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.     

Computational analysis of the steady states of the Sivashinsky model of hydrodynamic flame instability

In this work a numerical analysis of an integro-differential equation modelling the Darrieus–Landau instability of plane flame fronts was undertaken. A relatively new computational method based on saturated asymptotic approximations was used. Within the considered computational times a steady limiting shape of the flame front was not reached in large enough computational domains of size L?>?L_c . Instead, a smooth surface of an almost steadily shaped flame is repeatedly disturbed by small perturbations, resembling small cusps, appearing and disappearing randomly in time. The nature of these small cusps as well as of the steady limiting shape of the flame front was studied with a relatively new computational method.

The correlation between the critical length L_c and parameters of the computational algorithm and the computer precision was investigated. The calculations confirmed that, unlike the round-off errors, there is no significant link between the approximation accuracy of the algorithm and L_c . The obtained dependence of the critical length L_c on the magnitude of the round-off errors, considered as an external noise, was compared with the predictions given by other researchers. The agreement supports the idea of high sensitivity of solutions of the Sivashinsky equation to the external noise. A similarity between the appearance of small cusps on the surface of large enough flames governed by the Sivashinsky equation and streamwise streaks accompanying the loss of stability of the classic Hagen–Poiseuille flow was noted.     

Influence of radiation losses on the stability of premixed flames on a porous-plug burner

Analysis of the planar premixed flames on a porous plug was performed numerically for finite activation energy within the diffusive-thermal model. The paper is focused on the influence of radiation heat loses on the flame standoff distance and its linear stability. We show that the presence of volumetric heat losses limits the range of the mass flow range as well as it can promote the flame instabilities of different kinds, both oscillatory and cellular. The oscillatory instability, which for freely propagating flames can be usually observed for the Lewis number larger than one, in the porous-plug case occurs also for flames with unity and lower than unity Lewis number. For flames with Le < 1 both cellular and oscillatory instabilities can be observed simultaneously in a certain range of the mass flow rate.     

On intrinsic oscillation in radiation-affected diffusion flames

A linear stability analysis is conducted to study the onset of near-limit flame oscillation with radiative heat loss in 1-D chambered planar flames using multi-scale activation-energy asymptotics. The oscillatory instability near the radiation-induced extinction limit at large Damköhler numbers is identified, in additional to the one near the kinetic limit at small Damköhler numbers. It is shown that radiative loss assumes a similar role as varying the thermal diffusivity of the reactants. Thus, flame oscillation near the radiative limit is still thermal-diffusive in nature although it may develop under unity Lewis numbers. The unstable range of Damköhler numbers near the radiative limit shows quite similar parametric dependence on the Lewis numbers of reactants, Le_F and Le_O, the stoichiometry, ?, and the radiative loss as that near the kinetic limit. They both increase monotonically with Le_O and ? and increase then decrease with Le_F. Increasing radiative loss extends the parameter range under which flame oscillations may develop. However, they show different dependence on the temperature difference between the supplying reactants. Unless radiative loss approaches its maximum value the system can sustain, flame oscillation near the radiative limit is only possible within a limited range of ΔT, whereas it is promoted monotonically with decreasing ΔT near the kinetic limit. Furthermore, while radiative loss shows small effect on the nondimensional oscillation frequency, the dimensional frequency of flame oscillations near the radiative limit can be substantially smaller than that near the kinetic limit.     

Three-dimensional numerical simulations of cellular jet diffusion flames

Recent experimental investigations have demonstrated that the appearance of particular cellular states in circular non-premixed jet flames significantly depends on a number of parameters, including the initial mixture strength, reactant Lewis numbers, and proximity to the extinction limit (Damköhler number). For CO₂-diluted H₂/O₂ jet diffusion flames, these studies have shown that a variety of different cellular patterns or states can form. For given fuel and oxidizer compositions, several preferred states were found to co-exist, and the particular state realized was determined by the initial conditions. To elucidate the dynamics of cellular instabilities, circular non-premixed jet flames are modeled with a combination of three-dimensional numerical simulation and linear stability analysis (LSA). In both formulations, chemistry is described by a single-step, finite-rate reaction, and different reactant Lewis numbers and molecular weights are specified. The three-dimensional numerical simulations show that different cellular flames can be obtained close to extinction and that different states co-exist for the same parameter values. Similar to the experiments, the behavior of the cell structures is sensitive to (numerical) noise. During the transient blow-off process, the flame undergoes transitions to structures with different number of cells, while the flame edge close to the nozzle oscillates in the streamwise direction. For conditions similar to the experiments discussed, the LSA results reveal various cellular instabilities, typically with azimuthal wavenumber m = 1–6. Consistent with previous theoretical work, the propensity for the cellular instabilities is shown to increase with decreasing reactant Lewis number and Damköhler number.     

Effects of fuel Lewis number on flame spread over solids

Using a detailed two-dimensional numerical model, a systematic investigation has been made to study the effect of fuel Lewis number (Le_F = α/D_F) and mass transfer on flame spread over thin solids. The fuel Lewis number affects the flame spread rates for both concurrent and opposed flames over thin fuels. The dependence of the flame spread rate on Le_F for these two spreading modes is, however, not the same. In opposed flame spreads (zero-gravity, self-propagation, and normal gravity downward propagation), the flame spread rate vs. Le_F curve is non-monotonic with a maximum value occurring at an intermediate value of Le_F = 0.5. In steady, concurrent spread in zero-gravity with low-speed flow and a constant flame length, the flame spread rate decreases with Le_F in a monotonic manner. By using the computational model as a tool, the effects of fuel mass diffusion perpendicular to and parallel with the solid surface are isolated to obtain more physical insight on the two-dimensional aspect of fuel mass transfer on flame spread. In addition, the model has also been used to decouple the solid evaporation process so that the fuel diffusion effect in the gas-phase can be isolated. Both of these theoretical exercises contribute to the understanding of mass transfer effects on the flame spreading phenomena over solids.     

Thermal quenching and re-ignition of mixed pockets of reactants and products in gas explosions

An approximate solution of the problem of quenching and re-ignition of products/reactants pockets mixed by turbulence is presented. The approach is based on the analysis of thermal regimes of the pocket, but not on the concept of flame stretch. Critical conditions for quenching and re-ignition of the mixed pockets are obtained in a simplified analytical model, and applied to the problem of the sharp difference between the cases of weak and strong flame acceleration in gas explosions. The critical conditions of the mixed eddies in the turbulent flow are shown to depend on the size of the mixed eddies, mixture properties and turbulence intensity. The critical Karlovitz number, Ka, for thermal quenching is shown to increase with the ratio of densities between reactants and products, σ, and with the overall reaction order, n, and to decrease with the Zeldovich number β (dimensionless activation energy) and Lewis number, Le. For the smallest mixed pockets, which are about the size of the laminar flame thickness, the critical Ka-number defines the boundary of the domain of broken flamelets and distributed reaction zones. This number is shown to be of the same order of magnitude as that found from experiments and from direct numerical simulations. The critical conditions for thermal quenching of the largest pockets that can be mixed by turbulence are shown to be independent of the turbulent intensity and could be expressed as a function of σ on β, n, and Le. The mixture properties, thus, may prescribe certain types of flame behavior in turbulent flows. The corresponding critical conditions are linked to the sharp boundary between the cases of weak and strong flame acceleration, which was not satisfactorily explained in previous studies. These critical conditions are shown to have similar critical σ-values and general trends as the experimental data.     

Thermal expansion effect on the propagation of premixed flames in narrow channels of circular cross-section: Multiplicity of solutions,axisymmetry and non-axisymmetry

The present study examines, in presence of thermal expansion effects, the existence of the multiplicity of solutions previously reported within the context of diffusive-thermal modeling in [15], for lean premixed flames with low Lewis number (Le?<?1) propagating in narrow circular adiabatic channels subject to a Poiseuille flow. For this, direct numerical simulations have been carried out within the framework of variable-density Navier–Stokes equations and zero-Mach-number approximation. The simulations, conducted for both axisymmetric and three-dimensional cylindrical geometries, confirm the coexistence of multiple steady flame structures for a given flow rate. They show that axisymmetric flames concave towards the upstream are more unstable to three-dimensional perturbations than convex (toward the upstream) flames. This result evinces earlier findings obtained from stability analysis. The non-axisymmetry property of the flame is also found to push back the critical flashback limits at larger flow rate when compared to those predicted under the assumption of flame axisymmetry.     

Effect of Lewis number on premixed laminar lean-limit flames stabilized on a bluff body

In this paper, we present a study on the effect of Lewis number, Le, on the stabilization and blow-off of laminar lean limit premixed flames stabilized on a cylindrical bluff body. Numerical simulations and experiments are conducted for propane, methane and two blends of hydrogen with methane as fuel gases, containing 20% and 40% of hydrogen by volume, respectively. It is found that the Le?>?1 flame blows-off via convection from the base of the flame (without formation of a neck) when the conditions for flame anchoring are not fulfilled. Le?≤?1 flames exhibit a necking phenomenon just before lean blow-off. This necking of the flame front is a result of the local reduction in mass burning rates causing flame merging and quenching of the thin flame tube formed. The structure of these flames at the necking location is found to be similar to tubular flames. It is found that extinction stretch rates for tubular flames closely match values at the neck location of bluff-body flames of corresponding mixtures, suggesting that excessive flame stretch is directly responsible for blow-off of the studied Le?≤?1 flames. After quenching of the neck, the upstream part forms a steady and stable residual flame in the wake of the bluff body while the downstream part is convected away.     

Superconductivity of A15-and σ-phase of Nb-Ir

The superconducting properties of A15-, σ-, and tetragonal phases of the system Nb−Ir were investigated. The alloys were prepared by sintering and arc melting. They were subjected to optical and scanning electron microscopy. The lattice parameters were determined by x-ray diffraction technique. Superconducting transition temperatures,T _c , as well as upper critical fields,H _c2, were measured inductively and resistively. TheT _c -values of the σ-phase vary between 2.15 and 2.40 K whereas for the A15-phase they vary between 1.83 and 2.73 K. TheT _c -value of the tetragonal phase is 3.81 K. The upper critical fields of the tetragonal and the A 15-phase are nearly the same (≈13 kG) and lower compared with that of the σ-phase (≈18 kG). Several theoretically predicted values ofH _c2(0) are evaluated and compared with the experimental ones.     

Importance of direction of vibration on the onset of Soret-driven convection under gravity or weightlessness

This paper considers the influence of the direction of vibration on the stability threshold of two-dimensional Soret-driven convection. The configuration is an infinite layer filled with a binary mixture, which can be heated from below or from above. The limiting case of high-frequency and small-amplitude vibration is considered for which the time-averaged formulation has been adopted. The linear stability analysis of the quasi-mechanical equilibrium shows that the problem depends on five non-dimensional parameters. These include the thermal Rayleigh number ( Ra_T), the vibrational parameter (R), the Prandtl number ( Pr), the Lewis number (Le), the separation ratio (S) and the orientation of vibration with respect to the horizontal heated plate (). For different sets of parameters, the bifurcation diagrams are plotted Ra_c = f (S) and k_c = g(S), which are the critical thermal Rayleigh and the critical wave numbers, respectively. Our results indicate that, relative to the classical case of static gravity, vibration may affect all regions in Ra_c-S stability diagram. In the case of mono-cellular convection, by using a regular perturbation method, a closed-form relation for the critical Rayleigh number is found. Several physical situations in the presence or in the absence of gravity (micro-gravity) are discussed.     

An experimental realization of an unstrained, planar diffusion flame

A unique burner was constructed to experimentally realize a one-dimensional unstrained planar non-premixed flame, previously considered only in idealized theoretical models. One reactant, the fuel mixture in the current experiments, is supplied through a porous plug at the bottom of the combustion chamber and flows vertically up towards the horizontal flame. The crux of the design is the introduction of the oxidizer from above in such a way that its diffusion against the upward product flow is essentially one-dimensional, i.e., uniform over the burner cross-section. This feature was implemented by introducing the oxidizer into the burner chamber from the top through an array of 625 closely spaced hypodermic needles, and allowing the hot products to escape vertically up through the space between the needles. Due to the injection of oxidizer through discrete tubes, a three-dimensional “injection layer” exists below the exit plane of the oxidizer supply tubes. Experimental evidence suggests that this layer is thin and that oxidizer is supplied to the flame by 1-D counterdiffusion, producing a nearly unstrained flame. To characterize the burner, flame position measurements were conducted for different compositions and flowrates of H₂–CO₂ and O₂–CO₂ mixtures. The measured flame locations are compared to an idealized one-dimensional model in which only diffusion of oxidizer against the product flow is considered. The potential of the new burner is demonstrated by a study of cellular structures forming near the extinction limit. Consistent with previous investigations, cellular instabilities are shown to become more prevalent as the initial mixture strength and/or the Damköhler number are decreased. As the extinction limit is approached, the number of cells was observed to decrease progressively.     

A LES-CMC formulation for premixed flames including differential diffusion

A finite volume large eddy simulation–conditional moment closure (LES-CMC) numerical framework for premixed combustion developed in a previous studyhas been extended to account for differential diffusion. The non-unity Lewis number CMC transport equation has an additional convective term in sample space proportional to the conditional diffusion of the progress variable, that in turn accounts for diffusion normal to the flame front and curvature-induced effects. Planar laminar simulations are first performed using a spatially homogeneous non-unity Lewis number CMC formulation and validated against physical-space fully resolved reference solutions. The same CMC formulation is subsequently used to numerically investigate the effects of curvature for laminar flames having different effective Lewis numbers: a lean methane–air flame with Le_eff = 0.99 and a lean hydrogen–air flame with Le_eff = 0.33. Results suggest that curvature does not affect the conditional heat release if the effective Lewis number tends to unity, so that curvature-induced transport may be neglected. Finally, the effect of turbulence on the flame structure is qualitatively analysed using LES-CMC simulations with and without differential diffusion for a turbulent premixed bluff body methane–air flame exhibiting local extinction behaviour. Overall, both the unity and the non-unity computations predict the characteristic M-shaped flame observed experimentally, although some minor differences are identified. The findings suggest that for the high Karlovitz number (from 1 to 10) flame considered, turbulent mixing within the flame weakens the differential transport contribution by reducing the conditional scalar dissipation rate and accordingly the conditional diffusion of the progress variable.     

Critical behavior of electrical resistivity in amorphous Fe-Zr alloys

Electrical resistivity (ρ) of the amorphous (a-)Fe_100−c Zr _c (c=8.5, 9.5 and 10) alloys has been measured in the temperature range 77 to 300 K, which embraces the second-order magnetic phase transition at the Curie temperature point T _c. Analysis of the resistivity data particularly in the critical region reveals that these systems have a much wider range of critical region compared to other crystalline ferromagnetic materials. The value of T _c and specific heat critical exponent, α has the same values as those determined from our earlier magnetic measurements. The value of α for all the present investigated alloys are in close agreement with the values predicted for three-dimensional (3D) Heisenberg ferromagnet systems, which gives contradiction to the earlier results on similar alloys. It is observed from the analysis that the presence of quenched disorder does not have any influence on critical behavior.     

Diffusion flame instabilities in a 0.75 mm non-premixed microburner

We examine the cellular instabilities of laminar non-premixed diffusion flames that arise in a polycrystalline alumina microburner with a channel wall gap of dimension 0.75 mm. Changes in the flame structure are observed as a function of the fuel type (H₂, CH₄, and C₃H₈) and diluent. The oxidizer is O₂/inert. In contrast to previous observations on laminar diffusion flame instabilities, the current instabilities occur in the direction of flow above the splitter plate, and only occur for the heavier fuel types. They are not observed in a H₂–O₂ mixture, which will only support a continuous laminar flame inside our burner, regardless of the initial mixture strength and whether or not the flame is in near-quenching conditions. The only exception is when helium is added to the H₂–O₂ mixture, raising the effective Lewis numbers of both components.     

Hyperacceleration effects on turbulent combustion in premixed step-stabilized flames

Experimental results are presented from an investigation of the effects of large transverse accelerations on flame propagation and blowout limits in premixed step-stabilized flames. The accelerations, which exceed ±10,000 g in the present study, induce large body forces on the high-density reactants and low-density products. These body forces can substantially alter the flame propagation mechanisms and dramatically increase the flame blowout limits. Sustained centripetal accelerations a_c ≡ U²/R are created by flowing a premixed propane–air reactant stream with equivalence ratios 0.7  Φ  1.9 at various speeds U through a semicircular channel with radius R. A backward-facing step of height h on the radially outer (a_c > 0) or inner (a_c < 0) wall stabilizes the flame. For a_c > 0 the acceleration acts to force high-density reactants into the recirculation zone and low-density products into the reactant stream, while a_c < 0 forces hot products into the recirculation zone and impedes cold reactants from entering this zone. An otherwise identical straight channel provides corresponding baseline (a_c = 0) results for comparison. The flow speed U, equivalence ratio Φ, and step height h are systematically varied for a_c = 0, a_c > 0, and a_c < 0. Shadowgraph and chemiluminescence imaging show that as a_c→ +∞ the propagation of the flame across the channel becomes independent of the flame burning velocity and instead is primarily due to large-scale “centrifugal pumping” driven by the induced body forces. For a_c → −∞ the body forces effectively segregate reactants and products to produce a nearly flat flame. In both cases, for large |a_c| values the resulting blowout limits can be substantially higher than those at a_c = 0.     

Computational study on lean and rich combustion of flame ball,counterflow flame and planar flame: Their limits and stoichiometries

To investigate (fuel-)lean/rich limits and essential stoichiometries, i.e., the borders of lean/rich combustion, one-dimensional steady computations with detailed chemistry for flame balls, counterflow flames, and stretch-free planar flames were conducted using a CH₄/O₂/Xe mixture that has been used in microgravity experiments. As continuous converged solutions were obtained under lean/rich conditions, it was suggested that the existence of flame ball not only under lean but also under rich condition. Flame radii and temperatures of flame balls decreased and increased toward the lean/rich limits from their maximum and minimum values, respectively. The lean limits were wider in the order of the flame ball, counterflow flame, and stretch-free planar flame. Therefore, the lean flammability limit corresponded to the lean limit of the flame ball in the mixture. Conversely, the rich limits were wider in the order of the counterflow flame, stretch-free planar flame, and flame ball. Thus, the rich flammability limit corresponded to the rich limit of the counterflow flame in the mixture. Essential stoichiometry, which represents the actual stoichiometry depending on the dominant transport in near-flame front, was not uniquely determined as conventional stoichiometry (ϕ = 1); it was located between the equivalence ratio of ϕ = 1 and ϕ_c, where ϕ _c denotes the critical equivalence ratio is evaluated using the fuel and oxidizer Lewis number of a target mixture. The results indicated that the essential stoichiometry of the stretch-free planar flame corresponded to ϕ = 1, that of the flame ball corresponded to ϕ = ϕ _c, and that of the stretched flame was located between ϕ = 1 and ϕ _c depending on the stretch rate.     

Role of processing in improving the critical current of Ag/BPSCCO tapes

Silver-clad tapes of highT _c Bi-Pb-Sr-Ca-Cu-O superconductors have been fabricated through the powder-in-tube method. The critical current density, J _c , of a thick tape was 534 A.cm⁻² (77 K, 0 T). Subsequent rolling and sintering of the tapes led to a gradual decrease inJ _c, instead of the expected increase. This was caused by the microcracks developed in the core material by a rather drastic reduction during the rolling of the tapes. A modified and well controlled rolling technique, on the other hand, resulted in much improvedJ _c values. Repeated rolling and sintering resulted in a good grain alignment and no microcracks were observed. In the present studies, maximumJ _c of 1846 A.cm⁻² (77 K, 0 T) and 2.43 × 10⁴ A.cm⁻² (4.2 K, 0 T) have been obtained Optimization of the processing and sintering parameters are expected to lead to still higherJ _c values.     

Comparison of superconducting parameters of A 15- and σ-phases of Nb−Pt

The superconducting properties of A 15- and σ-phases of the system Nb−Pt were investigated. Alloys of compositions Nb₃Pt, Nb₂Pt, and Nb₆₂Pt₃₈ were prepared by arc melting and subjected to optical microscopic and x-ray analysis for structure determination. The transition temperatures were measured inductively as well as resistively. The temperature dependences of critical fields were measured up to 35 kG. The A 15-phase has aT _c value of 8.97K and a zero temperature upper critical fieldH _c2(0) of 100 kG as compared to aT _c value of 2.14K and anH _c2(0) value of 14kG for the σ-phase. A comparison with theoretical upper critical field values seems to indicate that a spin-orbit coupling mechanism is responsible for the higher value ofH _c2(0) in the case of the A 15-phase alloy. The temperature dependent resistance up to 300 K is also measured and discussed for both the phases.     

Fundamental burning velocities of meso-scale propagating spherical flames with H2, CH4 and C3H8 mixtures

This study is performed to experimentally examine the fundamental burning velocity characteristics of meso-scale outwardly propagating spherical laminar flames in the range of flame radius r_f approximately from 1 to 5 mm for hydrogen, methane and propane mixtures, in order to make clear a method for improving combustion of micro–meso scale flames. Macro-scale laminar flames with r_f > 7 mm are also examined for comparison. The mixtures have nearly the same laminar burning velocity (S_L0 = 25 cm/s) for unstretched flames and different equivalence ratios ?. The radius r_f and the burning velocity S_Ll of meso-scale flames are estimated by using sequential schlieren images recorded under appropriate ignition conditions. It is found that S_Ll of hydrogen and methane premixed meso-scale flames at the same r_f or the Karlovitz number Ka shows a tendency to increase with decreasing ?, whereas S_Ll of propane flames increases with ?. However, S_Ll tends to decrease with the Lewis number Le and the Markstein number Ma, irrespective of the type of fuel and ?. It also becomes clear that the optimum flame size and Ka to improve the burning velocity exist for some mixtures depending on Le and fuel types.