One-step Irreversible Reaction Research Articles

Numerical Simulation of Growth of Flame Formed in a Two-Dimensional Mixing Layer. 4th Report. Effects of Diffusion Flame on Mixing Properties.

The mixing properties of a two-dimensional reacting shear layer have been studied numerically. Effects of heat release by combustion on the mixing properties have been discussed based on the viewpoint of the transport of vorticity. The numerical simulation is concerned with an unstable, two-dimensional, two-stream, spatially developing, confined reacting shear layer. The numerical method is based on the modified HSMAC method which can handle the change in temperature. The chemical model is a one-step irreversible methane-oxygen reaction with a finite reaction rate defined by the Arrhenius law. The numerical results have revealed that in the reacting mixing layer the vorticity thickness and the carbon element mixing layer thickness defined by the difference in the carbon element mixture fraction of 99% between the fuel and the oxidizer flows, increase in comparison to the cold mixing layer. The baroclinic torque suppresses the vorticity and the viscous term to increase the vorticity thickness.

On the direct initiation of gaseous detonations by an energy source

A new criterion for the direct initiation of cylindrical or spherical detonations by a localized energy source is presented. The analysis is based on nonlinear curvature effects on the detonation structure. These effects are first studied in a quasi-steady-state approximation valid for a characteristic timescale of evolution much larger than the reaction timescale. Analytical results for the square-wave model and numerical results for an Arrhenius law of the quasi-steady equations exhibit two branches of solutions with a C-shaped curve and a critical radius below which generalized Chapman–Jouguet (CJ) solutions cannot exist. For a sufficiently large activation energy this critical radius is much larger than the thickness of the planar CJ detonation front (typically 300 times larger at ordinary conditions) which is the only intrinsic lengthscale in the problem. Then, the initiation of gaseous detonations by an ideal point energy source is investigated in cylindrical and spherical geometries for a one-step irreversible reaction. Direct numerical simulations show that the upper branch of quasi-steady solutions acts as an attractor of the unsteady blast waves originating from the energy source. The critical source energy, which is associated with the critical point of the quasi-steady solutions, corresponds approximately to the boundary of the basin of attraction. For initiation energy smaller than the critical value, the detonation initiation fails, the strong detonation which is initially formed decays to a weak shock wave. A successful initiation of the detonation requires a larger energy source. Transient phenomena which are associated with the intrinsic instability of the quasi-steady detonations branch develop in the induction timescale and may induce additional mechanisms close to the critical condition. In conditions of stable or weakly unstable planar detonations, these unsteady phenomena are important only in the vicinity of the critical conditions. The criterion of initiation derived in this paper works to a good approximation and exhibits the huge numerical factor, 106–108, which has been experimentally observed in the critical value of the initiation energy.

Simulation of a planar combustion wave

In this paper a planar combustion wave propagating in a gaseous mixture is simulated. The two-dimensional compressible Navier–Stokes equations for a reacting mixture of two species, burnt and unburnt gas, are considered. The unburnt gas is assumed to be converted into burnt gas by a one-step irreversible chemical reaction. The rate of production of the burnt gas is modelled according to the Arrhenius law. The resulting differential system is numerically integrated by means of a semi-implicit version of the alternating direction method. The scheme is so devised that its stability does not depend upon the speed of sound. If the computational grid is divided into n × m finite-difference cells, at each time step the algorithm requires the solution of n tridiagonal systems of m equations in m unknowns in the first stage, and of m tridiagonal systems of n equations in n unknowns in a second stage. All these systems are diagonally dominant with positive elements on the main diagonal and negative ones elsewhere. Thus existence and uniqueness of the numerical solution are assured. Finally, some computer examples are described and discussed.

Autoignition of a Turbulent Premixed Gas

Abstract Autoignition in a two-dimensional turbulent premixed gas al temperatures ranging from 1100 K to 1400 K was numerically simulated. Assuming one-step irreversible reaction, the physical parameters were arranged to simulate a 30% (2H2 + 02) + 70% N2 gas mixture. The temperature initially fluctuated about 1% resulting from a given isotropic compressible turbulent flow with an intensily of 25m/s. The temperature fluctuation affected the ignition delay time and the spacial heterogeneity of ignition. At low temperatures, the ignition occurred spottily and a propagating pressure wave appeared from the hot spot. The pressure wave completed the ignition process and strong pressure fluctuations remained. At high temperatures, almost homogeneous ignition occurred. The ignition delay time was decreased by the temperaiure fluctuations and showed a good agreement with the theoretical results of Arrhenius' law in homogeneous turbulent media. Large activation energy also contributed to heterogeneous autoignition.

Determination of germanium by potentiometric stripping analysis and adsorption potentiometric stripping analysis

Potentiometric stripping analysis was applied to determination of germanium(IV) in 0.2 M NH 3-NH 4Cl (pH 8.4) buffer solution at −1.8 V ( vs. Ag/AgCl), with dissolved oxygen or Hg(II) as oxidant. The sensitivity was 8.5 × 10 −9 M in the presence of 2.0 × 10 −5 M Hg(II) with plating for 15 min after deaeration for 20 min. Cyclic voltammetry revealed that GE(IV) å Ge at the surface of the mercury-film electrode in a one-step irreversible reduction reaction, and the Ge at the electrode was oxidized by dissolved oxygen in the solution. The presence of complexing agents such as Alizarin Red (ARS), which forms a Ge(IV) complex adsorbed at the electrode, improved the sensitivity by one order of magnitude. The presence of adsorption was revealed by the temperature coefficient, the electrocapillary curve and cyclic voltammetry. Ge-containing samples were analysed by the proposed methods and agreement with the results obtained by other methods was excellent.

Numerical simulation of hydrodynamic flame stability.

Unsteady motions of two-dimensional reactive flows have been simulated to investigate the hydrodynamic flame stability using the one-step irreversible chemical reaction model. The numerical model contains compressibility, viscosity, heat conduction, molecular diffusion, and convection. We have calculated the evolution of disturbed flame fronts and numerically reproduced the disturbance growing exponentially in time as predicted by the linear theory. The growth rate of the disturbance depending on the wave number was obtained and the critical wave number for neutral stability was determined. The calculated unstable region for the case of the Lewis number unity is slightly narrow compared with that of the linear theory because we consider the finite reaction thickness with the preheat zone in the simulation. The departure of the Lewis number from unity has great influence on the flame instability : the unstable region increases when the Lewis number is smaller than unity, and decreases when the Lewis number is larger than unity.

On the Quenching of a Diffusion Flame Near a Cold Wall

Abstract High activation energy asymptotic methods are used to derive an expression for the quenching distance for a diffusion flame undergoing the one-step irreversible reaction F + vO → P near a cold wall. The fluid-dynamic influences are disregarded by assuming a very small mass flux. The two-dimensionality of the problem is retained. This requires analysis of the temperature field in the pure (one-dimensional) diffusion flame region, in the pure premised flame regions, in the pure quenching region and in the so-called “Iriple-poinl region” where all of these separate zones meet. The functional form for the quenching distance is identical to that obtained by a simplified one-dimensional analysis; a larger numerical multiplicative factor accounts for the multidimensionality.

Cumulative effects of weak pressure waves during the induction period of a thermal explosion in a closed cylinder

It is shown that the accumulation of small-amplitude gasdynamic perturbations is able to accelerate the process of self-ignition of a homogeneous explosive mixture. For analytical simplicity, the chemical kinetics are represented by a one-step irreversible reaction with a large activation energy. A one-dimensional piston-cylinder geometry is considered, which allows a slow compression of the gas during the induction period. It is assumed that the rates of temperature increase due to the reaction and due to the compression are comparable. A two-timescale asymptotic expansion for small Mach numbers is performed considering the distinguished limit ME = O(1), where E is the non-dimensional activation energy, and M is the Mach number based on a characteristic speed of the gas motion. Gasdynamic-chemical interaction is observed at the second order, where the secular equations describing the evolution on the slow timescale explicitly show a cumulative influence.

An Asymptotic Analysis of Supersonic Reacting Mixing Layers

Abstract The purpose of this paper is to present an asymptotic analysis of the laminar mixing of and the simultaneous chemical reaction between parallel supersonic streams of two reacting species. The study is based on a one-step irreversible Arrhenius reaction and on large activation energy asymptotics. Esssenlially it extends the work of Linan and Crespo to include the effect of free shear and Mach number on the ignition regime, the deflagration regime and the diffusion flame regime. It is found that the effective parameter is the product of the characteristic Mach number and a shear parameter.

Numerical simulation of detonation initiation of combustible gases.

A numerical simulation of the initiation processes of gaseous detonation waves was performed by the Random-Choice Method (RCM) developed by Chorin. The initiator was high-pressure and high-temperature gas which was chemically inert. The chemical reaction was assumed to be a one-step irreversible reaction with its rate described the Arrhenius law. It was found that the initiation processes were strongly dependent on the total energy contained in the initiator gas. Local explosions were observed in the initiation processes and were found to be most essential in these processes.

Experimental and theoretical investigation of partially premixed diffusion flames at extinction

The structure and the mechanism of extinction of partially premixed diffusion flames is analyzed on the basis of a model that uses a one-step irreversible reaction with a large activation energy. Close to extinction the inner flame structure is essentially that of the Liñán diffusion flame regime with modifications of the boundary conditions due to partial premixing. Extinction conditions are derived for small fuel-to-air mass ratios. In this limit the ratio of the Damköhler numbers at quenching for the partially premixed to the unpremixed case does not depend on any additional parameters. Experiments on flat partially premixed diffusion flames are performed in an opposed flow burner between two ducts. A fuel stream of diluted methane and an oxidizer stream of diluted air was prepared. The diluent in both streams was nitrogen. Both streams were partially premixed by the other in such a way that the stoichiometric fuel-to-oxidizer mass ratio was the same as in the corresponding unpremixed diffusion flame. As predicted by the theory two nonequilibrium flame structures are observed. The ratio of the velocity gradients at extinction for the partially premixed to the unpremixed flames was compared with the theoretical results. In particular, the predicted increasing sensitivity of partially premixed flamelets to flame stretch when compared to initially unpremixed flows is verified.

Asymptotic Analysis of Laminar Flame Propagation with Variable Transport Coefficients

Abstract This paper reports an extended formula for the burning velocity of a steady one-dimensional, planar, adiabatic flame in the case of a one-step irreversible decomposition reaction. As a generalization of previous analyses, which were concerned with constant-property flames, variable transport coefficients and variable mean molecular weight are taken into account. The resulting effects on the burning velocity are discussed and explained on physical grounds. A distinguished downstream zone involving a convective-reactive-diffusive balance is discovered to exist for all reaction orders greater than unity and to influence the burning rate if the Lewis number differs from unity, more strongly than the variable-property effects for reaction orders of three or greater.

Mathematical modelling of spark-ignition engines

The flow field, scavenging efficiency, power output, heat transfer losses, and unburned hydrocarbon emissions have been numerically studied by means of a two-equation model of turbulence in a four-stroke, homogeneous-charge, spark-ignition engine. The engine is equipped with an intake valve, an exhaust valve, and a constant rate heat source which simulates the spark plug. Combustion has been modelled by means of a one-step irreversible chemical reaction whose rate is controlled by an Arrhenius-type expression. The numerical results indicate that the intake stroke is characterized by the formation of two eddies which persist in the compression stroke. Turbulence is generated at the shear layers of the air jet drawn into the cylinder, but its level decreases in the compression stroke. Due to the heat released by the spark plug and the chemical reaction, a spherical flame kernel is formed. This kernel evolves into a cylindrical flame when the flame front reaches the piston. Fuel remains unburnt at the corner between the cylinder head and the cylinder wall due to heat transfer losses. The numerical results also indicate that despite uncertainties about the turbulence and heat transfer models, an engine model such as the one studied here can be used to understand the flow field, heat transfer losses, scavenging efficiency, and power output in conventional spark-ignition engines. Such capabilities are very helpful in the development and optimization stages of engines. For example, here the engine model thermal and scavenging efficiencies are 15.69% and 94%, respectively. The peak pressure is 33 atm and occurs at 6° ATDC. The unburnt hydrocarbon emissions are 7.41% of the total fuel admitted into the cylinder.

On Diffusion Flames in Turbulent Shear Flows: Modeling Reactant Consumption in a Circular Fuel Jet

The turbulent portion of the circular fuel jet is analyzed for isobaric subsonic flow under fast direct one-step irreversible reaction between unpremixed fuel and oxidant. Mean spatial profiles for the dependent variables are found numerically from the governing nonlinear partial differential equations, based upon an explicit eddy diffusion and upon a mean rate of reactant consumption proportional to the product of the mean mass fraction of fuel, the mean mass fraction of oxidant, and the appropriate local characterization of the mean rate of strain. Experimental results are employed to evaluate the pertinent constants in the theoretical formulation of the model. I. Introduction T HE structure of the turbulent diffusion flame in the circular fuel-jet geometry is studied theoretically. As such, this represents an extension of the work by Bush, Feldman, and Fendell on the structure of turbulent diffusion flames in the planar fuel-jet1 and in the planar mixing-layer2 geometries. In this present paper, as in these previous papers, the emphasis is on the solution of a model formulation of the boundary-value problem for a turbulent diffusion flame in a flow geometry of practical interest, when the model is based upon the premise that the consumption of reactants and the generation of product(s) and chemical exothermicity are controlled by unsteady, inviscid, inertial, large-scale mixing. In this model, in time-average, for a direct one-step irreversible bimolecular chemical reaction, the mean rate of reactant consumption is taken to be related to the product of the mean mass fraction of oxidant, the mean mass fraction of fuel, and the magnitude of the principal mean strain rate (for the parabolic formulation appropriate for the thin shear layers of interest here). It is argued (as in Refs. 1 and 2) that, in general, the magnitude of the principal mean strain rate furnishes a characteristic frequency for the mean rate of local chemical activity in a turbulent diffusion flame in which macroscopic mixing is rate-controll ing. This explicit local algebraic (as opposed to field-type differential) expression adopted for the mean rate of chemical reaction is compatible with the adoption of an explicit local algebraic (eddy viscosity) expression for the mean rate of diffusive transport. The present model was first studied in detail for the planar mixing layer formed by two parallel streams.2 However, whereas the fully developed mixing layer is tractable for analysts, it is not tractable for experimentalists and, therefore, some empirical constants in the theory remained unassigned for lack of data. Experimentalists38 have treated the fuel jet exhausting into an oxidant-conta ining ambient, and, under the assumption that values for empirical factors may be transferable between geometries, solutions were

Bifurcation Phenomena in Burner-Stabilized Premixed Flames

Abstract The one-dimensional stability of an isobaric burner-stabilized premixed flame is investigated for arbitrary Lewis number and stoichiometry in the asymptotic limit of large activation energy. Assuming a one-step irreversible chemical reaction in which fuel and oxidizer react to form a product, a linear stability analysis is Used to calculate the neutral stability boundary in Lewis number-activation energy space as a function of incoming flow velocity (or equivalently, the burned temperature) The major result is that although a steady-state adiabatic flame is likely to be stable for typical parameter values, a value of the incoming flow velocity sufficiently less than the adiabatic flame speed is destabilizing to the extent that the unstable region becomes feasible for many flames. Consequently, if all other parameters are fixed, there exists for such flames a critical value of the incoming flow velocity at which the time-asymptotic solution to the time-dependent problem bifurcates from the nontriv...

Linear stability analysis of nonadiabatic flames: Diffusional-thermal model

The method of matched asymptotic expansions, in terms of a suitably reduced activation energy, is applied to investigate the effects of heat losses on linear stability of a planar flame, which is governed by a one-step irreversible Arrhenius reaction. The density change associated with the heat release is neglected in order to eliminate the Landau hydrodynamic instability. Attention is focused on diffusional-thermal instability mechanisms. The dispersion relation is obtained in terms of the diffusive properties of the limiting reactant and of the heat-loss intensity. For a given loss intensity-less than the critical value leading to extinction-the two steady planar regimes have different stability properties: (1) the “slow” regimes (which do not reduce to the adiabatic one when the heat-loss intensity goes to zero) are shown to be always unstable; and (2) for the “fast” regimes (which include and generalize the adiabatic one) cellular structures are predicted to occur when the limiting component is sufficiently light. If the limiting component is moderately light, the “fast” regimes are stable and unstructured in nearly adiabatic conditions; however, they are destabilized by an increase of heat losses and must exhibit cells before the extinction limit is reached. Similarly, for mixtures involving a realistically heavy limiting component, our analysis predicts the appearance of transverse travelling waves near the extinction limit.

On Diffusion Flames in Turbulent Shear Flows: Modeling Reactant Consumption in a Planar Fuel Jet

Abstract The turbulent portion of the planar fuel jet, for isobaric subsonic flow, under fast direct one-step irreversible reaction between unpremixed fuel and oxidant, is analyzed. Mean spatial profiles for the dependent variables are found numerically and analytically from the governing nonlinear partial differential equations, based on an explicit eddy diffusion and on a mean rate of reactant consumption proportional to the product of the mean mass fraction of fuel, the mean mass fraction of oxidant and the appropriate local characterization of the mean rate of strain. Results from the model are qualitatively, and, in many cases, quantitatively, compatible with experimental data.

On the stability of lin˜a´n's “premixed flame regime”

A linear stability analysis of Linan's (1974) premixed flame regime is carried out. Linan's problem concerns a laminar counterflow diffusion flame with a one-step irreversible reaction. In the present analysis, an infinitesimal disturbance of the steady-state solution is introduced, and the transient response of the system is assessed. It is shown that Linan's premixed flame may be unstable, and hence static extinction conditions cannot be applied.

The implications of the probability equations for turbulent combustion models

The physical foundations of combustion models employed in turbulent flow calculation procedures are examined by reference to the transport equation for the joint probability distribution of the scalars characterizing the system. It is shown that, with certain restrictions, an arbitrarily fuelled flame resulting from a one-step irreversible reaction can be characterized by two scalars, the total fuel mass fraction, f, and the mass fraction of products, c. This system includes the special cases of premixed and diffusion flames. The transport equation for the joint probability of f and c is introduced and discussed: it is shown that, in the limit of very rapid reaction, the distribution can be expressed in terms of two single probability distributions and a scalar, A, which represents the mass fraction of activated species. By deriving the transport equations for these quantities and modelling the unknown terms a closure is obtained which is used to assess existing combustion models. Lockwood and Naguib's [9] model for arbitrarily fuelled flames and the model for diffusion flames derived from it [6, 7] are sound in principle but improvements to detail are indicated. An alternative is provided for the eddy-break-up model [1] which is found to be deficient on mathematical and physical grounds.

An Asymptotic Analysis of Unsteady Diffusion Flames for Large Activation Energies

Abstract The limit of large activation energy is studied for the process of simultaneous mixing and chemical reaction of two reactants undergoing a one-step irreversible Arrhenius reaction. Consideration is restricted to problems of the evolution type—like unsteady mixing and boundary-layer combustion—for which the solution is uniquely determined in terms of the initial conditions. The continuous transition from the nearly-frozen to the near-equilibrium regimes is described. The analysis uncovers the existence of: (i) An ignition regime, in which a mixing layer develops with only minor effects of the chemical reaction, until a thermal runaway occurs somewhere within the mixing region; at this location chemical equilibrium then is established rapidly, (ii) A deflagration regime, in which premixed flames originate from the ignition point and move through the mixing region to burn completely the reactant not in excess. And (iii) a diffusion-flame regime, in which a thin diffusion flame, that is established when the deflagration wave crosses the surface where the reactants are present in stoichiometric proportions, consumes the excess reactants that could not be burned by the premixed flame. This is accomplished by a process in which the reactants diffuse through a thick layer of reaction products. There exists experimental evidence to support this rather complex picture deduced theoretically.