 Cococubed.com ZND Detonations

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Contact: F.X.Timmes
my one page vitae,
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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.

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.