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:
$$ \dfrac{dP}{dx} = \dfrac{v \phi}{v^2 - c_s^2} \hskip 0.5in \dfrac{dv}{dx} = - \ \dfrac{1}{\rho} \ \dfrac{\phi}{v^2 - c_s^2} \hskip 0.5in \dfrac{d\rho}{dx} = \dfrac{1}{v} \ \dfrac{\phi}{v^2 - c_s^2} \label{eq1} \tag{1} $$ $$ \phi = \left . \dfrac{\partial P}{\partial E} \right |_{\rho} \cdot \left [ \epsilon_{{\rm nuc}} - \left . \dfrac{\partial E}{\partial A} \right |_P \dfrac{dA}{dt} \right ] \label{eq2} \tag{2} $$ 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 the helium detonations shown below. While my ZND solver is currently out of comission, one can explore Kevin Moore's ZND solver.

image image

Here is the structure of a detonation in 2D and 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.