Transient process of methane-oxygen diffusion flame-street establishment in a microchannel

Abstract

“Flame-street” is an interesting diffusion flame behavior in which a series of flame-segments is separately distributed along the mixing layer in a narrow channel. This experimental phenomenon was experimentally and numerically investigated with the focus on the steady-state, thermo-chemical flame structures in previous literature. In the present paper, the dynamic formation process of a methane-oxygen diffusion flame-street structure was simulated with a reacting flow solver developed based on the open-source framework OpenFOAM. By imposing a certain amount of ignition-energy near the channel outlet, a reaction-kernel was formed and bifurcated. Subsequently, three separate flames were consecutively generated from this kernel and propagated within the channel. The whole process was completed within 15 ms and all the discrete flames were eventually in a steady-state. Interestingly, different propagation features were observed for the three flame segments: The leading flame experienced a flame shape/type change from a tribrachial structure in its fast-propagating phase to a long, trailing diffusion tail after being anchored to the inlet. The successive flame had a much lower propagation speed, keeping its two wing-like (fuel-lean premixed and fuel-rich premixed) structure while moving toward its stabilization location, which was approximately in the middle of the channel. The last flame, after the ignition source was turned-off, was immediately convected a bit downstream, and eventually featured a similar two-branch-like structure as the second one. Moreover, chemical insights for the premixed and diffusion branches of the leading flame were also provided with the change of significance of some key elementary reactions focused on, in order to attain a detailed profiling of the flame-type transition. This paper is a first-ever one discussing the transient formation of flame-streets in literature and is believed to be useful for obtaining a comprehensive understanding of this unique flame characteristics from a dynamic point of view.

Graphical abstract

Keywords

micro-combustion / flame-street / diffusion flame / mixing layer / flame propagation speed

1 Introduction

Micro-combustion (combustion occurring in combustors whose dimensions are on the order of the flame thickness) has become a “hot” topic over the last two decades because of its ability to exploit hydrocarbon fuels which feature notably higher energy density as compared to electrical batteries. Micro-combustion is thus considered a promising technology for miniature power and propulsion devices [1–4]. Intensive and extensive fundamental studies have been conducted around the world, focusing primarily on various methods to maintain/enhance flame stabilities [5], as well as some interesting flame behaviors that are unique to combustors at micro-scales (e.g., flames with repetitive extinction and ignition [6,7], periodic [8] or chaotic [9] flame oscillations, weak flames [10], various flame patterns in 2-D planar [11] and 3-D radial channels [12], etc.).

Apart from the above-mentioned flame behaviors that were extensively studied, the “flame-street” structure is another exotic phenomenon that was first observed in experiments [13–17]. A long diffusion flame sheet in a narrow channel was observed to split into several separated flame segments with local extinction/re-ignition in between. However, due to the difficulties in performing spatially-resolved measurements for temperature and species fields at such a small-scale, experimental investigations were not sufficient to reveal underlying physical mechanisms for this special flame-structure formation. On the other hand, no numerical studies were reported for the flame-streets for more than 10 years after the experimental observation. Not until recently were a very limited number of numerical studies published. Mohan and Matalon [18] established a simplified model with the assumptions of constant gas density, constant thermodynamic/transport properties, one-step reaction, and qualitatively reproduced the experimental observations. Kang et al. [19] and Mackay et al. [20] simulated the flame-street phenomenon with more realistic physical models and more detailed chemical kinetics, using their incompressible-like and fully compressible reacting flow code, respectively. Kang et al. [19] answered the question proposed by Prakash et al. [16] regarding the specific structures of the two-branch “hook”-like flame-segments in their experiments while the effects of combustor length/width influences as well as the ‧H and ‧O radicals wall quenching on flame behaviors were assessed by Mackay et al. [20]. Very recently, Sun et al. [21] parametrically studied the influence of some operation conditions (wall temperatures, inflow rates, and global equivalence ratios) on flame behaviors and the burner performances.

In this paper, for the purpose of a more comprehensive understanding of this unique flame behavior, the previous work on the steady-state structure of flame-street was extended to investigate the transient establishment of the methane-oxygen flame-street phenomenon starting from the flame ignition to its final steady-state, which will facilitate in explaining the formation of this specific flame structure from a dynamic point of view, by placing the focus on the quantitative description of this process from the aspects of flame propagation speed, flame-type transition, and chemistry profiles during the upstream propagation period of each flame-segment.

2 Numerical approach

Figure 1 shows the computational domain and flow directions of methane and oxygen streams of the 30 mm × 5 mm × 0.75 mm micro-combustor, which is identical to that used in Refs. [19,21], and is consistent with the dimensions of the Illinois’ combustor [13–16].

The micro-flame propagation problem was simulated using the transient, low-Mach number, and reacting flow code developed based on the open-source framework OpenFOAM. A brief flowchart of the loop structure of the numerical tool is demonstrated in Fig. 2. A detailed description of the numerics for this solver with governing equations solved as well as the spatial and temporal discretization schemes used can be found in Refs. [19,22].

The 32-species and 177-reaction chemical kinetics GRI-Mech 1.2 [23] was used, which was capable of accurately reproducing most of the methane combustion features such as heat release, flame speed, ignition delay, etc. On the other hand, as compared to the most complete (53-species and 325-reaction) mechanism GRI-Mech 3.0 [24] that also included propane and nitrogen chemistry, the use of GRI-Mech 1.2 to simulate methane-pure oxygen flames in this paper avoided some dispensable and non-essential species/reactions while was still able to provide detailed information regarding the production/consumption rates of critical species associated with certain key intermediate elementary reactions. Therefore, it was considered to achieve a good compromise between an accurate prediction of flame behaviors and a considerable saving in expensive computational costs. The boundary conditions (BCs) for the simulation were set as follows:

The inflow streams of CH₄ and O₂ were introduced at a room temperature of T₀ = 300 K, with flow rates of 100 standard cubic centimeter per minute (sccm) and 200 sccm respectively. Fully developed velocity profiles were set for both streams. Atmospheric pressure and zero-gradient conditions for all other variables were set at the channel outlet. No-slip BCs were applied at the combustor walls while different thermal conditions were prescribed for the top/bottom (constant and uniform temperature distribution of T_w = 800 K) and front/back sides (adiabatic), respectively. A uniform mesh with a mesh size of 0.05 mm was used in the computation. As the grid refinement study in Ref. [19] indicate, this mesh level was capable of offering sufficiently accurate results. Validation works were already performed, showing a good predictability of the flame features and behaviors against the experiment, which could be found in Ref. [21].

3 Numerical results

3.1 Overview of the flame-street formation process

At the start of the flame-street formation process, an energy input of 0.7 × 10¹⁰ W/m³ was exerted in a small zone (called the “ignition-zone” in this paper) near the channel outlet (x = 25.5–26.5 mm, y = 2–3 mm, z = 0.075–0.675 mm), in order to trigger the flame. This means of ignition can be viewed as to correspond to the experimental method of using an electrode discharge or a torch. It should be pointed out that the above-mentioned ignition-energy density and ignition-zone area were not selected arbitrarily. In fact, the integrated heat addition over this specific zone was approximately 20% of the total combustion heat release rate (HRR) for the steady-state flame-street (4.2 W versus 19.6 W). A smaller energy input (either lower energy density or ignition-zone area) was found not capable of igniting the flame within a reasonably short period of time (approximately 0.1 ms in this paper) while a larger energy input could lead to much higher acoustic perturbations in the flow. As exhibited in Fig. 3, a reaction zone was formed within a short time (approximately 0.1 ms) under the effect of externally imposed heat. When compared to the “cold” condition (t = 0 ms), it can be found that the stoichiometric mixture fraction line Z_st (a reaction-free parameter, equaling to the fuel mass fraction for an unburnt fuel/oxidizer mixture under stoichiometric conditions [19]) now protrudes locally near the ignition zone toward the fuel side (minus y direction), owing to the spatial redistribution of the streamlines around the reaction-kernel: the fuel and oxidizer streams diverge span-wisely from the ignition point while the y-axis velocity components were found to have greater absolute values at the fuel side than its oxidizer counterpart, thereby locally shifting the stoichiometric point slightly downwards.

At t≃ 0.2 ms, the reaction zone trifurcated into three parts. One was stabilized at the ignition location owing to the continuous heat addition. Another reaction front swept downstream the channel, consuming the unburned gas there. After a relatively short movement distance, it was then swiftly blown out of the combustor. The other was an upstream-moving flame with a fast propagation speed. During its propagation, it first exhibited a tribrachial structure (to be discussed quantitatively in Section 3.2) while its front progressively became increasingly narrower. Within less than 2 ms, the flame already reached the most upstream location and was thereby anchored to the channel inlet, with its shape turning into a long and thin sheet. At t≃ 4.0 ms, a new flamelet started to form in the ignition zone, subsequently dislocated the heat-addition-sustained reaction kernel and then propagated upstream. This flame moved much slower than the leading one which had been now already anchored). This can be attributed mainly to the much lower concentrations of fuel/oxidizer upstream the flame front, since a considerable amount has already been consumed by the leading flame. After about 6 ms (t≃ 10 ms), it reached a certain upstream location of the channel (x≃ 12.5 mm) and was eventually stabilized.

At t = 13.9 ms, the ignition source was switched off. After this point, the reaction kernel turned much thinner immediately, and was then convected a bit downstream to its final stabilization location within a short period of time. This is understandable considering that without external heat addition, its burning velocity decreases so that a new balance between the flow convection and burning velocity has to be established at a more downstream location. Finally at t = 15 ms the flame-street formation process was completed. Three stable but discrete flame segments (a leading, long tail plus two much shorter ones) can now be observed in the channel.

3.2 Flame-types transition

As mentioned earlier, the leading flame has experienced a shape transition during its propagation upstream. More detailed information can be found in Fig. 4 by plotting HRR contours at three instants of t = 1.0 ms, 1.6 ms, and 2.0 ms, which respectively correspond to the instants before, coincident with and after the shape transition. The terms RPF, LPF, and DF in the Fig. 4 denote the “rich premixed flame” wing, “lean premixed flame” wing, and trailing “diffusion flame,” respectively. The color bar range in Fig. 4 is adjusted for the purpose of visual distinction as the diffusion branch is much weaker than its premixed counterparts. For a typical tribrachial (triple) flame encountered in a diffusion mixing layer, the above-mentioned branches that are extending from a single point are the three essential components [25]. Span-wise profiles of the HRR, species mass fractions, and the parameter flame index (FI) at the locations 2 mm behind each flame edge point (x = 13.5, 4.2 and 2.0 mm, respectively) are also illustrated. Note the flame index (\mathrm{FI}=\cos \theta ={\displaystyle \frac{\nabla Y_{{\mathrm{CH}}_4}\cdot \nabla Y_{{\mathrm{O}}_2}}{\left|\nabla Y_{{\mathrm{CH}}_4}\right|\left|\nabla Y_{{\mathrm{O}}_2}\right|}}), taking into account the included angle between the gradients of fuel and oxidizer mass fractions [19], is typically used to tell the types of the flame — premixed (FI>0) or diffusion (FI<0). The points P1, P2, P3, P4, P5, P6, and P7 are the intersections between the sliced lines and the flame fronts of each branch (the local maximum HRR points).

At t = 1.0 ms when the flame was in its fastest burning phase, a tribrachial flame structure was observed. It was noticed that the diffusion branch was much weaker than its premixed counterparts, and was inclined to the fuel-rich side, similar to what was observed by Yamamoto et al. [26]. This trailing diffusion sheet was not completely aligned with the Z_st line, while they were gradually in a closer proximity to each other with the increase of downstream position, i.e., the span-wise distance between the two lines decreased as the stream-wise location increased. It is worth pointing out that in this stage, not all the whole DF sheet fell into the diffusion region (at least in terms of the rigorous FI indicator). The upstream part of the DF sheet, especially in the place near the “root,” was locally of the premixed type, e.g., the FI value at the point P2 was still larger than 0.

The situation changes notably as the flame propagated further upstream. At t = 1.6 ms, two premixed branches shrank by a large extent in their lengths, and got weakened in terms of the heat release rates. At the same time, the diffusion branch was found to be closer to the constant Z_st line as compared to the case at t = 1.0 ms. The local HRR peak at the DF branch (P5) grew considerably, and exceeded the peaks (P4 and P6) in the premixed wings. More importantly, this point has experienced a FI value-transition: it evolved from a positive FI for P2, went across a turning point, and now lied in the diffusion region with a negative FI for P5.

As the flame eventually reached the channel entrance, the diffusion branch got strengthened and turned into the only one that was able to be “visually” identified. Its premixed counterparts, however, were continuously weakened during the propagation of the flame in its last stage and became difficult to observe. Therefore, this leading flame is mainly a diffusion-type thin sheet, extending stream-wisely to quite a long distance.

The second upstream-propagating flame basically kept its main shape unchanged, as seen at t = 5.0 ms, 7.0 ms, and 12.0 ms in Fig. 5. The flame always consisted of a fuel-lean and a fuel-rich premixed wing, presenting a “new moon”-like flamelet structure, although it turned smaller and narrower as it gradually approached its final steady-state. The mechanisms of the stabilization of this type of flames were described by Daou et al. [27] and Cha et al. [28] (referred to as “tailless triple flames” and “short-length” flames, respectively): At low mixture fraction gradients (more downstream locations in the present channel), the trailing diffusion branch of a tribrachial flame can become relatively thick. As a result, it suffers substantially from heat losses and is then thereby extinguished. In contrast, the thickness of the premixed branches is almost independent of the mixture fraction gradient, which explains their survival in the presence of heat losses (at least at the present moderate level). Subsequently, the fresh reactants infill the quenched region. After a certain stream-wise distance, a new flame (the third flame in this paper) ignites in the downstream part of this trailing region owing to the high wall temperature (800 K in this case). It should be mentioned that the train of flame-segments can be “infinite” as long as the channel is sufficiently long, as explained in the above-discussed mechanism.

A flowchart that summarizes the whole transient formation process of the flame-street phenomenon is illustrated in Fig. 6.

3.3 Flame propagation speeds

The local propagation speeds S_loc of the two upstream-propagating flames (1st and 2nd in Fig. 7) were inspected. S_loc is the flame-tip moving velocity along the Z_st line relative to the projection of local gas flow velocity vector along Z_st.

As can be found in Fig. 7, S_loc,1st generally decreases as the flame moves more upstream while S_loc,2nd shows a non-monotonic trend: increasing first with time, and then gradually decreasing. Compared to the second upstream-propagating flame, the leading one has a much larger S_loc except for its last stage near entrance-anchoring. The main reason for this was that the upstream portion of the channel was filled with fresh reactants for the propagation of the first flame, leading to a rapid fuel/oxidizer consumption rate. However, during the propagation of the second flame, the first one had already been anchored to the channel inlet. As a result, its products considerably diluted the reactants prior to the second flame, which would decrease S_loc, 2nd to a large extent. It is also worth noting that at t≃ 1.5 ms, this flame has experienced a sudden decrease in its propagation speed, which was exactly the time point marking the beginning of the flame-type transition. After a relatively flat plateau for which the reaction intensity of the diffusion branch was significantly elevated while those of both the fuel-rich and fuel-lean premixed wings continuously got weakened, the flame propagation speed decreased again at t = 1.7 ms owing to the encounter of the “cold” fresh gases very near the inlet.

3.4 Chemical insights during flame-street formation

Finally, in order to attain a more comprehensive understanding of the flame-types transition during the flame-street formation from a chemical point of view, some critical elementary reactions in the GRI-Mech 1.2 [23] chemical kinetics were inspected for the above-mentioned seven local HRR points of P1, P2, P3, P4, P5, P6, and P7. Figures 8, 9, and 10 show the heat release rates at the seven points from some elementary reactions which contribute the largest proportions (each reaction accounts for at least 5%) of the total HRR (sum of heat release rates by all elementary reactions).

For the RPF branch, listed reactions that dominated the combustion heat release were similar for P1 (fast-burning phase) and P4 (flame type-transition phase), although the most predominant reaction shifted from “R10: O+ CH₃ ⇌ H+ CH₂O” for P1 to “R158: 2CH₃ (+ M) ⇌ C₂H₆ (+ M)” for P4. Moreover, some acetylene-participating (“R23: O+ C₂H₂ ⇌ CO+ CH₂”), methylene (in the singlet state)-participating (“R144: CH₂(S) + O₂ ⇌ H+ OH+ CO,” “R145: CH₂(S) + O₂ ⇌ CO+ H₂O”) and ethynyl radical-participating (“R171: C₂H+ O₂ ⇌ HCO+ CO”) reactions have become relatively insignificant as the flame propagates more upstream.

For the LPF branch, listed reactions and their relative contributions to the total HRR between the two phases (for P3 and P6) were even more similar. The only difference was that the reaction “R4: O+ HO₂ ⇌ OH+ O₂” turned into more important in contributions to the total HRR when the flame underwent type-transition.

The changes in chemistry profiles for the DF branch during flame propagation were much larger. When comparing the three points (P2 → P5 → P7), it was found that although the reaction “R10: O+ CH₃ ⇌ H+ CH₂O” that was a critical step in the oxidation pathway from CH₄ to CO₂ (CH₄→ CH₃→ CH₂O → HCO → CO → CO₂) [29] always played the most dominant role, the second crucial reaction in contributing heat release “R127: CH+ H₂O ⇌ H+ CH₂O” in the fast-propagation stage (P2) and the flame-type transition stage (P7), however, became much less important after the anchoring of the flame. Other weakened reactions in terms of the relative contributions to the total HRR included “R58: H+ CH₂O ⇌ HCO+ H₂,” “R90: OH+ C ⇌ H+ CO,” “R92: OH+ CH₂ ⇌ H+ CH₂O,” “R153: CH₃(S) + CO₂ ⇌ CO+ CH₂O,” and the endothermic reaction “R52: H+ CH₃ (+M) ⇌ CH₄ (+M).” On the other hand, a few reactions were also strengthened, such as “R84: OH+ H₂ ⇌ H+ H₂O” which was directly related to hydrogen radical formation and water production, and “R98: OH+ CH₄ ⇌ CH₃ + H₂O” which was one of the conversion pathways from methane to methyl radical.

For the second upstream-propagating flame, chemistry profiles of the important elementary reactions to the HRR contributions were found quite similar at the same branch (P₈, P₁₀, and P₁₂ for RPF, and P₉, P₁₁, and P₁₃ for LPF in Fig. 5) throughout the whole flame propagation period (not shown here).

4 Conclusions

The dynamic establishment process of the CH₄-O₂ flame-street phenomenon in a microchannel was first-ever numerically simulated and reported in this paper. The main conclusions are summarized as follows:

The whole process that was completed within 15 ms consisted of several key events that occurred consecutively: heat addition and reaction-kernel initiation → reaction-kernel trifurcation → leading flame propagation and type-transition → second flame generation and propagation → ignition source removing, and third flame evolution.

Different propagation features for the three flames were observed. The leading flame underwent a flame-shape and-type transition from a tribrachial structure in its fast-burning stage to a long, trailing diffusion sheet after the anchoring to the channel entrance. The successive flame with two premixed wings was observed to have quite a lower propagation speed, keep its main shape/structure unchanged, and be eventually stabilized at a certain stream-wise location of the channel. The third flame which had a similar two-branch-like structure as the second one, was stabilized at a downstream location slightly away from the ignition source.

Chemical insights for the three branches (RPF, LPF, and DF) of the leading flame during its propagation and type transition were provided. Elementary reactions that dominated the combustion heat release were similar during the whole process for the premixed wings, but were found different at various stages for the diffusion tail. After experiencing the flame-type transition and being anchored to the inlet, the carbon-abstraction reaction of methylidyne got weakened significantly while a few hydrogen radical formation and water production reactions, were in contrast, strengthened.

The time-accurate information with quantitative physical/chemical analysis is needed to comprehensively understand the transient characteristics of the flame-street phenomenon. Apart from the flame-ignition process discussed in this paper, other flame dynamics (e.g., flame dynamic response to the change of inlet conditions, flame repetitive- and self-oscillations at some operation conditions, etc.) will be investigated in the future.

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