The range of validity of the Rayleigh limit for computing mie scattering and extinction efficiencies

For the small particle limit for scattering by either absorbing or dielectric spheres, values of the size parameter are determined below which various approximate expressions for the scattering and extinction efficiencies are accurate to within 1%. Simple, analytical criteria for ensuring 1% accuracy are given in terms of the size parameter and the complex refractive index. A much broader range of refractive indices is considered than has been studied previously.     

Spontaneous ignition temperature for the compacted mixture of Ti–Al system: Theory and experimental comparisons

Spontaneous ignition of compacted mixture has been examined not only experimentally but also theoretically, relevant to materials synthesis by combustion for Ti–Al system. By varying compact and particle sizes, mixture ratio, and degree of dilution, spontaneous ignition temperature has been measured, which is determined from the inflection-point of the temporal variations of the surface temperature. It is found that the spontaneous ignition temperature decreases with increasing aspect ratio, defined as the ratio of the sample height and compact diameter, due to an establishment of the stationary temperature distribution in the radial direction in the compacted mixture, as the sample height becomes tall. It is also found that the spontaneous ignition temperature decreases with increasing size ratio, defined as the ratio of compact and particle diameters, due to an increase in the particle surface per unit spatial volume of the compacted mixture, caused by a decrease in the particle diameter and/or an increase in the compact diameter. By further examining its dependence on mixture ratio and/or degree of dilution, it is confirmed that the limit of flammability also exerts influences on the spontaneous ignition temperature. In addition, a fair degree of agreement, shown in experimental comparisons with theoretical results, indicates that the present formulation has captured the essential features of the spontaneous ignition of compacted mixture. Since this kind of particle size effect, especially, relevant to the spontaneous ignition of compacted mixtures, has not been captured in the previous studies, its elucidation can be considered not only notable but also useful, especially, in manipulating combustion process in materials synthesis.     

On the critical diameter and hotspot combustion of a double-base propellant

An analysis of experimental data on the critical diameter for burning of nitroglycerin-based propellant NB and on the temperature profiles in the combustion wave on a propellant sample in a heat-absorbing confinement was performed. It was demonstrated that, for cylindrical samples placed into a heat-absorbing confinement, there are two values of the critical diameter. The smallest value of the critical diameter (lower extinction limit) is associated with heat losses from the heat conduction zone and reaction zone of the condensed phase. The largest value of the critical diameter (upper extinction limit) is determined by heat losses from the condensed and gas phases. It was demonstrated that the value of the critical diameter is controlled by the maximum size of hotspots on the burning surface. For example, the mean critical diameter equals approximately twice the maximum hotspot size. Critical diameters characteristic of the range between the lower and upper limits range from a quarter to a half of the maximum hotspot size, with the process of extinction in this interval being of stochastic character.     

Phase transitions in binary mixtures of rodlike colloids and stiff polymers

A suspension of long rodlike colloids and long stiff polymers is modelled as a mixture of hard rods. The diameter of the colloid particle is finite, while the polymer is considered in the limit of zero diameter. Two types of first-order phase transition may occur in such mixtures: an isotropic-nematic phase transition if the density (or the pressure) is high enough, and a demixing transition involving two isotropic phases. The demixing transition has a critical point, and a triple point with one nematic and two isotropic phases may also exist. Phase diagrams are calculated. For the demixing isotropic-isotropic transition to be observed the ratio between the polymer length and the colloid length must exceed 0.36.     

Evidence for the transition from the diffusion-limit in aluminum particle combustion

This work presents experimental evidence that the transition from gas-phase diffusion-limited combustion for aluminum particles begins to occur at a particle size of 10 μm at a pressure of 8.5 atm. Measurements of the particle temperature by AlO spectroscopy and three-color pyrometry indicate that the peak temperature surrounding a burning particle approaches the aluminum boiling temperature as particle size is decreased to 10 μm when oxygen is the oxidizer. This reduction indicates that reactions are occurring at or near the particle surface rather than in a detached diffusion flame. When CO₂ is the oxidizer, the combustion temperatures remain near the aluminum boiling temperature for particles as large as 40 μm, indicating that the flame is consistently near the surface throughout this size range. Burn time measurements of 10 and 2.8 μm powders indicate that burn time is roughly proportional to particle diameter to the first power. The burn rates of micron- and nano-particles also show strong pressure dependence. These measurements all indicate that the combustion has deviated from the vapor-phase diffusion limit, and that surface or near-surface processes are beginning to affect the rate of burning. Such processes would have to be included in combustion models in order to accurately predict burning characteristics for aluminum with diameter less than 10 μm.     

Extinction characteristics of isolated n-alkane fuel droplets during low temperature cool flame burning in air

Large carbon number n-alkanes are a notable component in all real transportation fuels, and their chemical structure fosters substantial low temperature kinetic reactivity. Normal alkanes have been studied in various canonical configurations but rarely in systems with strong coupling between low temperature chemistry and transport for pure as well as for multi-component n-alkane mixtures. The Flame Extinguishment (FLEX) experiments onboard the International Space Station provided a unique platform for investigating low temperature multi-phase n-alkane and iso-alkane combustion. Among the many interesting phenomena experimentally observed, cool flame extinction can occur, accompanied by the concurrent formation of a surrounding cloud of condensed vapor. In this work we conduct numerical simulations of high and low temperature combustion of large, initially single-component n-heptane, n-decane and n-dodecane droplets. The role of initial droplet diameter, operating pressure, and n-alkyl carbon number on the extinction of hot and low temperature flames is investigated and compared against the available experimental data. While all three fuels exhibit similar hot flame behavior, cool flame activity increases with the carbon number, resulting in an increased cool flame temperature and decreased extinction diameter. Multi-cyclic “hot/cool flame transitions” are found in air as pressure is slightly increased above one atmosphere. The cyclic behaviors correspond to continuously varying hot and cool flame transitions across the high, low, and negative temperature coefficient (NTC) kinetic regimes. Further increase in pressure results in a second stage steady “Warm flame” transition. The extinction of hot and cool flame has a strong non-linear dependence on ambient pressure but as the hot flame extinction diameter increases with pressure the extinction diameter of the cool flame decreases. The computational results are compared with a recent asymptotic analysis of FLEX n-alkane cool flames.     

Cellular hotspot-type structure of the combustion wave of perchlorate ammonium

The non-one-dimensionality of the combustion wave of ammonium perchlorate was studied. An analysis of the surface of samples quenched by pressure drop and by coolant spray injection onto the burning surface, as well as extinction of samples with a diameter close to the quenching diameter, showed that, at pressures providing steady burning (2.5–7.0 MPa), the burning surface is nonplanar and nonuniform, but features a cellular hotspot-type pattern. Hotspots emerge and disappear at the burning surface, with their diameter and depth being pressure-dependent. The maximum diameter of hotspots depends on the pressure. It exceeds the characteristic thickness of the heat conduction zone by about two orders of magnitude but is smaller than the critical quenching diameter approximately twofold. Measurements of the electric conductivity of the surface layer and of the local luminosity of the flame revealed the existence of pulsations of approximately the same frequency. The period of these pulsations is close to the lifetime of hotspots. It was demonstrated that extinction curves for ammonium perchlorate obtained using pressure differ from the analogous curves for nitroglycerine-based propellants.     

Ignition and combustion of a falling, single sodium droplet

Ignition and combustion of a single sodium droplet has been studied experimentally, by use of a falling droplet. It is found that the ignition delay time increases first gradually and then rapidly, with decreasing initial temperature and/or oxygen concentration, and reaches the limit of ignitability, because of the suppression of surface reaction in the ignition stage. It is also found that with decreasing droplet diameter, the ignition delay time first decreases gradually, because of the decrease in the droplet mass to be heated, and then increases steeply, because of the enhancement of heat loss from the droplet surface. As for the effect of the relative speed, it is found that the ignition delay time increases with increasing relative speed, because of the enhanced heat loss. Experimental comparisons with the analytical results have also been conducted to elucidate dominant parameters, and it is confirmed that a set of comprehensive parameters in the literature can be useful in correlating dominant parameters that influence the ignition delay and/or the limit of ignitability. Furthermore, the analysis has been extended to determine the critical size for the ignition and that for the minimum ignition delay time. Combustion behavior after the ignition has also been examined, and it is found that d²-law can hold for the sodium droplet combustion. In addition, it is found that the burning rate-constant without forced convection has nearly the same value as those for usual hydrocarbon droplets, while the sodium combustion in air is quite similar to that of the usual hydrocarbon fuel in an oxidizer-rich environment.     

Concept and combustion characteristics of ultra-micro combustors with premixed flame

Under micro-scale combustion influenced by quenching distance, high heat loss, shortened diffusion characteristic time, and flow laminarization, we clarified the most important issues for the combustor of ultra-micro gas turbines (UMGT), such as high space heating rate, low pressure loss, and premixed combustion. The stability behavior of single flames stabilized on top of micro tubes was examined using premixtures of air with hydrogen, methane, and propane to understand the basic combustion behavior of micro premixed flames. When micro tube inner diameters were smaller than 0.4 mm, all of the fuels exhibited critical equivalence ratios in fuel-rich regions, below which no flame formed, and above which the two stability limits of blow-off and extinction appeared at a certain equivalence ratio. The extinction limit for very fuel-rich premixtures was due to heat loss to the surrounding air and the tube. The extinction limit for more diluted fuel-rich premixtures was due to leakage of unburned fuel under the flame base. This clarification and the results of micro flame analysis led to a flat-flame burning method. For hydrogen, a prototype of a flat-flame ultra-micro combustor with a volume of 0.067 cm³ was made and tested. The flame stability region satisfied the optimum operation region of the UMGT with a 16 W output. The temperatures in the combustion chamber were sufficiently high, and the combustion efficiency achieved was more than 99.2%. For methane, the effects on flame stability of an upper wall in the combustion chamber were examined. The results can be explained by the heat loss and flame stretch.     

An investigation of nonlinear dynamics of a thermal pulse combustor

Nonlinear dynamics of a thermal pulse combustor was investigated using a coupled fourth order lumped combustor model. The effects of optically thin radiation from the combustor gases to the wall are also investigated. The system response changes from steady combustion to extinction through oscillatory combustion as the wall temperature is lowered. The qualitative results suggest a transition to chaos through a period-doubling route prior to extinction. The presence of chaos is also confirmed by quantitative measures like correlation dimension and Lyapunov exponent. The system dynamics is qualitatively similar in presence and absence of radiation. However, inclusion of radiative heat loss leads to extinction at higher temperatures and also increases the predicted range of wall temperatures for which limit cycle behaviour is obtained. A measure for monitoring the proximity of the system to extinction has been developed using the time series data.     

Optical Cross-Sections of Soot Agglomerates: The model of the virtual refractive index and first-order multiple scattering

A new technique for the calculation of the optical properties of agglomerated spherical primary particles is presented. By means of the so-called virtual refractive index, the multiple scattering within the agglomerate is decribed by a modified Mie solution, thus avoiding restrictions with respect to the primary particle size. An additional benefit of the method is the small numerical expense required, permitting practical use for complex agglomerate structures such as real combustion aerosols. Utilizing this method, attention is focused on the calculation of the extinction cross-section of real combustion aerosols in order to discuss the results of multiple-wavelength extinction measurements within combustion systems. It is found that approximately the primary particle diameter is determined. Furthermore, the error that occurs can be avoided by means of the method presented without a detailed knowledge of the agglomerate size. Thus, the present work eliminates some current uncertainties inherent in optical combustion aerosol characterization.     

The Fokker-Planck equation in the second-order pitch angle approximation and its exact solution

The diffusive particle propagation and its pitch angle scattering is studied using kinetic equation of the Fokker-Planck form. The case is considered when charged particles preferable propagate along the strong mean magnetic field direction and undergo the pitch angle scattering with respect to it. The paper deals with solution of the equation for particle distribution function in the second-order approximation in the pitch angle. The exact analytical solution is obtained in an integral form. The well-known solution in the first-order pitch angle approximation can be restored performing the small time limit in the result. Unlike the first-order solution the obtained solution in the second approximation rightly shows that the pitch angle diffusion is closely connected with the particle transport along the mean magnetic field. The expression for particle density for the point instantaneous unidirectional source also has been obtained.     

Analytical study of stretched ultra-lean premixed flames within porous inert media

It has been shown both theoretically and experimentally that combustion within porous inert media can extend the flammability limits of reactant mixtures for unstretched stationary premixed flames. However little attention has been given to flames within porous media submitted to stretch conditions. This work presents a closed form approximate analytical solution for the problem of ultra-lean premixed flames within porous inert media subjected to small stretch rates in an impinging flow configuration against a constant temperature wall. The solution is obtained using the method of matched asymptotic expansions taking advantage of the large difference between the solid- and gas-phase thermal conductivities. The model allows for thermal nonequilibrium between the phases and is able to predict the flame temperature, velocity and position as function of the stretch rate. The results show that within porous media low stretch rates may increase the flame temperature, further extending the lean flammability limit of the reactant mixture when compared to planar flames. The model is restricted to low porosities, low stretch rates, low heat losses and intense interphase heat transfer.     

近场接收时颗粒的消光特性

讨论了在近场接收条件下颗粒的消光特性。计算表明：在近场接收时，颗粒的实际消光将性与远场接收相比，存在很大的区别－－实际消光纱数不但同颗粒的性质和大小有关，而且与颗烊在光束中的位置相联系。对于大颗粒，近场间的消光系数在数值上也有很大差异，如果采用近场接收来测量颗粒的大小，必须考虑这些因素的影响，否则将极大增加测量误差。还论述了近场接收时消光法测量颗粒时测量区定义中的问题，论证了如何能恰当定义测量区，     

Retrieval of spheroidal particle size distribution using the approximate method in spectral extinction technique

Retrieval of spheroidal particle size distribution using an approximate method in spectral extinction technique is proposed. The combined approximate method, which is the combination of Mie method and generalized eikonal approximation (GEA) method, is used as an alternative to the rigorous solutions to calculate the averaging extinction efficiency of spheroid. Based on the averaging extinction efficiency, the accuracy and limitations of the retrieval are then investigated. Moreover, the validity range and effect of the refractive index are also examined. The Johnson's S_B function in this paper is used as a versatile function to fit the commonly used particle size distribution functions in the dependent model. Simulations and experimental results show that the combined approximate method can be successfully applied to retrieval of spheroidal particle size distribution. In certain constraint conditions, the retrieval results demonstrate the high reliability and stability of the method. By using the combined approximate method, the complexity and computation time of the retrieval are significantly reduced, which is more suitable for quick and easy measurement. The method can also be used as a replacement when the rigorous solutions suffer computationally intractable difficulties.     

Combustion of a propellant and its extinction upon rapid depressurization: A comparison of theory and experiment

The combustion of a nitroglycerin-based propellant and its extinction as a result of exponential pressure decay was studied on a bomb-receiver setup. At moderate depths and rates of pressure decay, the transient process ends with adoption of a new steady-state combustion mode. There are critical values of the depth and rate of pressure decay above which combustion ceases. Numerical simulations are used to determine a relationship between the critical values of these quantities (extinction curves). The calculations are performed within the framework of the phenomenological theory of unsteady combustion of energetic condensed systems using known steady-state laws of propellant combustion. A comparison of experimental and theoretical results demonstrates their satisfactory agreement.     

受迫薛罗格双匣化学反应模型的随机共振

为了在理论上揭示高斯白噪声激励的薛罗格双匣化学反应模型对弱周期扰动的线性与非线性响应 ,分四态近似和两态近似两种情形 ,基于绝热近似与速率方程方法 ,解析导出线性的和非线性的敏感性以及信噪比的表达式 ,并与数值模拟结果进行比较 ,在一次谐波的意义上得到了解析结果与数值模拟结果的定量一致性 .理论上讲 ,该模型只能表现出奇次谐波的随机共振 ,但数值模拟结果也出现了二次谐波的随机共振 ,其原因可能归结为在数值模拟中有限频率的截断引入了误差 ,也可能归结为信号的高次谐波与背景噪声难以区分所致 .     

Einstein-Maxwell-Higgs solitons

A regular, localized solution of the classical theory of the gravitational field coupled to the electromagnetic field and to an auxiliary scalar field is presented, and an analytical form of this solution is obtained in a limiting case. This solution, which is interpreted, from the macroscopic point of view, as an extended charged particle, has a peculiar microscopic topology characterized by a fundamental length of the order of the classical electromagnetic radius of the particle. There is no lower limit to the mass-to-charge ratio of such a particle.     

Orientational averaging of integrated cross sections in the discrete dipole method

Using the discrete dipole method, exact and approximate analytical solutions for orientation-averaged cross sections for extinction, absorption, and scattering of light are obtained. The analytical solutions can be applied to the calculation of integrated cross sections of fractal clusters formed by primary particles with different optical properties (soot in air and aqueous suspensions of aggregates of polystyrene, gold, and silver nanoparticles). It is shown that two models of aggregates that differ only in trajectories (ballistic or Brownian) of primary particles and intermediate clusters and in average fractal dimensions give close values of averaged extinction cross sections.