Combustion effects in confined explosions

Results of shock-dispersed-fuel (SDF) explosion experiments are presented. The SDF charge consisted of a spherical 0.5-g PETN booster surrounded by 1 g of fuel, either flake aluminum (Al) powder or TNT. The charge was placed at the center of a sealed chamber. Three cylindrical chambers (volumes of 6.6, 20, and 40 l with L/D = 1) and three tunnels (L/D = 3.8, 4.65, and 12.5) were used to explore the influence of chamber volume and geometry on completeness of combustion. Detonation of the SDF charge created an expanding cloud of explosion product gases and hot fuel (Al or TNT). When this fuel mixed with air, it formed a turbulent combustion cloud that consumed the fuel and liberated additional energy (31 kJ/g for Al or 15 kJ/g for TNT) over and above detonation of the booster (6 kJ/g) that created the explosion. Static pressure gauges were the main diagnostic. Pressure and impulse histories for explosions in air were much greater than those recorded for explosions in nitrogen—thereby demonstrating that combustion has a dramatic effect on the chamber pressure. This effect increases as the confinement volume decreases and the excess air ratio approaches values between 2 and 3.5.     

Spherical combustion clouds in explosions

This study explores the properties of spherical combustion clouds in explosions. Two cases are investigated: (1) detonation of a TNT charge and combustion of its detonation products with air, and (2) shock dispersion of aluminum powder and its combustion with air. The evolution of the blast wave and ensuing combustion cloud dynamics are studied via numerical simulations with our adaptive mesh refinement combustion code. The code solves the multi-phase conservation laws for a dilute heterogeneous continuum as formulated by Nigmatulin. Single-phase combustion (e.g., TNT with air) is modeled in the fast-chemistry limit. Two-phase combustion (e.g., Al powder with air) uses an induction time model based on Arrhenius fits to Boiko’s shock tube data, along with an ignition temperature criterion based on fits to Gurevich’s data, and an ignition probability model that accounts for multi-particle effects on cloud ignition. Equations of state are based on polynomial fits to thermodynamic calculations with the Cheetah code, assuming frozen reactants and equilibrium products. Adaptive mesh refinement is used to resolve thin reaction zones and capture the energy-bearing scales of turbulence on the computational mesh (ILES approach). Taking advantage of the symmetry of the problem, azimuthal averaging was used to extract the mean and rms fluctuations from the numerical solution, including: thermodynamic profiles, kinematic profiles, and reaction-zone profiles across the combustion cloud. Fuel consumption was limited to $\sim $ 60–70 %, due to the limited amount of air a spherical combustion cloud can entrain before the turbulent velocity field decays away. Turbulent kinetic energy spectra of the solution were found to have both rotational and dilatational components, due to compressibility effects. The dilatational component was typically about 1 % of the rotational component; both seemed to preserve their spectra as they decayed. Kinetic energy of the blast wave decayed due to the pressure field. Turbulent kinetic energy of the combustion cloud decayed due to enstrophy $\overline{\omega ^{2}} $ and dilatation $\overline{\Delta ^{2}} $ .     

An empirical model for the ignition of explosively dispersed aluminum particle clouds

An empirical model for the ignition of aluminum particle clouds is developed and applied to the study of particle ignition and combustion behavior resulting from explosive blast waves. This model incorporates both particle ignition time delay as well as cloud concentration effects on ignition. The total mass of aluminum that burns is found to depend on the model, with shorter ignition delay times resulting in increased burning of the cloud. After the Al particles ignite, a competition for oxidizer between the booster detonation products and Al ensues. A new mass-averaged ignition parameter is defined and is observed to serve as a useful parameter to compare cloud ignition behavior. Investigation of this variable reveals that both peak ignition as well as the time required to attain peak ignition, are sensitive to the model parameters. The peak degree of dissociation in the fireball is about 19 % and the associated energy can play a significant role on the dynamics of the problem. The peak degree of ionization is about 2.9 % and the energy associated with this is much lower than the other controlling factors. Overall, this study demonstrates that the new ignition model developed captures effects not included in other combustion models for the investigation of shock-induced ignition of aluminum particle clouds.     

Higher-order accurate implicit time integration schemes for transport problems

The present paper is concerned with the numerical solution of transient transport problems by means of spatial and temporal discretization methods. The generalized initial boundary value problem of various nonlinear transport phenomena like heat transfer or mass transport is discretized in space by p-finite elements. After finite element discretization, the resulting first-order semidiscrete balance has to be solved with respect to time. Next to the classical generalized-α integration method predicated on the Newmark approach and the evaluation at a generalized midpoint also implicit Runge–Kutta time integration schemes, are presented. Both families of finite difference-based integration schemes are derived for general first-order problems. In contrast to the above-mentioned algorithms, temporal discontinuous and continuous Galerkin methods evaluate the balance equation not at a selected time instant within the timestep, but in an integral sense over the whole time step interval. Therefore, the underlying semidiscrete balance and the continuity of the primary variables are weakly formulated within time steps and between time steps, respectively. Continuous Galerkin methods are obtained by the strong enforcement of the continuity condition as special cases. The introduction of a natural time coordinate allows for the application of standard higher-order temporal shape functions of the p-Lagrange type and the well-known Gau?–Legendre quadrature of associated time integrals. It is shown that arbitrary order accurate integration schemes can be developed within the framework of the proposed temporal p-Galerkin methods. Selected benchmark analyses of calcium diffusion demonstrate the properties of all three methods with respect to non-smooth initial or boundary conditions. Furthermore, the robustness of the present time integration schemes is also demonstrated for the highly nonlinear reaction–diffusion problem of calcium leaching, including the pronounced changes of the reaction term and non-smooth changes of Dirichlet boundary conditions of calcium dissolution.     

Anisotropic density growth of bone—A computational micro-sphere approach

Bones are able to adapt their local density when exposed to mechanical loading. Such growth processes result in densification of the bone in regions of high loading levels and in resorption of the material in regions of low loading levels. This evolution and optimisation process generates heterogeneous distributions of bone density accompanied by pronounced anisotropic mechanical properties. While several constitutive models reported in the literature assume the growth process to be purely isotropic, only few studies focus on the modelling and simulation of anisotropic functional adaptation we can observe in vivo. Some of these few computational models for anisotropic growth characterise the evolution of anisotropy by analogy to anisotropic continuum damage mechanics while others include anisotropic growth but assume isotropic elastic properties.The objective of this work is to generalise a well-established framework of energy-driven isotropic functional adaptation to anisotropic microstructural growth and density evolution. We adopt the so-called micro-sphere concept, which proves to be extremely versatile and flexible to extend sophisticated one-dimensional constitutive relations to the three-dimensional case. In this work we apply this framework to the modelling and simulation of anisotropic functional adaptation by means of a directional density distribution, which evolves in time and in response to the mechanical loading condition. Several numerical studies highlight the characteristics and properties of the anisotropic growth model we establish. The formulation is embedded into an iterative finite element algorithm to solve complex boundary value problems. In particular, we consider the finite-element-simulation of a subject-specific proximal tibia bone and a comparison to experimental measurements. The proposed model is able to appropriately represent the heterogeneous bone density distribution. As an advantage over several other computational growth models proposed in the literature, a pronounced local anisotropy evolution is identified and illustrated by means of orientation-distribution-type density plots.     

Computational Material Forces in Micromorphic Continua

The micromorphic continuum theory is used to describe materials with significant microstructure which thus exhibit scaledependence (see e.g. [1], [2] [3]). Microcontinua are assumed to be attached to each physical point and may experience both stretch and rotation which are affine throughout the microcontinuum, nevertheless kinematically independent from the deformation on the macroscale. The additional kinematical quantities which account for the micro-deformation yield additional stresses and contributions to the balance of momentum. Additionally to the common finite-element approximation which here is a coupled problem to be solved for macro- and the micro-quantities, we apply the method of material forces, cf. [4], [5]. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Short pulse physics of quantum well structures

This paper reports some recent results of time-resolved studies of the carrier dynamics in GaAs/GaAlAs quantum well structures with picosecond and subpicosecond time resolution. These experiments have provided insight into carrier trapping, energy relaxation, and carrier recombination processes. Carrier trapping into the quantum well layers is very efficient and determines the decay of the GaAlAs luminescence even for 1 μm thick cladding layers. Carrier recombination is enhanced particularly at low temperatures. This effect has been attributed to the increased overlap of electron and hole (exciton) wavefunctions in the quasi-two-dimensional carrier system.     

Bilateral, difunctional nanosphere aggregates and their assembly mediated by polymer chains

We have developed an efficient method for producing difunctional, bilateral nanospheres. A monolayer of nanoparticles was prepared followed by deposition of a thin layer of metal. By varying the base particle and metal deposited, bilateral nanoparticles were formed. The different regions of the nanoparticles were selectively functionalized with polymer linkers containing specific terminal groups, thereby creating bilateral, difunctional nanoparticles. Subsequent covalent cross-linking of different nanoparticles enabled the formation of stable architectures with programmed hierarchy and controlled chemical composition.