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Chapman-Jouget Detonations

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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.

Given (i) a fuel's temperature, density and composition and (ii) that the fuel's ashes are in their equilibrium state (e.g., NSE in the nuclear case), then the Chapman-Jouget (CJ; 1890) detonation solution follows from solving the the mass and momentum equation (which defines the "Rayleigh line" ; see illustration below) $$ (P_2 - P_1) - (v_2 \rho_2)^2 \cdot (v_1 - v_2) = 0 \label{rayleigh} \tag{1} $$ together with the energy equation (which defines the "Hugoniot curve"; see illustration) $$ E_1 + q_{\rm nuc} - E_2 + \dfrac{1}{2} (P_1 + P_2) (v_1 - v_2) = 0 \label{hugoniot} \tag{2} $$ where $P$ is the pressure, $\rho$ is the density, $v$ is the material speed, $E$ is the specific internal energy, and $q_{\rm nuc}$ is the energy released by burning in going from the unshocked upstream material (subscript 1) to the final post-shock downstream material (subscript 2). These two algebraic equations are to be solved simultaneously with the two algebraic equations for the postshock NSE composition. This is a four-dimensional root find, but it can be done efficiently as two nested two-dimensional root finds.

The CJ solution tells you the (i) speed of the detonation and (ii) the thermodynamics of the ashes. The CJ solution doesn't tell you the (a) the width of the fuel-to-ash region, (b) the spatial variations of the variables, or (c) if the solution is a self-sustaining detonation.



The tool in cjdet.tar.xz generates CJ solutions using the helmholtz equation of state and relevant parts of the torch network. It will also compute the strong and weak solutions if one chooses to drive the system at a user-specified Mach number. If one wants what a Chapman-Jouget solution doesn't tell you, a ZND detonation might.


image
detonation speed is non-monotonic with density
image
why the detonation speed is non-monotonic



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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.