ZND Detonations


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Contact: F.X.Timmes
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Zeldovich, Von Neumann, and Doring (ZND, 1943) independently formed a set of differential equations for a 1D detonation which overcame the deficiencies of the Chapman-Jouget detonation model:
$$ \dfrac{dP}{dx} = \dfrac{v \phi}{v^2 - c_s^2} \hskip 0.5in \dfrac{dv}{dx} = - \ \dfrac{1}{\rho} \ \dfrac{\phi}{v^2 - c_s^2} \hskip 0.5in \dfrac{d\rho}{dx} = \dfrac{1}{v} \ \dfrac{\phi}{v^2 - c_s^2} \label{eq1} \tag{1} $$ $$ \phi = \left . \dfrac{\partial P}{\partial E} \right |_{\rho} = \left [ \epsilon_{{\rm nuc}} - \left . \dfrac{\partial E}{\partial A} \right |_P \dfrac{dA}{dt} \right ] \label{eq2} \tag{2} $$ The ZND solution gives the:
• width of the fuel-ash region
• spatial variation of the hydrodynamic and thermodynamic variables
• the self-sustating detonation solution
• global integrals which reduce to the Chapman-Jouget solution.

Solving for the structure of a ZND detonation can be considered a particular case of integrating a reaction network. For example, this 13 isotope alpha-chain network simultaneously solves the ZND equations the nuclear reaction equations. One can also explore the ZND solver by Kevin Moore.

Helium detonation, Pressure
Helium detonation, Temperature
Subsonic until the CJ point

Here is the structure of a detonation in 2D or 3D.


Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.