_{4}-H

_{2}-Air Mixtures

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Experimental characterization of the burning behavior of gaseous mixtures has been carried out, analyzing spherical expanding flames. Tests were performed in the Device for Hydrogen-Air Reaction Mode Analysis (DHARMA) laboratory of Istituto Motori—CNR. Based on a high-pressure, constant-volume bomb, the activity is aimed at populating a systematic database on the burning properties of CH_{4}, H_{2} and other species of interest, in conditions typical of internal combustion (i.c.) engines and gas turbines. High-speed shadowgraph is used to record the flame growth, allowing to infer the laminar burning parameters and the flame stability properties. Mixtures of CH_{4}, H_{2} and air have been analyzed at initial temperature 293÷305 K, initial pressure 3÷18 bar and equivalence ratio _{2} in the mixture was 0%, 20% and 30% (vol.). The effect of the initial pressure and of the Hydrogen content on the laminar burning velocity and the Markstein length has been evaluated: the relative weight and mutual interaction has been assessed of the two controlling parameters. Analysis has been carried out of the flame instability, expressed in terms of the critical radius for the onset of cellularity, as a function of the operating conditions.

No matter the claim and the quest for new answers to the needs of an energy-thirstier society, thermal conversion systems will play a key role in the energy supply chain. This awareness, along with the urgent need of CO_{2} reduction (currently the main driver of technology advance), has at least two direct consequences: the introduction in the energy cycle of CO_{2}-neutral fuels (biomass-derived) and the design/development of more efficient conversion systems. The latter point can be anticipated to have a larger practical impact than the former, given the majority of energy sources will be represented by fossil fuels for many years to come.

Sometimes placed in the category of “alternative” fuels, methane (CH_{4}) is indeed a hydrocarbon, sporting the peculiarity of the lowest C/H ratio, if compared to other fuels: by trivial reasoning, the less the carbon, the less the CO_{2}. This feature has boosted a renewed attention to CH_{4}, which represents the main constituent of natural gas. CH_{4} has been used with heat engines for a long time, even if with the status of a “niche” solution: as a fuel for internal combustion (i.c.) engines, it offers some advantages over gasoline, having wider flammable limits and better anti-knock characteristics, at the cost of a lower flame speed. A feasible opportunity to overcome the limits of CH_{4} is offered by H_{2}: adding H_{2} to CH_{4} (or natural gas) can improve the flame speed/stability and lower the lean operating limit. The overall effect is to extend the stable operation map to extreme conditions (e.g., high EGR).

Crucial for the development and design of i.c. engines and gas turbine combustors is the knowledge of laminar combustion properties: they offer the basis for modelling and simulation of flame-turbulence interaction. Data on the combustion properties of pure gaseous fuels are widely available in the literature [_{4} and H_{2}, obtained in conditions as close as possible to those of actual engines.

The project relies on an optically accessible constant-volume bomb (static _{0}, _{0}), the equivalence ratio, the relative composition of the mixture, the ignition energy can be varied in a meaningful range. A shadowgraph setup, based on a c.w. laser source and a CMOS camera, is used to follow the flame growth with high time and space resolution.

The present work was carried out in the above-described framework and deals specifically with the effect of the initial pressure and of the H_{2} amount on the combustion properties of CH_{4}-H_{2}-air mixtures.

The initial pressure varied between 3 and 18 bar; the H2 percentage varied from 0% to 30% (vol.): the equivalence ratio

The experimental tests yielded the (unstretched) laminar burning velocity and the Markstein length in each condition. These flame characteristics constitute a necessary input for the development and validation of theoretical models of laminar flame propagation. In addition, the interaction between laminar burning velocity and stretch (expressed by the Markstein length) allows to highlight the relation between flame and turbulence within the wrinkled thin laminar flamelet regime of premixed turbulent flames. These theoretical models, in turn, represent the basis for the design and testing of i.c. engines and/or combustors.

Other than the laminar burning characteristics, the phenomenon of flame instability has been explicitly analyzed, offering further details on flame properties. Under certain conditions, instability may wrinkle and break the flame front into small combustion cells: the effective flame front area increases, and the combustion process accelerates. Flame cellularity can be considered as an intermediate regime between laminar and turbulent combustion. Since its relevance in real combustion systems cannot be overlooked, the dependence of cellularity on both pressure and H_{2} amount was suitably investigated.

The general arrangement of the experimental layout is shown in

A total of 6 optical accesses are available: the larger viewports (

Four additional service ports are available, e.g., for the intake of the combusting mixture and the vent of the exhaust gases.

The mixture is ignited with an automotive inductive ignition system (energy ≤ 60 mJ), which was characterized recording the time evolution of the voltage drop and the current flow between the electrodes: this allowed to evaluate the power and energy release. Being known the electrical behaviour of the coil, the energy of discharge can be set in the range 0÷60 mJ, adjusting the time of charge (dwell time). The spark discharge takes place in the center of the chamber between two pointed-tip tungsten electrodes (dia. = 1 mm, gap = 1 mm).

Layout of the experimental apparatus.

A high-frequency dynamic pressure transducer detects pressure history during the combustion events. A metal-shielded, type K thermocouple is used to monitor the temperature of the gases, save for the combustion phase.

The gas handling system was designed to prepare combustible mixtures of variable composition with high accuracy, spanning a range of initial pressures, which included values of relevance in spark-ignition engine operation.

High purity gases (CH_{4}: 99.9995%, H_{2}: 99.999%, dry air: 99.999%, N_{2}: 99.9995%) are used to prepare the mixtures, relying on the partial pressures method [_{2} and pumped down to 10^{−}^{2} mbar. All the devices operate with a high degree of automation, to maximize safety and repeatability of the tests.

The entire lab conforms to current safety standards on the use of combustible gases, and is provided with interconnected gas leak sensors, cylinder cut-off devices and forced venting systems.

A parallel-beam direct shadowgraph layout [

Time-resolved, shadowgraph images of the spherical expanding flame allow to evaluate the laminar burning parameters, according to a well-known approach [_{u} (the flame radius on the

The stretched flame speed _{s} can then be evaluated as:

The obtained speed includes the stretch effects associated to the propagation of a flame surface, which experiences curvature and flow dynamic strain [

The relationship between flame speed and stretch has been thoroughly investigated. It depends on the mathematical model and the associated hypotheses. A detailed analysis leads to the _{s0} is the unstretched flame speed and _{b} is the burned gas Markstein length.

For weakly stretched flames, Equation (3) reduces to the

By plotting _{s} against α, it is possible to estimate (i) the unstretched flame speed _{s0} as the value assumed by _{s} at α = 0, and (ii) the Markstein length _{b} as the gradient of the best straight line fit. The Markstein length indicates how and to what extent the flame is influenced by the stretch. Positive _{b} are associated to flames with speed decreasing with stretch (which are stable), while in the case of negative _{b} the flame speed tends to increase with stretch, becoming unstable; moreover, the magnitude of _{b} indicates to what extent the flame propagation is influenced by the stretch.

The unstretched flame speed _{s0} refers to the limiting case of a plane flame front, with infinite radius and negligible curvature: in such a case, _{s0} can be related to the unstretched laminar burning velocity _{l0} through the following relation:
_{b} is the density of burned gases and ρ_{u} the density of unburned gases. Equation (5) holds true in the hypotheses of perfect gases, isobaric, adiabatic and equilibrium conditions.

The laminar flame thickness δ_{l} is a characteristic length, rather than an actual physical dimension: it’s meant to describe the extension of a reaction zone and different definitions have been proposed, based on the balance of mass, energy or momentum. In the current work, the hydrodynamic thickness has been used:
_{u} and μ_{u} are respectively the kinematic and dynamic viscosity of the unburned mixture [

An image processing routine has been implemented to infer the flame radius _{u} from the shadowgraph data: for each frame, the flame contour is traced and the area of the projected flame ball is evaluated; the radius is estimated as that of a circle of equal area to the flame. The time evolution of the flame radius _{u} offers the basis for the evaluation of the laminar parameters (_{l0} and _{b}).

In the present work, a linear dependence was assumed between the flame speed and the stretch, Equation (4): the validity of this postulation was corroborated “a posteriori” by the results.

The usual approach for the linear analysis consists of a series of steps, which makes use of Equations (1),(2),(4) and (5): a polynomial fit of r_{u} data is first performed; differentiation of the fit allows to obtain the stretched flame speed _{s} defined in Equation (1); being known _{s} and _{u}, the stretch rate α can be evaluated after Equation (2); according to Equation (4), linear-fit extrapolation of the flame speed to α = 0 gives the unstretched flame speed _{s0}, while the slope of the fit allows to estimate the burned gas Markstein length _{b}. The critical step in this approach resides in the polynomial differentiation, which is highly sensitive to the choice of the original data interval: this may introduce noise and lead to distorted profiles of _{s}, affecting both _{s0} and _{b}.

At least two different approaches have been proposed in the literature [

The solution to Equation (7) is:
_{1} is a constant to be determined.

The values of _{s0} and _{b} (along with _{1}) are obtained minimizing the following equation:
_{u} is the experimentally measured radius. The Lambert function _{0}(_{−1}(_{b} > 0 (that is _{0}) must be used, while for _{b} < 0, _{−1}(_{s0} and _{b} for each test case. The stretched flame speed and the stretch rate can be obtained differentiating Equation (8) with respect to time.

The following results refer to the combustion behaviour of CH_{4} and of CH_{4}-H_{2} mixtures, with a H_{2} fraction of 20% and 30% in volume: these values optimize the trade-off between additional technical complexity and performance benefits, allowing for a direct utilization of CH_{4}-H_{2} mixtures in current natural gas engines [_{0} varied in the range 293÷305 K, while the initial pressure _{0} was set at 3, 6, 12 and 18 bar (abs.). The study was limited to stoichiometric air-fuel mixtures (equivalence ratio

Time-resolved shadowgraph images of spherical expanding flames were used to infer the laminar flame parameters. As stated earlier, laminar analysis can be meaningfully carried out in the constant-pressure phase only, before the chamber pressure shows a sensible increment. Moreover, as stated by Bradley

The resulting measurement time-window starts after the ignition disturbances are over, and ends when the pressure shows an appreciable rise. In the present tests, spark energy was set at 20 mJ (electrical). Since the ignition system is inductive, only a small fraction of this energy is released in the breakdown phase (<10 ns), which (due to the high power peaks) drives the early kernel growth and induces likely perturbations in the flame [

Analysis of the flame radii in the early stages revealed no discernible evidence of ignition-induced effects: nonetheless, pending further investigation, a conservative criterion was applied, based on the morphology of the flame: flames with an aspect ratio (major axis/minor axis of the fitting ellipse) lower than 0.98 were discarded. Typical value for the minimum radius was about 4.5 mm.

As stated above, the maximum radius was obtained applying the constraint of constant pressure: typical value was ~9.5 mm, corresponding to ~27% of the chamber radius. This value meets the (_{u} < 0.3_{chamber}) criterion suggested by Burke

_{0} = 3 bar. The combustion behaviour is compared for CH_{4} and H_{2}-CH_{4} mixtures with a H_{2} content of 20% and 30% (vol.). Recording speed was 7000 fps (143 µs between consecutive frames) with a shutter speed of 1 µs; optical magnification ratio was 3.27:1, resulting in a spatial resolution of 15.3 pixel/mm. Flames appear smooth and virtually free of wrinkles; the crack shown for the 30% mixture is the self-similar development of initial ignition disturbances. The effect of H_{2} addition can be appreciated in the increased size of the flame ball at a given time.

Flame propagation in the isobaric phase for stoichiometric CH_{4} and H_{2}-enriched mixtures (20% and 30% vol.) at 3 bar and room temperature. Window dia. 65 mm.

The output of shadowgraph image processing is shown in _{0}, _{0}, % H_{2},

As mentioned earlier, the analytical solution delivers _{s0} and _{b} directly. The time evolution of _{s} can anyway be evaluated differentiating Equation (8). This allows one to trace the behavior of the stretched flame speed against α, as shown in _{2}, even in limited amounts, has always a positive effect on the flame speed.

Time evolution of flame radius. Stoichiometric CH_{4} and H_{2}-enriched mixtures (20% and 30% vol.) at room temperature. Starting pressure as indicated.

The unstretched laminar burning velocity _{l0}_{l0}, which bypass the evaluation of the expansion factor. The authors highlighted the drawbacks of the approach generally used in the literature, which requires the evaluation of the ratio ρ_{u}/ρ_{b}: this can introduce errors if any of the hypotheses behind Equation (5) are not satisfied. In the case of CH_{4}, they concluded that the “old” method delivers reliable results. In the present work, the expansion factor was obtained from the properties of the reactant species and of equilibrated adiabatic products, evaluated with the GASEQ code [

Evolution of the flame speed

The _{l0} values for CH_{4} are summarized in _{0}. As the starting pressure is increased from 3 to 18 bars, a decrease of the laminar burning velocity can be observed; _{l0} at 18 bar is about 40% of 3 bar. The comparison is proposed with the results from other research groups [_{l0} show a fairly good agreement with most of published data, save for the values of Halter, which appear slightly lower.

The variation of the burning velocity with initial pressure and temperature can be expressed by the simple empirical correlation [_{l0,r} is the laminar burning velocity at the reference temperature _{0,r} and pressure _{0,r}. In the present study, only the pressure dependence was evidenced.

The parameter β was optimized in the range 3÷18 bar, using 3 bar as the reference pressure. As shown in ^{2} is >0.99. In the case of CH_{4} the value of β is −0.45, which is bracketed between the findings of Gu _{4}-H_{2} mixtures show a minor reduction in the magnitude of β, which is proportional to the amount of H_{2}.

Unstretched laminar burning velocity as a function of the starting pressure, for stoichiometric CH_{4} at room temperature.

Effect of initial pressure on the unstretched laminar burning velocity. Solid lines represent fits obtained by Equation (11): values of β as indicated.

The effect of the addition of H_{2} to CH_{4} is twofold: the laminar burning velocity not only increases but becomes also less sensitive to the initial pressure.

The Markstein length is shown in _{4} at lower pressure, _{b} is positive, corresponding to a flame speed which increases as α decreases. As the pressure is increased, the Markstein length becomes smaller, and eventually negative: this result is in agreement with the findings of Gu _{4} flames up to 10 bar. The effect is probably related to the decrease of flame thickness associated to the pressure increment: this reduces the effect of curvature in counteracting the hydrodynamic instabilities.

Burned-gas Markstein length as a function of the starting pressure, for stoichiometric CH_{4} and H_{2}-enriched mixtures at room temperature.

The addition of H_{2} to CH_{4} has the anticipated effect [

Due to the combined effects of initial pressure and Hydrogen content, high-pressure CH_{4}-H_{2} flames are characterized by the lowest values of _{b}.

The obtained results confirm the selected procedure for data analysis as appropriate. Since −0.2 ≤ _{b} ≤ 0.2 mm, and the minimum flame radius used in the image processing is ~4.5 mm, the ratio |_{b}/_{u min}| results lower than ~0.045. According to Halter

The burned-gas Markstein length _{b} expresses how and how much the stretch rate affects the flame propagation. Aerodynamic stretch, induced by flame curvature, interacts with the propensity of the flame to develop instability (hydrodynamic and/or thermo diffusive). In this sense, _{b} can be considered an indicator of flame instability. Interestingly enough, the Markstein length is evaluated from the expanding flame in the constant-pressure regime, when the flame is smooth and there is little or no distortion (see e.g., _{b} has a predictive nature.

Evidence of flame instability, if any, appears afterwards, depending on the experimental setup. The flame travelling the chamber volume may go through various morphological alterations, characterized by the appearance and branching of large cracks and, eventually, fine cellular structures [_{2}-enriched CH_{4} mixtures, ignited at _{0} = 6 bar. Recording conditions were as in

Evolution of flame instability for stoichiometric CH_{4} and H_{2}-enriched mixtures (20% and 30% vol.). _{0} = 6 bar, _{0} = 298 K. Window dia. 65 mm.

It is worth stressing that these images refer to late stages of flame propagation, when the combustion process is no more isobaric.

At moderate values of the initial pressure (_{0} = 6 bar), the CH_{4} flame keeps its laminar shape until it approaches the chamber walls. The addition of H_{2} to the mixture, even in limited amount (20%), corresponds to the appearance of large cracks on the flame surface. This effect gets more striking as long as the flame travels the chamber, with the cracks being suddenly integrated by cellular structures [

As shown in _{0} = 12 bar: no matter the mixture composition, in all the cases the flame exhibits deviations from a smooth, laminar morphology. These phenomena take place earlier in the process (that is at smaller radii), if compared to _{0} = 6 bar. The typical sequence of large cracks followed by smaller, uniformly distributed “cells” is always present; if the amount of H_{2} is increased, cellular structures show up at earlier times.

Evolution of flame instability for stoichiometric CH_{4} and H_{2}-enriched mixtures (20% and 30% vol.). _{0} = 12 bar, _{0} = 298 K. Window dia. 65 mm.

As suggested by Law _{cr} for the onset of instability.

_{cr} as a function of the starting pressure, for different mixture compositions. All the flames at _{0} = 3 bar show a laminar behaviour, hence the lack of data points for this case.

At _{0} = 6 bar, CH_{4} flames show the appearance of cellular structures when the flame approaches the chamber wall: these points are greyed-out, since they are likely influenced by additional phenomena, like flame-wall interaction.

These results show that increasing the pressure, the critical radius gets smaller: the resulting picture is of a flame that departs earlier from the laminar regime, and mostly develops under a wrinkled regime. Adding H_{2} to CH_{4} further reduces _{cr} (_{2} to CH_{4} reduces _{cr} by 24% at 12 bar and by 21.5% at 18 bar.

The morphological analysis appears to confirm the trends from the flame stretch analysis. As shown in _{cr} exhibits a reasonable correlation with the Markstein length _{b}.

As far as the observed instabilities are concerned, it is well established that flame cellularity can be hydrodynamic and thermo-diffusional in nature (if body-force effects are absent).

Critical radius for the onset of flame instability as a function of the starting pressure, for stoichiometric CH_{4} and H_{2}-enriched mixtures at room temperature.

Critical radius for the onset of flame instability

Hydrodynamic instability is caused by the density difference across the flame. It is expressed by the thermal expansion ratio of the burned to the unburned mixtures, and is always present for all flames [

Thermo-diffusional instability originates from the diffusive disparity of heat conduction from the flame and reactant diffusion towards the flame; it may not be present, if the flame is equidiffusive [

In the case of a spherical expanding flame, cellular instability is initially suppressed by the strong curvature-induced stretch, associated with the corresponding small flame radii. As the flame expands, the stretch decreases, until a condition is reached in which cell development can no longer be suppressed and cells suddenly appear over the flame surface. This state depends on the combined effects of the hydrodynamic and diffusional–thermal instabilities.

The above-described transition can be expressed in terms of the critical Peclet number, obtained scaling the critical radius _{cr} by the laminar flame thickness δ_{l}. An expression has been proposed of _{cr} as the sum of two terms, corresponding to hydrodynamic and diffusional–thermal instabilities [

Being known _{cr} and _{b}, the comparison can be drawn between the Markstein number (defined as _{b}/δ_{l}) and _{cr}

Actually, in the present conditions, expressing the comparison in terms of non-dimensional parameters does not add to a better understanding of the phenomena.

Critical Peclet number

As shown in _{cr} suggests the flames are equidiffusive in nature [_{cr} to increase with

The described behaviour prevents a straightforward identification of the role of the hydrodynamic and thermo-diffusive terms in the global _{cr}. Pending a deeper theoretical analysis, a possible explanation of this apparent incongruity could reside in the different conditions in which _{b} and _{cr} have been evaluated: while the former is a parameter obtained in the isobaric phase of flame development, the latter was measured later, when the global pressure in the chamber was increasing. The unpredictability of the results could be due to the scaling by δ_{l}, since this parameter is meaningfully defined in the isobaric phase.

The effect of the initial pressure and of the H_{2} content on the combustion of CH_{4}-H_{2}-air mixtures was investigated studying spherical expanding flames. Laminar burning parameters (unstretched burning velocity, burned-gas Markstein length) and flame instability characteristics (critical radius for the onset of cellularity) were evaluated for mixtures with different H2 percentage (0%, 20% and 30% vol.), equivalence ratio _{0} = 293÷305 K and initial pressure _{0} = 3÷18 bar.

The obtained results allowed to assess quantitatively the effect of pressure and of H_{2} amount: the laminar burning velocity was found to decrease with the former and increase with the latter. The flame stability decreased when any of the two parameters was increased.

The laminar burning velocity and the Markstein length were found to be in good agreement with published data, wherever available. As a matter of fact, the present results extend the data published so far in literature, as far as high-pressure, stoichiometric H_{2}-enriched mixtures are concerned.

In agreement with the observed behaviour of the Markstein length, the results on flame cellularity highlight the increasing relevance of the phenomenon at high pressures and/or for significant concentrations of hydrogen.

The main findings can be summarized as follows:

If the initial pressure is increased, the laminar burning velocity decreases and the Markstein length becomes negative. In the case of CH_{4}, when _{0} is raised from 3 to 18 bar, _{l}_{0} decreases by ~40%. In the same conditions, _{b} shifts from about 0.20 to −0.07.

If H_{2} is added to CH_{4}, the burning velocity increases. At _{0} = 3 bar, _{l}_{0} increases by ~25% if the amount of H_{2} in the mixture is 30%. The Markstein length of H_{2}-enhanced mixtures is shifted to smaller values, if compared to pure CH_{4}, and becomes negative at _{0} > 6 bar.

The behaviour of _{l}_{0} _{0} follows a power law, with exponent β = −0.45 for CH_{4}. The magnitude of β decreases with the amount of H_{2}.

The critical radius for the onset of cellularity was found to decrease when either the pressure or the H_{2} content in the mixture were increased. At _{0} = 3 bar, regardless of the amount of H_{2}, no sign of instability was observed; at _{0} > 6 bar, the flame get increasingly unstable with the amount of H_{2}. The critical radius shows a good correlation with the Markstein length.

The present findings offer a quantitative frame of reference for the burning properties of CH_{4}-H_{2}, highlighting the specific features of the combustion process in condition typical of i.c. engines.

flame area (mm^{2})

Lewis number

_{b}

burned gas Markstein length (mm)

Markstein number (_{b}/δ_{l})

pressure (bar)

_{cr}

critical Peclet number (_{cr}/δ_{l})

_{cr}

critical flame radius (mm)

_{u}

cold flame front radius (mm)

temperature (K)

_{l0}

unstretched laminar burning velocity (cm/s)

_{s}

stretched flame speed (m/s)

_{s0}

unstretched flame speed (m/s)

flame stretch rate (s^{−}^{1})

pressure index in Equation (11)

temperature index in Equation (11)

equivalence ratio

gas density (kg/m^{3})

_{l}

laminar flame thickness (mm)

kinematic viscosity (m^{2}/s)

dynamic viscosity (kg/m·s)

initial

burned gas

laminar

reference

unburned gas

The research was partially supported by the Italian Ministry of Economic Development within the framework of the Program Agreement MiSE-CNR “Ricerca di Sistema Elettrico”. Discussions with Natale Rispoli of Istituto Motori-CNR about mathematical analysis were very helpful and highly appreciated.

_{4}/air premixed flames at high-pressure and high-temperature

_{4}-air mixtures by the three modes of the ignition spark

_{2}/O

_{2}/inert mixtures up to 60 atmospheres