Impact of swirl and bluff-body on the transfer function of premixed flames

The frequency response of three lean methane/air flames submitted to flowrate perturbations is analyzed for flames featuring the same equivalence ratio and thermal power, but a different stabilization mechanism. The first flame is stabilized by a central bluff body without swirl, the second one by the same bluff body with the addition of swirl and the last one only by swirl without central insert. In the two last cases, the swirl level is roughly the same. These three flames feature different shapes and heat release distributions, but their Flame Transfer Function (FTF) feature about the same phase lag at low frequencies. The gain of the FTF also shows the same behavior for the flame stabilized by the central insert without swirl and the one fully aerodynamically stabilized by swirl. Shedding of vortical structures from the injector nozzle that grow and rollup the flame tip controls the FTF of these flames. The flame stabilized by the swirler-plus-bluff-body system features a peculiar response with a large drop of the FTF gain around a frequency at which large swirl number oscillations are observed. Velocity measurements in cold flow conditions reveal a strong reduction of the size of the vortical structures shed from the injector lip at this forcing condition. The flame stabilized aerodynamically only by swirl and the one stabilized by the bluff body without swirl do not exhibit any FTF gain drop at low frequencies. In the former case, large swirl number oscillations are still identified, but large vortical structures shed from the nozzle also persist at the same forcing frequency in the cold flow response. These different flame responses are found to be intimately related to the dynamics of the internal recirculation region, which response strongly differs depending upon the injector used to stabilize the flame.     

Flame sheet dynamics of bluff-body stabilized flames during longitudinal acoustic forcing

Bluff-body stabilized flames are susceptible to combustion instabilities due to interactions between acoustics, vortical disturbances, and the flame. In order to elucidate these flow-flame interactions during an instability, an experimental and computational investigation of the flame-sheet dynamics of a harmonically excited flame was performed. It is shown that the flame dynamics are controlled by three key processes: excitation of shear layer instabilities by the axially oscillating flow, anchoring of the flame at the bluff body, and the kinematic response of the flame to this forcing. The near-field flame features are controlled by flame anchoring and the far-field by kinematic restoration. In the near-field, the flame response grows with downstream distance due to flame anchoring, which prevents significant flame movement near the attachment point. Theory predicts that this results in linear flame response characteristics as a function of perturbation amplitude, and a monotonic growth in magnitude of the flame-sheet fluctuations near the stabilization point, consistent with the experimental data. Farther downstream, the flame response reaches a maximum and then decays due to the dissipation of the vortical disturbances and action of flame propagation normal to itself, which acts to smooth out the wrinkles generated by the harmonic flow forcing. This behavior is strongly non-linear, resulting in significant variation in far-field flame-sheet response with perturbation amplitude.     

Accelerating flames in tubes—an analysis

Flame acceleration in tubes is studied. A tube filled with flammable mixture is closed at one end and open to the atmosphere at its second end. When ignition takes place near the closed end, it is well-known from experiments that the flame may accelerate, oscillate and eventually reach considerable speeds. A one-dimensional analysis is presented, based upon the assumption that the flame front propagates at a speed that is small compared to the speed of sound. The analysis leads to a construction of the complete unsteady solution. Results from the analysis and from a numerical simulation are compared. They are similar enough to validate the analysis. The tube acoustics are set in motion by the expansion of the fluid due to ignition at the closed end. Subsequently, both spectrum and amplitude evolve because of the motion of the temperature interface, and because of forcing by the flame front, which the analysis precisely quantifies. Oscillations in the front position are strong enough to result in flow reversal. In addition, the induced periodic acoustic acceleration of the temperature and density interface will periodically make the flame front Rayleigh–Taylor unstable, which should result in the dramatic increase in the propagation speed seen in experiments.     

Modelling of lifted turbulent diffusion flames in a channel mixing layer by the flame hole dynamics

The partial quenching structure of turbulent diffusion flames in a turbulent mixing layer is investigated by the method of flame hole dynamics as an effort to develop a prediction model for the turbulent flame lift off. The essence of the flame hole dynamics is derivation of the random walk mapping, from the flame-edge theory, which governs expansion or contraction of the quenching holes initially created by the local quenching events. The numerical simulation for the flame hole dynamics is carried out in two stages. First, a direct numerical simulation is performed for a constant-density fuel–air channel mixing layer to obtain the background turbulent flow and mixing fields, from which a time series of two-dimensional scalar-dissipation-rate array is extracted. Subsequently, a Lagrangian simulation of the flame hole random walk mapping, projected to the scalar dissipation rate array, yields a temporally evolving turbulent extinction process and its statistics on partial quenching characteristics. In particular, the probability of encountering the reacting state, while conditioned with the instantaneous scalar dissipation rate, is examined to reveal that the conditional probability has a sharp transition across the crossover scalar dissipation rate, at which the flame edge changes its direction of propagation. This statistical characteristic implies that the flame edge propagation instead of the local quenching event is the main mechanism controlling the partial quenching events in turbulent flames. In addition, the conditional probability can be approximated by a heavyside function across the crossover scalar dissipation rate.     

Flame dynamics

This lecture describes recent theoretical developments associated with the dynamics of flames, obtained primarily by exploiting the various temporal and length scales involved in the combustion process. In premixed flames the focus is on flame-flow interactions that occur during the nonlinear development of hydrodynamically unstable large-scale flames, or during the propagation of curved flames in two-dimensional channels. The second part of the paper deals with non-premixed and partially premixed flames, where the focus is on understanding the nature of diffusive-thermal instabilities including the effect of thermal expansion, and on stabilization mechanisms of edge flames, which possess characteristics of both premixed and diffusion flames. The results presented in this talk illustrate how simplified models, when analyzed to their extreme, yield predictions of qualitative nature with physical insight that have advanced our understanding of combustion. This insight can be used to guide the experimental efforts, explain observations and validate large-scale numerical simulations.     

Compressible turbulent flame speeds of highly turbulent standing flames

In this paper we present the first measurement of turbulent burning velocities of a highly turbulent compressible standing flame induced by shock-driven turbulence in a Turbulent Shock Tube. High-speed schlieren, chemiluminescence, PIV, and dynamic pressure measurements are made to quantify flame–turbulence interaction for high levels of turbulence at elevated temperatures and pressure. Distributions of turbulent velocities, vorticity and turbulent strain are provided for regions ahead and behind the standing flame. The turbulent flame speed is directly measured for the high-Mach standing turbulent flame. From measurements of the flame turbulent speed and turbulent Mach number, transition into a non-linear compressibility regime at turbulent Mach numbers above 0.4 is confirmed, and a possible mechanism for flame generated turbulence and deflagration-to-detonation transition is established.     

Characteristics of self-excited spinning azimuthal modes in an annular combustor with turbulent premixed bluff-body flames

In this paper we investigate self-excited azimuthal modes in an annular combustor with turbulent premixed bluff-body stabilised flames. Previous studies have shown that both swirl and equivalence ratio influence modal dynamics, i.e. the time-varying nature of the modes. However, self-excited azimuthal modes have not yet been investigated in turbulent flames without bulk swirl, which do not generate any preferential flow in either azimuthal direction, and may therefore lead to different behaviour. Joint probability density functions of the instability amplitudes at various flowrates and equivalence ratios showed a strong bi-modal response favouring both ACW and CW spinning states not previously observed. Operating conditions leading to a bi-modal response provide a unique opportunity to investigate whether the structure of the global fluctuating heat release rate of self-excited spinning modes in both directions exhibit similar dynamics and structure. This was investigated using high-speed OH* chemiluminescence images of the annular combustor and a new rotational averaging method was applied which decomposes the spinning components of the global fluctuating heat release rate. The new rotational averaging, which differs from standard phase-averaging, produces spatial averages in a frame of reference moving with the spinning wave. The results show that the structure of the fluctuating heat release rate for spinning modes is highly asymmetric as characterised by large, crescent shaped regions of high OH* intensity, located on the far side of each flame, relative to the direction of the azimuthally propagating pressure wave. In comparison with interacting swirling flames, these results indicate that the previously observed radial asymmetry of OH* fluctuations may be introduced through advection by local swirl.     

Methane flames in a jet impinging onto a wall

Traditionally, research has focused on positive stretch in the stagnation flow and negative stretch along the Bunsen flame. Only a very limited amount of research has been devoted to studying the behavior of a conical Bunsen flame established in a stagnation flow, which is significantly affected by the combined effects of the curvature stretch and the aerodynamic straining. This investigation is aimed at studying the characteristics of laminar conical premixed flames in an impinging jet flow experimentally and theoretically. First, we analyze the transport processes of a nonreactive impinging jet flow numerically. For lower burner-to-plate distance, the potential core becomes concave at the top. Hence, a conical Bunsen flame established in such a flow field may suffer positive flow stretch. The predicted flame shapes using a simple model incorporated with the numerical results agree well with the experimental observations. Flame shapes exhibit double-solution characteristics in a certain range of methane concentrations. Experimentally, by following different paths of adjusting methane concentration (decreasing from rich to lean or increasing from lean to rich), two different flame configurations (planar or conical flame) may exist at the same flow conditions, namely burner-to-plate distance, inlet velocity, and methane concentration. At the higher (or lower) critical methane concentration, the transition from a flat flame to a conical flame (or from a conical flame to a flat flame) occurs. The calculation of stretch and measurement of flame temperature for the low inlet velocity, 0.8 m/s, show that the stretch of a conical flame established in a stagnation flow is negative (dominated by the flame curvature). However, it is important to emphasize that at high velocity, e.g., U_in = 1.6 m/s, a negatively stretched flame tip can suffer positive flow stretch. This significant finding has been verified in the experiment since the conical flame tip is higher than the positively stretched flat flame.     

Structure and dynamic response of radiative diffusion flames

Nitrogen-diluted hydrogen burning in air is modeled numerically using a constant density and one-step reaction model in a plane two-dimensional counterflow configuration. An optically thin assumption is used to investigate the effects of radiation on the dynamics, structure, and extinction of diffusion flames. While there exist dual steady-state extinction limits for the 1D radiative flame response, it is found that as the 1D radiative extinction point is approached the 1D low-stretch diffusion flame exhibits oscillatory response, even with sub-unity Lewis number fuel. These radiation-induced limit cycle oscillations are found to have increasing amplitude and decreasing frequency as the stretch rate is reduced. Flame oscillation eventually leads to permanent extinction at the stretch rate which is larger than the steady-state radiative extinction value. Along the 1D radiative response curve, the transition from 1D flame to 2D structure and the differences in the resulting 2D flame patterns are also examined using a variety of initial profiles, with special emphasis on the comparison of using the initial profiles with and without a flame edge. Similar to the previous studies on the high-stretch adiabatic edge flames using the same configuration, the high-stretch radiative flames are found to resist 1D blow-off quenching through various 2D structures, including propagating front and steady cellular flames for initial profiles with and without flame edges. For all initial profiles studied, the low-stretch radiative flames are also found to exhibit different 2D flame phenomena near the 1D radiative extinction limit, such as transient cellular structures, steady cellular structures, and pulsating ignition fronts. Although the results demonstrate the presence of low-stretch and high-stretch 2D bifurcation branches close to the corresponding 1D extinction limits irrespective of the initial profile used, particular 2D flame structures in certain stretch rate range are initial profile dependent. The existence of two-dimensional flame structures beyond the 1D steady-state radiative extinction limit suggests that the flammable range is expanded as compared to that predicted by the 1D model. Hence, multi-dimensional flame patterns need to be accounted for when determining the flammability limits for a given system.     

Effect of conical intersection of benzene on non-adiabatic dynamics

The effect of conical intersection on the excited dynamics of benzene is studied by ab initio theory of electronic structure, which provides an important insight into photophysical and photochemical reactions. Based on the CASSCF(6,6)/6-31+G(d, p) method, the topological structures of conical intersections S₁/S and S₂/S₁ of benzene, as well as the optimal structures of the ground state (S) and excited states (S₁, S₂), are determined. The energy minima of the S₁ state and S₂ state are estimated at 4.608 eV and 6.889 eV, respectively. In addition, the energy values of the conical intersections of S₁/S and S₂/S₁ are predicted to be 5.600 eV and 6.774 eV. According to the topological structures and energy values of the S₂/S₁ and S₁/S conical intersections, the photophysical behavior of benzene excited to the S₂ state and the effects of the S₂/S₁ and S₁/S conical intersections are discussed in detail.     

Transient soot dynamics in turbulent nonpremixed ethylene-air counterflow flames

The dynamics of soot formation in turbulent ethylene-air nonpremixed counterflow flames is studied using direct numerical simulation (DNS) with a semi-empirical soot model and the discrete ordinate method (DOM) as a radiation solver. Transient characteristics of soot behavior are studies by a model problem of flame interaction with turbulence inflow at various intensities. The interaction between soot and turbulence reveals that the soot volume fraction depends on the combined effects of the local conditions of flow, temperature, and fuel concentration, while the soot number density depends predominantly on the high temperature regions. Depending on the relative strength between mixing and reaction, the effects of turbulence on the soot formation lead to three distinct paths in deviating the data points away from the laminar flame conditions. It is found that turbulence has twofold effects of increasing the overall soot yield by generating additional flame volume and of reducing soot by dissipating soot pockets out of high-temperature regions. The relative importance between the two effects depends on the relative length scales of turbulence and flame, suggesting that a nonmonotonic response of soot yield to turbulence level may be expected in turbulent combustion.     

Inhibition of hydrogen–oxygen flames by iron pentacarbonyl at atmospheric pressure

The chemistry of inhibition of laminar premixed hydrogen–oxygen flames by iron pentacarbonyl at atmospheric pressure was studied experimentally and by numerical simulation. Flame speed and chemical structure were analyzed. Flame burning velocities and inhibition effectiveness were measured and simulated for various equivalence ratios. The concentration profiles of a number of Fe-containing products of Fe(CO)₅ combustion, including Fe, FeO₂, FeOH, and Fe(OH)₂, were first measured using probing molecular beam mass spectrometry in an atmospheric-pressure H₂/O₂/N₂ flame. A comparison of the experimental and modeling results shows that they are in satisfactory agreement with each other, indicating that the reaction mechanism proposed previously for flame inhibition by iron pentacarbonyl is adequate for predicting the chemical structure of flames. The key recombination stages of active species catalyzed by Fe-containing species for flames of various stoichiometries can be determined by calculations of the production rates of H and O atoms and OH radicals as well as by analysis of the kinetic model.     

Hydrodynamic and chemical scaling for blow-off dynamics of lean premixed flames stabilized on a meso-scale bluff-body

Direct numerical simulations were conducted to investigate the effect of two parameters, density ratio and laminar flame speed, on the conditions of the onset of local extinction and blow-off of lean premixed flames, stabilized on a meso-scale bluff-body in hydrogen-air and syngas–air mixtures. A total of six simulation cases were considered as isolated comparison of the two parametric effects of the fluid dynamic instability and flame time scale. For all cases under study, the general flame development towards the blow-off limit showed a sequence of five distinct modes, with possible cyclic patterns among the different modes for a range of velocity conditions. The onset of local extinction was observed during the asymmetric vortex shedding and vortex street mode. As the density ratio is decreased, the flow inunder reviewstability is promoted through the increased sinuous mode, and such behavior was properly scaled by the Strouhal number. Although the blow-off velocity is altered by the fluid dynamic effects, the condition for the onset of local extinction and blow-off was mainly dictated by the competition between flow residence time associated with the lateral flame motion and ignition delay of the local mixtures. Time scale analysis supported the validity of the findings across all the cases investigated.     

Experimental measurements of geometric properties of turbulent stratified flames

Combustion under stratified conditions is common in many systems. However, relatively little is known about the structure and dynamics of turbulent stratified flames. Two-dimensional imaging diagnostics are applied to premixed and stratified V-flames at a mean equivalence ratio of 0.77, and low turbulent intensity, within the corrugated flame range. The present results show that stratification affects the mean turbulent flame speed, structure and geometric properties. Stratification increases the flame surface density above the premixed flame levels in all cases, with a maximum reached at intermediate levels of stratification. The flame surface density (FSD) of stratified flames is higher than that of premixed flames at the same mean equivalence ratio. Under the present conditions, the FSD peaks at a stratification ratio around 3.0. The FSD curves for stratified flames are further skewed towards the product side. The distribution of flame curvature in stratified flames is broader and more symmetric relative to premixed flames, indicating an additional mechanism of curvature generation, which is not necessarily due to cusping. These experiments indicate that flame stratification affects the intrinsic behaviour of turbulent flames and suggest that models may need to be revised in the light of the current evidence.     

Burning velocity of triple flames with gentle concentration gradient

We investigated the local flame speed of a two-dimensional, methane-air triple flame in a rectangular burner. The velocity fields and the concentration profiles were measured with particle image velocimetry and the Rayleigh scattering method, respectively. There was a requisite combination of initial velocity and initial concentration gradient for consistency of the local concentration gradient at the leading edge of the flame. In these cases, the flame curvatures were also consistent. Accordingly, the burning velocity, defined as local flow velocity at the triple point, was determined by the flame curvature. The burning velocity increased with increasing flame curvature, when the curvature was near zero. After that, the burning velocity decreased with increasing curvature. The peak value thus exceeded the adiabatic one-dimensional laminar burning velocity. Comparing the effects of the measured flame stretch rate on the flow strain κ_s and flame curvature κ_c, κ_s is larger and increases more rapidly than κ_c for flame curvatures satisfying 1/R_f < 250 m⁻¹ and then becomes constant while κ_c still increases for 250 m⁻¹ < 1/R_f, so that κ_c becomes much larger than κ_s. There is also a peak in burning velocity at roughly the transition in flame curvature specified above. Therefore, the burning velocity for a low concentration gradient correlates with the flame stretch rate.     

Verification of the inverted temperature gradient condition via molecular dynamics simulation

We perform molecular dynamics simulations to verify the critical condition for the existence of an inverted temperature profile in the vapor between two liquid slabs at slightly different temperatures. Reasonable agreement is found between the kinetic theory based condition and simulations. The deviation from theory can be explained by deviation from ideal gas behavior on which the kinetic condition is based and by deviation in the MD from diffuse boundary conditions, which are used in deriving the kinetic condition.     

Nonlinear kinematic response of premixed flames to harmonic velocity disturbances

This paper analyzes the nonlinear dynamics of premixed flames responding to harmonic velocity disturbances. These nonlinear dynamics were studied by solving a constant flame speed front tracking equation for the flame’s response to harmonically oscillating velocity disturbances. The solution to these equations is used to quantify the transfer function relating the ratio of the normalized flame area to velocity fluctuations, G = (A′/A_o)/(u′/u_o), upon the amplitude of velocity oscillations, ε = u′/u_o. Due to nonlinearities, the amplitude of this transfer function relative to its linear value decreases with increasing amplitude of velocity oscillation, u′/u_o. In contrast, the transfer function phase exhibits almost no amplitude dependence. The velocity amplitude where transfer function nonlinearities become significant depends strongly upon three parameters: a Strouhal number, St = ωL_f/u_o (where L_f is the flame length), the ratio of the flame length to width, β = L_f/R, and the flame shape in the absence of perturbations (i.e., conical, inverted wedge, etc.). In the linear case, the transfer function, G, depends only upon an algebraic combination of the first two parameters, given by St₂ = St (1 + β²)/β². In general, however, G exhibits a distinct dependence upon both parameters St and β. In particular, we show that the nonlinear response of G is an intrinsically dynamic phenomenon; i.e., its quasi-steady response (St 1) is purely linear. As such, nonlinearity is enhanced with increasing Strouhal numbers. In contrast, nonlinearity is suppressed at large β values; as such, the response of a long flame remains quite similar to its linear value, even at large ε values where the flame front exhibits substantial corrugation and cusping. Finally, we show that the response of conical flames remains much more linear at comparable disturbance amplitudes than for “V” or wedge-shaped flames. These predictions are shown to be consistent with available experimental data.