Flame propagation in narrow channels

Resumo

The sudden arrival of the climate change hurries fundamental research on a wide variety of topics trying to slow it down and counteract its effects. One of the examples is the study of alternative fuels (e.g., methane and hydrogen) to gradually replace oil and coal in the upcoming energy transition towards a totally renewable power generation scenario. Furthermore, scientific investigation focusing on combustion in confined geometries is also interesting in safety-related scenarios, as well as in the development of small burners, or even improving the efficiency of the existing and upcoming internal combustion engines. Combustion of premixed alternative gaseous fuels involves several instabilities, affecting the overall performance and security of confined power generation systems. For example, the density and viscosity gradient generated by the highly exothermic chemical reaction, the influence of buoyancy on the propagating front or the inequality between mass and heat diffusion of the mixtures, may promote unstable behaviours of the flame. These instabilities modify the dynamics of the flames due to the wrinkling and folding of the reaction front in several ways. Particularly, the flames may couple with the acoustic waves produced in the combustion chamber, commonly referred to as thermoacoustics, generating a strong pulsation of the reactive front throughout its propagation in a combustion chamber, which can also be transmitted to the holding structure and, therefore, lead to a catastrophic failure. This dissertation aims to study the stability of premixed gaseous flames propagating in semi-confined narrow geometries. The spotlight focuses on the so-called thermoacoustic instabilities and a previously unknown propagation regime, introduced here, for ultra-lean highly-diffusive flames. The methodology consists of the evaluation of experimental studies to assess the effect of different parameters (e.g., fuel, mixture composition, energy losses, gravity) on their onset. For such purpose, we modified a Hele-Shaw cell to perform as a combustion chamber. A Hele-Shaw cell was originally used by Hele-Shaw and Saffman and Taylor to study viscous effects on different fluids. It is a simple domain formed by two parallel plates separated -ideally- by an infinitesimal gap. In real configurations, the gap between the plates h should be much smaller than both the length L and width W of the cell. Furthermore, to promote the appearance of thermoacoustic instabilities, we opened the ignition end and closed the opposite one so that the flames propagate towards a closed wall in all cases. The vibratory motion of premixed flames was firstly reported by Mallard and Le Chatelier. These were baptized as thermoacoustic instabilities, which appear as a result of the coupling between the flames and the acoustic pressure waves that remain trapped in confined or semi-confined combustion chambers, that can potentially lead to critical failure of the system. Following the original Rayleigh's criterion, the pressure waves are amplified -theoretically- if they are in phase with the unsteady heat released by the flame. This transfer of energy between the front and the acoustic waves competes against the different damping mechanisms that arise in real configurations, such as viscous layers or heat losses. The competition between various effects may lead to an amplification, thus yielding a destabilizing effect, or to an attenuation of the acoustic waves. We present in the first part of this thesis an experimental study of premixed flames propagating in the said quasi-two-dimensional geometry (Hele-Shaw cell), where the viscous damping mechanisms can be adjusted by changing the channel thickness and visual inspection can provide quantitative data. We aim to contribute to the understanding of the transition between the primary and secondary instabilities for different gaseous hydrocarbons and ether fuels, chosen mostly because of their unalike diffusive characteristics and their potential future clean fuels. Given a constant geometry of the combustion chamber, we first study the combustion of methane, propane and dimethylether (DME) blends with air, minimizing buoyancy effects (i.e., the flames propagate horizontally) and changing the composition of the burned mixture. Regarding thermoacoustics, all the fuels undergo two regimes of acoustic coupling. Lean enough (rich) propane and DME (methane) flames oscillate smoothly, given the relatively low interaction with the acoustic waves, at the primary thermoacoustic regime, and keep their slightly wrinkled outline (due to the hydrodynamic instability) during their whole journey along the channel. Richer (leaner) flames than a critical value -mixture dependent- show a strong coupling with the acoustic waves and develop the secondary thermoacoustic instability, characterized by a violent oscillatory motion of the front, related to high acoustic pressures, at the eigenfrequency determined by the conditions of the chamber (i.e., geometry, average temperature, position of the front, etc.). The shape of the reactive front changes from the characteristic smoothly-wrinkled Darrieus-Landau front to become very stretched, generating lobes with the shape of fingers with long tails. Later, we rotate the combustion chamber to burn vertical downward-propagating flames and account for the stabilizing effect of buoyancy on the dynamics of the flames. The differences found are not of major importance. The only alterations are the presence of a slightly chaotic dynamics and local quenching when close to the flammability limits, that is dictated by each particular fuel, due to the strong influence of buoyancy-induced velocities. Therefore, it is possible to compare the previous results to the ones obtained for lean hydrogen-air buoyant mixtures, which were only burn vertically in a similar geometry. Despite being such and special fuel (because of its high mass diffusivity), hydrogen flames obtained with lean mixtures behave qualitatively as methane flames: rich-enough downward-propagating flames begin to vibrate smoothly, under the primary acoustic regime described before. Flames of mixtures leaner than a critical value are able to transit to the secondary oscillating regime. The only difference is the flame shape prior to the interaction with acoustics. Lean hydrogen reactive fronts show a more wrinkled front because the thermodiffusive instability is present in such highly diffusive flames with Lewis number, which compares thermal and mass diffusivity, much lower than the unity. Additionally, we reduce the channel thickness for a stoichiometric non-buoyant DME flame and different hydrogen-air mixtures, of variable composition and traveling downwards, to evaluate heat losses and acoustic damping via viscous effects. They result to be almost negligible -mixture dependent- until reaching sufficiently thin geometries, where acoustics begin to be attenuated, and eventually totally removed, due to the interaction with the acoustic boundary layer and the increasing heat losses to the surrounding walls. Regarding hydrogen, the region of equivalence ratio for the secondary thermoacoustic instability diminishes, showing an additional transition for very lean flames. There, the reactive front breaks into several smaller flames, leaving colder corridors of unburned mixtures. The feedback of the acoustic waves becomes weaker there, where the density gradient is lower and, therefore, such broken flames show less interaction with acoustics. To close this first part, we test flames travelling upwards, finding that the Rayleigh-Taylor instability becomes dominant for sufficiently small values of the Froude number -that compares gravity to inertial effects-, obtained for lean and rich enough flames that propagate slowly. Flames governed by this instability develop less wrinkled fronts than those propagating to the opposite direction, and remain unresponsive to the interaction with acoustics. This behaviour becomes critical for lean hydrogen and methane flames, that do vibrate strongly and build up pressure peaks up to 3/5 kPa if gravity is negligible or stabilizing, but they show zero feedback with acoustic when propagating upwards. We give a direct and clear connection between thermoacoustics and the shape of the front. On light of our experimental results, the Markstein number arises as the best candidate to characterize the thermoacoustic transition because of its decrease towards rich (propane and DME) and lean (methane and hydrogen) flames. Therefore, the onset of the pulsations is observed for Markstein numbers below a critical value, reinforcing the numerical results provided by some authors. Moreover, the simulations carried out in several numerical studies concluded that short wavelength perturbations colonize the front when the Markstein number is lower, as we found for the flames tested. Therefore, our empirical observations and the numerical findings appoint the front shape and its malleability to an external perturbation, that is the Markstein number, as the possible parameter triggering the transition between the different instability modes identified in this part of the dissertation. Markstein proposed that local changes of the instantaneous burning velocity and temperature can be directly related to the local curvature of the flame front. That is done by the afterwards-named Markstein number, a semi-phenomenological parameter defined as the ratio between the Markstein length and the flame thickness, used as the proportionality factor between the speed deviations from the laminar burning velocity and the comprised effects of curvature, strain and flame surface. This mixture-dependent magnitude proved itself very valuable in the study of general stability of flame fronts, leading to a better understanding of Darrieus-Landau, Rayleigh-Taylor and thermoacoustic instabilities. Nevertheless, its definition and the related theoretical analyses found in the literature only apply for equidiffusional (with a similar thermal and mass diffusivity, that is, a Lewis number close to one) mixtures, and are not accurate enough to describe the vibratory hydrogen flames, only found for considerably lean mixtures Lewis number with an approximate value of 0.3, considered in our experiments. The previous part of the thesis analyses how the combination of different parameters may trigger thermoacoustic instabilities in narrow channels. As we showed, one of the interesting conclusions is that acoustic-flame interactions are less important, and eventually disappear, when the relative importance of heat losses grows either because the flames propagate in sufficiently narrow channels or because the fuel concentration is close to the lower flammability limit. Taking advantage of this, we eliminate the acoustic out of the problem in the second part of the thesis and focus on flames governed by other phenomena, such as heat losses or fuel diffusivity. From a theoretical point of view, this limit can be achieved by reducing to zero the channel thickness. Experimentally, this assumption implies a strong increment of the relative importance of heat losses that can be induced by reducing the gap distance between the solid walls, reaching thicknesses down to 1 mm, or reducing the heat released by the flame. These two alternatives will be also tested in forthcoming paragraphs, using hydrogen as fuel. Hydrogen is one of the preferred alternative fuel options to produce energy, as presented before, either in fuel cells or in combustion systems. In comparison to conventional hydrocarbons, some of the main concerns of power generation technologies based on hydrogen are the potential safety issues associated to its use. The small size of the H2 molecule brings along a higher permeation of the fuel through solid walls, especially in non-metallic containers, that significantly increases the risk of undesired leaks. Additionally, its high reactivity, with a lean-flammability limit around %H2= 4 at Earth's gravity, and ignition energy as low as 0.02 mJ, ten times lower than conventional hydrocarbons, makes hydrogen more prone to undesired deflagrations and explosions when leaks take place in reduced spaces without ventilation. Furthermore, the dim visible emissions and weak heat radiated from lean hydrogen flames make their detection extremely difficult. Safety-related issues, such as fuel leakage, undesired ignition or explosion accidents, have motivated new fundamental studies. Besides the most destructive events, such as detonations and material combustion, one of the main challenges when using hydrogen is to detect and control very lean and slow-burning flames that can deliver undesired hot spots into flammable regions. These reactive kernels can travel in favour or against gravity under different circumstances. The description of this variety of new regimes in confined lean-burning processes is imperative to design updated prevention strategies, in particular for hydrogen-based systems. To this purpose, we first predict two novel propagation regimes with a simplified quasi-2D numerical simulation which considers the limit where the separation between plates is asymptotically small compared to any other length scale of the problem. The transverse gradients of pressure, temperature and mass fraction can be neglected in the first approximation, with the viscous-dominated velocity adopting a Poiseuille parabolic profile that relates to pressure gradients in the two dimensions considered by means of Darcy-like expressions. Moreover, the contribution of acoustic pressure changes naturally disappears from both the state and energy equations given the applied simplifications. In the adiabatic case, our results recovered the dynamics of unstable cell growth and the development of diffusive-thermal instabilities found previously in some works. However, when conductive heat losses are included, our transient numerical calculations show the existence of isolated circle or comet-like flame cells travelling along the combustion chamber in the limit of slow propagation velocity. The two-dimensional equivalent to a flame ball arises stabilized by means of conductive heat losses. The dynamics of the found isolated flame cells is very different depending on the orientation of the combustion chamber. In horizontal vessels, stable one or two-headed comet-like flames are formed in both open-closed (OC) and closed-open (CO) configurations for moderately large heat losses to the enclosing walls. Both the size of the flame cell and its travelling velocity remain constant. Larger values of the heat loss parameter make the flame to adopt a semi-circular shape to maintain the temperature high enough to sustain the reaction before total quenching happens. When propagating in favour of gravity, the dynamics of the isolated flame cells change. In the OC configuration, the flame adopts a semi-circular shape that undergoes a random walk with several flame-splitting episodes that form alternative paths branching off from a main flame cell pathway that is determined by the buoyancy forces. On the contrary, in the CO configuration, the semi-circular flame cells are stable and propagate along the chamber with constant shape and velocity. Larger values of the heat losses parameter are necessary to extinguish the flame compared to the non-buoyant case. However, for propagation against the influence of gravity, only comet-like stable flames were observed in our calculations. Values of the extinction heat losses parameter are much smaller than upwards propagating flames, and not large enough to enable the generation of the circular regime. Finally, we demonstrate empirically how flames with very low fuel concentration undergo the unprecedented propagation regimes predicted before in gaps narrower than 6 mm. The increasing influence of heat losses was checked by reducing either the combustion chamber thickness or the concentration of hydrogen, keeping the other constant. When the losses were not intense enough, the expected continuous front was found. Once the transfer of heat to the walls exceeds a critical value, the front destabilizes triggering a new propagation mode. The flames split cyclically to fulfil a fractal-like circulation that looks like the pathway formed by different living mechanisms, such as starving bacteria or fungi. Further increment of the relative heat losses makes the flame cells to move steady without splitting. Furthermore, differential diffusion plays a fundamental role in the formation of both circle or comet-like flames. When the fuel does not diffuse at a sufficient velocity, the flames were found to extinguish as a continuous front once the heat losses to the walls are high enough. The discovery of the propagation regimes described before opens new research lines and leaves unanswered questions regarding near-limit hydrogen combustion in narrow geometries. As the use of hydrogen in the near future is expected to increase, we anticipate a raising concern about the safety of hydrogen-powered devices that will motivate the exploration of interactions between different phenomena that may unveil unknown flame behaviours relevant in the development of safety measures.