No Arabic abstract
The sensitizing effect of cavities in the form of microbubbles on the shock initiation of a homogeneous liquid explosive is studied computationally. While the presence of voids in an explosive has long been known to induce so-called hot spots that greatly accelerate the global reaction rate, the ability to computationally resolve the details of the interaction of the shock front with heterogeneities existing on the scale of the detonation reaction zone has only recently become feasible. In this study, the influence of the spatial distribution of air-filled cavities has been examined, enabled by the use of graphic processing unit (GPU) accelerated computations that can resolve shock initiation and detonation propagation through an explosive while fully resolving features at the mesoscale. Different spatial distributions of cavities are examined in two-dimensional simulations, including regular arrays of cavities, slightly perturbed arrays, random arrays (with varying minimum spacing being imposed on the cavities), and randomly distributed clusters of cavities. The presence of the cavities is able to reduce the time required to initiate detonation---for a given input shock strength---by greater than 50%, in agreement with previous experimental results. Randomly distributing the cavities results in a 15-20% decrease in detonation initiation time in comparison to a regular array of cavities. Clustering the cavities---as would occur in the case of agglomeration---results in an additional 10% decrease in detonation initiation time in comparison to random arrays. The effect of clustering is shown not to be a result of the clusters forming an effectively larger cavity, but rather due to interactions between clusters upon shock loading occurring on the microscale.
Two-dimensional, meso-resolved numerical simulations are performed to investigate the complete shock-to-detonation transition (SDT) process in a mixture of liquid nitromethane (NM) and air-filled, circular cavities. The shock-induced initiation behaviors resulting from the cases with neat NM, NM with an array of regularly spaced cavities, and NM with randomly distributed cavities are examined. For the case with randomly distributed cavities, hundreds of cavities are explicitly resolved in the simulations using a diffuse-interface approach to treat two immiscible fluids and GPU-enabled parallel computing. Without invoking any empirically calibrated, phenomenological models, the reaction rate in the simulations is governed by Arrhenius kinetics. For the cases with neat NM, the resulting SDT process features a superdetonation that evolves from a thermal explosion after a delay following the passage of the incident shock wave and eventually catches up with the leading shock front. For the cases wherein mesoscale heterogeneities are explicitly considered, a gradual SDT process is captured. These two distinct initiation behaviors for neat NM and heterogeneous NM mixtures agree with experimental findings. Via examining the global reaction rate of the mixture, a unique time scale characterizing the SDT process, i.e., the overtake time, is measured for each simulation. For an input shock pressure less than approximately $9.4~mathrm{GPa}$, the overtake time resulting from a heterogeneous mixture is shorter than that for neat NM. This sensitizing effect is more pronounced for lower input shock pressures. A random distribution of cavities is found to be more effective in enhancing the SDT process than a regular array of cavities. Statistical analysis on the meso-resolved simulation data provides more insights into the mechanism of energy release underlying the SDT process.
Dynamics of ethylene autoignition and Deflagration-to-Detonation Transition (DDT) in a one-dimensional shock tube are numerically investigated using a skeletal chemistry including 10 species and 10 reactions. Different combustion modes are investigated through considering various premixed gas equivalence ratios (0.2 to 2.0) and incident shock wave Mach numbers (1.8 to 3.2). Four ignition and DDT modes are observed from the studied cases, i.e., no ignition, deflagration combustion, detonation after reflected shock and deflagration behind the incident shock. For detonation development behind the reflected shock, three autoignition hot spots are formed. The first one occurs at the wall surface after the re-compression of the reflected shock and contact surface, which further develops to a reaction shock because of the explosion in the explosion regime. The other two are off the wall, respectively caused by the reflected shock rarefaction wave interaction and reaction induction in the compressed mixture. The last hot spot develops to a reaction wave and couples with the reflected shock after a DDT process, which eventually leads to detonation combustion. For deflagration development behind the reflected shock, the wave interactions, wall surface autoignition hot spot as well as its induction of reaction shock are qualitatively similar to the mode of detonation after incident shock reflection, before the reflected shock rarefaction wave collision point. However, only one hot spot is induced after the collision, which also develops to a reaction wave but cannot catch up with the reflected shock. For deflagration behind the incident shock, deflagration combustion is induced by the incident shock compression whereas detonation occurs after the shock reflection.
We evaluate the effect of boundary layer losses on two-dimensional H2/O2/Ar cellular detonations obtained in narrow channels. The experiments provide the details of the cellular structure and the detonation speed deficits from the ideal CJ speed. We model the effect of the boundary layer losses by incorporating the flow divergence in the third dimension due to the negative boundary layer displacement thickness, modeled using Mirels theory. The cellular structures obtained numerically with the resulting quasi-2D formulation of the reactive Euler equations with two-step chain-branching chemistry are found in excellent agreement with experiment, both in terms of cell dynamics and velocity deficits, provided the boundary layer constant of Mirels is modified by a factor of 2. A significant increase in the cell size is found with increasing velocity deficit. This is found to be very well captured by the induction zone increase in slower detonations due to the lower temperatures in the induction zone.
Turbulence structure resulting from multi-fluid or multi-species, variable-density isotropic turbulence interaction with a Mach 2 shock is studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles density play in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that the density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic velocity gradient tensor, PDF$(Q^ast, R^ast)$, as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multi-species case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetrical PDF$(Q^ast, R^ast)$ in heavy fluid regions, while the light fluid regions retain the characteristic tear-drop shape. To understand this behavior and the return to standard turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants are studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multi-fluid case, making them critically important to the flow dynamics and turbulence structure.
The present study addresses the reaction zone structure and burning mechanism of unstable detonations. Experiments investigated mainly two-dimensional methane-oxygen cellular detonations in a thin channel geometry. The sufficiently high temporal resolution permitted to determine the PDF of the shock distribution, a power-law with an exponent of -3, and the burning rate of unreacted pockets from their edges - through surface turbulent flames with a speed approximately 3-7 times larger than the laminar one at the local conditions. Numerical simulations were performed using a novel Large Eddy Simulation method where the reactions due to both auto-ignition and turbulent transport and treated exactly at the sub-grid scale in a reaction-diffusion formulation. The model is an extension of Kerstein & Menons Linear Eddy Model for Large Eddy Simulation to treat flows with shock waves and rapid gasdynamic transients. The two-dimensional simulations recovered well the amplification of the laminar flame speed owing to the turbulence generated mainly by the shear layers originating from the triple points and subsequent Richtmyer-Meshkov instability associated with the internal pressure waves. The simulations clarified how the level of turbulence generated controlled the burning rate of the pockets, the hydrodynamic thickness of the wave, the cellular structure and its distribution. Three-dimensional simulations were found in general good agreement with the two-dimensional ones, in that the sub-grid scale model captured the ensuing turbulent burning once the scales associated with the cellular dynamics, where turbulent kinetic energy is injected, are well resolved.