Effective Lewis Number Research Articles

Burning velocity and statistical flame front structure of turbulent premixed flames at high pressure up to 1.0 MPa

Statistical flame front structure of turbulent premixed flames at high pressure up to 1.0MPa was measured on a nozzle-type Bunsen burner with OH-PLIF technique. Turbulent burning velocity, flame surface density and flame brush thickness, as well as the local curvature and radius of curvature were derived from the experimental OH-PLIF images. Turbulence–flame interaction was analyzed based on the geometric parameters combined with laminar flame properties and turbulence length scales. Results show that the flame wrinkles at high pressure are dominated by small scale cusps superimposed with large scale flame branches which is a general characteristic of the turbulent premixed flames at high pressure. ST/SL increases remarkably with u′/SL and the influence of elevated pressure on ST/SL is significant. This is mainly due to the increase of flame front area caused by the turbulence wrinkling. Flame surface density significantly increases with the increase of pressure indicating that there is a large amount of fine cusps and small wrinkles in the flame front at high pressure. This would be due to the enhancement of the flame instability represented by effective Lewis number Leeff and flame intrinsic instability scale li. With the increase of turbulence intensity, the Σ at high pressure increases while slightly decreases at normal pressure. The most frequent length scale of the flame front moves to smaller value and the possibility increases with the increase of u′/SL for all pressures. The effect of flame intrinsic instability on finer flame front at high pressure is mainly on the formation of a large number of convex structures which enlarge the effective contact surface between flame front and unburned reactants, resulting in the increase of ST/SL.

A Comparative Study of Different Reaction Models for Turbulent Methane/Hydrogen/Air Combustion

Reaction modelling of methane/hydrogen combustion has two important aspects. First, such mixtures may be used in future in combustion devices like gas turbines and gas engines in the frame of the demand for efficient energy storage systems, where the amount of hydrogen in natural gas delivering systems may vary according to varying hydrogen production from renewable energies. Second, this can be an important aspect for safety, as such mixtures may occur in disastrous situations and calculations may allow the prediction of safety issues. Modelling of such mixed fuel combustion processes is non-trivial due to the involved preferential diffusion effects, coming from the different diffusivities of methane and hydrogen. In turbulent flame modelling, this topic is of special interest, as also thermo-diffusive instabilities and local influence of the local burning velocity near leading edges of the flame seem to be of importance even for highly turbulent flames. This numerical work deals therefore with a comparative study of five different turbulent combustion models - Bray-Moss-Libby, Linstedt-Vaos (LV), a modified version LV, Turbulent Flamespeed Closure, and Algebraic Flame Surface Wrinkling model - to the situation of turbulent methane/hydrogen/air flames. Validation is done with extensive experimental data obtained by a low swirl burner in the group by Cheng. Besides a basic case with pure methane/air, special emphasis is laid on flames with 40 to 100 % hydrogen content by volume. It is shown that for such methane/hydrogen fuel mixtures common reaction rate models are not sufficient where the fuel effects are included only via a laminar flame speed. Instead, a recently proposed reaction model with the incorporation of an effective Lewis number of the fuel mixture is found to work rather well. This is of both, practical as well as theoretical importance, as for the latter it confirms controversially discussed assumptions of the influence of preferential diffusion.

Experimental validation of Lewis number and convection effects on the smoldering combustion of a thin solid in a narrow space

This paper presents numerical and experimental results of the smoldering propagation along a thin solid in a narrow space. This study particularly focuses on the formation of a fingering pattern caused by an instability mechanism—an important phenomenon from a fire safety point of view because the formation of such a pattern increases the smoldering velocity. Two-dimensional numerical simulations are first conducted to show, similarly to previous theoretical studies, that a fingering pattern including the split and local extinction of fingertip is formed only when the Lewis number is well below unity. The accuracy of the near-equidiffusive (i.e., the Lewis number near unity) approximation for such a low Lewis number is also tested. Then, the predicted influence of the Lewis number is experimentally confirmed by burning paper sheets having different Lewis numbers. It is also demonstrated (both numerically and experimentally) that a fingering pattern can be formed without convection effects.

Effect of variable gravity on thermal instability of rotating nanofluid in porous medium

Effect of variable gravity on the onset of thermal convection in a horizontal layer of rotating nanofluid in a porous medium is investigated. For the porous medium Darcy model is used. A linear stability analysis based upon normal mode technique is used to find solution of the fluid layer confined between two free-free boundaries. Rayleigh numbers on the onset of stationary convection and oscillatory convection have been derived by using Galerkin method. Graphs have been plotted to study the effect of Taylor number (rotation), Lewis number and variable gravity parameter on the stationary convection.

He와 Ar으로 희석된 합성가스 화염에서 루이스 수와 선호확산효과

Numerical study is conducted to grasp flame characteristics in <TEX>$H_2/CO$</TEX> syngas counterflow diffusion flames diluted with He and Ar. An effective fuel Lewis number, applicable to premixed burning regime and even to moderately-stretched diffusion flames, is suggested through the comparison among fuel Lewis number, effective Lewis number, and effective fuel Lewis number. Flame characteristics with and without the suppression of the diffusivities of H, <TEX>$H_2$</TEX>, and He are compared in order to clarify the important role of preferential diffusion effects through them. It is found that the scarcity of H and He in reaction zone increases flame temperature whereas that of <TEX>$H_2$</TEX> deteriorates flame temperature. Impact of preferential diffusion of H, <TEX>$H_2$</TEX>, and He in flame characteristics is also addressed to reaction pathways for the purpose of displaying chemical effects.

Effects of Soret diffusion on spherical flame initiation and propagation

Dynamics of spherical flame initiation and propagation with Soret diffusion are investigated using large-activation-energy asymptotic analysis. Under the assumptions of constant density and quasi-steady flame propagation, a general correlation between the flame propagating speed and flame radius considering Soret diffusion and external energy deposition is derived. Emphasis is placed on assessing the effects of Soret diffusion on spherical flame propagation speed, Markstein length, and critical ignition condition. The stretched flame speed is found to be increased and reduced by the Soret diffusion of light and heavy fuels, respectively. For both light and heavy fuels, the absolute value of Markstein length increases after including Soret diffusion, indicating that premixed flames become more sensitive to stretch rate with Soret diffusion. It is found that the Markstein length can be characterized by an effective Lewis number which includes the effects of Soret diffusion. Moreover, Soret diffusion is shown to affect the ignition process since the spherical flame kernel is highly stretched. For large hydrocarbon fuels with high Lewis numbers, the minimum ignition power becomes much larger after considering Soret diffusion.

Thermal instability of a nonhomogeneous power-law nanofluid in a porous layer with horizontal throughflow

Despite the experimental observation of shear-thinning rheological behavior depending on the nanoparticle volume fraction, nanofluids were treated as either Newtonian or viscoelastic fluids in previous studies on thermal convection. In this work, taking into account the shear-thinning rheology, Brownian diffusion and thermophoresis of nanofluids, the onset of thermal convection in a nonhomogeneous nanofluid-saturated porous layer with throughflow is investigated. The power-law model is adopted to describe the shear-thinning behavior of nanofluids. The combined effects of Lewis number, Péclet number and power-law index on the thermal instability are analyzed. It is found that the most unstable perturbations are transverse rolls, and both traveling-wave and oscillatory modes may occur. The critical Rayleigh number can be significantly reduced or increased with the increasing power-law index, mainly depending on the value of Péclet number. Furthermore, the decrease of Lewis number can promote or suppress the onset of thermal convection, depending on whether the nanoparticle distribution at the basic state is bottom-heavy or top-heavy.

Quantification of extinction mechanism in counterflow premixed flames

The extinction mechanisms of stretched premixed flames have been investigated numerically for the fuels of CH4, C3H8, H2, CO and for the mixture fuels of CH4+H2 and CO+H2 by adopting symmetric double premixed flames in a counterflow configuration. The local equilibrium temperature concept was used as a measure of energy loss or gain in order to quantify the extinction mechanism by preferential diffusion and/or incomplete reaction. The energy loss ratio from preferential diffusion arising from non-unity Lewis number and the loss ratio from incomplete reaction were calculated at various equivalence ratios near flame extinction. The results showed that the extinction of lean H2, CH4, CH4+H2, CO+H2, and rich C3H8 premixed flames was caused by incomplete reaction due to insufficient reaction time, indicating that the effective Lewis number was smaller than unity, while the effect of preferential diffusion resulted in energy gain. However, the extinction of rich H2, CH4, CH4+H2, CO+H2, and lean C3H8 premixed flames was affected by the combined effects of preferential diffusion and incomplete reaction indicating that the effective Lewis number was larger than unity. In CO premixed flames, incomplete reaction was dominant in both lean and rich cases due to the effective Lewis number close to unity. The effect of H2 mixing to CO is found to be quite significant as compared to CH4+H2 cases, which can alter the flame behavior of CO flames to that of H2.

Laminar flame speed and Markstein length of syngas at normal and elevated pressures and temperatures

Synthetic gas, or syngas, is a popular alternative fuel for gas turbine industry. However, the composition of syngas is complex which complicates the combustor design. In this study, a dual-chambered pressure-release type combustion apparatus was developed and used for measurements of laminar flame speed which could be operated at high pressures and temperatures. The laminar flame speeds of syngas were measured at normal and elevated pressures and temperatures. The effects of Lewis number, flame temperature, pressure and initial temperature on the laminar flame speed and Markstein length of typical syngas mixtures were investigated. The results showed that the unstretched laminar flame speed increased with the increase of Lewis number and flame temperature, and that it decreased with the increase of pressure. The Markstein length decreased with the increase of pressure and initial temperature. It was found that the Markstein length was less sensitive to change of initial temperature than that of pressure. Furthermore, the performance on theoretical model for Markstein length using different Lewis numbers was examined. It was found that for syngas, the diffusion-based effective Lewis number rather than the volume or heat release-based Lewis number should be used to evaluate the Markstein length from the theoretical model.

Structure of a high Karlovitz n-C7H16 premixed turbulent flame

Results from a series of direct numerical simulations (DNS) of a high Karlovitz, slightly lean (ϕ=0.9), n-C7H16/air premixed turbulent flame are presented. The flame is statistically flat and is subjected to an inflow of homogeneous isotropic turbulence. A 35-species and 217-reaction mechanism (Bisetti et al., 2012) [17] is used to represent the chemistry. Two simulations have been performed: one with unity Lewis number to asses the effects of turbulence on the flame structure in the absence of differential diffusion, and the other with non-unity Lewis numbers to analyze how turbulence affects differential diffusion. The Karlovitz numbers are 280 and 220 respectively. The first simulation reveals that the flame is strongly affected by turbulence as enhanced mixing largely thickens the preheat zone. However, the turbulent flame structure (i.e. the correlation between species and temperature) is similar to that of a one-dimensional flat flame, suggesting that turbulence has limited effet on the flame in temperature space, in the absence of differential diffusion. In the second simulation, the flame structure is affected by turbulence, as differential diffusion effects are weakened. It is suggested that this result is attributed to the fact that turbulence drives the effective species Lewis numbers towards unity through an increase in effective species and thermal diffusivities. Finally, the reaction zones of both the unity and the non-unity Lewis number turbulent flames remain thin, and are locally broken (only to some extent for the unity Lewis number flame, and more strongly for non-unity).

Effects of Lewis number, density ratio and gravity on burning velocity and conditional statistics in stagnating turbulent premixed flames

DNS is performed to analyse the effects of Lewis number (Le), density ratio and gravity in stagnating turbulent premixed flames. The results show good agreement with those of Lee and Huh (Combustion and Flame, Vol. 159, 2012, pp. 1576–1591) with respect to the turbulent burning velocity, ST, in terms of turbulent diffusivity, flamelet thickness, mean curvature and displacement speed at the leading edge. In all four stagnating flames studied, a mean tangential strain rate resulting in a mean flamelet thickness smaller than the unstretched laminar flame thickness leads to an increase in ST. A flame cusp of positive curvature involves a superadiabatic burned gas temperature due to diffusive–thermal instability for an Le less than unity. Wrinkling tends to be suppressed at a larger density ratio, not enhanced by hydrodynamic instability, in the stagnating flow configuration. Turbulence is produced, resulting in highly anisotropic turbulence with heavier unburned gas accelerating through a flame brush by Rayleigh–Taylor instability. Results are also provided on brush thickness, flame surface density and conditional velocities in burned and unburned gas and on flame surfaces to represent the internal brush structures for all four test flames.

Sound generation by premixed flame annihilation with full and simple chemistry

This paper presents a numerical study of sound generation by premixed laminar flame annihilation with full and simple chemistry. Planar annihilation is examined from lean (ϕ=0.5) to rich (ϕ=3) conditions, which correspond to (effective) Lewis numbers ranging from 0.5 to 2.0 respectively. The full chemistry simulations use a well known detailed mechanism for hydrogen-air mixtures [1,2]. The simple chemistry simulations are tuned such that the freely propagating laminar flame speed matched those from the detailed chemistry simulations at the same equivalence ratio.These simulations examine two, related issues. First, they are used to confirm whether the Lewis number plays a significant role in the sound generation process, as our previous, simple chemistry studies have found [3,4]. More generally, these simulations seek to determine whether the use of simple chemistry to model sound generation is reasonable. The importance of the Lewis number is confirmed, and the use of simple chemistry is found to be reasonable in some cases.

Numerical study of unstable hydrogen/air flames: Shape and propagation speed

Extensive numerical simulations with detailed chemistry and transport are performed to identify the range of dominance (in terms of equivalence ratio and domain size) of the hydrodynamic instability, the shape of the structures that evolve at long times, and their propagation speed. The calculations were performed in two-dimensional domains of lateral extent 3–100 flame thicknesses. Hydrogen/air mixtures ranging from rich (ϕ=2) to lean conditions (ϕ=0.5) were considered, expecting that thermo-diffusive effects will start becoming important only at the lean end. The initial growth of a perturbed planar flame front is found to agree qualitatively, and to a large extent even quantitatively, with the asymptotic theoretical predictions. Beyond linearity it is shown that the dynamics depend strongly on the equivalence ratio (or on the effective Lewis number of the mixture) and the domain lateral size. For stoichiometric and rich mixtures, the flame shape is generally characterized by a single-cusp structure that propagates at a constant speed. The propagation speed increases with increasing lateral domain size and asymptotes to a value nearly 24% larger than the laminar flame speed. For the lean mixtures, the flame does not assume a well-defined structure even after a long time. It is regularly contaminated by small cells that result from thermo-diffusive effects and cause a significant increase in the propagation speed (nearly 60% above the laminar flame speed) that varies continuously in time. Except for the lean cases, the simulation results compare well with the asymptotic hydrodynamic theory both in the flame shape and propagation speed.

Modelling paradigms for MILD combustion

Three-dimensional Direct Numerical Simulation (DNS) data of methane-air MILD combustion is analysed to study the behaviour of MILD reaction zones and to identify a suitable modelling paradigm for MILD combustion. The combustion kinetics in the DNS was modelled using a skeletal mechanism including non-unity Lewis number effects. The reaction zones under MILD conditions are highly convoluted and contorted resulting in their frequent interactions. This leads to combustion occurring over a large portion of the computational volume and giving an appearance of distributed combustion. Three paradigms, standard flamelets, mild flame elements (MIFEs) and PSR, along with a presumed PDF model are explored to estimate the mean and filtered reaction rate in MILD combustion. A beta function is used to estimate the presumed PDF shape. The variations of species mass fractions and reaction rate with temperature computed using these models are compared to the DNS results. The PSR-based model is found to be appropriate, since the conditional averages obtained from the DNS agree well with those obtained using the PSR model. The flamelets model with MIFEs gives only a qualitative agreement because it does not include the effects of reaction zone interactions.

The influence of radiation on the flame propagation through micro organic dust particles with non-unity Lewis number

In this paper, the analytical study of effects of radiation and non-unity Lewis number on the laminar premixed flames of organic dust clouds has been done. The research is focused on a combustion model for premixed flames and the flame structure is composed of preheat-vaporization, narrow reaction and finally the post-flame zone. The normalized governing equations with help of boundary and matching conditions are solved by perturbation method. The results show that increasing equivalence ratio and decreasing Lewis number are resulted in the increase of flame temperature and burning velocity. For the sake of this model validation, fuel conversion is compared by published experimental data and shows an acceptable agreement.

Streamline segment statistics of premixed flames with nonunity Lewis numbers.

The interaction of flame and surrounding fluid motion is of central importance in the fundamental understanding of turbulent combustion. It is demonstrated here that this interaction can be represented using streamline segment analysis, which was previously applied in nonreactive turbulence. The present work focuses on the effects of the global Lewis number (Le) on streamline segment statistics in premixed flames in the thin-reaction-zones regime. A direct numerical simulation database of freely propagating thin-reaction-zones regime flames with Le ranging from 0.34 to 1.2 is used to demonstrate that Le has significant influences on the characteristic features of the streamline segment, such as the curve length, the difference in the velocity magnitude at two extremal points, and their correlations with the local flame curvature. The strengthenings of the dilatation rate, flame normal acceleration, and flame-generated turbulence with decreasing Le are principally responsible for these observed effects. An expression for the probability density function (pdf) of the streamline segment length, originally developed for nonreacting turbulent flows, captures the qualitative behavior for turbulent premixed flames in the thin-reaction-zones regime for a wide range of Le values. The joint pdfs between the streamline length and the difference in the velocity magnitude at two extremal points for both unweighted and density-weighted velocity vectors are analyzed and compared. Detailed explanations are provided for the observed differences in the topological behaviors of the streamline segment in response to the global Le.

An a priori model for the effective species Lewis numbers in premixed turbulent flames

An a priori model for the effective species Lewis numbers in premixed turbulent flames is presented. This a priori analysis is performed using data from a series of direct numerical simulations (DNS) of lean (ϕ=0.4) premixed turbulent hydrogen flames, with Karlovitz number ranging from 10 to 1562 (Aspden et al., 2011). The conditional mean profiles of various species mass fraction versus temperature are evaluated from the DNS and compared to unstretched laminar premixed flame profiles. The turbulent flame structure is found to be different from the laminar flame structure. However, the turbulent flame can still be mapped onto a laminar flame with an appropriate change in the Lewis numbers of the different species. A transition from “laminar” Lewis numbers to unity Lewis numbers as the Karlovitz number increases is clearly captured. A model for those effective Lewis numbers with respect to the turbulent Reynolds number is developed. This model is derived from a Reynolds-averaged Navier–Stokes (RANS) formulation of the reactive scalar and temperature balance equations. The dependency of the effective Lewis numbers on the Karlovitz number instead of the Reynolds number is discussed in this paper. Unfortunately, given that the ratio of the integral length to the laminar flame thickness is fixed throughout this series of DNS, a change in the Karlovitz number is equivalent to a change in the Reynolds number. Incorporating these effective Lewis numbers in simulations of turbulent flames would have several impacts. First, the associated laminar flame speed and laminar flame thickness vary by a factor of two through the range of obtained effective Lewis numbers. Second, the turbulent premixed combustion regime diagram changes because a unique pair of laminar flame speed and laminar flame thickness cannot be used, and a dependency on the effective Lewis numbers has to be introduced. Finally, a turbulent flame speed model that takes into account these effective Lewis numbers is proposed.

High accuracy numerical investigation of double-diffusive convection in a rectangular enclosure with horizontal temperature and concentration gradients

Double-diffusive convection of a binary mixed fluid in a rectangular enclosure with horizontal temperature and concentration gradients is numerically investigated. The problem with thermal Rayleigh numbers of 104 and 105, the Prandtl number being range of [0.015,12], the Lewis number being range of [0.05,100], the buoyancy ratio of 0.8, and the height-to-width aspect ratio of 2 are considered. A compact difference method with fully fourth-order accuracy and high resolution in space, involving a, at least, fourth-order upwind compact scheme suggested for approximation of the nonlinear convective terms, a fourth-order symmetrical compact scheme to discretize the viscous terms and the third-order TVD Runge–Kutta method employed for time discretization, is proposed for solving this unsteady double-diffusive convection problem. The effects of Prandtl and Lewis numbers on flow structure, the temperature and concentration distribution are investigated and discussed for Ra=104 and 105 respectively in a rectangular enclosure with the aspect ratio A=2. A bifurcation for the double-diffusive convection is captured with the variation of Prandtl number, and two different types of periodic flow motion with Lewis number in different ranges are observed.

Comparative study on the effect of CO2 and H2O dilution on laminar burning characteristics of CO/H2/air mixtures

A study on the effect of CO2 and H2O dilution on the laminar burning characteristics of CO/H2/air mixtures was conducted at elevated pressures using spherically expanding flames and CHEMKIN package. Experimental conditions for the CO2 and H2O diluted CO/H2/air/mixtures of hydrogen fraction in syngas from 0.2 to 0.8 are the pressures from 0.1 to 0.3 MPa, initial temperature of 373 K, with CO2 or H2O dilution ratios from 0 to 0.15. Laminar burning velocities of the CO2 and H2O diluted CO/H2/air/mixtures were measured and calculated using the mechanism of Davis et al. and the mechanism of Li et al. Results show that the discrepancy exists between the measured values and the simulated ones using both Davis and Li mechanisms. The discrepancy shows different trends under CO2 and H2O dilution. Chemical kinetics analysis indicates that the elementary reaction corresponding to peak ROP of OH consumption for mixtures with CO/H2 ratio of 20/80 changes from reaction R3 (OH + H2 = H + H2O) to R16 (HO2+H = OH + OH) when CO2 and H2O are added. Sensitivity analysis was conducted to find out the dominant reaction when CO2 and H2O are added. Laminar burning velocities and kinetics analysis indicate that CO2 has a stronger chemical effect than H2O. The intrinsic flame instability is promoted at atmospheric pressure and is suppressed at elevated pressure for the CO2 and H2O diluted mixtures. This phenomenon was interpreted with the parameters of the effective Lewis number, thermal expansion ratio, flame thickness and linear theory.

Effect of Lewis Number on Unsteady Double Diffusive Buoyancy Induced Flow in a Triangular Solar Collector with Corrugated Wall

A numerical investigation has been carried out in this paper to study the effect of varying Lewis number on the nature of heat and mass transfer in a triangular solar collector at unsteady condition. The triangular solar collector consists of two inclined glass covers and an absorber plate. The situation studied here resembles heat transfer phenomena in solar collectors and hence a thorough study on the effect of different parameters dictating this kind of heat transfer is essential. Bottom corrugated wall is subjected to high temperature and high concentration. Finite element method was employed to solve the unsteady dimensionless governing equations of continuity, momentum, energy and concentration of the problem. Calculations were carried out for Raleigh number ranging from 104 to 106 and for dimensionless time parameter = 0.1, 0.5 and 1. For the conditions mentioned here the effect of varying local and overall Nusselt and Sherwood number at those conditions are discussed. A comprehensive explanation follows each result.