Delay time for fine particle ignition within gas with fluctuating temperature

The Pontryagin equation was applied to calculating the average time for the random process escaping the assign interval: this gives the average delay time for waiting of particle ignition moment in a turbulent flow of gas. A direct numerical simulation method was developed for gas temperature fluctuations with assigned autocorrelation function and particle temperature fluctuations due to exothermal chemical reaction. The method was based on numerical solution of a system of stochastic differential equations. Results of direct simulation were validated through comparing with the analytical solution available for particles without exothermal reaction. Analytical calculations and results of direct numerical simulation for the delay time of particle ignition are in agreement.     

Mathematical combustion model of nanoaluminum-air suspension

This paper presents a combustion model of a nano-aluminum-air (nAl-air) suspension. The special feature of the model is performing a local mathematical model of the oxidant diffusion through an aluminum oxide layer on the particle surface taking into account the aluminum-oxidant reaction to simulate the combustion of nano-size aluminum (nAl) particles. The oxidation rate of the aluminum particles and the associated with this process the rate of heat release are determined from the solution of the local combustion problems for the entire set of nAl particles in the suspension. To obtain the suspension state parameters we solve the equation system, which includes the energy conservation equations for the gas and particles, the mass-conservation equation for the gas-dispersed mixture and the motion equations for the gas and particles controlling for the particle velocity lag. The model considers gas expansion and thus gas and particle motion. The developed model does not require setting the ignition temperature of nAl particles. The study provides the calculated propagation rate of the combustion front in the nAl-air suspension depending on the nAl mass concentration and on the initial temperature of the suspension.     

Screening of a charged particle field in rarefied ionized gas

A self-consistent field of a charged micron-size particle placed in a rarefied ionized gas is created by both free ions moving along infinite trajectories and trapped ions moving in closed orbits. The character of screening of the particle field is analyzed under dynamic conditions in a nonequilibrium plasma where the temperature (or the mean energy) of electrons greatly exceeds the ion temperature. Under these conditions, trapped ions are generated in a restricted region of the particle field where the transitions between closed ion orbits resulting from resonant charge exchange dominate. This leads to a higher number density of trapped ions compared to that of free ions. The parameters of the self-consistent field of the particle and ions are found when free or trapped ions determine the screening of the particle field, and a similarity law is established for a simultaneous variation of the number density of plasma particles and the particle size. In dusty plasmas of the Solar System, which result from the interaction of the solar wind with dust, formation of trapped ions increases the plasma number density compared to that in the solar wind.     

镁颗粒群非稳态着火过程数值模拟

建立了镁颗粒群着火的一维非稳态有限影响体模型, 数值模拟颗粒群中镁颗粒的着火过程. 研究表明, 当镁颗粒表面反应加剧之后,颗粒相温度急剧上升, 迅速达到着火, 而其周围气相的温升速率却远小于颗粒的温升速率; 在着火过程中气相温度只在颗粒表面附近升高比较明显, 整体温度升高不大. 分析了颗粒群内部参数和环境参数对镁颗粒群着火的影响. 随颗粒浓度的增加, 颗 粒群变得易于着火, 其着火时间变短, 但颗粒浓度增大到一定程度后, 继续增大该值将对颗粒群的着火起消极作用. 环境压力对颗粒群着火的影响比较小,在1-5 atm范围内颗粒群的着火性能基本不变. 气相中氧气浓度对颗粒群的着火性能影响也不显著, 但当氧气浓度过小时, 对着火过程的影响将大大增强.颗粒粒径、气相/颗粒相初温、辐射源温度对颗粒 群着火的影响巨大,小粒径、高温度促使颗粒群快速着火.数值模拟与文献中试验 结果的变化趋势相一致.     

Effect of polymorphic phase transformations in alumina layer on ignition of aluminium particles

The mechanism of aluminium oxidation is quantified and a simplified ignition model is developed. The model describes ignition of an aluminium particle inserted in a hot oxygenated gas environment: a scenario similar to the particle ignition in a reflected shock in a shock tube experiment. The model treats heterogeneous oxidation as an exothermic process leading to ignition. The ignition is assumed to occur when the particle's temperature exceeds the alumina melting point. The model analyses processes of simultaneous growth and phase transformations in the oxide scale. Kinetic parameters for both direct oxidative growth and phase transformations are determined from thermal analysis. Additional assumptions about oxidation rates are made to account for discontinuities produced in the oxide scale as a result of increase in its density caused by the polymorphic phase changes. The model predicts that particles of different sizes ignite at different environment temperatures. Generally, finer particles ignite at lower temperatures. The model consistently interprets a wide range of the previously published experimental data describing aluminium ignition.     

Relativistic kinetics of phonon gas in superfluids

The relativistic kinetic theory of the phonon gas in superfluids is developed. The technique of the derivation of macroscopic balance equations from microscopic equations of motion for individual particles is applied to an ensemble of quasi-particles. The necessary expressions are constructed in terms of a Hamilton function of a (quasi-)particle. A phonon contribution into superfluid dynamic parameters is obtained from energy-momentum balance equations for the phonon gas together with the conservation law for superfluids as a whole. Relations between dynamic flows being in agreement with results of relativistic hydrodynamic consideration are found. Based on the kinetic approach a problem of relativistic variation of the speed of sound under phonon influence at low temperature is solved.     

SERS from light localization positions

The proposed model allows to analyze reasons for surface enhanced Raman scattering (SERS) by molecules adsorbed onto surface of metal particles. It considers multiple inelastic scattering of a photon, which moves along a closed loop inside a system of closely packed small metallic particles. During this motion, the photon undergoes multiple exchanges with the medium by the same amount of energy corresponding to excitation in the system of charge density fluctuations, which are permanently present in the system. The energy of such fluctuations can be an arbitrary value, with magnitude of less than the energy of incident photon. Probability of the excitation is very high and comparable with the probability of resonance excitation of the dipole surface plasmon in a separate particle. Strong local fields related to these fluctuations exist over entire frequency range from infrared up to ultraviolet. The reason for the photon motion along the closed loop is related to constructive interference of amplitudes corresponding to two alternative ways of the loop passing; clockwise and counter clockwise. Probability of such motion is calculated. Peculiarities of behavior of charge density fluctuations allow explaining some specific features of flicker noise. Copyright © 2013 John Wiley & Sons, Ltd.     

Transport theory for quantum crystals

A correlation function approach is developed to treat non-equilibrium phenomena of quantum crystals at low frequency and long wavelength within the renormalized harmonic approximation (RHA). The derivation of the transport equations is carried out by studying the hierarchy of equations of motion for the retarded Green's functions of a pure, nonprimitive, nonionic, anharmonic lattice. Using a factorization technique to take into account the most important terms due to the particle fluctuations and the leading contributions to the hydrodynamic singularities of the phonon self-energy, we find a differential equation for the displacement field and a generalized transport equation for the phonon gas. The microscopic RHA expressions for the local temperature, the local heat density and the energy current are derived; the quasiparticle parameters (elastic constants, generalized Grüneisen parameters, quasiparticle interaction) entering the equations of motion are shown to be consistent with the RHA. In the hydrodynamic regime the general equations are reduced to two coupled differential equations for the lattice deformations and for the local temperature. Then only the displacement-displacement, the displacement-energy density and the energy density-energy density correlation functions show macroscopic fluctuations; for these functions thermodynamical sum-rules are derived.     

Numerical investigation of pulverized coal particle group combustion using tabulated chemistry

The ignition and combustion of coal particle groups are investigated numerically in a laminar flow reactor. The Flamelet Generated Manifold method is extended to account for the complex mixture of gases being released during devolatilization, which is calculated with a competing two-step model. A second mixture fraction is introduced to include the mixing with the second methane fuel stream. The interactions of the gas phase with particles are modeled within a fully coupled Euler-Lagrange framework. To investigate the influence of particle groups on ignition and combustion, successively increasing densities of particle streams have been analyzed. The ignition delay time is increased significantly by higher particle densities. This delay is validated successfully with the available measurements. Moreover, the shape of the volatile flame was found to be strongly influenced by the particle number density inside the flame. A transition from spherical flames around single particles to a conical flame around the particle cloud could be found in numerical results as well as in experiments. As the primary mechanism for the substantial ignition delay and the formation of the flame, the increased heat transfer from the gas-phase to the particle group, resulting in lower gas-phase temperatures, was identified.     

Multiple band electron-phonon transport theory: II. Derivation of transport equation

For an electron-phonon system with several equivalent bands a closed set of integral equations is solved self-consistently using real-time Green's functions. A multiple-band Peierls-Boltzmann equation is deduced from the Bethe-Salpeter equation for the electron density. Relaxation-time approximation together with local particle number conservation allows the calculation of the dielectric response and the displacement response generalized for the multiple-band case. The poles of the latter response function, essentially governed by electron density fluctuations, determine three coupled modes. A soft-mode instability is found in agreement with A15- compounds.     

Auto-ignition of methane–air mixtures flowing along an array of thin catalytic plates

In this paper, the heterogeneous ignition of a methane–air mixture flowing along an infinite array of catalytic parallel plates has been studied by inclusion of gas expansion effects and the finite heat conduction on the plates. The system of equations considers the full compressible Navier–Stokes equations coupled with the energy equations of the plates. The gas expansion effects which arise from temperature changes have been considered. The heterogeneous kinetics considers the adsorption and desorption reactions for both reactants. The limits of large and small longitudinal thermal conductance of the plate material are analyzed and the critical conditions for ignition are obtained in closed form. The governing equations are solved numerically using finite differences. The results show that ignition is more easily produced as the longitudinal wall thermal conductance increases, and the effects of the gas expansion on the catalytic ignition process are rather small due to the large value of the activation energy of the desorption reaction of adsorbed oxygen atoms.     

DSM-LPDF两相湍流模型及旋流两相流动的模拟

本文由流体－颗粒速度的拉氏联合概率密度函数（ＰＤＦ）输运方程出发,用Ｓｉｍｏｎｉｎ建议的Ｌａｎｇｅｖｉｎ模型封闭颗粒所遇到流体瞬时速度的条件期望项,并用Ｍｏｎｔｅ Ｃａｒｌｏ方法直接求解 ＰＤＦ输运方程,将其和求解流体雷诺应力方程模型的有限差分方法结合,建立了雷诺应力－拉氏ＰＤＦ（ＤＳＭ－ＬＰＤＦ,简称ＤＬ）两相湍流模型．用此模型模拟了旋流数为０．４７的突扩旋流气粒两相流动,并与文献中ＰＤＰＡ实验和用类似于单相流动湍流模型封闭方法的时平均统一二阶矩（ＵＳＭ）模型的预报进行了对比．     

Stochastic modeling of evaporating sprays within a consistent hybrid joint PDF framework

In the present study, a framework for modeling two-phase evaporating flow is presented, which employs an Eulerian–Lagrangian–Lagrangian approach. For the continuous phase, a joint velocity-composition probability density function (PDF) method is used. Opposed to other approaches, such PDF methods require no modeling for turbulent convection and chemical source terms. For the dispersed phase, the PDF of velocity, diameter, temperature, seen gas velocity and seen gas composition is calculated. This provides a unified formulation, which allows to consistently address the different modeling issues associated with such a system. Because of the high dimensionality, particle methods are employed to solve the PDF transport equations. To further enhance computational efficiency, a local particle time-stepping algorithm is implemented and a particle time-averaging technique is employed to reduce statistical and bias errors. In comparison to previous studies, a significantly smaller number of droplet particles per grid cell can be employed for the computations, which rely on two-way coupling between the droplet and gas phases. The framework was validated using established experimental data and a good overall agreement can be observed.     

Ignition and combustion of a dense powder jet of micron-sized aluminum particles in hot gas

Aiming at the potential implementation of aluminum as a primary fuel in powder-fueled ramjets or engines, this work seeks to investigate the ignition and combustion characteristics of a dense gas-suspended jet of micron-sized aluminum particles in a hot flow with controlled temperature and compositions. Aluminum particles with a mean diameter of 40 µm are aerosolized using a custom-made feeder and carried into the burner by a nitrogen stream. The powder jet with a particle density of up to 1–3 kg/m³ can be ignited and burned violently at a surrounding gas temperature as low as 1500 K. The lowered ignition temperature of the powder jet can be attributed to a cooperative mechanism resulting in fast reactions. Meanwhile, the ignition delay time decreases from ∼25 to ∼5 ms when the surrounding temperature increases from 1500 to 2200 K. The burning powder jet generates strong luminance and AlO emission signals detected by a spectrometer. Particle image velocimetry (PIV) and camera pyrometry are used to derive the two-dimensional velocity and average projected temperature distribution, respectively. Furthermore, a high-speed camera with a microscopic lens captures the transition from dispersed combustion to group combustion that forms a large-scale flame column wrapping the entire powder jet. The aluminum oxide produced in the columnar flame forms a large number of nanosized smoke particles in the condensation region. Finally, a numerical model considering the collective effect of the powder jet is developed to predict the particle temperature history during the ignition stage, which shows good agreement with the temperature profiles derived from camera pyrometry and PIV techniques.     

Heat and mass transfer at gas-phase ignition of grinded coal layer by several metal particles heated to a high temperature

Characteristics of gas-phase ignition of grinded brown coal (brand 2B, Shive-Ovoos deposit in Mongolia) layer by single and several metal particles heated to a high temperature (above 1000 K) have been investigated numerically. The developed mathematical model of the process takes into account the heating and thermal decomposition of coal at the expense of the heat supplied from local heat sources, release of volatiles, formation and heating of gas mixture and its ignition. The conditions of the joint effect of several hot particles on the main characteristic of the process–ignition delay time are determined. The relation of the ignition zone position in the vicinity of local heat sources and the intensity of combustible gas mixture warming has been elucidated. It has been found that when the distance between neighboring particles exceeds 1.5 hot particle size, an analysis of characteristics and regularities of coal ignition by several local heat sources can be carried out within the framework of the model of “single metal particle / grinded coal / air”. Besides, it has been shown with the use of this model that the increase in the hot particle height leads, along with the ignition delay time reduction, to a reduction of the source initial temperatures required for solid fuel ignition. At an imperfect thermal contact at the interface hot particle / grinded coal due to the natural porosity of the solid fuel structure, the intensity of ignition reduces due to a less significant effect of radiation in the area of pores on the heat transfer conditions compared to heat transfer by conduction in the near-surface coal layer without regard to its heterogeneous structure.     

Exploring the thermodynamics of a two-dimensional Bose gas

Using in situ measurements on a quasi-two-dimensional, harmonically trapped (87)Rb gas, we infer various equations of state for the equivalent homogeneous fluid. From the dependence of the total atom number and the central density of our clouds with chemical potential and temperature, we obtain the equations of state for the pressure and the phase-space density. Then, using the approximate scale invariance of this 2D system, we determine the entropy per particle and find very low values (below 0.1k(B)) in the strongly degenerate regime. This shows that this gas can constitute an efficient coolant for other quantum fluids. We also explain how to disentangle the various contributions (kinetic, potential, interaction) to the energy of the trapped gas using a time-of-flight method, from which we infer the reduction of density fluctuations in a nonfully coherent cloud.