Effects of Fuel Lewis Number on Localised Forced Ignition of Globally Stoichiometric Stratified Mixtures: a Numerical Investigation

The influences of fuel Lewis number LeF on localised forced ignition of globally stoichiometric stratified mixtures have been analysed using three-dimensional compressible Direct Numerical Simulations (DNS) for cases with LeF ranging from 0.8 to 1.2. The globally stoichiometric stratified mixtures with different values of root-mean-square (rms) equivalence ratio fluctuation (i.e. ϕ′= 0.2, 0.4 and 0.6) and the Taylor micro-scale lϕ of equivalence ratio ϕ variation (i.e. lϕ/lf= 2.1, 5.5 and 8.3 with lf being the Zel’dovich flame thickness of the stoichiometric laminar premixed flame) have been considered for different initial rms values of turbulent velocity u′. A pseudo-spectral method is used to initialise the equivalence ratio variation following a presumed bi-modal distribution for prescribed values of ϕ′ and lϕ/lf for global mean equivalence ratio 〈ϕ〉=1.0. The localised ignition is accounted for by a source term in the energy transport equation that deposits energy for a stipulated time interval. It has been observed that the maximum values of temperature and the fuel reaction rate magnitude increase with decreasing LeF during the period of external energy deposition. The initial values of LeF, u′/Sb(ϕ=1), ϕ′ and lϕ/lf have been found to have significant effects on the extent of burning of the stratified mixtures following localised ignition. For a given value of u′/Sb(ϕ=1), the extent of burning decreases with increasing LeF. An increase in u′ leads to a monotonic reduction in the burned gas mass for all values of LeF in all stratified mixture cases but an opposite trend is observed for the LeF=0.8 homogeneous mixture. It has been found that an increase in ϕ′ has adverse effects on the burned gas mass, whereas the effects of lϕ/lf on the extent of burning are non-monotonic and dependent on ϕ′ and LeF. Detailed physical explanations have been provided for the observed LeF, u′/Sb(ϕ=1), ϕ′ and lϕ/lf dependences.

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abstract: A parametric study of forced ignition at the mixing layer between air and air carrying fine monosized fuel droplets is done through one-step chemistry direct numerical simulations to determine the influence of the size and volatility of the droplets, the spark location, the droplet-air mixing layer initial thickness and the turbulence intensity on the ignition success and the subsequent flame propagation. The propagation is analyzed in terms of edge flame displacement speed, which has not been studied before for turbulent edge spray flames. Spark ignition successfully resulted in a tribrachial flame if enough fuel vapour was available at the spark location, which occurred when the local droplet number density was high. Ignition was achieved even when the spark was offset from the spray, on the air side, due to the diffusion of heat from the spark, provided droplets evaporated rapidly. Large kernels were obtained by sparking close to the spray, since fuel was more readily available. At long times after the spark, for all flames studied, the probability density function of the displacement speed was wide, with a mean value in the range 0.55 – 0.75 S L , with S L the laminar burning velocity of a stoichiometric gaseous premixed flame. This value is close to the mean displacement speed in turbulent edge flames with gaseous fuel. The displacement speed was negatively correlated with curvature. The detrimental effect of curvature was attenuated with a large initial kernel and by increasing the thickness of the mixing layer. The mixing layer was thicker when evaporation was slow and the turbulence intensity higher. However, high turbulence intensity also distorted the kernel which could lead to high values of curvature. The edge flame reaction component increased when the maximum temperature coincided with the stoichiometric contour. The results are consistent with the limited available experimental evidence and provide insights into the processes associated with ignition of practical spray flames.

title: Ignition and flame quenching in flowing gaseous mixtures
abstract: The influence of pressure, velocity, turbulence intensity, turbulence scale and mixture composition on minimum ignition energy and quenching distance in flowing gaseous mixtures is examined experimentally for methane and propane fuels. In some experiments, the nitrogen in the air is replaced by various inert gases such as carbon dioxide, helium or argon, while in others the nitrogen is either partly or totally replaced by oxygen. The tests are conducted at room temperature in a 9 cm square working section through which the combustible mixture is arranged to flow at various levels of pressure, turbulence and velocity. At each test condition, the spark energy required to ignite the flowing mixture is measured for several gap widths in order to establish the optimum gap width corresponding to minimum ignition energy. From analysis of the relevant combustion and heat transfer processes involved, expressions for the prediction of quenching distance in flowing mixtures are derived. Support for the model employed in this analysis is demonstrated by a close level of agreement between theoretical predictions of quenching distance and corresponding values calculated from the experimental data on minimum ignition energy obtained over a wide range of mixture compositions and flow conditions.

title: Effects of Energy Deposition Characteristics on Localised Forced Ignition of Homogeneous Mixtures
abstract: The effects of the characteristic width of the energy deposition profile and the duration of energy deposition by the ignitor on localised forced ignition of stoichiometric and fuel-lean homogeneous mixtures have been analysed using simplified chemistry three-dimensional compressible Direct Numerical Simulation (DNS) for different values of root-mean-square turbulent velocity fluctuation. The localised forced ignition is modelled using a source term in the energy transport equation, which deposits energy in a Gaussian manner from the centre of the ignitor over a stipulated period of time. It has been shown that the width of ignition energy deposition and the duration over which ignition energy is deposited have significant influences on the success of ignition and subsequent flame propagation. An increase in the width of ignition energy deposition (duration of energy deposition) for a given amount of ignition energy has been found to have a detrimental effect on the ignition event, which may ultimately lead to misfire. Moreover, an increase in u′ gives rise to augmented heat transfer rate from the hot gas kernel, which in turn leads to a reduction in the extent of overall burning for both stoichiometric and fuel-lean homogeneous mixtures but the detrimental effects of high values of u′ on localised ignition are particularly prevalent for fuel-lean mixtures.

title: Boundary conditions for direct simulations of compressible viscous flows
abstract: Procedures to define boundary conditions for Navier-Stokes equations are discussed. A new formulation using characteristic wave relations through boundaries is derived for the Euler equations and generalized to the Navier-Stokes equations. The emphasis is on deriving boundary conditions compatible with modern non-dissipative algorithms used for direct simulations of turbulent flows. These methods have very low dispersion errors and require precise boundary conditions to avoid numerical instabilities and to control spurious wave reflections at the computational boundaries. The present formulation is an attempt to provide such conditions. Reflecting and non-reflecting boundary condition treatments are presented. Examples of practical implementations for inlet and outlet boundaries as well as slip and no-slip walls are presented. The method applies to subsonic and supersonic flows. It is compared with a reference method based on extrapolation and partial use of Riemann invariants. Test cases described include a ducted shear layer, vortices propagating through boundaries, and Poiseuille flow. Although no mathematical proof of well-posedness is given, the method uses the correct number of boundary conditions required for well-posedness of the Navier-Stokes equations and the examples reveal that it provides a significant improvement over the reference method.

title: Numerical experiments in homogeneous turbulence
abstract: The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.

title: A numerical study on flame stability at the transition point of jet diffusion flames
abstract: Flame stability of a fuel jet diffusion flame was studied numerically by using finite rate chemistry. The flow is time dependent and plane two-dimensional, and the chemical reaction is described by simplified, overall one-step kinetics. The variable parameters are the jet Reynolds number, P Rc o and Damkohler number, Da o : and three types of flame stability behavior were observed depending on values of these parameters. The first one is the local and occasional extinction at the transition point from a laminar to a turbulent flame. When Re 0 is kept at a rather high value and Da 0 is decreased, local extinction at the transition point begins to occur at a certain critical value. The occasional extinction is caused at the instant when the local scalar dissipation rate in the reaction zone becomes too large, producing a rupture in the reaction zone layer. The rupture is quickly connected again to recover the continuous reaction zone layer. As Da 0 is decreased further, however, the frequency of rupture increases, and at another critical value, complete extinction is produced at the transition point, leaving a short, residual rim flame immediately downtream of the injector. This is the second type of flame stability. As Da 0 is decreased further, the third and final stability characteristic is observed: the blow-off of the whole flame from the injector rim. When the flme is extinguished completely at the transition point, most of the injected fuel flows downstream as a fuel jet entraining the surounding air to produce a lifted, turbulent diffusion flame in the downstream flow. This study of the structure of the flame has shown that it is actually an ensemble of instantaneous local premixed, diffusion., and partially premixed flames.

title: Ignition probabilities in turbulent mixing flows
abstract: The paper describes experiments on ignitability carried out in a turbulent jet of natural gas. The turbulence properties of this jet, in terms of its mean and fluctuating velocity and concentration parameters have been extensively measured using laser Raman spectroscopy, and in the 17th Combustion Symposium the authors presented a theory in which the turbulent concentration parameters were used to derive a flammability factor and predict ignition probability. By using a single spark source this theory has been tested and results are presented which demonstrate the validity of the theory and define the flammable boundary of the jet. The results confirm that in a turbulent flow it is not meaningful to consider just the mean concentration in order to define the flammability or probability of ignition. However, in the absence of intermittency, this probability will approach zero when the mean falls below about half the lower flammable limit.

title: Ignition Characteristics Of Turbulent Jet Flows
abstract: Releases of flammable materials from chemical plant are a hazard since their dispersion down to safe levels only occurs at some distance from their source. Within this distance, accidental ignition can give rise to fires or explosions. This paper describes the development of computational fluid dynamic models capable of predicting the ignition hazards presented by turbulent releases of flammable materials. A mathematical model, based on solutions of the fluid flow equations, is described, with a prescribed probability density function (pdf) approach used to determine the distribution of conserved scalar quantities. Three distributions are explored, and their ability to simulate experimental data in jet and wake flows, in isolation of fluid flow calculations, is tested. A composite pdf (consisting of β- and δ- functions, and a power law distribution for the viscous super-layer) demonstrates excellent agreement with data, particularly in those regions of a flow that contain significant intermittency Coupling of this pdf with flow field calculations yields reasonable predictions of scalar pdfs in a methane jet, with probabilities of ignition implied from measured and predicted pdfs being in close accord. The results demonstrate that prescribed pdf methods are likely to be capable of predicting ignition probabilities in many practical flows.

title: AN EXPERIMENTAL STUDY OF FREELY PROPAGATING TURBULENT PROPANE/AIR FLAMES IN STRATIFIED INHOMOGENEOUS MIXTURES
abstract: Experiments of freely propagating turbulent flames in nonhomogeneous propane/air mixtures are performed for various initial distributions of heterogeneities and compared with homogeneous cases. For various flame propagation times, laser tomography and planar laser-induced fluorescence on acetone are performed simultaneously to characterize the flame-front structure as well as the local mixture fraction in front of the flame. The two-dimensional scalar fields are characterized by a mean stratified mixture fraction field, symmetrical around ignition, and by a fluctuation field. The scalar scales are determined from the spatial autocorrelation coefficients and are compared with the turbulence scales, because the turbulence grid is responsible for the mixing. From the flame contours, global parameters (flame radii and wrinkling ratio) and local curvature distributions are also studied to evaluate the contribution of heterogeneities on the topology of the turbulent flame front. At the early stages of flame propagation, the flame structure is weakly affected by the local heterogeneities. Then, at higher propagation times, the heterogeneities tend to smooth the wrinkling produced by the turbulent flow field. A characteristic scale of flame curvature is then compared with the integral length scale of the flow field, L T , and scalar scale L Z . For heterogeneous conditions, the flame front presents small wrinkles with positive and negative curvatures equally distributed all around the flame with a characteristic size strongly depending on L Z .

title: Numerical simulation of turbulent propane–air combustion with nonhomogeneous reactants
abstract: High-resolution two-dimensional numerical simulations have been performed for premixed turbulent propane–air flames propagating into regions of nonhomogeneous reactant stoichiometry. Simulations include complex chemical kinetics, realistic molecular transport, and fully resolved hydrodynamics (no turbulence model). Aerothermochemical conditions (pressure, temperature, stoichiometry, and turbulence velocity scale) approach those in an automotive gasoline direct-injection (GDI) engine at a low-speed, part-load operating condition. Salient findings are as follows: (1) There is no leakage of the primary fuel (propane) behind an initial thin premixed heat-release zone. This “primary premixed flame” can be described using a monotonic progress variable and laminar premixed flamelet concepts. (2) For the conditions simulated, differences in global heat release and flame area (length) between homogeneous and nonhomogeneous reactants having the same overall stoichiometry are small. (3) Beyond three-to-four flame thicknesses behind the primary flame, practically all hydrocarbon fuel has broken down into CO and H2. (4) The rate of heat release in the “secondary reaction zone” behind the primary premixed flame is governed by turbulent mixing and the kinetics of CO2 production. Mixture-fraction-conditioned secondary heat release, CO, and CO2 production rates are qualitatively similar to results from a first-order conditional moment closure (CMC) model; CMC gives poor results for H2, H2O, and radical species. Description of the secondary heat release using steady laminar diffusion flamelet concepts is problematic. (5) Of the chemical species considered, HCO mass fraction or the product of CH2O and OH mass fractions correlates best with local heat-release rate  . (6) Computational considerations demand modifications to chemical mechanisms involving C3H7 and CH3CO. Specific changes are proposed to strike a satisfactory balance between accuracy and computational efficiency over a broad range of reactant stoichiometry.

title: Statistical Analysis of Displacement Speed in Turbulent Stratified Flames: A Direct Numerical Simulation Study
abstract: Statistically planar turbulent stratified flames under different initial root mean square turbulent velocity fluctuation u′ levels are simulated for global equivalence ratios  = 1.0 and  = 0.7 using 3-dimensional compressible direct numerical simulations (DNS) with a modified single-step Arrhenius-type chemistry. For the simulations of stratified flames, a sinusoidal variation of equivalence ratio is introduced in the unburned reactants ahead of the flame. The simulation parameters are chosen in such a manner that the combustion situation belongs to the thin reaction zones regime in all cases. The DNS data has been used to analyze the statistical behavior of the displacement speed S d and its components (i.e., the reaction rate component S r , the normal molecular diffusion component S n , the tangential diffusion component S t , and the component arising due to reactant inhomogeneity S ξ) and their curvature and tangential strain rate dependence. The mean behavior of displacement speed S d and its local strain rate and curvature dependences have been analyzed in detail in terms of the statistical behaviors of the various components of displacement speed (i.e., S r , S n , S t , and S ξ). It has been observed that the contribution of S d due to reactant inhomogeneity S ξ is negligible in comparison to the other components and therefore S d is most significantly affected by the contribution of (S r + S n + S t ). The displacement speed S d statistics are presented in terms of its marginal probability density functions (PDFs) as well as its joint PDFs with curvature and tangential strain rate. It has been observed that S d shows a nonlinear negative correlation with curvature but the correlation strength decreases with increasing u′. The tangential strain rate response of S d has also been found to be dependent upon the turbulence velocity fluctuation level u′ with weak correlation in higher initial u′ cases and a modest positive correlation in the lower u′ cases. It has been found that the marginal PDFs of S r and S n in stratified flames show significant differences in comparison to the corresponding PDFs obtained for perfectly premixed flames with the same values of global equivalence ratio and u′. However, the local curvature and strain rate dependences of S d and its components are found to be qualitatively similar to the corresponding statistical behaviors obtained for perfectly premixed flames with the same values of global equivalence ratio and u′. It has been demonstrated that the curvature dependence of S d has important implications in the context of modeling the curvature stretch term in the Flame Surface Density transport equation.