Allen L. Kuhl

Simulation of Enhance-Explosive Devices in Chambers and Tunnels

Shock-dispersed fuel (SDF) explosives use a small chemical charge to disperse a combustible fuel that burns in the post-detonation environment. Here, we model an SDF explosive in which the dispersed fuel is flake aluminum. We present a multiphase flow model that combines a second-order Godunov-type discretization coupled with a structured adaptive mesh refinement scheme. We use this model to simulate several calorimeter geometries and compare the simulations with experimental results.

Model of Non‐Premixed Combustion of Aluminium—Air Mixtures

Shock‐induced dissemination and burning of aluminum particles in air is numerically simulated using the equilibrium chemistry approach for describing the equation of state of reacting two‐phase media. Since the initial mixture is non‐premixed it was necessary to develop a new model. Its predictive abilities and advantages are demonstrated.

Gasdynamic model of dilute two-phase combustion fields

A gasdynamic model of two-phase combustion fields is proposed. The model is based on an extension of our dilute heterogeneous-continuum formulation, where now the particle phase is modeled thermodynamically as a particle gas (with a pressure p2, temperature T2, and internal energy u2, given by the kinetic theory for hard spheres with γ2 = 5/3), thereby, resulting in particle gas conservation laws for mass, momentum, and total energy. The particles also possess a thermal storage capacity, expressed in terms of an internal energy of the solid es = csTs with its own temperature Ts, and the corresponding energy conservation law. The consequence of this formulation is that both phases are hyperbolic, but decoupled; so each phase has it own complete set of eigenvalues and eigenvectors. The conservation laws for each phase can be integrated with a high-order Godunov scheme. Phases are coupled only through drag, heat, and mass transfer. The model is used to simulate aluminum particle combustion in a shock-dispersed-fuel explosion. Taking advantage of the point symmetry inherent in this problem, the flow field is azimuthally averaged in θ and φ directions to extract the mean and root-mean-square radial profiles of the thermodynamic fields, velocity fields, and reaction zone profiles. We find that the particle gas pressure influences the flow only during the initial phase of particle acceleration: as the compaction wave moves through the powder, followed by the rarefaction wave from the free surface. Thereafter, the particle pressure decays rapidly and particle accelerations are dominated by drag. Nevertheless, this seems to affect the dispersion process because the combustion cloud shape is somewhat different from previous results.

On the Structure of Self-Similar Detonation Waves in TNT Charges

A phase-plane method is proposed to model flow fields bounded by constant-velocity detonation waves propagating in TNT charges. Similarity transformations are used to formulate the problem in the phase plane of non-dimensional sound speed Z versus non-dimensional velocity F. The formulation results in two coupled ordinary differential equations that are solved simultaneously. The solution corresponds to an integral curve Z(F) in the phase plane, starting at the Chapman-Jouguet (CJ) point and terminating at the singularity A, which is the sonic point within the wave. The system is closed by computing thermodynamic variables along the expansion isentrope passing through the CJ point, forming, in effect, the complete equation of state of the thermodynamic system. The CJ condition and isentropic states are computed by the Cheetah thermodynamic code. Solutions are developed for planar, cylindrical, and spherical detonations. Species profiles are also computed; carbon graphite is found to be the predominant component (≈10 mol/kg). The similarity solution is used to initialize a 1D gas-dynamic simulation that predicts the initial expansion of the detonation products and the formation of a blast wave in air. Such simulations provide an insight into the thermodynamic states and species concentrations that create the initial optical emissions from TNT fireballs.

AMR Code Simulations of Turbulent Combustion in Confined and Unconfined SDF Explosions

A heterogeneous continuum model is proposed to describe the dispersion and combustion of an aluminum particle cloud in an explosion. It combines the gasdynamic conservation laws for the gas phase with a continuum model for the dispersed phase, as formulated by Nigmatulin. Inter-phase mass, momentum and energy exchange are prescribed by phenomenological models. It incorporates a combustion model based on the mass conservation laws for fuel, air and products; source/sink terms are treated in the fast-chemistry limit appropriate for such gasdynamic fields, along with a model for mass transfer from the particle phase to the gas. The model takes into account both the afterburning of the detonation products of the booster with air, and the combustion of the Al particles with air. The model equations were integrated by high-order Godunov schemes for both the gas and particle phases. Numerical simulations of the explosion fields from 1.5-g Shock-Dispersed-Fuel (SDF) charge in a 6.6 liter calorimeter were used to validate the combustion model. Then the model was applied to 10-kg Al-SDF explosions in a vented two-room structure and in an unconfined height-of-burst explosion. Computed pressure histories are in reasonable (but not perfect) agreement with measured waveforms. Differences are caused by physical-chemical kinetic effects of particle combustion which induce ignition delays in the initial reactive blast wave and quenching of reactions at late times. Current simulations give initial insights into such modeling issues.

Riemann solver for the Nigmatulin model of two-phase flow

The two-phase model of Nigmatulin (Dynamics of Multiphase Media, 1991) is revisited and a second order Godunov solver is constructed for the corresponding Riemann problem using a seven wave structure. This model differs from the well established Baer-Nunziato model (International J. Multiphase Flow, Vol. 12, No. 6, 1986, pp. 861-889) in that it treats the solid phase as incompressible, and also accounts for thermal as well as elastic energies for the solid phase. Numerical results are presented for three classes of Riemann problems, demonstrating the accuracy of the method. The effect of inter-granular stress on the flow physics is investigated and it is shown that this term results in faster wave speeds for higher stresses. This study confirms that the Nigmatulin model can also be useful for the study of two-phase flows.

Turbulent combustion in aluminum-air clouds for different scale explosion fields

This paper explores “scaling issues” associated with Al particle combustion in explosions. The basic idea is the following: in this non-premixed combustion system, the global burning rate is controlled by rate of turbulent mixing of fuel (Al particles) with air. From similarity considerations, the turbulent mixing rates should scale with the explosion length and time scales. However, the induction time for ignition of Al particles depends on an Arrhenius function, which is independent of the explosion length and time. To study this, we have performed numerical simulations of turbulent combustion in unconfined Al-SDF (shock-dispersed-fuel) explosion fields at different scales. Three different charge masses were assumed: 1-g, 1-kg and 1-T Al-powder charges. We found that there are two combustion regimes: an ignition regime—where the burning rate decays as a power-law function of time, and a turbulent combustion regime—where the burning rate decays exponentially with time. This exponential dependence is typi...

Simulation of the reflected blast wave from a C-4 charge

The reflection of a blast wave from a C4 charge detonated above a planar surface is simulated with our ALE3D code. We used a finely-resolved, fixed Eulerian 2-D mesh (167 μm per cell) to capture the detonation of the charge, the blast wave propagation in nitrogen, and its reflection from the surface. The thermodynamic properties of the detonation products and nitrogen were specified by the Cheetah code. A programmed-burn model was used to detonate the charge at a rate based on measured detonation velocities. Computed pressure histories are compared with pressures measured by Kistler 603B piezoelectric gauges at 7 ranges (GR = 0, 5.08, 10.16, 15.24, 20.32, 25.4, and 30.48 cm) along the reflecting surface. Computed and measured waveforms and positive-phase impulses were similar, except at close-in ranges (GR < 5 cm), which were dominated by jetting effects.

Securing infrastructure from high explosive threats

Lawrence Livermore National Laboratory (LLNL) is working with the Department of Homeland Securitys Science and Technology Directorate, the Transportation Security Administration, and several infrastructure partners to characterize and help mitigate principal structural vulnerabilities to explosive threats. Given the importance of infrastructure to the nations security and economy, there is a clear need for applied research and analyses (1) to improve understanding of the vulnerabilities of these systems to explosive threats and (2) to provide decision makers with time-critical technical assistance concerning countermeasure and mitigation options. Fully-coupled high performance calculations of structural response to ideal and non-ideal explosives help bound and quantify specific critical vulnerabilities, and help identify possible corrective schemes. Experimental validation of modeling approaches and methodologies builds confidence in the prediction, while advanced stochastic techniques allow for optimal use of scarce computational resources to efficiently provide infrastructure owners and decision makers with timely analyses.

Numerical Simulation of the Combustion of Aluminum Shock-Dispersed-Fuel Charges

For many explosives, only a fraction of the chemical energy is released in the detonation. Calorimetry data for TNT from Ornellas (1984) shows that when the ambient gas is inert, there is substantially less total energy released than when the ambient gas is air. This data indicates that burning of the explosion byproducts plays a key role in the overall energetics of the system. In this paper, we briefly discuss the models and the numerical methods used for the simulations and present the computational results. We also discuss future directions our work on the development of SDF explosives