Nonpremixed Edge-flames Research Articles

The combined effects of chemical reaction order and stoichiometry on nonpremixed edge flames

We examined in this work the combined effects of chemical reaction order n and the stoichiometric mixture fraction on the propagation of nonpremixed edge flames in a counterflow configuration. We began by formulating the problem mathematically using the constant density thermo-diffusive model. The problem was then solved numerically using the finite element method. It has been shown that the reaction order and stoichiometry have an interchangeable role in modifying flame propagation. The study has shown that triple flames exist only for a limited range of values of both the chemical reaction order n and the stoichiometric mixture fraction . Over such values, modifying n and were found to have a great impact on many characteristics related to the flame structure, such as the flame location, the extent of both the premixed flame wings and the trilling diffusion flame, and the flame curvature. In addition, the flame location was found to vary subjected to the value of the reaction order in a manner similar to that observed by varying the mixture fraction. The study also identified the influence of the fuel Lewis number on the flame propagation and was found that the effect of is more pronounced when the reaction order differs from unity. Finally, the study has examined the role of the strain rate on the flame propagation and concluded that the effect of the chemical order n is negligible for stoichiometric mixtures but tends to be significant for off-stoichiometric mixtures.

Stationary edge flames in a wedge with hydrodynamic variable-density interaction

The behavior of nonpremixed edge flames to low and high strains in a wedge-shaped region are simulated and studied in detail. The chemistry is modeled by a one-step mechanism and transport by constant coefficient Fickian diffusion, as a qualitative model describing the physical mechanisms in the thermochemistry of combustion of hydrocarbon fuels. The reactive zero-Mach-number Navier-Stokes equations are used to describe the flow, both in a thermodiffusive regime (constant density) and a hydrodynamically-coupled regime (variable density). This configuration is an adaptation of the experimental opposed inclined jet geometry long used at the University of Southern California, but made stationary by the addition of a sink at the apex of the wedge. This crucial modification enables the stable presence of stationary edge flames, and it allows the study of advancing and retreating edge flames in the low and high strain regimes. The dependence of the edge flames speed on strain rate, stoichiometry, and Lewis numbers is discussed and compared to previous studies.

Propagation and extinction of premixed edge-flames

The propagation rates (Uedge) of edge-flames in premixed hydrocarbon-oxygen-inert mixtures were measured as a function of global strain rate (σ), mixture strength, and (by changing fuel and inert type) Lewis number (Le). Using a counterflow slot-jet burner with electrical heaters at both ends to anchor the flame edges, both advancing (positive Uedge) and retreating (negative Uedge) edge-flames were characterized. Results are presented for both twin (premixed gas against premixed gas) and single (premixed gas against cold inert gas) edge-flames in terms of the effects of a non-dimensional strain rate (ε) and non-dimensional heat loss (κ) on a scaled propagation rate. Uedge showed a strong dependence on Le and flames images show that high (low) Le lead to weaker (stronger) edge-flame burning intensity. Uedge for single edge-flames scaled with the square root of the unburned to burned gas density ratio in a manner similar to nonpremixed flames whereas for premixed flames Uedge scaled linearly with density ratio. Edge-flames exhibited two extinction limits corresponding to a high-σ strain induced limit and a low-σ heat loss induced limit; a simple description of the low-σ limits was proposed and found to correlate well with experiments in twin-premixed, single-premixed, and nonpremixed edge-flames over more than a two-decade range of κ. Results are in good qualitative and reasonable quantitative agreement with simple theories except that retreating twin edge-flames in high-Le mixtures are predicted theoretically but were not observed experimentally.

Edge flame propagation via parallel electric fields in nonpremixed coflow jets

Recent investigations suggested that the primary influence of an electric field on a flame is flow modification caused by ionic wind, and that negative ions produced by the electron impact attachment should play a key role in the bi-directional ionic wind. In order to prove this hypothesis in electric fields parallel to the propagating flames, we designed a coflow experiment with laminar lifted flames in vertical electric fields produced by a nozzle and ground electrode installed over the flame. We found that applying DC and AC increased the flame displacement speed, and decreased the unburned velocity even to negative velocity. Velocity measurements revealed the influence of the electric body force on the flow volume, indicating the importance of the electron impact attachment when the nozzle was charged with positive voltage. The flame propagation speeds were estimated by subtracting the unburned velocity from the displacement speed, and were well correlated with those of stationary lifted flames without an applied electric field as a function of flame curvature. This supported our hypothesis that the effect of the electric field is reflected in the flow modification, and that the flame is affected by the modified flow. It also suggested that the propagation direction of premixed or nonpremixed edge flames can be manipulated by coupling the appropriate electric fields.

Effect of stoichiometric mixture fraction on nonpremixed H2O2N2 edge-flames

The influences of stoichiometric mixture fraction ( Z st ) and global strain rate ( σ ) on the shapes and propagation rates ( U edge ) of nonpremixed edge-flames in H 2 N 2 /O 2 N 2 mixtures were investigated using a counterflow slot-jet apparatus. Both positive and negative U edge were observed depending on dilution level, Z st and σ . At low Z st only continuous flames were observed whereas at sufficiently high Z st , where a shift from more oxygen-deficient to more fuel-deficient conditions at the reaction zone occurs, broken structures characteristic of low Lewis number premixed flames were observed which enabled combustion under conditions where no flames could be sustained at lower Z st , even for the same dilution level. At sufficiently high σ these broken structures could transition from advancing edge-flames to isolated, stationary flames, particularly for highly-diluted mixtures. These findings were in surprisingly good agreement with theoretical predictions. Appropriate scalings of these behaviors for different mixtures based on computed 1D extinction strain rates were identified. Nonpremixed H 2 N 2 /O 2 N 2 edge-flames have profoundly different responses to Z st than corresponding hydrocarbon edge-flames, which is shown to be due to differences in the chemistry and Lewis numbers of the two fuels.

Effects of mixture fraction on edge-flame propagation speeds

The propagation speeds (Uedge) of nonpremixed edge-flames were measured as a function of stoichiometric mixture fraction (Zst) and global strain rate (σ) for several fuel/oxidant/diluent combinations using a counterflow slot-jet burner. It was found that for fuel Lewis number (Lef) ≈ 1 and oxidant Lewis number (Leo) ≈ 1 with fixed σ, Uedge increases monotonically with increasing Zst. In contrast, for Lef > 1 and Leo ≈ 1 with fixed σ, Uedge exhibits a minimum, typically at Zst ≈ 0.3, except for dimethyl ether which showed Uedge montonically decreasing with increasing Zst. These results indicate that Zst has both chemical and Lewis number effects on nonpremixed edge-flame speeds. For Lef ≈ Leo ≈ 1, chemical effects dominate over the whole range of Zst whereas for Lef> 1 and Leo ≈ 1, Lewis number effects become important at low Zst. It is shown that all observed Uedge vs. Zst trends are consistent with computed values of extinction strain rate (σext) of these mixtures in a 1D counterflow, thus σext serves as a simple surrogate for predicting edge-flame behavior.

Propagating nonpremixed edge-flames in a counterflow, annular slot burner under DC electric fields

Characteristics of propagating nonpremixed edge-flames were investigated in a counterflow, annular slot burner. A high-voltage direct current (DC) was applied to the lower part of the burner and the upper part was grounded, creating electric field lines perpendicular to the direction of edge-flame propagation. Upon application of an electric field, an ionic wind is caused by the migration of positive and negative ions to lower and higher electrical potential sides of a flame, respectively. Under an applied DC, we found a significant decrease in edge-flame displacement speeds unlike several previous studies, which showed an increase in displacement speed. Within a moderate range of field intensity, we found effects on flame propagation speeds to be negligible after correcting the flame displacement speed with respect to the unburned flow velocity ahead of the flame edge. This indicates that the displacement speed of an edge-flame strongly depends on ionic wind and that an electric field has little or no impact on propagation speed. The ionic wind also influenced the location of the stoichiometric contour in front of the propagating edge in a given configuration such that a propagating edge was relocated to the higher potential side due to an imbalance between ionic winds originating from positive and negative ions. In addition, we observed a steadily wrinkled flame following transient propagation of the edge-flame, a topic for future research.

Time evolution of propagating nonpremixed flames in a counterflow, annular slot burner under AC electric fields

The mechanism behind improved flame propagation speeds under electric fields is not yet fully understood. Although evidence supports that ion movements cause ionic wind, how this wind affects flame propagation has not been addressed. Here, we apply alternating current electric fields to a gap between the upper and lower parts of a counterflow, annular slot burner and present the characteristics of the propagating nonpremixed edge-flames produced. Contrary to many other previous studies, flame displacement speed decreased with applied AC voltage, and, depending on the applied AC frequency, the trailing flame body took on an oscillatory wavy motion. When flame displacement speeds were corrected using measured unburned flow velocities, we found no significant difference in flame propagation speeds, indicating no thermal or chemical effects by electric fields on the burning velocity. Thus, we conclude that the generation of bidirectional ionic wind is responsible for the impact of electric fields on flames and that an interaction between this bidirectional ionic wind and the flame parameters creates visible and/or measurable phenomenological effects. We also explain that the presence of trailing flame bodies is a dynamic response to an electric body force on a reaction zone, an area that can be considered to have a net positively charged volume. In addition, we characterize the wavy motion of the transient flame as a relaxation time independent of mixture strength, strain rate, and Lewis number.

Nonlinear dynamical behaviour of intrinsic thermal-diffusive oscillations of laminar flames with varying premixedness

This study focuses on the thermal-diffusive oscillations of the full spectrum of co-flow laminar flames—from premixed to non-premixed through partially premixed flames for Lewis numbers sufficiently greater than unity. A premixedness parameter is identified using the analytical solution to the mixing field downstream of a splitter plate. Different premixedness levels ranging from zero (fully non-premixed) to unity (fully premixed) are then used as Dirichlet data for inlet concentrations of the reactants to the flame. The initial value problem is numerically solved by adopting a thermo-diffusive model and single-step finite rate chemical reaction and using higher-order compact schemes. A thumb-shaped region in the Damköhler number – premixedness parameter space is identified as corresponding to limit cycle oscillations of the flame. This fills the gap between what is reported for the pulsating instability of non-premixed edge flames recently and fully premixed flames earlier. The thumb-shaped region enlarges with increase in the Lewis number in the range of 1.5–1.7, with marked increase in the oscillatory amplitude of the total heat release. A subcritical Hopf bifurcation is seen to occur at the boundary of this region in the above parametric space. The mechanism of oscillations is studied: hysteresis is found between the upstream and downstream propagation of the flame due to the thermal-diffusive imbalance. The oscillations are plotted in the phase space of the domain-integrated mass and heat diffusive fluxes of and to the reactants. The area of the limit cycle peaks at a particular Damköhler number and premixedness parameter and drops to zero on both sides in this parametric space.

Local Stretch Rates at Non-stationary Non-premixed Edge Flames

Local Stretch Rates at Non-stationary Non-premixed Edge Flames

Multidimensional flamelet-generated manifolds for partially premixed combustion

Flamelet-generated manifolds have been restricted so far to premixed or diffusion flame archetypes, even though the resulting tables have been applied to nonpremixed and partially premixed flame simulations. By using a projection of the full set of mass conservation species balance equations into a restricted subset of the composition space, unsteady multidimensional flamelet governing equations are derived from first principles, under given hypotheses. During the projection, as in usual one-dimensional flamelets, the tangential strain rate of scalar isosurfaces is expressed in the form of the scalar dissipation rates of the control parameters of the multidimensional flamelet-generated manifold (MFM), which is tested in its five-dimensional form for partially premixed combustion, with two composition space directions and three scalar dissipation rates. It is shown that strain-rate-induced effects can hardly be fully neglected in chemistry tabulation of partially premixed combustion, because of fluxes across iso-equivalence-ratio and iso-progress-of-reaction surfaces. This is illustrated by comparing the 5D flamelet-generated manifold with one-dimensional premixed flame and unsteady strained diffusion flame composition space trajectories. The formal links between the asymptotic behavior of MFM and stratified flame, weakly varying partially premixed front, triple-flame, premixed and nonpremixed edge flames are also evidenced.

Dynamics and quenching of non-premixed edge-flames in oscillatory counterflows

The dynamics of non-premixed edge-flames, including the generation of cellular structures, in an unsteady, symmetric counterflow are examined for positive rates of strain. A one-step reaction is assumed, ν Y F + ν X O → ν p P , in which the oxidizer Lewis number is 1. For a variety of Damköhler numbers, we examine the edge-flame evolution for two values of the fuel Lewis number Le Y , 0.3 and 1, and two values of the initial mixture fraction γ, 0.36 and 1, representing fuel lean and stoichiometric supply conditions. For Le Y = 0.3 and γ = 0.36 , unsteady forcing can convert non-cellular edge-flames into ones containing various characteristics of near- or sub-limit cellular structures, including drifting, splitting and stationary flame strings. The transition regimes between the different edge-flame structures are examined as a function of the amplitude and frequency of the strain rate variations in the unsteady counterflow and also as a function of the instantaneous and equivalent strain rate functions. For Le Y = 0.3 and γ = 1 , while no cellular edge-flames can be generated for steady counterflows, we show that cellular structures can be observed in the presence of unsteady forcing. For Le Y = 1 and γ = 1 , it is shown that unsteady forcing can significantly modify the mean propagation speeds of both ignition and failure waves. Finally, the quenching boundaries of two-dimensional edge-flames induced by the unsteady counterflow are examined for Le Y = 0.3 , γ = 0.36 and Le Y = 1 , γ = 1 .

Statistics of relative and absolute velocities of turbulent non-premixed edge flames following spark ignition

2-D projections of turbulent non-premixed edge flame propagation velocities following spark ignition have been measured in the opposed-jet geometry using simultaneous high-speed OH-PLIF/PIV. The difference in the thickness of the edge between the flame sheet from the OH-PLIF images and the evaporated droplets from the PIV images was about 1–1.5 mm, and generally did not effect the calculation of the absolute flame speed, V abs. The local flow velocity in the direction of the flame velocity was calculated and resulted in a measurement of the relative propagation velocity, V r. It was found that, after an initial transient due to the plasma expansion, the mean 〈 V abs〉 increased with time and radial distance as the flame travelled outwards and 〈 V abs〉 increased with the bulk velocity U b. The fluctuations in V abs also increased with U b. The mean relative propagation velocity, 〈 V r〉, for all flames was about 0.75 S L, but increased slightly to 1 S L by the inner burner rim. The RMS of V r was close to 〈 V r〉. The PDF of V r was wide with very little content above 3 S L and a non-negligible content at negative relative speeds, i.e. retreating fronts. The measured statistics are in good agreement with 3-D DNS results. Separate analysis of images from successful and failed ignition events shows that the PDF of V r for the failed ignition has relatively lower values than the successful. This PDF peaks at about 0.25 S L, with higher probability of negative V r. The measured value of 〈 V r〉/ S L is a new result and provides insight on the time taken to fully ignite non-premixed combustion in applications such as the relight of gas turbines.

Premixed Edge-Flames in Spatially-Varying Straining Flows

Premixed-gas flames subject to steady spatially-varying straining flows were studied to examine one aspect of premixed flames in strongly turbulent flows where strain rate gradients are present and local strain rates may be high enough to cause local flame-front extinguishment. The spatially-varying straining flows were created using a counterflow slot-jet burner with slightly non-parallel jet exits. When the flow configuration was premixed combustible gas vs. cold inert gas, so that only a single flame was produced, steady flame “edges” could be created where the flame would exist in the low-strain region but would be extinguished in the high-strain region. When the flow configuration was premixed gas vs. premixed gas, twin flames would exist in the low-strain region that converged to a corner-like tip in the high-strain region. For both configurations the local strain at the location of the stationary flame edge was somewhat lower than the strain required to extinguish flames in the same mixture subject to a spatially uniform strain. The difference was greater for the twin-flame configuration, particularly at high Lewis number (Le). Due to diffusive-thermal instabilities, cellular flames were observed at low Le and travelling-wave patterns were observed at high Le. Le effects also led to the formation of isolated “flame tubes” rather than continuous fronts at sufficiently low Le and high strain rates. All of these results are consistent with recent theoretical predictions. These results indicate that “laminar flamelet” models of premixed turbulent combustion may be reasonably accurate for single flames over a wide range of Le and twin flames with Le close to unity, even at conditions approaching those where local flame quenching occurs, but may not be accurate for twin-flames except for Le near unity. This finding is somewhat different from previous experimental and theoretical results for nonpremixed edge-flames, where more substantial differences between uniform flames and edge-flames were found for all Le.

Nonpremixed edge flames in spatially varying straining flows

Nonpremixed flames subject to steady but spatially varying straining flows were studied to examine one aspect of nonpremixed flames in strongly turbulent flows or near quenching conditions (e.g., near a burner rim), where strain-rate gradients are present and local strain rates may be high enough to cause local flame-front extinguishment. The spatially varying straining flow were created using an opposed slot-jet burner with slightly nonparallel jet exits. The most significant observation was that steady flame “edges” could be created where the flame would exist in the low-strain region but would be extinguished in the high-strain region. The local strain at the location of the stationary flame edge was almost always lower than the strain required to extinguish flames in the same mixture subject to a spatially uniform strain. The strain rate at the edge-flame location was independent of the strain-rate gradient and gradual transitions from edge-flame behavior to uniformly strained flame behavior were not observed, indicating that conventional nonpremixed flames and edge flames are quite distinct structures yet each has well-defined properties. At the flame edge, interferometer images indicate a region of locally intense burning and an abrupt transition to nonburning conditions away from the edge. These observations were found to be qualitatively consistent with recent theoretical models of flame edges. These results indicate that “laminar flamelet” models of nonpremixed turbulent combustion may require reevaluation at conditions approaching those where local flame quenching occurs. It is proposed that these models could be improved by adding edge-flame libraries to existing laminar flamelet libraries.