Chapman-Jouget Detonations


Astronomy Research
   Radiative Opacity
   2024 Neutrino Emission from Stars
   2023 White Dwarfs & 12C(α,γ)16O
   2023 MESA VI
   2022 Earendel, A Highly Magnified Star
   2022 Black Hole Mass Spectrum
   2021 Skye Equation of State
   2021 White Dwarf Pulsations & 22Ne
   Software Instruments
     Stellar equation of states
     EOS with ionization
     EOS for supernovae
     Chemical potentials
     Stellar atmospheres

     Voigt Function
     Jeans escape
     Polytropic stars
     Cold white dwarfs
     Adiabatic white dwarfs

     Cold neutron stars
     Stellar opacities
     Neutrino energy loss rates
     Ephemeris routines
     Fermi-Dirac functions

     Polyhedra volume
     Plane - cube intersection
     Coating an ellipsoid

     Nuclear reaction networks
     Nuclear statistical equilibrium
     Laminar deflagrations
     CJ detonations
     ZND detonations

     Fitting to conic sections
     Unusual linear algebra
     Derivatives on uneven grids
     Pentadiagonal solver
     Quadratics, Cubics, Quartics

     Supernova light curves
     Exact Riemann solutions
     1D PPM hydrodynamics
     Hydrodynamic test cases
     Galactic chemical evolution

     Universal two-body problem
     Circular and elliptical 3 body
     The pendulum


     Zingale's software
     Brown's dStar
     GR1D code
     Iliadis' STARLIB database
     Herwig's NuGRID
     Meyer's NetNuc

AAS Journals
   2024 AAS YouTube
   2024 AAS Peer Review Workshops

2024 ASU Energy in Everyday Life
2024 MESA Classroom
Outreach and Education Materials

Other Stuff:
   Bicycle Adventures

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.

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



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.