Hydrodynamic instabilities in gaseous detonations: comparison of Euler, Navier–Stokes, and large-eddy simulation

A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier–Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier–Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier–Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier–Stokes computations, which appear to be fully combusted when large-eddy simulation is employed

Nonlinear cellular dynamics of the idealized detonation model: Regular cells

High-resolution numerical simulations of cellular detonations are performed using a parallelized adaptive grid solver, in the case where the channel width is very wide. In particular, the nonlinear response of a weakly unstable ZND detonation to two-dimensional perturbations is studied in the context of the idealized one-step chemistry model. For random perturbations, cells appear with a characteristic size in good agreement with that corresponding to the maximum growth rate from a linear stability analysis. However, the cells then grow and equilibrate at a larger size. It is also shown that the linear analysis predicts well the ratio of cell lengths to cell widths of the fully developed cells. The evolutionary dynamics of the growth are nonetheless quite slow, in that the detonation needs to run of the order of 1000 reaction lengths before the final size and equilibrium state is reached. For sinusoidal perturbations, it is found that there is a large band of wavelengths/cell sizes which can propagate over very long distances (~1000 reaction lengths). By perturbing the fully developed cells of each wavelength, it is found that smaller cells in this range are unstable to symmetry breaking, which again results in cellular growth to a larger final size. However, a range of larger cell sizes appear to be nonlinearly stable. As a result it is found that the final cell size of the model is non-unique, even for such a weakly unstable, regular cell case. Indeed, in the case studied, the equilibrium cell size varies by 100% with different initial conditions. Numerical dependencies of the cellular dynamics are also examined

High-resolution numerical simulation and analysis of Mach reflection structures in detonation waves in low-pressure H₂:O₂:Ar mixtures: a summary of results obtained with adaptive mesh refinement framework AMROC

Numerical simulation can be key to the understanding of the multidimensional nature of transient detonation waves. However, the accurate approximation of realistic detonations is demanding as a wide range of scales needs to be resolved. This paper describes a successful solution strategy that utilizes logically rectangular dynamically adaptive meshes. The hydrodynamic transport scheme and the treatment of the nonequilibrium reaction terms are sketched. A ghost fluid approach is integrated into the method to allow for embedded geometrically complex boundaries. Large-scale parallel simulations of unstable detonation structures of Chapman-Jouguet detonations in low-pressure hydrogen-oxygen-argon mixtures demonstrate the efficiency of the described techniques in practice. In particular, computations of regular cellular structures in two and three space dimensions and their development under transient conditions, that is, under diffraction and for propagation through bends are presented. Some of the observed patterns are classified by shock polar analysis, and a diagram of the transition boundaries between possible Mach reflection structures is constructed

Combustion in thermonuclear supernova explosions

Type Ia supernovae are associated with thermonuclear explosions of white dwarf stars. Combustion processes convert material in nuclear reactions and release the energy required to explode the stars. At the same time, they produce the radioactive species that power radiation and give rise to the formation of the observables. Therefore, the physical mechanism of the combustion processes, as reviewed here, is the key to understand these astrophysical events. Theory establishes two distinct modes of propagation for combustion fronts: subsonic deflagrations and supersonic detonations. Both are assumed to play an important role in thermonuclear supernovae. The physical nature and theoretical models of deflagrations and detonations are discussed together with numerical implementations. A particular challenge arises due to the wide range of spatial scales involved in these phenomena. Neither the combustion waves nor their interaction with fluid flow and instabilities can be directly resolved in simulations. Substantial modeling effort is required to consistently capture such effects and the corresponding techniques are discussed in detail. They form the basis of modern multidimensional hydrodynamical simulations of thermonuclear supernova explosions. The problem of deflagration-to-detonation transitions in thermonuclear supernova explosions is briefly mentioned.Comment: Author version of chapter for 'Handbook of Supernovae,' edited by A. Alsabti and P. Murdin, Springer. 24 pages, 4 figure

Linear and nonlinear dynamics of cylindrically and spherically expanding detonation waves

The nonlinear stability of cylindrically and spherically expanding detonation waves is investigated using numerical simulations for both directly (blast) initiated detonations and cases where the simulations are initialized by placing quasi-steady solutions corresponding to different initial shock radii onto the grid. First, high-resolution one-dimensional (axially or radially symmetric) simulations of pulsating detonations are performed. Emphasis is on comparing with the predictions of a recent one-dimensional linear stability analysis of weakly curved detonation waves. The simulations show that, in agreement with the linear analysis, increasing curvature has a rapid destabilizing effect on detonation waves. The initial size and growth rate of the pulsation amplitude decreases as the radius where the detonation first forms increases. The pulsations may reach a saturated nonlinear behaviour as the amplitude grows, such that the subsequent evolution is independent of the initial conditions. As the wave expands outwards towards higher (and hence more stable) radii, the nature of the saturated nonlinear dynamics evolves to that of more stable behaviour (e.g. the amplitude of the saturated nonlinear oscillation decreases, or for sufficiently unstable cases, the oscillations evolve from multi-mode to period-doubled to limit-cycle-type behaviour). For parameter regimes where the planar detonation is stable, the linear stability prediction of the neutrally stable curvature gives a good prediction of the location of the maximum amplitude (provided the stability boundary is reached before the oscillations saturate) and of the critical radius of formation above which no oscillations are seen. The linear analysis also predicts very well the dependence of the period on the radius, even in the saturated nonlinear regimes. Secondly, preliminary two-dimensional numerical simulations of expanding cellular detonations are performed, but it is shown that resolved and accurate calculations of the cellular dynamics are currently computationally prohibitive, even with a dynamically adaptive numerical scheme

A numerical study of detonation diffraction

An investigation of detonation diffraction through an abrupt area change has been carried out via a set of two-dimensional numerical simulations parameterized by the activation energy of the reactant. Our analysis is specialized to a reactive mixture with a perfect gas equation of state and a single-step reaction in the Arrhenius form. Lagrangian particles are injected into the flow as a diagnostic tool for identifying the dominant terms in the equation that describes the temperature rate of change of a fluid element, expressed in the shock-based reference system. When simplified, this equation provides insight into the competition between the energy release rate and the expansion rate behind the diffracting front. The mechanism of spontaneous generation of transverse waves along the diffracting front is carefully analysed and related to the sensitivity of the reaction rate to temperature. We study in detail three highly resolved cases of detonation diffraction that illustrate different types of behaviour, super-, sub- and near-critical diffraction

Type Ia Supernova Explosion Models: Homogeneity versus Diversity

Type Ia supernovae (SN Ia) are generally believed to be the result of the thermonuclear disruption of Chandrasekhar-mass carbon-oxygen white dwarfs, mainly because such thermonuclear explosions can account for the right amount of Ni-56, which is needed to explain the light curves and the late-time spectra, and the abundances of intermediate-mass nuclei which dominate the spectra near maximum light. Because of their enormous brightness and apparent homogeneity SN Ia have become an important tool to measure cosmological parameters. In this article the present understanding of the physics of thermonuclear explosions is reviewed. In particular, we focus our attention on subsonic (``deflagration'') fronts, i.e. we investigate fronts propagating by heat diffusion and convection rather than by compression. Models based upon this mode of nuclear burning have been applied very successfully to the SN Ia problem, and are able to reproduce many of their observed features remarkably well. However, the models also indicate that SN Ia may differ considerably from each other, which is of importance if they are to be used as standard candles.Comment: 11 pages, 4 figures. To appear in Proc. 10th Ann. Astrophys. Conf. "Cosmic Explosions", Univ. of Maryland 1999, eds. S.S. Holt and W.W. Zhan