Cococubed.com Chapman-Jouget Detonations
Home Astronomy Research    2024 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      Phyllotaxis      MESA      MESA-Web      FLASH      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    Illustrations    Presentations 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
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