An analytical study of droplet combustion under microgravity: Quasi-steady transient approach

An analytical model based on an assumption of combined quasi-steady and transient behavior of the process is presented to exemplify the unsteady, sphero-symmetric single droplet combustion under microgravity. The model used in the present study includes an alternative approach of describing the droplet combustion as a process where the diffusion of fuel vapor residing inside the region between the droplet surface and the flame interface experiences quasi-steadiness while the diffusion of oxidizer inside the region between the flame interface and the ambient surrounding experiences unsteadiness. The modeling approach especially focuses on predicting; the variations of droplet and flame diameters with burning time, the effect of vaporization enthalpy on burning behavior, the average burning rates and the effect of change in ambient oxygen concentration on flame structure. The modeling results are compared with a wide range of experimental data available in the literature. It is shown that this simplified quasi-steady transient approach towards droplet combustion yields behavior similar to the classical droplet theory.     

Influence of pressure-driven gas permeation on the quasi-steady burning of porous energetic materials

A theoretical two-phase-flow analysis is developed to describe the quasi-steady propagation, across a pressure jump, of a multi-phase deflagration in confined porous energetic materials. The difference, or overpressure, between the upstream (unburned) and downstream (burned) gas pressure leads to a more complex structure than that which is obtained for an unconfined deflagration in which the pressure across the multi-phase flame region is approximately constant. In particular, the structure of such a wave is shown by asymptotic methods to consist of a thin boundary layer characterized by gas permeation into the unburned solid, followed by a liquid-gas flame region, common to both types of problem, in which the melted material is preheated further and ultimately converted to gaseous products. The effect of gas flow relative to the condensed material is shown to be significant, both in the porous unburned solid as well as in the exothermic liquid-gas melt layer, and is, in turn, strongly affected by the overpressure. Indeed, all quantities of interest, including the burn temperature, gas velocity and the propagation speed, depend on this pressure difference, leading to a significant enhancement of the burning rate with increasing overpressure. In the limit that the overpressure becomes small, the pressure gradient is insufficient to drive gas produced in the reaction zone in the upstream direction, and all gas flow relative to the condensed material is directed in the downstream direction, as in the case of an unconfined deflagration. The present analysis is particularly applicable to those types of porous energetic solid, such as degraded nitramine propellants that can experience significant gas flow in the solid preheat region and which are characterized by the presence of exothermic reactions in a bubbling melt layer at their surfaces.     

Size effect on electric-double-layer capacitances of conducting structures

The charge storage in an electrical double-layer capacitor is dependent on the accumulation of ions on the interface between electrolyte and conducting material and the spatial distribution of ions in electrolyte. In this work, we study the effect of local curvature on the concentration of ions on the interface between electrolyte and electrode from the framework of thermodynamics and incorporate the concentration of ions on the interface in the analysis of the spatial distribution of ions for symmetric binary electrolytes. Semi-analytical results of the integral electrical-double-layer capacitances per unit area under the condition of large Debye-Hückel constant are obtained for spherical particle and cylindrical rod, which reveal the contribution of interface energy between the conducting material and the electrolyte to the storage of charge. For spherical cavity and cylindrical pore at small electric potential, the solution of the electric potential for linearized Poisson-Boltzmann equation is used in the calculation of the integral electrical-double-layer capacitances per unit area, which are dependent on the sizes of the cavity and pore and independent of the interface energy between the conducting material and the electrolyte. For spherical cavity and cylindrical pore at large electric potential, the integral double-layer capacitances are dependent on the interface energy.     

Influences of interfacial damage on the effective wave velocity in composites with reinforced particles

The scattering of elastic waves by a spherical particle with imperfect interface and the multiple scattering by many spherical particles with imperfect interface are studied in this paper. First, the scattering of elastic waves by a spherical particle with imperfect interface, i.e. spring interface model, is studied. Then, the multiple scattering by random distributed particles with interfacial damage in a composite material is investigated. The equations to evaluate velocity and attenuation of effective waves defined by statistic averaging are given. Furthermore, based on the established relation between the effective velocity and interfacial constants, a method to evaluate the interfacial damage nondestructively from the ultrasonic measure data is proposed. The numerical simulation is performed for the Sic-Al composites. The effective velocity is computed to show the influences of interface damage. By using the genetic algorithm, the interfacial damage is evaluated from the synthetic experimental data with various levels of error. The numerical results show the feasibility of the method proposed to approximately evaluate the interfacial damage in a composite material with reinforced particles based on ultrasonic data. Supported by the National Natural Science Foundation of China (Grant Nos. 10672019 and 10272003)     

Fixed-grid method for the modelling of unsteady partial oxidation of a spherical coal particle

The main goal of this work is the development of a fixed-grid method to model unsteady partial oxidation of a solid with implicit tracking of the interface. As a first step diffusive oxidation of a spherical coal particle is considered. The energy and species conservation equations formulated in spherical coordinates are discretised using the finite-volume approach. The boundary conditions for the temperature and species mass fractions at the solid–gas interface are modelled via special source terms activated in the interface cells. The numerical model was validated against analytic one- and two-film models for coal combustion in a dry-air atmosphere. Very good agreement was obtained. Based on the model developed a numerical study was carried out on the influence of water vapour on the partial oxidation of a spherical coal particle. Numerous numerical simulations were performed for particle diameters in the range 200×10^?6 m to 2×10^?2 m. The ambient temperature was varied in the range between 700 and 3000 K. The analysis of results showed that the addition of H₂O has an influence on the solution convergence due to the catalytic effect of water in the coal monoxide oxidation reaction making the whole system stiffer. However, at the same time, it was found that if the ambient mass fraction of water vapour is below 1×10^?3, its influence on combustion rates is minimal. The results of numerical simulations obtained for higher H₂O concentration (>1×10^?3) are discussed.     

In-situ flame particle tracking based on barycentric coordinates for studying local flame dynamics in pulsating Bunsen flames

Flame particles (FP) are massless, virtual particles which follow material points on the flame surface. This work presents a tracking algorithm for FPs which utilizes barycentric coordinates. The methodology can be used with any cell shape in the computational mesh and allows computationally fast spatial interpolation as well as efficient determination of the intersection of FP trajectories with iso-surfaces. In contrast to previous flame particle tracking (FPT) approaches, the code is fully parallelized and can therefore be used in-situ during the simulation. It also includes fully parallelized computation of flame consumption speed by integrating reaction rates along a line normal to the flame surface at each FP position. Direct numerical simulations of laminar pulsating premixed hydrogen–air Bunsen flames serve as validation cases and showcase the added value of tracking material points for studying local flame dynamics. Exciting the inlet flow harmonically with frequencies equal to the inverse flame time scale leads to a pulsating mode where the flame front is corrugated. Ten times higher frequencies nearly resemble the steady state solution. The FPs are seeded along the flame surface and are used to track the unsteady diffusive, convective and chemical contributions at arbitrary points on the flame front over time. Their trajectories reveal a phase shift between the unsteady flame stretch rate and local flame speed of the order of 0.1 flame time scales for rich hydrogen flames. This is caused by a time delay between straining and stretch due to curvature. The reason is that diffusive processes follow the time signal of curvature while chemical processes are most strongly affected by the straining rate, which dominates the high Lewis number hydrogen flames investigated. This time history effect may help to explain the large scattering in the correlation of local flame speed with flame stretch found in turbulent flames.     

Modelling of the influence of dihedral angle,volume fractions,particle size and coordination on the driving forces for sintering of dual phase systems

The equilibrium shape of solid particles in an aggregate immersed in a liquid or in a gas results from the minimization of interface energy. A model is developed for expressing the dependence of the solid–solid and solid–second phase interface areas on the system parameters: phase volume fractions, dihedral angle, particle size and coordination. The model aims at allowing quantitative assessment of the role of these parameters on the driving force for sintering. The representative volume element is a cone of which the apex angle accounts for the average particle coordination. In order to comply with the uniformity of interface curvature, the solid–second phase interfaces are described using the mathematics of the Delaunay surfaces. The results are compared with the solutions obtained by approximating the interface shape by the revolution of an arc of circle around the cone axis. This approximation does not involve a significant loss of precision.     

The comparison between the Mie theory and the Rayleigh approximation to calculate the EM scattering by partially charged sand

The Mie theory and Rayleigh approximation are two basic methods to study the EM scattering of uncharged spherical particle, and when the particle radius is much smaller than the incident wavelength, they are equivalent, but whether the Rayleigh approximation is still equivalent to Mie theory when we use them to calculate the EM scattering of small charged particle, there is still no any report published to discuss this problem. In this paper we make some comparisons between Mie theory and Rayleigh approximation to solve the EM scattering of partially electrification spherical particles. The results showed that the Mie theory would be more suitable to calculate the scattering of charged spherical particles.     

Embedded particle size distribution and its effect on detonation in composite explosives

This paper discusses the effects of stochastically varying inert particle parameters on the long-term behaviour of detonation front propagation. The simulation model involves a series of cylindrical high explosive unit cells, each embedded with an inert spherical particle. Detonation shock dynamics theory postulates that the velocity of the shock front in the explosive fluid is related to its curvature. In our previous work, we derived a series of partial differential equations that govern the propagation of the shock front passing over the inert particles and developed a computationally efficient simulation environment to study the model over extremely long timescales. We expand upon that project by randomising several properties of the inert particles to represent experimental designs better. First, we randomise the particle diameters according to the Weibull distribution. Then we discuss stochastic particle spacing methods and their effects on the predictability of the shock wave speed. Finally, we discuss mixtures of plastic and metal particles and material inconsistency among the particles.     

Influence of different interfaces on laser propulsion in water environment

The dynamics of laser-induced semispherical cavitation bubbles are investigated by means of an optical beam deflection method. The bubbles were generated in water in the vicinity of three different interfaces: including water–air, water–colloid and water–solid, and also in the bulk. Numerical simulation shows that the propelled surface obtains more energy and longer propulsion from the semispherical bubble than from the spherical bubble during the first expansion of the bubble. The collapse time of the quasi-semispherical bubble is significantly less than the Rayleigh collapse time of the spherical bubble for all the cases considered in this work. The influence of water–air or water–solid interfaces on the collapse time of a semispherical bubble is similar to that of a spherical bubble. As the bubble energy grows, the effect of the water–colloid interface changes gradually from that of the water–solid to that of the water–air interface. In other words, the energy of the bubble dictates whether the water–colloid interface behaves as a water–solid or a water–air interface.     

On the mechanism of hotspot initiation of detonation

A mechanism of the initiation of hotspots in heterogeneous solid high explosives was considered. It was demonstrated that the growth of hotspots may be associated with the propagation of a thermal wave in the deflagration regime only at an early stage of the process. The growth at later stages occurs in the reactive shock regime, a finding that renders the assumption about a very high deflagration wave velocity redundant.     

非球形水下爆炸气泡坍塌机制

 为研究非球形水下爆炸气泡的坍塌机制和射流特性,采用水下爆炸实验和数值模拟相结合的手段,研究了典型的柱形装药自由场水下爆炸气泡的运动过程。实验结果与数值模拟结果符合较好,通过对比发现,非球形水下爆炸气泡坍塌所形成的射流与球形气泡坍塌射流的行为存在差异。研究结果表明：非球形气泡的坍塌过程与气泡初始形态的局部曲率半径有关,初始气泡表面曲率半径大的区域的初始膨胀速度较曲率半径小的区域的小,坍塌时刻也较早,导致气泡产生非球形坍塌。     

Nanoscale deformation of a liquid surface

We study the interaction between a solid particle and a liquid interface. A semianalytical solution of the nonlinear equation that describes the interface deformation points out the existence of a bifurcation behavior for the apex deformation as a function of the distance. We show that the apex curvature obeys a simple power-law dependency on the deformation. Relationships between physical parameters disclose the threshold distance at which the particle can approach the liquid before capillarity provokes a "jump to contact." A prediction of the interface original position before deformation takes place, as well as the attraction force measured by an approaching probe, are produced. The results of our analysis agree with the force curves obtained from atomic force microscopy experiments over a liquid puddle.     

The role of interfacial layers in the enhanced thermal conductivity of nanofluids: A renovated Hamilton–Crosser model

We previously developed a renovated Maxwell model for the effective thermal conductivity of nanofluids and determined that the solid/liquid interfacial layers play an important role in the enhanced thermal conductivity of nanofluids. However, this renovated Maxwell model is limited to suspensions with spherical particles. Here, we extend the Hamilton--Crosser model for suspensions of nonspherical particles to include the effect of a solid/liquid interface. The solid/liquid interface is described as a confocal ellipsoid with a solid particle. The new model for the three-phase suspensions is mathematically expressed in terms of the equivalent thermal conductivity and equivalent volume fraction of anisotropic complex ellipsoids, as well as an empirical shape factor. With a generalized empirical shape factor, the renovated Hamilton--Crosser model correctly predicts the magnitude of the thermal conductivity of nanotube-in-oil nanofluids. At present, this new model is not able to predict the nonlinear behavior of the nanofluid thermal conductivity.     

强声波作用下煤颗粒周围气体的振荡流动特性

根据二维非稳态层流的质量和动量守恒方程,研究强声波作用下煤颗粒周围气体的振荡流动特性.入射波的振幅远大于颗粒特征长度,声雷诺数小于20.根据通用微分方程的解,详细分析不同声雷诺数与斯特劳哈尔数下,颗粒壁面的流场分布、轴向压力梯度、切向应力及分离角的分布,发现在低频（~50 Hz）时,颗粒壁面轴向压力梯度、切向应力及流动分离角的分布主要受曲率效应影响,其变化规律与振荡速度的幅值变化相对应;在高频时（~5 000 Hz）,颗粒壁面轴向压力梯度、切向应力及流动分离角的分布同时受到曲率效应和流动加速度的影响.为进一步研究强声波强化煤颗粒燃烧提供理论基础.     

Effects of endothermic chain-branching reaction on spherical flame initiation and propagation

A theoretical model is developed to describe the spherical flame initiation and propagation. It considers endothermic chain-branching reaction and exothermic recombination reaction. Based on this model, the effects of endothermic chain-branching reaction on spherical flame initiation and propagation are assessed. First, the analytical solutions for the distributions of fuel and radical mass fraction as well as temperature are obtained within the framework of large activation energy and quasi-steady assumption. Then, a correlation describing spherical flame initiation and propagation is derived. Based on this correlation, different factors affecting spherical flame propagation and initiation are examined. It is found that endothermicity of the chain-branching reaction suppresses radical accumulation at the flame front and thus reduces flame intensity. With the increase of endothermicity, the unstretched flame speed decreases while both flame ball radius and Markstein length increases. Endothermicity has a stronger effect on the stretched flame speed with larger fuel Lewis number. The Markstein length is found to increase monotonically with endothermicity. Furthermore, the endothermicity of the chain-branching reaction is shown to affect the transition among different flame regimes including ignition kernel, flame ball, propagating spherical flame, and planar flame. The critical ignition power radius increases with endothermicity, indicating that endothermicity inhibits the ignition process. The influence of endothermicity on ignition becomes relatively stronger at higher crossover temperature or higher fuel Lewis number. Moreover, one-dimensional transient simulations are conducted to validate the theoretical results. It is shown that the quasi-steady-state assumption used in theoretical analysis is reasonable and that the same conclusion on the effects of endothermic chain-branching reaction can be drawn from simulation and theoretical analysis.     

Theory of gaseous detonations

The objective of the present paper is to review some developments that have occurred in detonation theory over the last ten years. They concern nonlinear dynamics of detonation fronts, namely patterns of pulsating and/or cellular fronts, selection of the cell size, dynamical self-quenching, direct (blast) or spontaneous initiation, and transition from deflagration to detonation. These phenomena are all well documented by experiments since the sixties but remained unexplained until recently. In the first part of the paper, the patterns of cellular detonations are described by an asymptotic solution to nonlinear hyperbolic equations (reactive Euler equations) in the form of unsteady (sometime chaotic) and multidimensional traveling-waves. In the second part, turning points of quasi-steady solutions are shown to correspond to critical conditions of fully unsteady problems, either for (direct or spontaneous) initiation or for spontaneous failure (self-quenching). Physical insights are tentatively presented rather than technical aspects. The challenge is to identify the physical mechanisms with their relevant parameters, and more specifically to explain how the length-scales involved in detonation dynamics are larger by two order of magnitude (at least) than the length-scale involved in the steady planar traveling-wave solution (detonation thickness).     

Refraction in media with a negative refractive index

We show that an electromagnetic (EM) wave undergoes negative refraction at the interface between a positive and negative refractive index material, the latter being a properly chosen photonic crystal. Finite-difference time-domain (FDTD) simulations are used to study the time evolution of an EM wave as it hits the interface. The wave is trapped temporarily at the interface, reorganizes, and, after a long time, the wave front moves eventually in the negative direction. This particular example shows how causality and speed of light are not violated in spite of the negative refraction always present in a negative index material.     

Particle Size Influence on the Effective Permeability of Composite Materials

The energy method, which estimates the effective permeability of composite material is proposed. We approximate the effective static magnetic permeability by energy method and Maxwell-Garnett method for spherical particles dispersing system. Considering the effect of the interface layer between the medium and the particle, we study the nanoparticles embedded in a medium exactly. The interface layer property plays a significant factor for the effective permeability of the composite material in which nano-sized particles embedded.