1/cells_revised.pdf |archive-date=2017-07-05}}</ref> To date, none has adequately described how the structure is formed and sustained behind unconfined waves.