Small Lewis Numbers Research Articles

Suppression of the turbulent kinetic energy and enhancement of the flame-normal Reynolds stress in premixed jet flames at small Lewis numbers

We report the effects of the Lewis number on the turbulent kinetic energy, Reynolds stresses, and scalar fluxes in premixed jet flames with strong mean shear. The direct numerical simulation (DNS) of piloted turbulent premixed jet flames is performed under the same condition except for different Lewis numbers to isolate the Lewis number effects. The turbulence intensity within the mean flame brush is found to decay more rapidly along the axial distance with a smaller Lewis number. This Lewis number dependence results from the coupling of the mean shear and the combustion heat release, where the mean shear is the primary source of turbulence production. We show that, under the strain imposed by the mean shear and turbulence fluctuation, the heat release of premixed jet flames is significantly enhanced at the Lewis number smaller than unity, which is represented by the rising flamelet consumption speed and flame surface area. As a consequence, the mean shear within the flame brush is suppressed at small Lewis numbers via the dilatation effect, and the weakened mean shear production causes the fast turbulence suppression along the axial direction. The enhanced heat release at small Lewis numbers also increases the flame-normal Reynolds stress, and leads to the counter-Boussinesq behavior of the shear Reynolds stress and the counter-gradient transport of scalar fluxes. We model the Lewis number effects on local turbulence and scalar transport using the stretched laminar flame speed and thickness, and achieve overall good estimations of the flame-normal Reynolds stress and scalar transport at small Lewis numbers.

Hess Law Applicability to Heterogeneous Combustion Reactions Resulting to Non-Monotonicity of Enthalpy Distribution in Them

The definition of reaction irreversibility (reversibility) available now in literature does not allow for determining this reaction peculiarity before a practice. Moreover, in mathematical terms, such a definition is not universal and leads actually to the denial of any similarity in physicochemical processes, in particular in combustion waves. We have considered the irreversibility of reactions from the mathematical viewpoint as independence of a reaction rate on the concentration of products directly. As a result, in terms of Lei numbers, we have formulated conditions sufficient for the enthalpy of reagents to be a complete differential (or a thermodynamic potential) and independent of the reaction path. And conversely, the conditions necessary for that enthalpy of reagents are significantly dependent on the reaction path (Le ≌ 1). A comparison of the conclusions we obtained with the data from experiments available in the literature showed a good agreement with them and put an edge on the question of determining the irreversibility (reversibility) of reactions in the scientific community. We have shown that the small values of the diffusion coefficients of reagents Di compared to the thermal diffusivity coefficient κ, and with them, the corresponding small Lewis numbers (Lei = Di/κ << 1) for the most heterogeneous combustion synthesis systems, are the sufficient conditions for the enthalpy of reactions (H) to be a complete differential of the systems states and, vice versa, a strong similarity appears between the enthalpy and concentration fields at Le ≌ 1.

Effect of non-ambient pressure conditions and Lewis number variation on direct numerical simulation of turbulent Bunsen flames at low turbulence intensity

The instantaneous flame front structure of high pressure turbulent premixed Bunsen flames has been analyzed for a wide range of characteristic Lewis numbers using a new Direct Numerical Simulation (DNS) database. High pressure turbulent premixed flames of lean-light fuels are likely to feature both thermo-diffusive and Darrieus–Landau instabilities. As the effects of these instabilities are eclipsed by intense turbulence, the present analysis focuses on flames located at the border of the wrinkled and corrugated flamelets regimes. The flame morphology has been characterized by the skewness and kurtosis of the probability density function (PDF) profiles of the mean and Gaussian curvatures. While skewness alone is not sufficient as a marker to distinguish between thermo-diffusive and Darrieus–Landau instabilities, it has been found that excess kurtosis of Gaussian curvature possibly can be used to distinguish between both instabilities. Further, the inner cut-off length and the fractal dimension have been computed for characterization of flame scales and for parameterization of wrinkling factor models. It has been observed that increasing pressure and decreasing Lewis number give rise to flame instabilities which results in an increased fractal dimension and a decreased inner cut-off scale. For high pressure flames with Lewis numbers around unity, the inner cut-off scale scales very well with the critical wavelength for flame instabilities determined from the theoretical analysis by Matalon and Matkowsky (1982). For small sub-unity Lewis numbers, the flames become unconditionally unstable and the critical wavelength loses its meaning, while the inner cut-off scales continues to decrease with Lewis number and the fractal dimension continues to increase up to a limit of about 7/3. The present findings are in excellent agreement with experimental observations from literature and theoretical analysis of flame instabilities.

Natural Convection in a Non-Newtonian Fluid: Effects of Particle Concentration

In this paper we study the buoyancy driven flow of a particulate suspension between two inclined walls. The suspension is modeled as a non-linear fluid, where the (shear) viscosity depends on the concentration (volume fraction of particles) and the shear rate. The motion of the particles is determined by a convection-diffusion equation. The equations are made dimensionless and the boundary value problem is solved numerically. A parametric study is performed, and velocity, concentration and temperature profiles are obtained for various values of the dimensionless numbers. The numerical results indicate that due to the non-uniform shear rate, the particles tend to concentrate near the centerline; however, for a small Lewis number (Le) related to the size of the particles, a uniform concentration distribution can be achieved.

Effects of water droplet evaporation on initiation, propagation and extinction of premixed spherical flames

In this study, we develop a simplified theoretical model for flame initiation, propagation and extinction in premixed gas mixture containing water droplets, by considering water droplet evaporation in pre-flame or/and post-flame zones. The Eulerian droplet model with simplified evaporation sub-model is employed, while for gas phase the assumptions of constant-density, quasi-steady and large activation energy are made. Analytical correlations describing different flame regimes and transitions among flame balls, propagating spherical flames and planar flames are then derived to investigate the spherical flame initiation, propagation and extinction, with emphasis on the effects of water droplet evaporation on spherical flames at different Lewis numbers. Five different flame regimes are observed and discussed for droplets evaporation in pre-flame or/and post-flame zones. It is found that the droplets with larger heat exchange coefficient are more effective in reducing flame propagation speed and temperature but increasing the vaporization front. Moreover, the cooling effect of evaporation heat loss plays an important role on flame regimes and their transitions. At the relatively large heat exchange coefficient, the total evaporation heat loss from pre-flame and post-flame zones reaches its maximum at an intermediate flame radius. The cooling effect is strong enough to quench the flame and results in the self-extinguishing flame. In addition, the combined effects of stretch rate and Lewis number compete with the evaporation heat loss from droplet evaporation. For small Lewis number, the flammability limits can be achieved through self-extinguishing flames, whereas for large Lewis number the flames approach their flammability limits in their evolution into planar flames. For ignition of spherical flames, if the droplet-laden mixture is intrinsically non-flammable, although a propagating flame kernel can be initiated, however it would still be quenched due to evaporation heat loss at a critical radius. The minimum ignition energy increases with heat exchange coefficient and Lewis number.

Dynamic transition of dendrite orientation in the diffusive spinodal decomposition of binary mixtures under a thermal gradient

While the spinodal decomposition of mixtures in unbounded systems has been largely investigated, little is known about phase separation constrained within a slab. In this study, spinodal decomposition of a very viscous regular binary mixture bounded within two walls cooled at different temperatures is simulated by using the diffuse interface model in 2D. Under a temperature gradient, phase separation starts from the cooler wall forming dendritic structures growing anisotropically with time. Two remarkably different dynamics are identified depending on whether heat propagates slower or faster than mass. For small thermal conductivity (i.e., small Lewis number), dendrites grow parallelly to the temperature gradient, keeping such an alignment until the steady-state. On the other hand, for large Lewis number, during the early stages phase separation proceeds within stripes oriented along iso-temperature lines, i.e., with dendrites aligned perpendicularly to the temperature gradient, which, however, gradually shift their orientation parallel to the temperature gradient as the steady-state is approached. Such a dynamic transition of dendrite orientation upon a temperature gradient when heat propagates faster than mass is found to hold also for non-equimolar mixtures and for different species thermal conductivities. These results shed light on the dynamics of phase separation in constrained systems and anisotropic conditions.

Impact of an insoluble surfactant on the thresholds of evaporative Bénard-Marangoni instability under air.

It is known that the addition of an insoluble surfactant to a Bénard-Marangoni (BM) layer heated from below or cooled from above can give rise to a supplementary, oscillatory mode of instability. Here the objective is to see how exactly this plays out in the framework of a recently studied and experimentally tested case of a non-long-wavelength BM instability driven by diffusion-limited evaporation into air in isothermal surroundings. Linear stability analysis is accomplished within a now standard reduction to a one-sided model. In the absence of surfactant, we just recover the classical Pearson problem, albeit with an evaporation-specific wavenumber-dependent Biot number potentially attaining large values for strongly volatile liquids. Adding a surfactant not only sharply stabilizes the monotonic Pearson-like mode, but also leads to a more dangerous oscillatory mode, a parametric study of which is here undertaken. Although slanted towards the evaporative case, the present study is also of interest from the general viewpoint of the Pearson problem + an insoluble surfactant, the results for which are scarce in the literature without being obscured by further effects. In particular, an asymptotic analysis based on small interfacial Lewis numbers (diffusion coefficients) is undertaken near the codimension-2 point.

Radiation Effects on the Thermodiffusive Instability of Premixed Flames on a Cylindrical Porous Flame Holder

A linear analysis method was used to investigate the mechanics of radiation heat loss and mass transfer in the porous wall of premixed annular flames and their effect on thermodiffusive instability. The dispersion relation between the disturbance wave growth rate and wavenumber was calculated numerically. Results showed that radiation heat loss elevated the annular flame slightly away from the porous wall. In the annular flame with small Lewis numbers, radiation heat loss changed the thermodiffusive instability from a pulsating to a cellular state, while for the large Lewis numbers, only the pulsating instability was represented. Increasing radiation heat loss and the radius of the porous wall enhanced the instability of the annular flames. Heat losses decreased with the continued increase in thickness of the porous wall and the decrease in porosity. Annular flames with long-wave mode along the angular direction were more unstable than the shortwave mode.

極低温環境における予混合火炎の固有不安定性（未燃ガス温度と熱損失の影響）

The effects of unburned-gas temperature and radiative heat loss on the intrinsic instability of premixed flames in cryogenic environment were studied. Unsteady reactive flow was calculated numerically, based on the compressible Navier-Stokes equation including chemical reaction and radiative heat loss. As the unburned-gas temperature became lower, the growth rate decreased and the unstable range narrowed, which was due to the reduction of the burning velocity of a planar flame. Considering radiative heat loss, the growth rate was smaller and the unstable range was narrower. On the other hand, the normalized growth rate increased as the unburned-gas temperature became lower. This was due to the strength of thermal-expansion effects and to the enlargement of Zeldovich numbers. Furthermore, cellular flames appeared owing to intrinsic instability. As the unburned-gas temperature became lower, the normalized burning velocity of a cellular flame increased. When radiative heat loss was considered, the normalized burning velocity of a cellular flame increased at small Lewis numbers and remained at Lewis number of unity.

Magnetic field effect on Soret driving free convection in an inclined porous cavity saturated by a conducting binary mixture

Purpose – The purpose of this paper is to study analytically and numerically the effect of a transverse magnetic field on the separation of species induced in an inclined rectangular porous cavity saturated with an electrically conducting mixture. Design/methodology/approach – The porous layer is assumed homogeneous and submitted from its long sides to uniform heat fluxes and to a magnetic field of strength B. The Darcy model combined with the Boussinesq approximation are used to study the heat and solute transfer in the medium. An analytical solution is developed on the basis of the parallel flow approximation. Numerical simulations are also performed in order to validate the analytical solution. The controlling parameters of this problem are the thermal Rayleigh number, the inclination of the enclosure, the separation parameter, the Hartmann number and the Lewis number. Findings – For given values of the thermal Rayleigh number, the inclination of the enclosure, the separation parameter and the Lewis number, there is an optimal magnetic field which leads to a maximum of separation. At relatively high Rayleigh numbers, where convection destroys the separation process, it is possible, with an optimal choice of the Hartman number, to recover a good level of separation. Research limitations/implications – Since the problem is governed by several parameters (five parameters), only the Darcy model was used in this study instead of the Darcy-Brinkman extended model even if the latter model allows to cover the pure fluid and Darcy porous media as limiting cases. Practical implications – In separation experiments, it is very difficult technically to work with small Rayleigh numbers due to technical difficulties. However, the process of separations is canceled at high Rayleigh number by the strength of convection which causes a mixing in the binary mixture. This study shows that, by using adequate combinations of the controlling parameters, it becomes possible to reach a good level of separation even at relatively high Rayleigh numbers. Originality/value – Optimum choice of the magnetic field and the inclination of the cavity may lead to a good level of the separation process. For large Lewis numbers, the separation vanishes far above and far below the optimal Ha. However, for small Lewis numbers, an important level of separation is maintained for any Ha located below the optimal value of the latter parameter.

Modeling curvature effects in diffusion flames using a laminar flamelet model

The goal of this paper is to investigate the effects of curvature of mixture fraction iso-surfaces on the transport of species in diffusion flames. A general flamelet formulation is derived mathematically considering both curvature effects and differential diffusion effects. These theoretical results suggest that curvature does not play a role in the transport process irrespective of the flame curvature if species transport is described with a unity Lewis number. On the other hand, a curvature-induced term becomes explicit when differential diffusion effects are considered, and it acts as a convective term in mixture fraction space. It is found that this term needs to be taken into account when the radius of curvature is comparable or smaller than the local flame thickness. For the proper integration of the flamelet equations, the scalar dissipation rate and curvature dependences on mixture fraction are modeled by considering two basic curved one-dimensional flame configurations. The flamelet equations accounting for curvature effects are solved with various prescribed curvature values. Results indicate that the mass fraction profiles of species with very small or large Lewis numbers are shifted significantly in mixture fraction space by the inclusion of curvature. Differential diffusion effects are enhanced by negative curvature values and suppressed by positive curvature values. In cases where flame curvature is not uniform, the curvature-induced convective term generates gradients along mixture fraction iso-surfaces, which enhance tangential diffusion effects. Budget analysis is performed on an axisymmetric laminar coflow diffusion flame to highlight the importance of the curvature-induced convective term compared to other terms in the full flamelet equation. A comparison is made between full chemistry simulation results and those obtained using planar and curved flamelet-based chemistry tabulation methods.

Non-linear stability bounds for a horizontal layer of a porous medium with an exothermic reaction on the lower boundary

We use the energy method to find regions of stability for a horizontal layer of a Darcy porous medium with an exothermic reaction on the lower layer. The results are compared to the linear instability results for this model found by Scott and Straughan [16]. It is shown that there is a region in which sub-critical instabilities may occur, but for small Lewis numbers, 0<Le<10, the non-linear stability boundary is reasonably close to the linear instability boundary. The effect of varying the parameters of the reaction on the stability curve is discussed.

Nonlinear dynamics of long-wave Marangoni convection in a binary mixture with the Soret effect

We investigate the nonlinear dynamics of long-wave Marangoni convection in a 2D binary-liquid layer heated from below. Free surface deformations and the Soret effect are taken into account. We employ the set of evolution equations derived in earlier work in the case of small Galileo and Lewis numbers and solve it numerically with periodic boundary conditions. We validate our numerical solution by comparison between the results obtained via two different numerical methods, as well as by comparison with the prior analytical results. We study the transitions between the nonlinear regimes emerging at finite supercriticality values and find a rich variety of patterns. In a sufficiently large computational domain, we observe multistability of waves chaotic in time and spatially replicated periodic and quasiperiodic solutions. For sufficiently high values of the Marangoni number, we also observe a breakdown of model equations.

The Instability of Flame Fronts in Premixed Combustion of Low-Temperature Gases (Effects of Unburned-Gas Temperature)

We performed two-dimensional unsteady calculations of reactive flows, based on the compressible N-S equation, to study the effects of unburned-gas temperature on the instability of flame fronts. As the unburned-gas temperature became lower, the growth rate decreased and the unstable range narrowed. This was due mainly to the reduction of the burning velocity of a planar flame. The normalized growth rate increased with a decrease of the unburned-gas temperature, and the normalized unstable range widened at Lewis numbers smaller than unity. This was because that the thermal-expansion effects became stronger owing to the increase of the temperature ratio of burned and unburned gases, and that the diffusive-thermal effects strengthened at Lewis numbers smaller than unity owing to the increase of the Zeldovich number. Moreover, the cellular shape of flame fronts formed, which was due to intrinsic instability. The normalized burning velocity of a cellular flame increased as the unburned-gas temperature became lower, especially in premixed flames with small Lewis numbers.

On the extraction of laminar flame speed and Markstein length from outwardly propagating spherical flames

Large discrepancies among the laminar flame speeds and Markstein lengths of methane/air mixtures measured by different researchers using the same constant-pressure spherical flame method are observed. As an effort to reduce these discrepancies, one linear model (LM, the stretched flame speed changes linearly with the stretch rate) and two non-linear models (NM I and NM II, the stretched flame speed changes non-linearly with the stretch rate) for extracting the laminar flame speed and Markstein length from propagating spherical flames are investigated. The accuracy and performance of the LM, NM I, and NM II are found to strongly depend on the Lewis number. It is demonstrated that NM I is the most accurate for mixtures with large Lewis number (positive Markstein length) while NM II is the most accurate for mixtures with small Lewis number (negative Markstein length). Therefore, in order to get accurate laminar flame speed and Markstein length from spherical flame experiments, different non-linear models should be used for different mixtures. The validity of the theoretical results is further demonstrated by numerical and experimental studies. The results of this study can be used directly in spherical flame experiments measuring the laminar flame speed and Markstein length.

Effects of Pressure on Laminar and Turbulent Burning Velocities of Ethanol Premixed Flames

Spherically propagating laminar and turbulent flames at elevated pressures in a large volume chamber were studied for ethanol / air mixtures. The properties of the ethanol flame at elevated pressures, especially the burning velocity and the effects of the flame stretch acting upon it are quit important for the modeling of combustion in internal combustion engines. Experiments were carried out in the wide range of the equivalence ratio from 0.8 to 1.4 at two turbulence intensities of 0.80 and 1.59m/s varying the initial pressure from 0.10 to 0.50MPa. The unstretched laminar burning velocity decreased with increasing initial pressure. The ratio of turbulent burning velocity to unstretched laminar burning velocity increased with increasing the turbulence Karlovitz number. This ratio of the burning velocities was large for rich flames. Thermo-diffusive effects might be more influential to rich ethanol flames because of their small Lewis number. The ratio of turbulent to laminar burning velocity was also found to increase with increasing initial pressure.

Marangoni convection in a binary liquid layer with Soret effect at small Lewis number: Linear stability analysis

We consider surface-tension-driven convection in a layer of a binary mixture. A linear stability problem is studied in the presence of both thermocapillary and solutocapillary effects. Assuming the Lewis and Biot numbers to be small, we develop the long wave theory and find both monotonic and oscillatory modes. Three various modes of oscillatory convection exist depending on the ratio between the small parameters. In the case of finite but sufficiently small values of the Biot and Lewis numbers, linear stability thresholds are determined numerically. The numerical results agree well with those found analytically.

F217 エタノール予混合火炎の層流および乱流燃焼速度に及ぼす圧力の影響(OS3 バイオマス・新燃料・環境技術)

Spherically propagating laminar and turbulent flames at elevated pressures in a large volume bomb were studied for ethanol-air mixtures. Experiments were carried out at the equivalence ratio 0.8, 1.0 and 1.4 varying the initial pressure from 0.10 to 0.50MPa. Turbulence intensity of the mixture was 0.80 and 1.59m/s. The unstretched laminar burning velocity, U_l decreased as the initial pressure increased. The ratio of the turbulent burning velocity to U_l increased with increasing the ratio of turbulence intensity to U_l and turbulence Karlovitz number. This burning velocity ratio was large for rich flames. Thermo-diffusive effects might be more influential to rich ethanol flames because of the small Lewis number. This burning velocity ratio was also found to increase with increasing initial pressure.

Long-wave Marangoni instability in a binary liquid layer on a thick solid substrate

We consider a system which consists of a layer of an incompressible binary liquid with a deformable free surface, and a thick solid substrate subjected to a differential heating across it. We investigate the long-wave thermosolutal Marangoni instability in the case of asymptotically small Lewis and Galileo numbers for finite capillary and Biot numbers with the Soret effect taken into account. We find both long-wave monotonic and oscillatory modes of instability in various parameter domains of Biot and Soret numbers. In the domain of finite wave numbers the monotonic instability is found, but the minimum of the monotonic neutral curve is shown to be located in the long-wave region. A set of nonlinear evolution equations is derived for the description of the spatiotemporal dynamics of the oscillatory instability. The weakly nonlinear analysis is carried out for the monotonic instability.

Numerical study of thermodiffusive flame structures interacting with adiabatic walls using an adaptive multiresolution scheme

We report on numerical simulations of planar, circular, and spherical thermodiffusive flames in one, two and three space dimensions, respectively. Attention is focused on the interaction of spherical flames with adiabatic walls or equivalently on their interaction with their mirror image. The numerical scheme is based on an adaptive multiresolution discretization which allows self-adaptive grid refinement in regions of the thin reaction zone. We show that the Lewis number determines the behaviour of the flame–wall interaction. When the flame is approaching the wall, we observe for Lewis numbers smaller than unity that the reaction rate is decreased, for unitary Lewis number the reaction rate neither increases nor decreases, and for Lewis numbers larger than unity the reaction rate increases. Due to tangential diffusion the flame front curvature is also modified, i.e. for small Lewis numbers the spherical flame contracts, for large Lewis numbers it spreads out, while for a unitary Lewis number the flame front remains perpendicular to the wall. The observed phenomena present similarities with capillarity effects in fluid mechanics when a droplet hits a wall.