On the stability of stretched flames

It is shown that the well known difficulty concerning the unconditional stability of a planar flame sustained in a stagnation-point flow is due to the infinite aspect length scale of the system. In finite geometries occurring in numerical and laboratory experiments the flame may well become unstable provided the flow-induced stretch is weak enough.     

Impact of the gravity field on stability of premixed flames propagating between two closely spaced parallel plates

The stability of a planar flame front propagating between two parallel adiabatic plates inclined at an arbitrary angle is investigated in the frame of narrow-channel approximation. It is demonstrated that buoyancy forces can suppress the hydrodynamic (Darrieus–Landau) and cellular (diffusive-thermal) instabilities for sufficiently large value of the gravity parameter for the case of downward-propagating flames. The stability analysis reveals that in the case of oscillatory diffusive-thermal instability, the flame front cannot be stabilized in the similar way. Finally, the stability results are compared satisfactorily with unsteady numerical simulations.     

Microstructural stability of the Kirkendall plane in solid-state diffusion

In a diffusion-controlled interaction, the Kirkendall plane, as marked by inert particles placed at the original contact surface of a reaction couple, need not be unique. Multiple planes can develop, and sometimes the Kirkendall plane does not exist at all. A phenomenological approach is introduced to rationalize the Kirkendall-effect-mediated migration of macroscopic inclusions inside a diffusion zone.     

On the behaviour of organic gel multi-size spray diffusion flames

The recently reported, experimentally observed, unusual behaviour of organic gellant-based fuel droplets which, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion is incorporated in a phenomenological manner in a model of a two-dimensional arbitrary multi-size spray diffusion flame. Non-unity Lewis numbers are permitted for the fuel vapour and oxidant. A combined analytical/numerical solution of the governing equations is presented and used to investigate how a spray's initial polydispersity and the frequency of oscillatory evaporation influence the combustion field. It is demonstrated that the initial droplet size distribution and the frequency of evaporation of the burning gel droplets can have an acute impact both on the homogeneous diffusion flame shape, height and width and on the thermal field downstream of the flame front. Hot spots of individual (or clusters of) burning droplets can be created and under certain operating conditions can lead to hotter temperatures than experienced in the main homogeneous flame. The intensity of these hotspots, their number and location are sensitive to spray related parameters. In realistic combustion chambers there is a danger inherent in the existence of hotspots in undesirable regions as they can damage the structural integrity. Other computed results demonstrate that, in relation to the spray diffusion flames obtained using an equivalent purely liquid fuel spray, the use of a gel fuel spray can lead, under certain operating conditions, to a reduction in flame height and temperature. The latter effect is critical when considering flame extinction.     

Mechanical instabilities of bubble clusters between parallel walls

We have carried out a systematic study of buckling-like mechanical instabilities in simple two- (2D) and three-dimensional (3D) symmetric foam clusters sandwiched between parallel planar walls. These instabilities occur when the wall separation w is reduced below a critical value, w^*, for which the foam surface energy E reaches its minimum, E^*. The clusters under investigation consist of either a single bubble, or of twin bubbles of fixed equal sizes (areas A in 2D or volumes V in 3D), which are either free to slide or pinned at the confining walls. We have numerically obtained w^* for both free and pinned 2D and 3D clusters. Furthermore, we have calculated the buckled configurations of 2D twin bubbles, either free or pinned, and of 3D free twin bubbles, whose energy is independent of w and equal to the minimum energy E^* of the unbuckled state. Finally, we have also predicted the critical w_t^* at which the terminal configurations under extension of 2D and 3D single and twin bubbles are realised. Experimental illustrations of these transitions under compression and extension are presented. Our results, together with others from the literature, suggest that a bubble cluster bounded by two parallel walls is stable only if the normal force it exerts on the walls is attractive, i.e., if dE/dw > 0; clusters that cause repulsion between the walls are unstable. We correlate this with the distribution of film orientations: films in a stable cluster cannot be too parallel to the confining walls; rather, their average tilt must be larger than for a random distribution of film orientations.     

On the absence of diffusion in a semiinfinite one-dimensional system

For obvious reasons, the self-diffusion coefficient in bounded many-body systems must be strictly zero, provided that it is defined as the limit of [R(t)–R(0)]²/(2td) whent grows indefinitely [d is the dimensionality,R() is the position of a given particle at time]. Thus, the time integral of the velocity correlation function is strictly zero. A system of hard points on a half-infinite line with a reflective wall at the origin does exhibit this property of absence of diffusion, since each particle has an average position. We study in detail the difference between the velocity correlation functions of the infinite and of the half-infinite systems.     

Analytic solution to the problem of the couette flow in a plane channel with infinitely large parallel walls

An analytic (in the form of a Neuman series) solution to the problem of the Couette flow in a plane channel with infinitely large parallel walls is constructed using the kinetic approach in the isothermal approximation. For the basic equation, the Bhatnagar-Gross-Krook (BGK) model of the kinetic Boltzmann equation is used, while the boundary condition is determined by the diffuse reflection model. The mass flux through half the channel thickness in the direction parallel to the channel walls as well as the nonzero component of the viscous stress tensor are calculated taking into account the constructed distribution function. The results are compared with analogous data obtained by numerical methods.     

The differential diffusion effect of the intermediate species on the stability of premixed flames propagating in microchannels

The propagation of premixed flames in adiabatic and non-catalytic planar microchannels subject to an assisted or opposed Poiseuille flow is considered. The diffusive–thermal model and the well-known two-step chain-branching kinetics are used in order to investigate the role of the differential diffusion of the intermediate species on the spatial and temporal flame stability. This numerical study successfully compares steady-state and time-dependent computations to the linear stability analysis of the problem. Results show that for fuel Lewis numbers less than unity, Le_F < 1, and at sufficiently large values of the opposed Poiseuille flow rate, symmetry-breaking bifurcation arises. It is seen that small values of the radical Lewis number, Le_Z, stabilise the flame to symmetric shape solutions, but result in earlier flashback. For very lean flames, the effect of the radical on the flame stabilisation becomes less important due to the small radical concentration typically found in the reaction zone. Cellular flame structures were also identified in this regime. For Le_F > 1, flames propagating in adiabatic channels suffer from oscillatory instabilities. The Poiseuille flow stabilises the flame and the effect of Le_Z is opposite to that found for Le_F < 1. Small values of Le_Z further destabilise the flame to oscillating or pulsating instabilities.     

On the chemical characteristics and dynamics of n-alkane low-temperature multistage diffusion flames

We demonstrate experimentally, perhaps for the first time, the existence of low-temperature multistage diffusion flames of n-alkanes. Multistage diffusion flames of n-heptane, n-decane, and n-dodecane are established in an atmospheric counterflow burner. Planar laser-induced fluorescence, chemiluminescence, and thermometry are used to probe the structures of such flames. In the first flame zone, the majority of the fuel is partially oxidized via low-temperature peroxy chemistry. In the second flame zone, the intermediate species produced are further oxidized via intermediate-temperature chemistry. The two stages of the flame are coupled such that significant fuel and oxidizer leakage occur, respectively, from the first and second reaction zones. The fuel is then further consumed, in the second stage, after the radical pool is replenished by the oxidation of the intermediates. The structure of the n-alkane multistage flame is found to be consistent with that previously observed for acyclic ethers. Owing to the different classes of temperature-dependent chemistries dominating the first and second stages, the reaction zone structure of multistage diffusion flames is dramatically influenced by the reactant concentrations and flame temperatures. The first stage is relatively favored at lower temperatures whereas the second stage is favored at elevated temperatures. Moreover, near extinction where the flame temperature is low, the multistage flame dynamics are controlled by the first oxidation stage, governed by peroxy chemistry, whereas the second oxidation stage, governed by intermediate chemistry, is dominant near high-temperature ignition conditions. Finally, by doping the oxidizer with ozone, we demonstrate the role of ozone doping on the multistage flame structure and the existence of a separate low-temperature ozone-assisted burning mode.     

平行圆柱面导热形状因子的保角变换法

本文采用保角变换将两个平行偏心的等温圆柱面之间的稳态导热变换为同心同轴的圆柱面之间的导热,得到稳态导热情况下偏心圆筒壁、两平行圆柱面以及地下埋管与地面之间等三种实际情况下的导热形状因子,为简化热流量计算提供方便,为对其机理的认识拓展新思路.     

On the dynamics of interaction between a moving mass and an infinite one-dimensional elastic structure at the stability limit

The paper herein deals with the study of the dynamic behaviour generated by the instability of the vibration of a loaded mass, uniformly moving along an Euler-Bernoulli beam on a viscoelastic foundation, induced by the anomalous Doppler waves excited in the beam. This issue is relevant for the case of modern trains travelling along a track with soft soil when the trains speed exceeds the phase velocity of the waves induced in the track. The model corresponds to a railway vehicle reduced to a loaded wheel running along a (half) track. The beam takes account of the bending stiffness of the rail and the mass of the track, including the mass of the rail, semi-sleepers and half of the ballast layer, where the viscoelastic foundation represents the subgrade. The model includes the wheel/rail Hertzian contact and it allows the simulation of the possibility of contact loss. The nonlinear equations of motion are integrated using a numerical approach based on the Green’s function method. When the vibration becomes unstable, the system evolution is a limit cycle characterised by a succession of shocks, due to the action of two opposite factors: the anomalous Doppler waves that pump energy at the interface between the moving mass and the beam, thus forcing the mass to take off, and the static load that push the mass downwards. The frequency of the shocks increases at higher velocity and the magnitude of the impact force decreases; the most dangerous velocity is the critical one, which represents the stability limit of the linear approximation of the motion equations. The transient behaviour that precedes the limit cycle appearance is being analysed. The Hertzian contact influences the time history of the limit cycle and the magnitude of the impact force and, therefore, it is essential to be included in the model. To the authors’ knowledge, this problem has never been dealt with.     

On transient behavior of non-premixed counter-flow diffusion flames within the REDIM based model reduction concept

In the present work non-stationary behavior of the counter-flow diffusion flame is examined in the context of the recently developed approach of model reduction called REaction–DIffusion Manifolds (REDIM) method. It is a natural extension of the ILDM approach which takes into account both the chemical reaction and the diffusion processes. It has been developed to treat both premixed and non-premixed regimes of combustion. In this work we investigate the ability of the concept to describe transient processes of extinction and re-ignition. A very simple flame configuration and transport model are considered in this current study for the sake of transparency because the main focus is on the transient and non-stationary behavior of flames. H₂/O₂/N₂ combustion system is considered in a non-premixed counter-flow diffusion 1D flame configuration. This study shows how the REDIM concept performs in the transient regimes; it interprets the effect of local extinction and reigniting phenomena using detailed and reduced models. It shows how the unstable/transient behavior of a detailed system can be successfully accounted with the help of the REDIM based reduced model.     

Phase behaviors in binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in binary mixture of diblock copolymers confined between two parallel walls are investigated by using cell dynamics simulation of the time-dependent Ginzburg-Landau theory. The morphological dependence of the wall-block interaction and the distance between walls (confinement degree) has been systematically studied, and the effect of repulsive interactions between different monomers is also discussed. It is interesting that multiple novel morphological transitions are observed by changing these factors, and various multilayered sandwich structures are formed in the mixture. Furthermore, the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed. From the simulation, we find that much richer morphologies can form in binary mixture of diblock copolymers than those in pure diblock copolymer. Our results provide an insight into the phase behaviors under parallel walls confinement and may provide guidance for experimentalists. This model system can also give a simple way to realize orientational order transition in soft materials through confinement.     

On the existence of steady-state gaseous microgravity spherical diffusion flames in the presence of radiation heat loss

Whether steady-state gaseous microgravity spherical diffusion exist in the presence of radiation heat loss is an important fundamental question and has important implications for spacecraft fire safety. In this work, experiments aboard the International Space Station and a transient numerical model are used to investigate the existence of steady-state microgravity spherical diffusion flames. Gaseous spherical diffusion flames stabilized on a porous spherical burner are employed in normal (i.e., fuel flowing into an ambient oxidizer) and inverse (i.e., oxidizer flowing into an ambient fuel) flame configurations. The fuel is ethylene and the oxidizer oxygen, both diluted with nitrogen. The flow rate of the reactant gas from the burner is held constant. It is found that steady-state gaseous microgravity spherical diffusion flames can exist in the presence of radiation heat loss, provided that the steady-state flame size is less than the flame size for radiative extinction, and the flame develops fast enough that radiation heat loss does not drop the flame temperature below the critical temperature for radiative extinction (1130 K). A simple model is provided that allows for the identification of initial conditions that can lead to steady-state spherical diffusion flames. In the spherical, infinite domain configuration, the characteristic time for the diffusion-controlled system to effectively reach steady-state is found to be on the order of 100,000 s. Despite a narrow range of attainable conditions, flames that exhibit steady-state behavior are observed aboard the ISS for up to 870 s, even with the constraint of a finite boundary. Steady-state flames are simulated using the numerical model for over 100,000 s.     

Phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls are investigated by using a cell dynamics simulation of the time-dependent Ginzburg-Landau theory.The morphological dependence of the wall-block interaction and the distance between walls(confinement degree) has been systematically studied,and the effect of repulsive interactions between different monomers is also discussed.It is interesting that multiple novel morphological transitions are observed by changing these factors,and various multilayered sandwich structures are formed in the mixture.Furthermore,the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed.From the simulation,we find that much richer morphologies can form in a binary mixture of diblock copolymers than those in a pure diblock copolymer.Our results provide an insight into the phase behaviors under parallel wall confinement and may provide guidance for experimentalists.This model system can also give a simple way to realize orientational order transition in soft materials through confinement.