In recent years, boundary layer flame flashback (BLF) has re-emerged as a technological and operational issue due to the more widespread use of alternative fuels as a part of a global effort to ...promote carbon neutrality. While much understanding has been achieved in experiments and simulations of BLF in the past decades, the theoretical modeling of BLF still largely relies on the progress made as early as the 1940s, when the critical gradient model (CGM) for the laminar flame flashback was proposed by Lewis and von Elbe. The CGM does not account for the modification of the upstream flow by the flame, which has been recently shown to play a role in BLF. The aim of the present work is to gain additional insight into the effects of thermal gas expansion and confinement on the flame-flow interaction in laminar BLF. Two-dimensional simulations of the confined laminar BLF in a channel are performed in this work. The parametric study focuses on the channel width, the thermal gas expansion coefficient, and the heat losses to the wall. This study evaluates the influence of these factors on the critical condition for the flame flashback. By varying the channel width, it is demonstrated that at the critical condition, the incoming flow in narrow channels is modified globally by the thermal gas expansion, while in wider channels, the flow modification by the flame tends to be more local. In narrow channels, a non-monotonic dependence of the critical-condition centerline velocity on the channel width has been identified. The variation of the heat loss to the wall confirms that the wall’s thermal conditions can significantly alter the flashback limit, with the flashback propensity being larger when the thermal resistance of the wall is high. To assess the general applicability of the CGM, the flame consumption speed and the flow velocity near the wall are quantified. The results confirm that the assumption of flame having no influence on the upstream flow, employed in the CGM, is not fulfilled under confinement for a realistic thermal gas expansion. This results in a general disagreement between the simulations and the CGM, which implies that the thermal expansion effects should be accounted for when considering the confined boundary layer flashback limits. It is shown that the critical velocity gradient increases with the gas expansion coefficient for the given channel width and wall thermal condition.
The mechanism of finger flame acceleration at the early stage of burning in tubes was studied experimentally by Clanet and Searby Combust. Flame 105 (1996) 225 for slow propane-air flames, and ...elucidated analytically and computationally by Bychkov et al. Combust. Flame 150 (2007) 263 in the limit of incompressible flow. We have now analytically, experimentally and computationally studied the finger flame acceleration for fast burning flames, when the gas compressibility assumes an important role. Specifically, we have first developed a theory through small Mach number expansion up to the first-order terms, demonstrating that gas compression reduces the acceleration rate and the maximum flame tip velocity, and thereby moderates the finger flame acceleration noticeably. This is an important quantitative correction to previous theoretical analysis. We have also conducted experiments for hydrogen–oxygen mixtures with considerable initial values of the Mach number, showing finger flame acceleration with the acceleration rate much smaller than those obtained previously for hydrocarbon flames. Furthermore, we have performed numerical simulations for a wide range of initial laminar flame velocities, with the results substantiating the experiments. It is shown that the theory is in good quantitative agreement with numerical simulations for small gas compression (small initial flame velocities). Similar to previous works, the numerical simulation shows that finger flame acceleration is followed by the formation of the “tulip” flame, which indicates termination of the early acceleration process.
It has been previously demonstrated that thermal gas expansion might have a role in boundary layer flashback of premixed turbulent flames Gruber et al., J Fluid Mech 2012, inducing local ...flow-reversal in the boundary layer's low-velocity streaks on the reactants’ side of the flame and facilitating its upstream propagation. We perform a two-dimensional numerical investigation of the interaction between a periodic shear flow and a laminar premixed flame. The periodic shear is a simplified model for the oncoming prolonged streamwise velocity streaks with alternating regions of high and low velocities found in turbulent boundary layers in the vicinity of the walls. The parametric study focuses on the amplitude and wavelength of the periodic shear flow and on the gas expansion ratio (unburnt-to-burnt density ratio). With the increase of the amplitudes of the periodic shear flow and of the gas expansion, the curved flame velocity increases monotonically. The flame velocity dependence on the periodic shear wavelength is non-monotonic, which is consistent with previous theoretical studies of curved premixed flame velocity. The flame shape that is initially formed by the oncoming periodic shear appears to be metastable. At a later stage of the flame propagation, the flame shape transforms into the stationary one dominated by the Darrieus-Landau instability.
The understanding of the boundary layer flame flashback (BLF) has considerably improved in recent decades, driven by the increasing focus on clean energy and the need to address the operational ...issues associated with flashback. This study investigates the influence of the Lewis number (Le) on symmetric flame shapes under the critical conditions for a laminar boundary layer flashback in cylindrical tubes. It has been found that the transformation of the flame shape from a mushroom to a tulip happens in a tube of a given radius, as the thermal expansion coefficient and Le are modified. A smaller Lewis number results in a local increase in the burning rate at the flame tip, with the flame being able to propagate closer to the wall, which significantly increases the flashback propensity, in line with previous findings. In cases with a Lewis number smaller than unity, a higher thermal expansion results in a flame propagation happening closer to the wall, thus facing a weaker oncoming flow and, consequently, becoming more prone to flashback. For Le > 1, the effect of the increase in the thermal expansion coefficient on the flashback tendency is much less pronounced.
Numerical simulations of spontaneous flame acceleration are performed within the problem of flame transition to detonation in two-dimensional channels. The acceleration is studied in the extremely ...wide range of flame front velocity changing by 3 orders of magnitude during the process. Flame accelerates from realistically small initial velocity (with Mach number about 10(-3)) to supersonic speed in the reference frame of the tube walls. It is shown that flame acceleration undergoes three distinctive stages: (1) initial exponential acceleration in the quasi-isobaric regime, (2) almost linear increase in the flame speed to supersonic values, and (3) saturation to a stationary high-speed deflagration velocity. The saturation velocity of deflagration may be correlated with the Chapman-Jouguet deflagration speed. The acceleration develops according to the Shelkin mechanism. Results on the exponential flame acceleration agree well with previous theoretical and numerical studies. The saturation velocity is in line with previous experimental results. Transition of flame acceleration regime from the exponential to the linear one, and then to the constant velocity, happens because of gas compression both ahead and behind the flame front.
In the present study, thermoacoustic oscillations of a flame propagating from an open to a closed end of an narrow channel with adiabatic walls are studied numerically. The study revisits the ...importance of hydrodynamic instability and flame symmetry for both primary and secondary acoustic instabilities. For a non-symmetric slanted flame, the primary instability is linked to the development of the hydrodynamic instability, resulting in a corrugated flame front. Spectral Proper Orthogonal Decomposition (SPOD) was employed to demonstrate that the mode at the fundamental frequency is closely associated with the nonlinear behavior of the hydrodynamic cells at the flame front. For the secondary instability of a non-symmetric flame, resonance between the acoustic waves at the fundamental mode and the hydrodynamic modes was observed, without a clear emergence of the parametric instability. For a symmetric flame, the parametric acoustic instability can be more easily observed in a narrow channel. For a symmetric flame, SPOD of the fundamental frequency suggests the formation of a mixture pocket at the centerline, that can potentially invert the flame front, while the first harmonic is related to the flame front inversion process.
Statistically steady supersonic deflagrations are numerically investigated in narrow channels with strong thermal expansion and heat loss. Four modes of flame propagation are observed, namely, ...extinction, low-speed deflagration, high-speed deflagration, and DDT. It is determined that larger thermal expansion facilitates initiation of high-speed deflagrations while the heat loss can suppress the transition to detonation. The high-speed deflagration mode is shown to be the result of the dynamic balance between thermal expansion and wall heat loss. The limits of high-speed deflagration in terms of the thermal expansion and heat loss coefficients are determined. The statistically steady oscillatory high-speed deflagrations propagate at average velocities close to half of the CJ detonation velocity. The dynamics of the flame front and shock waves are visualized using numerical schlieren. Periodic acceleration and deceleration of the leading shock are identified, and the mechanism of DDT suppression is elucidated.
The diffusive-thermal pulsating instability of Le>1 flames can considerably alter global quantities such as the flammability limit and mass burning rate, making its study practically relevant. In the ...present study we investigate the behavior of pulsating flames in unsteady flow fields using one-dimensional and two-dimensional flame simulations of laminar premixed rich hydrogen/air flame in a counterflow configuration, focusing on the response of the flame to imposed fluctuations in strain rate and equivalence ratio. These effects become important when the flame propagates in an unsteady flow field, for example, in turbulent flows. In the case of strain rate forcing, the flame is found to undergo oscillatory extinction if the forcing frequency is less than the pulsation frequency. For strain rate forcing frequencies higher than the pulsation frequency, the flame is found to be largely unresponsive to the upstream flow velocity fluctuations. The parametric study for equivalence ratio forcing shows that the pulsating instability is promoted with increasing inlet velocity, increasing amplitude and mean value of the imposed composition fluctuation. At the same time, it is observed that increasing the frequency of the imposed oscillations may attenuate the pulsating instability. Moreover, it is found that a flame subjected to pulsating extinction may be able to sustain pulsating combustion if forced with high-frequency inlet composition variation. Based on the insights gained from one-dimensional simulations, two-dimensional simulations of these pulsating flames are performed to provide additional insights on the shape and location of cells and cusp formation in these flames.
It has been previously demonstrated that thermal gas expansion might have a role in boundary layer flashback of premixed turbulent flames, inducing local flow-reversal in the boundary layer's ...low-velocity streaks on the reactants’ side of the flame and facilitating its upstream propagation. Here, we perform a two-dimensional numerical investigation of the interaction between a periodic shear flow and a laminar premixed flame. The periodic shear is a simplified model for the oncoming prolonged streamwise velocity streaks with alternating regions of high and low velocities found in turbulent boundary layers in the vicinity of the walls. The parametric study focuses on the amplitude and wavelength of the periodic shear flow and on the gas expansion ratio (unburnt-to-burnt density ratio). With the increase of the amplitudes of the periodic shear flow and of the gas expansion, the curved flame velocity increases monotonically. The flame velocity dependence on the periodic shear wavelength is non-monotonic, which is consistent with previous theoretical studies of curved premixed flame velocity. The flame shape that is initially formed by the oncoming periodic shear appears to be metastable. At a later stage of the flame propagation, the flame shape transforms into the stationary one dominated by the Darrieus-Landau instability.
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