SCI Publications

The growth of hydrocarbon molecules up to sizes of incipient soot is computed in premixed laminar flames using kinetic Monte Carlo and molecular dynamic methodologies (AMPI code). This approach is designed to preserve atomistic scale structure (bonds, bond angles, dihedral angles) as soot precursors evolve into three-dimensional structures. Application of this code to aliphatic (acetylene) and aromatic (benzene) flame environments is able to explain results in the literature on the differences in properties of soot precursors from these two classes of flames, particularly relating to H/C ratio, particle sphericity, and depolarization ratio.

An application of the Reaction Class Transition State Theory/Linear Energy Relationship (RC-TST/LER) is presented for the evaluation of the thermal rate constants of hydrogen abstraction reactions by H atoms from Polycyclic Aromatic Hydrocarbons (PAH). Two classes of reactions have been considered, namely hydrogen bonded to six- and five-membered rings, respectively, and twenty-two reactions have been used to develop the RC-TST/LER parameters. B3LYP and BH&HLYP density functional theory methods were used to calculate necessary potential energy surface information. Detailed analyses of RC-TST/LER reaction factors lead to the conclusion that rate constants for any reaction in these two classes can be approximated by those of its corresponding principal reaction corrected by the reaction symmetry factor. Specifically, for hydrogen abstraction from six-membered rings such as naphthalene and pyrene, k(T) = (σ/σ_H+C6H6) k_H+C6H6 = (σ/6)1.42 × 10⁸T^1.77 exp(−6570/T)(cm³/mol·s), and for hydrogen abstraction from five-membered rings such as acenaphthylene and acephenanthrylene, k(T) = (σ/σ_H+C12H8) k_H+C12H8 = (σ/2)3.27 × 10⁸T^1.71 exp(−8170/T) (cm³/mol·s), where σ is the reaction symmetry number.

In this paper, we solve the two-dimensional advection-diffusion equation with random transport velocity. The generalized polynomial chaos expansion is employed to discretize the equation in random space while the spectral hp element method is used for spatial discretization. Numerical results which demonstrate the convergence of generalized polynomial chaos are presented. Specifically, it appears that the fast convergence rate in the variance is the same as that of the mean solution in the Jacobi-chaos unlike the Hermite-chaos. To this end, a new model to represent compact Gaussian distributions is also proposed.

Keywords: generalized polynomial chaos, advection-diffusion, stochastic modeling

We study the viscous Burgers' equation subject to perturbations on the boundary conditions. Two kinds of perturbations are considered: deterministic and random. For deterministic perturbations, we show that small perturbations can result in O(1) changes in the location of the transition layer. For random perturbations, we solve the stochastic Burgers' equation using different approaches. First, we employ the Jacobi-polynomial-chaos, which is a subset of the generalized polynomial chaos for stochastic modeling. Converged numerical results are reported (up to seven significant digits), and we observe similar 'stochastic supersensitivity' for the mean location of the transition layer. Subsequently, we employ up to fourth-order perturbation expansions. We show that even with small random inputs, the resolution of the perturbation method is relatively poor due to the larger stochastic responses in the output. Two types of distributions are considered: uniform distribution and a 'truncated' Gaussian distribution with no tails. Various solution statistics, including the spatial evolution of probability density function at steady state, are studied.

Keywords: generalized polynomial chaos, stochastic Burgers' equation, supersensitivity, random boundary conditions

Many physical systems, such as natural porous media, are highly heterogeneous and characterized by parameters that are uncertain due to the lack of sufficient data. This uncertainty (randomness) occurs on a multiplicity of scales. We focus on random composites with the two dominant scales of uncertainty: large-scale uncertainty in the spatial arrangement of materials and small-scale uncertainty in the parameters within each material. We propose an approach that combines random domain decompositions and polynomial chaos expansions to account for the large and small scales of uncertainty, respectively. We present a general framework and use one-dimensional diffusion to demonstrate that our combined approach provides robust, nonperturbative approximations for the statistics of system states.

Keywords: random fields, moment equations, random domain decomposition, polynomial chaos

Polymer bonded explosives are particulate composites containing a high volume fraction of stiff elastic explosive particles in a compliant viscoelastic binder. Since the volume fraction of particles can be greater than 0.9 and the modulus contrast greater than 20 000, rigorous bounds on the elastic moduli of the composite are an order of magnitude different from experimentally determined values. Analytical solutions are also observed to provide inaccurate estimates of effective elastic properties. Direct finite element approximations of effective properties require large computational resources because of the complexity of the microstructure of these composites. An alternative approach, the recursive cells method (RCM) is also explored in this work. Results show that the degree of discretization and the microstructures used in finite element models of PBXs can significantly affect the estimated Young's moduli.

Polymer bonded explosives (PBXs) are particulate composites containing explosive particles and a continuous binder. The elastic modulus of the particles, at room temperature and higher, is often three to four orders of magnitude higher than that of the binder. Additionally, the explosive particles occupy high volume fractions, often greater than 90%. Both experimental and numerical determination of macroscopic properties of these composites is difficult. High modulus contrast mock PBXs provide a means of relatively inexpensive experimentation and validation of numerical approaches to determine properties of these materials. The goal of this investigation is to determine whether the effective elastic properties of monodisperse glass–estane mock PBXs can be predicted from two-dimensional micromechanics simulations using the finite element (FEM) method. In this study, the effect of representative volume element (RVE) size on the prediction of two-dimensional properties is explored. Two-dimensional estimates of elastic properties are compared with predictions from three-dimensional computations and with experimental data on glass–estane composites containing three different volume fractions of spherical glass beads. The effect of particle debonding on the effective elastic properties is also investigated using contact analyses. Results show that two-dimensional unit cells containing 10–20 circular particles are adequate for modelling glass–estane composites containing less than 60% glass particles by volume. No significant difference is observed between properties predicted by the two- and three-dimensional models. FEM simulations of RVEs, containing particles that are perfectly bonded to the binder, produce estimates of Young's modulus that are higher than the experimental data. Incorporation of debonding between particles and the binder causes the effective Young's modulus to decrease. However, the results suggest that cracks in the composite may play a significant role in determining the effective properties of mock polymer bonder explosives composed of glass and estane. The FEM simulations indicate that two-dimensional models that incorporate debonds and cracks can be used to obtain accurate estimates of the effective properties of glass–estane composites and possibly of PBXs.