Search

An approach for the calibration of an advanced programmed burn (PB) model for detonation performance calculations in high explosive systems is detailed. Programmed burn methods split the detonation performance calculation into two components: timing and energy release. For the timing, the PB model uses a Detonation Shock Dynamics (DSD) surface propagation model, where the normal surface speed is a function of local surface curvature. For the energy release calculation and subsequent hydrodynamic flow evolution, a Pseudo-Reaction-Zone (PRZ) model is used. The PRZ model is similar to a reactive burn model in that it converts reactants into products at a finite rate, but it has a reaction rate dependent on the normal surface speed derived from the DSD calculation. The PRZ reaction rate parameters must be calibrated in such a way that the rate of energy release due to reaction in multi-dimensional geometries is consistent with the timing calculation provided by the DSD model. Our strategy for achieving this is to run the PRZ model in a detonation shock-attached frame in a compliant 2D planar slab geometry in an equivalent way to a reactive burn model, from which we can generate detonation front shapes and detonation phase speed variations with slab thickness. In this case, the D n field used by the PRZ model is then simply the normal detonation shock speed rather than the DSD surface normal speed. The PRZ rate parameters are then iterated on to match the equivalent surface front shapes and surface phase speed variations with slab thickness derived from the target DSD model. For the purposes of this paper, the target DSD model is fitted to the performance properties of an idealised condensed-phase reactive burn model, which allows us to compare the detonation structure of the calibrated PRZ model to that of the originating idealised-condensed phase model. [ABSTRACT FROM AUTHOR]

The dynamics of steady detonation propagation in a two-dimensional, high explosive circular arc geometry are examined computationally using a reactive flow model approach. The arc is surrounded by a low impedance material confiner on its inner surface, while its outer surface is surrounded either by the low impedance confiner or by a high impedance confiner. The angular speed of the detonation and properties of the steady detonation driving zone structure, i.e. the region between the detonation shock and sonic flow locus, are examined as a function of increasing arc thickness for a fixed inner arc radius. For low impedance material confinement on the inner and outer arc surfaces, the angular speed increases monotonically with increasing arc thickness, before limiting to a constant. The limiting behaviour is found to occur when the detonation driving zone detaches from the outer arc surface, leaving a region of supersonic flow on the outer surface. Consequently, the angular speed of the detonation becomes insensitive to further increases in the arc thickness. For high impedance material confinement on the outer arc surface, the observed flow structures are significantly more complex. As the arc thickness increases, we sequentially observe regions of negative shock curvature on the detonation front, reflected shock formation downstream of the reaction zone, and eventually Mach stem formation on the detonation front. Subsequently, a region of supersonic flow develops between the detonation driving zone and the Mach stem structure. For sufficiently wide arcs, the Mach stem structure disappears. For the high impedance material confinement, the angular speed of the detonation first increases with increasing arc thickness, reaches a maximum, decreases, and then limits to a constant for sufficiently large arc thickness. The limiting angular speed is the same as that found for the low impedance confiner on the outer arc surface. [ABSTRACT FROM AUTHOR]

We study the physics of steady detonation wave propagation in a two-dimensional circular arc via a Detonation Shock Dynamics (DSD) surface evolution model. The dependence of the surface angular speed and surface spatial structure on the inner arc radius (Ri), the arc thickness (Re-Ri, where Re is the outer arc radius) and the degree of confinement on the inner and outer arc is examined. We first analyse the results for a linear Dn-κ model, in which the normal surface velocity Dn = DCJ(1 - Bκ), where DCJ is the planar Chapman-Jouguet velocity, κ is the total surface curvature and B is a length scale representative of a reaction zone thickness. An asymptotic analysis assuming the ratio B/Ri ≪ 1 is conducted for this model and reveals a complex surface structure as a function of the radial variation from the inner to the outer arc. For sufficiently thin arcs, where (Re - Ri)/Ri = O(B/Ri), the angular speed of the surface depends on the inner arc radius, the arc thickness and the inner and outer arc confinement. For thicker arcs, where (Re - Ri)/Ri = O(1), the angular speed does not depend on the outer arc radius or the outer arc confinement to the order calculated. It is found that the leading-order angular speed depends only on DCJ and Ri, and corresponds to a Huygens limit (zero curvature) propagation model where Dn = DCJ, assuming a constant angular speed and perfect confinement on the inner arc surface. Having the normal surface speed depend on curvature requires the insertion of a boundary layer structure near the inner arc surface. This is driven by an increase in the magnitude of the surface wave curvature as the inner arc surface is approached that is needed to meet the confinement condition on the inner arc surface. For weak inner arc confinement, the surface wave spatial variation with the radial coordinate is described by a triple-deck structure. The first-order correction to the angular speed brings in a dependence on the surface curvature through the parameter B, while the influence of the inner arc confinement on the angular velocity only appears in the second-order correction. For stronger inner arc confinement, the surface wave structure is described by a two-layer solution, where the effect of the confinement on the angular speed is promoted to the first-order correction. We also compare the steady-state arc solution for a PBX 9502 DSD model to an experimental two-dimensional arc geometry validation test. [ABSTRACT FROM AUTHOR]

ABSTRACT Astrophysical fluid dynamical problems rely on efficient numerical solution techniques for hyperbolic and parabolic terms. Efficient techniques are available for treating the hyperbolic terms. Parabolic terms, when present, can dominate the time for evaluating the solution, especially when large meshes are used. This stems from the fact that the explicit time-step for parabolic terms is proportional to the square of the mesh size and can become unusually small when the mesh is large. Multigrid-Newton-Krylov methods can help, but usually require a large number of iterations to converge. Super TimeStepping schemes are an interesting alternative, because they permit one to take very large overall time-steps for the parabolic terms while using only a modest number of explicit time-steps. Super TimeStepping schemes of the type used in astrophysics have, so far, been only first-order accurate in time and prone to instabilities. In this paper, we present a Runge-Kutta method that is based on the recursion sequence for Legendre polynomials, called the RKL2 method. RKL2 is a time-explicit method that permits us to treat non-linear parabolic terms robustly and with large, second-order accurate time-steps. An s-stage RKL2 scheme permits us to take a time-step that is ∼ s2 times larger than a single explicit, forward Euler time-step for the parabolic operator. This permits an s-fold gain in computational efficiency over explicit time-step sub-cycling. For modest values of ' s', the advantage can be substantial. The stability properties of the new schemes are explored and they are shown to be stable and positivity preserving for linear operators. We document the method as it is applied to the anisotropic thermal conduction operator for dilute, magnetized, astrophysical plasmas. Implementation-related details are discussed. The RKL2 Super TimeStepping scheme has been implemented in the riemann code for computational astrophysics. We explain the method for picking an s-stage RKL2 scheme for the parabolic terms and show how it can be integrated with a hyperbolic system solver. The method's simplicity makes it very easy to retrofit the s-stage RKL2 scheme to any problem with a parabolic part when a well-formed spatial discretization is available. Several stringent test problems involving thermal conduction in astrophysical plasmas are presented and the method is shown to perform robustly and efficiently on all of them. [ABSTRACT FROM AUTHOR]