Zeldovich Number Research Articles

The Effects of Unburned-Gas Temperature and Heat Loss on the Diffusive-Thermal Instability of Premixed Flames

The effects of unburned-gas temperature and heat loss on the diffusive-thermal instability of premixed flames were studied by two-dimensional unsteady calculations of reactive flows, based on the diffusive-thermal model equation, under the conditions of constant temperature jump through flame fronts. As the unburned-gas temperature became higher, the growth rate increased and the unstable range widened at Lewis numbers smaller than unity, which was due mainly to the increase of the burning velocity of a planar flame. As for the growth rate and unstable range normalized by the burning velocity of a planar flame, the former decreased and the latter narrowed. This was due to the reduction of Zeldovich numbers. In addition, the normalized growth rate increased and the normalized unstable range widened when the heat loss was taken into account. This indicated that the heat loss had a pronounced influence on the diffusive-thermal instability of premixed flames with high unburned-gas temperature. Furthermore, the cellular shape of flame fronts formed owing to diffusive-thermal instability. The normalized burning velocity of a cellular flame decreased as the unburned-gas temperature became higher, and increased when the heat loss was taken into account. Compared with high-temperature premixed flames where the adiabatic flame temperature was constant, the normalized level of instability intensity was low. This was because of small Zeldovich numbers.

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.

Numerical investigation on effects of high initial temperatures and pressures on flame behavior of CO/H2/Air mixtures near the dilution limit

This study investigates effects of initial temperatures and pressures on dilution limits of CO/H2/air mixtures by numerical simulation of one-dimensional laminar premixed flames of CO/H2/air mixtures (50%CO–50%H2). Maximum flame temperatures, laminar flame speeds, mass burning rates and flame thickness near the dilution limits are analyzed. Results reveal that the dilution limits are extended at the elevated initial temperatures. The laminar flame speeds and mass burning rates at the dilution limits increase with the elevation of initial temperature, however, the flame thickness at the dilution limits decreases with increasing pressures and increases slightly with elevated initial temperature. The decreased flame thickness renders the flamelet modeling more favorable for turbulent combustion at elevated pressure conditions. The ratio of the flame thickness to the reaction thickness and the Zeldovich number increase first and then decrease with increasing pressure, but the non-monotonic trend of ratio of flame thickness to reaction thickness with the increasing pressures is unnoticeable. Sensitivity analysis suggested that the non-monotonic trend of the Zeldovich number could be caused by the combined effects of following elementary reactions: H + O2 + M → HO2 + M, 2HO2 → H2O2 + O2 and H2O2 + M → 2OH + M.

Solution of adiabatic and nonadiabatic combustion problems using step-function reaction models

We consider the use of step-functions to model Arrhenius reaction terms for traveling wave solutions to combustion problems. We develop a methodology by which the Arrhenius reaction rate term is replaced by a suitably normalized step-function. The resulting model introduces interior interfaces and allows the conservation equations for energy and species to be solved explicitly within the subdomains bounded by the interfaces. The problem can then be reduced to a small number of nonlinear algebraic equations governing appropriate interface conditions. We apply this methodology to a variety of single-reaction problems and show that the resulting solutions agree with those obtained by the well-known front δ-function) approximations for large Zeldovich numbers. We then consider multiple reaction problems, specifically problems involving two independent reactions and problems involving sequential reactions. For these problems we compare the results with simpler front models as well as with Arrhenius kinetics. We show that the step-function models are generally superior to the front models where available and agree, both qualitatively and with reasonable quantitative accuracy, with solutions obtained via full Arrhenius kinetics.

Linear Stability Analysis of Pulsating Flame Propagation Through an Organic Dust Particle Cloud with Different Lewis Numbers and Heat Radiation Effects

In this article, a new mathematical model is presented that encompasses flame propagation through a two-phase mixture of uniformly distributed organic fuel particles and air. In this analytical study, which is conducted in the framework of a thermal-diffusive model assuming the Lewis number to be varying, and taking into account thermal radiation effect induced from flame front into unburned zone, the flame structure is divided into four integral zones. The system of governing equations is rewritten in the perturbed form with a perturbed flame front, and the time-related solutions are analyzed by using the method of small harmonic perturbations. The main goal of this study is to ascertain to what extent the laws of unsteady conservation damp or amplify the perturbation. As a result, the onset of pulsating instability is computed for both planar and wrinkled dust flames with respect to the variation of wavenumbers, as well as Lewis, Damköhler, and Zeldovich numbers, and also the thermal radiation effect. One of the noticeable results is that the position of pulsating-instability boundary for the flame propagation into the organic dust cloud is strongly affected by the induced thermal radiation, as the onset of pulsating instability under this circumstance becomes more likely. Also, the thermal radiation is an important factor in significantly reducing the frequency of pulsations at the onset of pulsating instability in the combustion of an organic dust-particle cloud.

NONLINEARITY EFFECT OF TRANSPORT PROPERTIES ON COMBUSTION OF VOLATILE ORGANIC PARTICLES

This paper presents the structure of laminar, one-dimensional, and steady-state flame propagation in a uniform cloud of volatile organic particles. In this model, it is assumed that particles vaporize to yield a gaseous fuel. In order to study the effects of thermal conductivity and thermal diffusion on combustion of organic particles, an asymptotic analysis, based on the large Zeldovich number or high rate of reaction, is used. In the preheat zone, the rate of chemical reaction is small, and transfer phenomena play a significant role in temperature and mass distributions. Therefore, according to the kinetic theory of gases, thermal conductivity (λ) and diffusion coefficient (D) are considered to be proportional to T1/2 and T3/2, respectively. Finally, flame characteristics for different equivalence ratios of solid mixture for different Lewis numbers are reported. Results show that both flame temperature and burning velocity increase with rise in the Lewis number.

Pulsating regime of magnetic deflagration in crystals of molecular magnets

The stability of a magnetic deflagration front in a media of molecular magnets, such as ${\mathrm{Mn}}_{12}$ acetate, is considered. It is demonstrated that stationary deflagration is unstable with respect to one-dimensional perturbations if the energy barrier of the magnets is sufficiently high in comparison with the release of Zeeman energy at the front; their ratio may be interpreted as an analog to the Zeldovich number, as found in problems of combustion. When the Zeldovich number exceeds a certain critical value, a stationary deflagration front becomes unstable and propagates in a pulsating regime. Analytical estimates for the critical Zeldovich number are obtained. The linear stage of the instability is investigated numerically by solving the eigenvalue problem. The nonlinear stage is studied using direct numerical simulations. The parameter domain required for experimental observations of the pulsating regime is discussed.

An analytical study of the effects of vaporization of twodimensional laminar droplets on a triple flame

The structure of triple flame propagation in combustion systems, containing uniformly distributed volatile fuel droplet was analyzed. The analysis was established for a one-step irreversible reaction with an asymptotic limit, where the value of the Zeldovich Number is large. Here, using unit Lewis number, the analytical results for the triple flame temperature were obtained considering two sections. In the first section, a non-vaporizing fuel stream was studied and in the second section, a volatile droplet fuel stream was taken into account. It is presumed that the fuel droplets vaporize to yield a gaseous fuel of known chemical structure, which is subsequently oxidized in the gaseous phase. Here two different cases are studied. In the first case, only the velocity parallel to the reactant flow was considered; while for the latter one, the vertical velocity was considered in addition. The energy equations were solved and the temperature field equations are presented. The results are first presented for a non-vaporizing fuel and compared to the experiment results. In addition, some other results of the temperature field for a vaporizing fuel stream are demonstrated within the comparison between the abovementioned cases which revealed the effect of the considering the vertical velocity component on the flame temperature field.

Linear stability analysis of spherically propagating thermal frontal polymerization waves

Spherically propagating frontal polymerization (FP) waves were observed for the first time in condensed media. After a brief period of ignition in a spherical domain by an external UV source, the front began to expand radially. Once the front attained a critical size, it became unstable, resulting in so-called ‘spin modes’. These spin modes are manifested as slightly raised regions that travel on the surface of the expanding spherical front. The onset of these instabilities from a stable, uniformly propagating spherical front can be described by a linear stability analysis. The bifurcation parameter is the Zeldovich number which is related to the activation energy of the reaction. A basic solution was constructed which describes a spherically symmetric outward propagating front of radius R. An asymptotic analysis was then employed under the assumption that R is large. This corresponds to the case where the conditions of ignition do not affect front propagation. It was found to leading order that the front propagates at a constant velocity and corrections to velocity due to curvature have been determined. The linear stability analysis shows that for the Zeldovich number in a certain range, there exists a situation in which the sphere will be unstable but will recover its stability in time as it expands.

Turbulent burning velocity predictions using transported PDF methods

The joint-scalar transported PDF approach is applied to compute freely propagating turbulent premixed flames with burning velocities determined for a range of turbulence intensities and fuel mixtures. The computed cases include rich hydrogen, stoichiometric and lean methane and stoichiometric ethane flames. The aim of the study is to investigate the sensitivity of predictions to different closure elements and to explore the predictive capabilities of the method. The work features extended chemistry closures with a systematically reduced mechanism featuring 142 reactions, 15 solved and 14 steady-state species applied for methane and ethane flames. A detailed sub-mechanism featuring 21 reactions and 9 solved species was used for the hydrogen flames. It is shown that the scaling of turbulent burning velocities with respect to turbulence intensity variations can be significantly improved through the application of an extended multi-scale scalar dissipation rate closure. Furthermore, the impact of molecular transport in physical space is explored through the derivation and inclusion of an explicit correction term applicable at the leading flame edge. It is shown that the impact is modest for fuels such as hydrogen and ethane, but that it can be expected to be significant for fuels with large Zeldovich numbers.

A Resonant Response of Self-Pulsating Spray-Flame Submitted to Acoustic Wave

Recently, experiments and theoretical investigations have shown that spray flame can exhibit oscillatory regimes for standard set of parameters. Theoretical and numerical investigations on flame propagation in two-phase premixtures have put forward an intrinsic (and robust) mechanism based on the interaction between the locus where droplets vaporize and the reaction zone. This mechanism invokes neither droplet inertia (very small droplets are studied) nor differential diffusive effects (pulsations take place for unity Lewis number, too). Self-oscillations of spray-flame occur as in a supercritical Hopf bifurcation, controlled by Zeldovich number (Ze, the reduced activation energy), the onset threshold being on the order of . The issue addressed in this contribution is whether acoustic wave and self-pulsating spray-flame can interact. This study was carried out in the open-loop context: a spray-flame was submitted to small amplitude fluctuations of pressure; the gain toward acoustics was found as depending on Zeldovich number because energy transfer is found magnified in the case of a close-frequency fit between acoustic resonator and natural spray-flame oscillations. Moreover, energy transfer is found as of resonant type.

Numerical study on combustion of diluted methanol-air premixed mixtures

The effect of nitrogen dilution on the premixed combustion characteristics and flame structure of laminar premixed methanol-air-nitrogen mixtures are analyzed numerically based on an extended methanol oxidation mechanism. The laminar burning velocities, the mass burning fluxes, the adiabatic flame temperature, the global activation temperature, the Zeldovich number, the effective Lewis number and the laminar flame structure of the methanol-air-nitrogen mixtures are obtained under different nitrogen dilution ratios. Comparison between experiments and numerical simulations show that the extended methanol oxidation mechanism can well reproduce the laminar burning velocities for lean and near stoichiometric methanol-air-nitrogen mixtures. The laminar burning velocities and the mass burning fluxes decrease with the increase of nitrogen dilution ratio and the effect is more obvious for the lean mixture. The effective Lewis number of the mixture increases with the increase of nitrogen dilution ratio, and the diffusive-thermal instability of the flame front is decreased by the nitrogen addition. Nitrogen addition can suppress the hydrodynamic instability of methanol-air-nitrogen flames. The decrease of the mole fraction of OH and H is mainly responsible for the suppressed effect of nitrogen diluent on the chemical reaction in the methanol-air-nitrogen laminar premixed flames, and the NOx and formaldehyde emissions are decreased by the nitrogen addition. methanol, dilution, premixed combustion, numerical analysis With increasing concern about fuel shortage and air pollution control, researches on improving engine fuel economy and reducing exhaust emissions have become the major topics in combustion and engine studies. Because of limited reserves of crude oil, the development of alternative-fuel engines has attracted more attention in the engine community. Alternative fuels usually are clean fuels compared with traditional diesel fuel and gasoline fuel in the engine combustion process. The introduction of these alternative fuels is beneficial to the solution of the fuel shortage and reduction of engine exhaust emissions. Nowadays, clean alternative fuels mainly include hydrogen, compressed natural gas (CNG), liquid petroleum gas (LPG), dimethyl ether (DME), and alcohols in internal combustion engines application

Laminar burning velocities and Markstein lengths of premixed methane/air flames near the lean flammability limit in microgravity

Effects of flame stretch on the laminar burning velocities of near-limit fuel-lean methane/air flames have been studied experimentally using a microgravity environment to minimize the complications of buoyancy. Outwardly propagating spherical flames were employed to assess the sensitivities of the laminar burning velocity to flame stretch, represented by Markstein lengths, and the fundamental laminar burning velocities of unstretched flames. Resulting data were reported for methane/air mixtures at ambient temperature and pressure, over the specific range of equivalence ratio that extended from 0.512 (the microgravity flammability limit found in the combustion chamber) to 0.601. Present measurements of unstretched laminar burning velocities were in good agreement with the unique existing microgravity data set at all measured equivalence ratios. Most of previous 1-g experiments using a variety of experimental techniques, however, appeared to give significantly higher burning velocities than the microgravity results. Furthermore, the burning velocities predicted by three chemical reaction mechanisms, which have been tuned primarily under off-limit conditions, were also considerably higher than the present experimental data. Additional results of the present investigation were derived for the overall activation energy and corresponding Zeldovich numbers, and the variation of the global flame Lewis numbers with equivalence ratio. The implications of these results were discussed.

Intrinsic Instability of Premixed Flames at Sufficiently Low Activation Energy

The intrinsic instability of premixed flames at sufficiently low activation energy was studied by two-dimensional unsteady calculations of reactive flows, based on the compressible Navier-Stokes equation including a one-step irreversible chemical reaction. A sinusoidal disturbance with small amplitude was superimposed on a planar flame to obtain the relation between the growth rate and wave number, i.e. the dispersion relation, and the average local burning velocity of a cellular flame. When the Lewis number was smaller (larger) than unity, the growth rate and the average local burning velocity decreased (increased) as activation energy became lower, because of the decrease of the Zeldovich number. When the Lewis number was unity, the growth rate decreased slightly at sufficiently low activation energy, and the average local burning velocity was almost constant. In addition, the dependence of the average local burning velocity on the Lewis number became weaker at sufficiently low activation energy.

Experimental Study on Combustion Characteristics of N2-Diluted Diethyl Ether−Air Mixtures

Combustion characteristics of diethyl ether-air-N2 diluent are studied at different initial temperatures, equivalence ratios, and dilution ratios using an outwardly expanding spherically flame and high-speed schlieren photography system. The effects of these parameters on laminar burning velocity, Markstein length, and Zeldovich number are analyzed. The results show that laminar burning velocity is increased with the increase of the initial temperature and is decreased with the increase of the dilution ratio. The maximum value of the laminar burning velocity is presented at the equivalence ratio of 1.0. The Markstein length is decreased with the increase of the initial temperature and equivalence ratio. Except for the equivalence ratio of 1.2, the Markstein length is increased with the increase of the dilution ratio, indicating that the increase of the initial temperature and equivalence ratio enhances the diffusional-thermal instability of the flame front but the increase of the dilution ratio reduces the diffusional-thermal instability. The density ratio is decreased, and the flame thickness is increased with the increase of the dilution ratio, indicating that the hydrodynamic instability is suppressed. The Zeldovich number is increasedwiththeincreaseofthedilutionratioandisdecreasedwiththeincreaseoftheinitialtemperature. The Zeldovich number gives the lowest value at the equivalence ratio of 1.0, where the adiabatic temperature gives the maximum value. A formula of laminar flame velocity is correlated with initial conditions based on the experimental data.

The effects of radiation and particle size on the pyrolysis of biomass particles

This article presents the structure of laminar, one-dimensional, and steady-state flame propagation in uniformly premixed wood particles. In order to predict the effect of radiation and particle size on the pyrolysis of biomass particles, the flame structure is divided into three regions: a preheat vaporization zone where the rate of the gas-phase chemical reaction is small; a narrow reaction zone composed of three zones (gas, tar, and char combustion) where convection and the rate of vaporization of the fuel particles are small; and finally a convection zone where diffusive terms in the conservation equation are small. In this model, it is assumed that fuel particles vaporize first to yield a gaseous fuel of known chemical structure. The analysis is performed in the asymptotic limit, where the value of the characteristic Zeldovich number is large and the equivalence ratio is larger than unity (i.e. ϕu≥1). The overall investigation of this study leads to a novel non-linear burning velocity correlation. Consequently, the impacts of radiation and particle size as determining factors on the combustion properties of biomass particles are declared in this research.

Novel analytical model for predicting the combustion characteristics of premixed flame propagation in lycopodium dust particles

This paper presents the effects of the temperature difference between gas and particle, different Lewis numbers, and heat loss from the walls in the structure of premixed flames propagation in a combustible system containing uniformly distributed volatile fuel particles in an oxidizing gas mixture. It is assumed that the fuel particles vaporize first to yield a gaseous fuel, which is oxidized in a gas phase. The analysis is performed in the asymptotic limit, where the value of the characteristic Zeldovich number is large. The structure of the flame is composed of a preheat zone, reaction zone, and convection zone. The governing equations and required boundary conditions are applied in each zone, and an analytical method is used for solving these equations. The obtained results illustrate the effects of the above parameters on the variations of the dimensionless temperature, particle mass friction, flame temperature, and burning velocity for gas and particle.

Numerical study on laminar burning velocity and NO formation of premixed methane–hydrogen–air flames

Abstract Numerical study on laminar burning velocity and NO formation of the premixed methane–hydrogen–air flames was conducted at room temperature and atmospheric pressure. The unstretched laminar burning velocity, adiabatic flame temperature, and radical mole fractions of H, OH and NO are obtained at various equivalence ratios and hydrogen fractions. The results show that the unstretched laminar burning velocity is increased with the increase of hydrogen fraction. Methane-dominated combustion is presented when hydrogen fraction is less than 40%, where laminar burning velocity is slightly increased with the increase of hydrogen addition. When hydrogen fraction is larger than 40% , laminar burning velocity is exponentially increased with the increase of hydrogen fraction. A strong correlation exists between burning velocity and maximum radical concentration of H + OH radicals in the reaction zone of premixed flames. High burning velocity corresponds to high radical concentration in the reaction zone. With the increase of hydrogen fraction, the overall activation energy of methane–hydrogen mixture is decreased, and the inner layer temperature and Zeldovich number are also decreased. All these factors contribute to the enhancement of combustion as hydrogen is added. The curve of NO versus equivalence ratio shows two peaks, where they occur at the stoichiometric mixture due to Zeldovich thermal-NO mechanism and at the rich mixture with equivalence ratio of 1.3 due to the Fenimore prompt-NO mechanism. In the stoichiometric flames, hydrogen addition has little influence on NO formation, while in rich flames, NO concentration is significantly decreased. Different NO formation responses to stretched and unstretched flames by hydrogen addition are discussed.

Laminar burning velocities and combustion characteristics of propane–hydrogen–air premixed flames

An experimental study on laminar burning characteristics of the spherically expanding premixed propane–hydrogen–air flames was conducted at room temperature and atmospheric pressure. The unstretched laminar burning velocity, the laminar flame thickness, the Markstein number, the Zeldovich number and the global Lewis number were obtained over a range of equivalence ratios and hydrogen fractions. The influence of hydrogen addition on the laminar burning velocities and the flame front instabilities were analyzed. The results show that the unstretched laminar burning velocity increases, the laminar flame thickness decreases and the peak value of unstretched laminar burning velocity shifts to the richer mixture side with the increase of hydrogen fraction. When hydrogen fraction in the fuel is less than 60%, the Markstein number decreases with the increase of equivalence ratio, and the flame behavior is similar to that of propane–air flames. When hydrogen fraction is larger than 60%, the flame behavior is similar to that of hydrogen–air flames. At equivalence ratio less than 1.2, the Markstein number decreases with the increase of hydrogen fraction, indicating flame destabilization by hydrogen addition. At equivalence ratio larger than 1.2, the Markstein length increases with the increase of hydrogen fraction, indicating the stabilization of flame by hydrogen addition. In the case of lean mixture combustion, the Zeldovich number decreases with the increase of hydrogen addition, indicating the lowering of activation temperature of the mixture. The global Lewis number decreases with the increase of hydrogen fraction, and this indicates the increase of preferential-diffusion instabilities by hydrogen addition.

Premixed flames with a reversible reaction: propagation and stability

We consider the effect of the reversibility of the chemical reaction on the propagation and stability of laminar premixed flames, an important realistic aspect which has received little attention in the literature. For the sake of analytical tractability and clarity of the results, the thermodiffusive approximation of constant density is adopted, along with the simple framework of a single reversible reaction of the form F P whose forward and backward rates follow an Arrhenius law. An asymptotic analysis is carried out for large values of an effective Zeldovich number β, and yields expressions for the flame speed U with arbitrary values of the Lewis numbers of the fuel, Le F , and the product, Le P . In particular, although U is found to decrease monotonically with the reversibility parameter r as expected, β turns out to be typically a non-monotonic function of r. The linear stability of the planar solution is then investigated, with particular emphasis on the influence of Le P , which did not appear in other studies. This is achieved by generalizing the so-called near-equidiffusional flame (NEF) approximation to the reversible case, which allows the stability problem to be reduced to that of the irreversible case, by an appropriate combination of variables. An effective reduced Lewis number is thus found to be the single control parameter in the resulting dispersion relation. The expression derived for the latter is used to delimit the stability and instability regions in the Le F -Le P -r space.