Piloted ignition and extinction for solid fuels

Piloted ignition of solid fuels is investigated by simulating the transport and chemical reaction in a counter-flow arrangement where a known fuel (methane) is supplied through a porous burner and the power and the location of the igniter are varied. The porous burner arrangement simulates a pyrolyzing solid fuel at constant temperature by separating the gas phase from the solid conduction and pyrolysis phenomena. An Arrhenius one-step global reaction and a simplified transport model with Lewis number equal to one were used in the simulation. Only quasi-steady conditions are considered for the gas phase in this work because the response time for the solid phenomena is, in general, much larger than the response diffusion time for the gaseous phenomena. The relation of piloted ignition to extinction is also investigated. The effect of Damköhler number on ignition and extinction and the effect of the igniter on ignition are presented through a characteristic S curve obtained by plotting the evolving maximum temperature as a function of fuel mass flux. Based on the S-shaped curve (representing the maximum temperature in the system versus the mass flux of fuel), the relationship between the piloted ignition and extinction turning points and mass fluxes has been demonstrated in this paper. The piloted ignition turning point gradually approaches the extinction turning point with increasing Damköhler number and also with increasing power of the igniter. The ignition mass flux is found to depend basically on three parameters, Damköhler number, the location of the igniter and the power of the igniter all expressed in dimensionless forms.     

On the sublimit solution branches of the stripe patterns formed in counterflow diffusion flames by diffusional–thermal instability

The nonlinear dynamics of striped diffusion flames, formed in a two-dimensional counterflow by diffusional–thermal instability with Lewis numbers sufficiently less than unity, is investigated numerically by examining various two-dimensional flame-structure solutions bifurcating from the one-dimensional steady solution. The Lewis numbers for fuel and oxidizer are identically set to be 0.3, and an overall single-step Arrhenius-type chemical reaction with a Zel'dovich number of 7 is employed as the chemistry model. Particular attention is focused on the flame-stripe solution branches in the sub-extinction regime and on the hysteresis encountered during the transition between different solution branches. In the numerical simulations, a nonlinear solution with eight stripes is first realized from the one-dimensional solution at a Damköhler number slightly greater than the extinction Damköhler number. The eight-stripe solution survives Damköhler numbers much smaller than the extinction Damköhler number until successive bifurcations, leading to the doubling of the pattern wavelength, occur at the subsequent forward-transition conditions. At the first forward-transition Damköhler number occurs the transition to a four-stripe solution, which in turn transits to a two-stripe solution at the second forward-transition Damköhler number, a value somewhat smaller than the first. However, further transition from a two-stripe solution to a one-stripe solution is not always possible even if a one-stripe solution can be accessed independently for particular initial conditions. The Damköhler-number ranges and shapes for the two-stripe and one-stripe solutions are found to be virtually identical, implying that each stripe could be an independent structure if the distance between stripes is sufficiently large. By increasing the Damköhler number, backward transitions can be observed. In comparison with the forward-transition Damköhler numbers, the corresponding backward-transition Damköhler numbers are always much greater, thereby indicating significant hysteresis between the stripe patterns of strained diffusion flames.     

Use of the two-moment boundary condition in the problem of rarefied gas slip over a solid cylindrical surface

The slip velocity of a rarefied gas nonuniform in temperature and mass velocity is calculated for gas slip over the surface of a right circular cylinder. The calculation uses the two-moment boundary condition in an approximation linear in Knudsen number. Corrections to the slip velocity that are due to the interface curvature, volume temperature stresses, and nonuniform temperature distribution in the Knudsen layer are studied as func-tions of the accommodation coefficients in the first two moments of the distribution function. The Bhatnagar-Gross-Krook model of the Boltzmann kinetic equation is employed as the basic equation for the gas state.     

Fast,non-diffusive ignition of a gaseous reacting mixture subject to a point energy source

The ignition of a gaseous reactive mixture subject to a localized energy source is analysed using large activation energy asymptotics. The energy released by the source results in a thermal non-uniformity in a small region of the gas. We distinguish two different regimes, non-diffusive and diffusive, depending on the dominant cooling mechanism during the ignition stage: expansion effects or heat conduction. We focus on the non-diffusive ignition, considering the energy source as instantaneous. We show the existence of a critical value of a Damköhler number, defined as the ratio of the characteristic times of the expansion waves and chemical reaction, such that ignition only occurs for supercritical values at a well-defined ignition time, which is calculated numerically. The ignition process for a non-instantaneous energy source is also described in terms of an initial inert heating stage and a shorter reactive stage ending in thermal runaway for supercritical values of the Damköhler number.     

Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model(DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation.It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model.Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model.To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified.     

Transient convective burning of interactive fuel droplets in single-layer arrays

The transient convective burning of n-octane droplets interacting within single-layer arrays in a hot gas flow perpendicular to the layer is studied numerically, with considerations of droplet surface regression, deceleration due to the drag of the droplets, internal liquid motion, variable properties, non-uniform liquid temperature and surface tension. Infinite periodic arrays, semi-infinite periodic arrays with one row of droplets (linear array) or two rows of droplets, and finite arrays with nine droplets with centers in a plane are investigated. All arrays are aligned orthogonal to the free stream direction. This paper compares the behavior of semi-infinite periodic arrays and finite arrays with the behavior of previously studied infinite periodic arrays. Furthermore, it identifies the critical values of the initial Damköhler number for bifurcations in flame behavior at various initial droplet spacing for all these arrays. The initial flame shape is either an envelope flame or a wake flame as determined by the initial Damköhler number, the array configuration and the initial droplet spacing. The critical initial Damköhler number separating initial wake flames from initial envelope flames decreases with increasing interaction amongst droplets at intermediate droplet spacing (when the number of rows in the array increases or the initial droplet spacing decreases for a specific number of rows in the array). In the transient process, an initial wake flame has a tendency to develop from a wake flame to an envelope flame, with the moment of wake-to-envelope transition advanced for the increasing interaction amongst droplets at intermediate droplet spacing. For the array with nine droplets with centers in a plane, the droplets at different types of positions have different critical initial Damköhler number and different wake-to-envelope transition time for initial wake flame.     

Bifurcation characteristics and flame dynamics of a ducted non-premixed flame with finite rate chemistry

The influence of system parameters such as the flame location, Peclet number and Damköhler number on the bifurcation characteristics and flame dynamics of a ducted non-premixed flame with finite rate chemistry is presented in this paper. In the bifurcation plot with flame location as the bifurcation parameter, subcritical Hopf bifurcation is found for lower values of flame location and supercritical Hopf bifurcation for higher values of flame location, for all the Damköhler numbers used in this study. The flame shapes are captured at eight different phases of a cycle of time series data of acoustic velocity at both the fold and Hopf points for bifurcation with flame location as the parameter. We find that the range of flame height variations at the Hopf point is more than the range of flame height variations obtained at the fold point. We also find that the flame oscillates in the same phase as pressure fluctuation but in a phase different from both velocity and heat release rate fluctuations in the region of hysteresis for bifurcation with flame location. The non-dimensional hysteresis width is plotted as a function of Damköhler number for variation of flame location in the subcritical region. An inverse power law relation is found between the non-dimensional hysteresis width and the Damköhler number. The bifurcation plot with Peclet number as parameter shows a subcritical Hopf bifurcation.     

Numerical investigation of laminar cross-flow non-premixed flames in the presence of a bluff-body

A knowledge of flame stability regimes in the presence of cylindrical bluff-bodies of various dimensions is essential to design non-premixed burners. The reacting flow field in such cases is reported to be three-dimensional and unsteady. In the literature, only a few experimental investigations with limited measurements are available. Therefore, in this work, a detailed numerical study of laminar cross-flow non-premixed methane–air flames in the presence of a square cylinder is presented. The flow, temperature, species and reaction fields have been predicted using a comprehensive transient three-dimensional reacting flow model with detailed chemical kinetics and variable thermo-physical properties, in order to get a good insight into the flame stabilisation phenomena. Further, analyses of quantities such as local equivalence ratio, cell Damköhler number, species velocity, net consumption rate of methane, which are not easily obtained through experiments even with detailed diagnostics, have been carried out. The influence of the flow field due to varying inlet velocity of the oxidiser, in the presence of the bluff-body, on flame anchoring location has been analysed in detail. Local equivalence ratio contours obtained from non-reacting flow calculations are seen to be quite useful in analysing the mixing process and in the prediction of flame anchoring locations when the flames are not separated. Cell Damköhler number has been calculated using cell size, species velocity of the fuel, which is a derived quantity, and the net reaction rate of the fuel. The flame zone, which is customarily inferred from the contours of temperature, CO and OH, is also shown to be predicted well by the contour line corresponding to a Damköhler number equal to unity. The net reaction rate of CH₄ and the net rates of two dominant reactions, which consume methane, show clearly the variation in the flame anchoring locations in these three cases. Further, the three-dimensionality of these flames are analysed by plotting the mean temperature contours in y–z planes. Finally, the unsteadiness in the separated flame case is analysed.     

Multiple speeds of flame edge propagation for Lewis numbers above one

Edges of diffusion flames in a counterflow burner are examined numerically for Lewis greater than unity. When the speed of propagation is plotted against Damköhler for a range of Lewis a fold bifurcation is observed. It is shown that there exist stable positively and negatively propagating edges for some Damköhler and Lewis number pairs. It is further shown that changed local conditions can lead to a transition from positive (advancing into the unburnt gasses) to negative (receding) propagation.     

微圆管进口区气体流动与换热特性研究

对微圆管进口区运用一阶速度滑移和温度跳跃边界,考察了Kn、动量调和及热调和系数对流动与换热特性的影响机理和规律.模拟结果表明:流动进口段长度随Kn增加而增加,但随动量调和系数减小而减小;热进口段长度随Kn增加而增加,但随动量调和系数及热调和系数减小而减小;Nu数随Kn增加及热调和系数减小而减小,但随动量调和系数减小而增加.     

微尺度振荡Couette流的格子Boltzmann模拟

采用有效多松弛时间-格子Boltzmann方法(Effective MRT-LBM)数值模拟了微尺度条件下的振荡Couette和Poiseuille流动. 在微流动LBM中引入Knudsen边界层模型,对松弛时间进行修正. 模拟时平板或外力以正弦周期振动,Couette流中考虑了单平板振动、上下板同相振动这两类情况. 研究结果表明,修正后的MRT-LBM模型能有效用于这类非平衡的微尺度流动模拟;对于Couette流,随着Kn数的增大,壁面滑移效应变得越明显. St越大,板间速度剖面的非线性特性越剧烈;两板同相振荡时,若Kn,St均较小,板间流体受到平板拖动剪切的影响很小,板间速度几乎重叠在一起;在振荡Poiseuille流动中,St数增大到一定值时,相位滞后现象减弱;相对于Kn数,St数对振荡Couette 和Poiseuille流中不同位置处速度相位差的产生有较大影响. 关键词： 格子Boltzmann方法 有效MRT模型 Knudsen层 振荡流     

Light Induced Drift and Heat Transfer of One-Component Gas in a Capillary

The processes of heat transfer and drift of rarefied gas in a capillary due to velocity-selective excitation of atoms by monochromatic light have been investigated. On the basis of kinetic equation the kinetic coefficients defining surface and bulk mechanisms of light induced transfer phenomena in dependence on the Knudsen number, the ratio of the rate of radiative decay of the excited level to the frequency of intermolecular collisions and the accommodation coefficient were calculated.     

Simulation of micro- and nano-scale flows via the lattice Boltzmann method

We use the lattice Boltzmann method (LBM) for analysis of high and moderate Knudsen number phenomena. Simulation results are presented for microscale Couette and Poiseuille flows. The slip velocity, nonlinear pressure drop, and mass flow rate are compared with previous numerical results and/or experimental data. The Knudsen minimum is successfully predicted for the first time within the LBM framework. These results validate the usage of the LBM based commercial, arbitrary geometry code PowerFLOW for simulating nanoscale problems.     

The role of unequal diffusivities in ignition and extinction fronts in strained mixing layers

We have studied flame propagation in a strained mixing layer formed between a fuel stream and an oxidizer stream, which can have different initial temperatures. Allowing the Lewis numbers to deviate from unity, the problem is first formulated within the framework of a thermo-diffusive model and a single irreversible reaction. A compact formulation is then derived in the limit of large activation energy, and solved analytically for high values of the Damköhler number. Simple expressions describing the flame shape and its propagation velocity are obtained. In particular, it is found that the Lewis numbers affect the propagation of the triple flame in a way similar to that obtained in the studies of stretched premixed flames. For example, the flame curvature determined by the transverse enthalpy gradients in the frozen mixing layer leads to flame-front velocities which grow with decreasing values of the Lewis numbers.

The analytical results are complemented by a numerical study which focuses on preferential-diffusion effects on triple flames. The results cover, for different values of the fuel Lewis number, a wide range of values of the Damköhler number leading to propagation speeds which vary from positive values down to large negative values     

Thermal modes of a plug flow reactor with a liquid–liquid heterogeneous system

The thermal modes of a flow plug reactor with an exothermic chemical reaction are numerically simulated. A heterogeneous reaction system consisting of two immiscible liquids is studied: one of the liquids (dispersed phase) in the form of droplets is distributed in the other (dispersion phase). The characteristics of the thermal modes of the reactor at various values of two governing parameters, the Damköhler number and the rate of extraction of the dissolved substance from the dispersed phase into the dispersion phase is examined. Two modes of chemical reaction in the reactor are demonstrated to be possible: low-temperature and high-temperature. Critical criteria of thermal ignition are formulated. The dependence of the structure of the thermal wave on the governing parameters is investigated.     

Homoclinic bifurcations in radiating diffusion flames

We analyse the dynamics of a model describing a planar diffusion flame with radiative heat losses incorporating a single step kinetic using timestepping techniques for Lewis number equal to one. We construct the full bifurcation diagram with respect to the Damköhler number including the branches of oscillating solutions. Based on this analysis we found, for the first time, homoclinic bifurcations that mark the abrupt disappearance of the nonlinear oscillations near extinction as reported in experiments.     

Light-induced heat and mass transfer in a single-component gas in a capillary

A theoretical analysis is presented of light-induced heat and mass transfer in a single-component gas in a capillary tube at arbitrary Knudsen numbers. Surface and collisional mechanisms of transfer are analyzed, due to differences in accommodation coefficient and collision cross section between excited-and ground-state particles, respectively. Analytical expressions for kinetic coefficients characterizing the gas drift and heat transfer in a capillary tube are obtained in the limits of low and high Knudsen numbers. Numerical computations are performed for intermediate Knudsen numbers. Both drift and heat fluxes are determined as functions of the light beam frequency. In the case of an inhomogeneously broadened absorption line, the light-induced fluxes are found to depend not only on the sign, but also on the amount, of light beam detuning from the absorption line center frequency.     

Heat and mass transfer in a gas in a capillary induced by light with nonuniform intensity distribution over the beam cross section

An analysis is presented of the heat and drift fluxes induced by velocity-selective light absorption in a single-component gas in a capillary tube. The light intensity distribution across the beam is assumed to have a Gaussian profile. Kinetic equations are solved numerically to calculate flux profiles and kinetic coefficients quantifying the contributions of surface and collisional mechanisms to light-induced transfer as functions of the Knudsen number, the ratio of the rate of radiative decay of the exited level and intermolecular collision frequency, accommodation coefficient, and the ratio of the tube radius to the light beam radius.     

An elementary model for the validation of flamelet approximations in non-premixed turbulent combustion

The fundamental soundness of three flamelet models for non-premixed turbulent combustion is examined on the basis of their performance in an idealized model problem that merges ideas from the laminar asymptotic theory for non-premixed flames and rigorous homogenization theory for the diffusion of a passive scalar. The overall flame configuration is stabilized by a mean gradient in the passive scalar: large Damköhler number asymptotics results are available for the laminar case to quantify the finite-rate effects that cause the flame to depart from its equilibrium state; the same results can also be used to incorporate higher-order corrections in the approximation of the reactive variables in terms of the passive scalar. The use of such flamelet approximations has been extended well beyond the laminar regime as they lie at the core of practical strategies to simulate non-premixed flames in the turbulent regime: the flamelet representation avoids the problem of turbulence closure for the reactive variables by replacing it by the presumably much simpler closure problem for a passive scalar. It is precisely the validity of this substitution outside the laminar regime that is addressed here in the idealized context of a class of small-scale periodic flows for which extensive rigorous results are available for the passive scalar statistics. Results for this simplified problem are reported here for significant wide ranges of Peclet and Damköhler numbers. Asymptotic convergence is observed in terms of the Damköhler number, with a convergence rate that is found to match the laminar predictions and appears relatively insensitive to the Peclet number. The passive scalar dissipation plays a key role in achieving higher-order corrections for the finite-rate case: replacing its pointwise value by an averaged value is convenient practically and can be rigorously motivated for the class of flows studied here, but while it does achieve an overall improvement over the lower-order equilibrium model, the simplification compromises the higher asymptotic convergence observed with the original finite-rate flamelet model with exact local dissipation.(Some figures in this article are in colour only in the electronic version; see www.iop.org)     

层间稀薄气体传热对多层绝热材料性能的影响分析

通过建立的热量传递模型,分析了不同的气体稀薄程度(Knudsen数)时,气体传热对多层绝热材料有效热导率和各层温度分布的影响。分析表明:由多层绝热材料真空度变化引起的稀薄气体传热量波动较大,在10—60层/cm层密度范围,真空度低于100Pa时,Kn数属于自由分子状态区域和中间压强区域,此时材料的有效热导率随残留气体热适应系数的增大而减小,并随着真空度的降低而增大;当残留气体为空气时,为保证多层材料的绝热性能,尽量维持真空度不低于10-2Pa。同时分析表明,为有效降低低真空下稀薄气体传热对多层绝热性能的影响,可以采用综合热适应系数较低的气体置换夹层中的空气,以减少低真空多层绝热材料的有效热导率,改善绝热性能。