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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 1) the fuel's temperature, density and composition and 2) that the ashes exist in their equilibrium state (e.g., NSE in the nuclear case), then the Chapman-Jouget (1890) detonation solution follows from solving the the mass and momentum "rayleigh line" equation $$ (P_2 - P_1) - (v_2 \rho_2)^2 \cdot (v_1 - v_2) = 0 \label{rayleigh} \tag{1} $$ together with the energy "hugoniot" equation $$ E_1 + q_{\rm nuc} - E_2 + \dfrac{1}{2} (P_1 + P_2) (v_1-v_2) = 0 \label{hugoniot} \tag{2} $$ 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 euqations are to be solved simultaneously with the two algebraic equations for the postshock equilibrium composition (NSE). 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 (1) speed of the detonation and (2) the thermodynamics of the ashes. The CJ solution doesn't tell you the (1) the width of the fuel-to-ash region, (2) the spatial variations of the variables, and (3) if the solution is a self-sustaining detonation.



The instrument in public_cjdet.tbz generates CJ detonation solutions. It will also compute the strong and weak detonation solutions if one chooses to drive the detonation at a user-specified Mach number. If one wants what the Chapman-Jouget solution doesn't tell you, a ZND detonation might.


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detonation speed
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why speed is non-monotonic
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detonation regimes


 



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.