Tulip flame - the mechanism of flame front inversion

Combustion and Flame 161 (2014) 3051–3062

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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e

Tulip flame - the mechanism of flame front inversion Bogdan Ponizy ⇑, Alain Claverie, Bernard Veyssière Institut Polytechnique de Poitiers Pprime, UPR 3346 CNRS, ENSMA, BP 40109, 86961 Futuroscope-Chasseneuil du Poitou, France

a r t i c l e

i n f o

Article history: Received 21 March 2014 Received in revised form 1 June 2014 Accepted 3 June 2014 Available online 8 July 2014 Keywords: Flame propagation Tulip flame

a b s t r a c t The paper explains the mechanism of tulip flame formation in horizontal combustion chambers closed at the ignition end. The explanations are based essentially on the PIV images and the direct visualization of the process. The obtained results demonstrate that the tulip flame is a purely hydrodynamic phenomenon which results from the competition between the backward movement of deflected burned gases expanding from the lateral flame skirts and the forward movement of unburned gases accelerated in the phase of finger-shaped flame. In some configurations a supplementary global movement imposed by the confinement (for example: acoustic waves) is superposed on the two above mentioned, and modifies the parameters of the process. The results also prove that the intrinsic instabilities of the flame front (Rayleigh–Taylor, Richtmyer–Meshkov or Darrieus–Landau) are not involved in this process. The convex shape of the flame front has no influence on the phenomenon. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction The so-called tulip flame is a particular shape of the flame front with inverted curvature, which can be often observed during the laminar flame propagation in elongated, closed or half-open (at the end opposite the ignition) combustion chambers. The process of flame propagation in such a chamber was described by many researchers and will be discussed in detail later in the paper. Here we just mention its four essential phases: (a) hemispherical expansion of the ignition kernel; (b) axial expansion of elongated finger-shaped laminar flame front with continuously growing surface area; (c) rapid reduction of the flame surface area (when the flame skirt reaches the side walls) and deceleration of the flame front followed by the inversion of its curvature; (d) oscillatory propagation of the tulip flame up to the end of the chamber. In long chambers, a kind of tubes, the inversion of the flame front curvature can reverse and repeat itself a number of times in any one ignition. Since more than eighty years, when first images of tulip flame were published by Ellis and his colleagues [1–3], this phenomenon puzzles researchers in the domain of combustion and gives occasion to various interpretations and hypotheses. One of the earliest suggested an interaction with pressure waves generated by the flame. Indeed, Markstein [4,5] demonstrated that ⇑ Corresponding author. Address: Laboratoire de Combustion et de Détonique, Ecole Nationale Supérieure de Mécanique et d’Aérotechnique, 1 Avenue Clément Ader, BP 40109, 86961 Futuroscope Cedex, France. Fax: +33 5 49 49 81 76. E-mail address: [email protected] (B. Ponizy).

the inversion of the flame shape can result from the interaction of a curved flame front with a counter propagating planar shock wave. However, shock waves of pressure ratio 1.3 or higher, like those generated artificially in Markstein’s experiment, are hardly observed in the early phase of laminar flame propagation when the inversion of the flame front occurs, and Markstein himself indicated [5] that earlier investigation [6] with weaker, sound wave used as disturbance gave rather inconclusive results. Latter experimental works [7–13] put into evidence that a first significant pressure perturbation in the above described process of flame propagation may be produced (in the form of rarefaction wave) at the moment of the rapid decrease of the flame surface area due to the extinction of lateral flame skirt in contact with chamber side walls. Before this moment only a monotonous smooth pressure increase is observed. A series of weak compression waves generated in the phases of flame acceleration and then reflected at the chamber ends can only slightly modify the flame speed and the pressure growth in the chamber. There is no doubt that the rarefaction wave triggers subsequent acoustic oscillations but the question remains open whether this wave is directly involved in the onset of the tulip-shaped flame front. Leyer [7], on the basis of his experiments with short rectangular (10  4  2.5 cm3) closed chamber hypothesized that the interaction of the rarefaction wave and previously emitted compression waves may lead to the backward motion of the unburned gases which brings about the inversion of the flame front curvature. Measurements of instantaneous flow velocity performed by Dunn-Rankin et al. [13] and Starke and Roth [9] using laser Doppler

http://dx.doi.org/10.1016/j.combustflame.2014.06.001 0010-2180/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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anemometry did not permit to confirm or reject this hypothesis. They showed indeed that the far-field unburned gas motion was always positive but were less conclusive concerning the flow field in the vicinity of the flame front because the position of the front was difficult to determine precisely (the run-to-run variations in flame arrival time were about 10% in their experiments). However, numerical study [9,13,14] seem to indicate that the axial component of the unburned gas velocity remains positive, at least until the beginning of the inversion of flame front curvature. Furthermore, if the flame front inversion was linked with the interaction of pressure waves the time of this inversion, should depend on the chamber length and the acoustic losses, while experiments of Clanet and Searby [10] demonstrated that this time was mainly function of the laminar burning velocity and the radius of the chamber. Starke and Roth [9] relate the onset of tulip flame with Markstein’s experiments through the effect of Taylor instabilities. They consider that the deceleration in unburned gas velocity resulting from the reduction of the flame front area is comparable with that found behind the shock wave in Markstein’s experiments, and acts in similar way via the instability. This idea was later taken up by Clanet and Searby [10] who tried to provide a quantitative proof. On the basis of the Taylor oscillator equation coupled with a simple geometrical model for flame propagation they calculated the time of the tulip inversion occurrence and compared it with the measured one. The discrepancy between both results was about 10%. The model demands however some experimental data like the moment at which the flame touches the side walls of the chamber, position of the flame tip at this moment, variation in time of the position of trailing edge of flame skirt, which are not easy to determine with good precision. A completely different approach to the tulip flame phenomenon was proposed by Dold and Joulin [15] who believe that the tulip flame has little or nothing to do with the deceleration in gas velocity caused by the reduction of the flame area. By means of numerical simulation based on the modified Michelson–Sivashinsky equation they demonstrated that combined influence of front curvature, geometric nonlinearity and Darrieus–Landau hydrodynamic instability are sufficient to produce the inversion of the flame front. Darrieus–Landau instability itself or associated with other flame generated hydrodynamic instabilities is also put forward by some researchers to explain various results obtained in their numerical simulations without, however, convincing arguments. Bychkov et al. [16] suppose that the Darrieus–Landau instability is responsible not only for the first but also for all the subsequent inversions of the flame front curvature in a long half-open tube, while the experiments of Kerampran [11,12] proved that all the inversions except the first one result from the acoustic oscillations. In 1986, on the basis of experimental and numerical results with a closed rectangular chamber (38 mm  38 mm  155 mm), DunnRankin et al. [13] arrived to the conclusion that the initial perturbation of the convex flame front comes from a radial gradient in the axial velocity created by the confinement of the chamber. According to the authors, when the flame reaches the side walls the faster flow near the walls, analogous to a squish flow, pulls the flame ahead while the leading edge of the flame begins to decelerate approaching to the closed downstream end of the chamber. The initial distortion is unstable (Darrieus–Landau instability!) and continues to grow, forming a cusp which develops into the ‘‘tulip’’. In his more recent paper Dunn-Rankin [17] associates the flame front inversion rather with a recirculation in the burned gases observed in schlieren images. He supposes that this recirculation is generated by the curved flame itself because the expansion of burned gases normal to the convex flame surface deflects the flow behind the flame front toward the center line. Similarly

to his earlier conclusions, the recirculation acts here only as an initial trigger for the Darrieus–Landau instability which grows to the full tulip. Results of numerical simulation performed by Gonzales et al. [14] confirm the presence of a reverse flow in the burned gases behind the flame. They also exhibit the transversal velocity gradient along the flattened front, subsequent to the squish flow near the side walls and the deceleration of the central part of the flame. However, according to the authors those phenomena are so intertwined that it is difficult to distinguish causes from consequences. Similarly, their paper neither confirms nor excludes the participation of the Darrieus–Landau instability in the tulip front inversion. The authors consider that although this instability is compatible with the tulip shape, it affects the flattened front less rapidly than the confined flow field can do during tulip formation process. Different opinions concern also the role played by the dynamic viscosity and especially the wall friction. Marra and Continillo [18] find it important while other researches consider that this role is negligible [10,14] or even that an excessive wall friction precludes the tulip phenomenon [14]. Finally, two general conclusions may be drawn from the bibliographic analyse: – there are many possible causes of the tulip phenomenon but none is certain; – tulip flame is a very ‘‘complaisant’’ phenomenon. It can be reproduced by all presented models in spite of opposite assumptions (viscous or non-viscous flow, potential or rotational, compressible or incompressible). In this situation it seems clear that a unique way to elucidate definitely the process of flame front inversion in the tulip flame phenomenon consists in returning back to the experiment. Indeed, the past 20 years have seen a rapid development of planar imaging techniques which offer a much more profound insight into the instantaneous local structure of the flow than the point probing techniques like LDV. In particular, we were interested by TimeResolved PIV method which has achieved a good level of practical application to combustion engineering. We expect that the obtained results clarify definitely the mechanism of tulip flame formation.

2. Experimental set-up and procedure The experiments were carried out in cylindrical elongated plexiglas transparent chambers of various length (LC) and diameter (/C). The essential detailed analysis of flame transformation was performed with chamber /C = 0.1 m, LC = 0.785 m closed at both ends. Other configurations (/C = 0.1 m, LC = 0.385 m; /C = 0.1 m, LC = 0.320 m; /C = 0.07 m, LC = 1.99 m; /C = 0.07 m, LC = 3.0 m) were used to verify the influence of chamber dimensions. The chamber /C = 0.1 m, LC = 0.785 m was also tested with a simple opening at the downstream end (a kind of uncovered vent) or connected to a duct (like in ducted venting). The chamber /C = 0.1 m, LC = 0.320 m was tested only with a duct. The tube /C = 0.07 m, LC = 1.99 m was closed at both ends or opened at downstream end. The tube /C = 0.07 m LC = 3.0 m was used only as opened at downstream end. All the experiments were carried out with stoichiometric propane–air mixture at initial atmospheric temperature and pressure. Before each experiment the chamber was first evacuated and then filled to atmospheric pressure with the mixture prepared earlier and stored under pressure (the open chambers and those with the vents were, during this manipulation, closed by a cap which was next removed just before firing).

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Ignition was achieved by a small electrically (10 V) heated wire, placed on the axis, mainly near the closed, rear end of the chamber but some experiments were also performed with the ignition at the center of the chamber (chambers: /C = 0.1 m, LC = 0.785 m and /C = 0.1 m, LC = 0.320 m). The birth of the flame front was monitored by an ionization gauge IIGN located near the ignition (Fig. 1). Overpressure variations in the vessel were recorded by a KISTLER piezoelectric gauge (PG). The flame propagation inside the vessel and the tube was visualized by means of a CMOS high speed camera (Photron APX-RS3000). Detailed investigation of gas dynamics in the chamber was performed using a high-speed Particle Image Velocimetry system (FlowMaster LaVision) based on a dual cavity laser Nd:YLF (New Wave Research Pegasus). In our experiments the laser was run at up to 9 kHz with 4–20 ls delay between frames. The mentioned earlier camera Photron was synchronized with laser pulses through a timing unit box and the synchronization was triggered by the ionization gauge IIGN. The flow field investigation was performed mainly at 3 kHz (PIV) but in some experiments up to 4.5 kHz. The flow was seeded with particles of zirconium oxide (ZrO2) which diameter was inferior to 15 lm. As the high melting point of ZrO2 is estimated to 2715 °C, the gas velocity could be measured in both: fresh and burned gases. A special seeding strategy was adapted to obtain a correct and uniform powder screen inside the chamber. First, a small amount of powder was carefully distributed along the axis on the chamber ground. Next, the chamber was closed by a cap, the gas was evacuated and the mixture was slowly introduced. Just before the ignition the chamber was turned upside down around its horizontal axis and slightly taped. Considering the chamber with aspect ratio (LC//C) close to 8:1, an effort was made to perform PIV experiments with 20 cm length windows, leading to a resolution of 198 lm/pixel. The resulting PIV images in contiguous sections were then juxtaposed to reconstitute the global flow pattern. In order to precisely locate the

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investigated windows all the chambers were marked on their outside surfaces with vertical lines at intervals 10 cm, except for the first and the last sections which had 9.8 cm about. In this investigation, focus was made on the symmetry plane of the chamber; the maximum acquisition rate is then 5 kHz with 1024  512 pixels for each section. Vector calculation was obtained by means of multi-pass crosscorrelation beginning by cells of 64  64 pixels and down to cells of 32  32 pixels, the distance between velocity vectors was dx = 6 mm offering a relevant resolution to streamlines determination. The PIV expectations rely here mostly on a better understanding of the phenomenon than an accurate measurement of gas speed that would have required stronger optical magnification. Recordings were performed intentionally without filter on the camera, enabling collection of both: PIV signal (from Mie diffusion of powder) and flame front location (from integrated flame radiation). In this way the raw PIV images given by the camera exhibit the vectors of gas velocity as well as the flame front (if it is present in the investigated window at a given instant) seen in the background of PIV fields. By using different artificial colors in postprocessing we can fairly well discern both elements. However, when the images are next presented in gray mode the discernment may be more difficult, especially in zones saturated due to higher particle concentration (Fig. 2a). Moreover, in images reduced for publication the vector orientation, thus the gas movement in the chamber, is hardly seen. For this reason the raw images were treated as shown in Fig. 2b. First, manipulating the artificial background colors, the flame front was exposed and marked with black points. Next, in gray mode, the contrast and luminosity of images were increased in order to remove the saturated zones and expose clearly the velocity vectors. Finally, the different streamlines as well as their orientations were marked by the thick lines with arrows. There is no relation between the length of these lines and the values of flow velocities. The flow velocities correspond to the

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from IIGN Fig. 1. Experimental setup: IGN, ignition (electrically heated wire); VP, vacuum pump; MI, mixture inlet; V, valves; PG, pressure gauge; IIGN, ionization gauge; C, cradle; LS, dual cavity laser Nd:YLF; LSG, laser sheet generator; HEM, high-energy mirror; TuB, timing unit box; PIV cam, camera Photron APX-RS3000; COMP, acquisition computer.

Fig. 2. Example of post-treatments of PIV images: (a) original raw image in gray mode; (b) treated image.

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length of the original vectors and the reference value of 5 m/s is given in one of the image corner.

3. Results and discussion 3.1. Tulip flame formation in a closed chamber Images in Fig. 3 are a typical example of flame propagation in a closed elongated chamber of moderate aspect ratio (LC//C ffi 8). (Note: Two horizontal lines visible in each image are steel rods which held tight the end-plates of the chamber.) One can clearly distinguish the four phases mentioned in Introduction. The first image (t = 5 ms) corresponds to the hemispherical expansion of the ignition kernel. Three subsequent images – to the phase of axial expansion of laminar flame with elongated finger-shaped front and continuously growing surface area. Shortly before t = 27 ms the flame skirt at the lateral walls begins to vanish and the flame surface area decreases rapidly. Consequently, the flame front flattens and slows down. Next, starting from t = 33 ms about, we observe the characteristic inversion of flame front curvature. Once the tulip shape is fully settled (at about t = 43 ms) the flame continues to propagate in this form to the end of the chamber without any discernible oscillations. (Note: The last phase of propagation is very slow and lasts up to 210 ms about.)

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In the images from t = 64 ms to t = 88 ms we can also distinguish in Sections 3 and 2 the vortexes mentioned in [13,14,17]. Figure 4 displays the time evolution of the chamber pressure (P), the progress of two points of the flame front (Xc – on the axis and Xr – at the radius 38 mm) and the variation of the length of the flame skirt at the side walls (Ls), all obtained from the same run that the images of Fig. 3. The length of the flame skirt was determined as a distance between the most advanced point of the flame front and the last visible point of the flame skirt at the side walls. To better define the skirt the contrast and luminosity of images were increased compared to Fig. 3 (examples of such a treatment can be seen later in images of Fig. 11 from the chamber with central ignition). Anyway it is very difficult to determine precisely the beginning of the flame skirt extinction. Approximately, this moment corresponds to the intersection of the extrapolated curve Ls and the curve Xc in Fig. 4, it is at t  26.3 ms. (Note: The curve Ls in Fig. 4 corresponds to the flame skirt at the bottom of the chamber. The upper skirt vanishes slightly earlier due to the convection of burned gases.) Figure 4 shows that the inversion of the flame front curvature occurs with a practically constant mean position of the front. The central point moves back at the same speed than the lateral point advances. Another interesting feature is that the flame skirt shortens more slowly when the flame front changes to a backward pointing cusp. We can also mention the change in the slope of chamber pressure after the flame skirt begins to disappear, the effect already demonstrated by all precedent papers. Three first phases of flame propagation may be better understood with help of PIV images presented in Figs. 5–10. These images are taken from recordings of three runs, each focused on different two-section window (S1–S2, S2–S3 and S3–S4, see Fig. 3), but four to seven runs were performed for each window. The recordings which were chosen for presentation have the best concordance of the flame front timing with the run presented in Figs. 3 and 4. As mentioned in Section 2, the thick dotted curves in PIV images indicate the flame front position. The trailing edges of the flame skirt are however hardly seen in PIV images so they are not defined precisely in the presented figures. The two first images of Fig. 5 correspond to a very initial phase of flame propagation, usually defined as a hemispherical expansion of the ignition kernel. Actually, as these images demonstrate, for slow flames like that of propane–air mixture used in our

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Fig. 4. Pressure evolution and flame front progress in closed chamber /C = 0.1 m, LC = 0.785 m. P, pressure; Xc, position of the central point of the flame front (on the axis); Xr, position of the flame front point at the radius 38 mm; Ls, length of the flame skirt. Vertical dashed line T indicates the beginning of the flame front inversion.

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Fig. 5. Initial phases of flame propagation in closed chamber /C = 0.1 m, LC = 0.785 m (3000 PIVim/s).

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Fig. 6. Beginning of the backward flow in the chamber.

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Fig. 8. Flow pattern just before the beginning of flame front inversion.

experiment the hemispherical shape practically does not exist. The buoyancy force pushes quickly the upper part of the flame front towards the lateral wall. Consequently, just 3.3 ms after the ignition a great part of gases burned at the upper front expands first towards the center line of the chamber, to be finally deflected downstream in axial direction. At t = 9.3 ms almost all streamlines crossing the flame front are directed horizontally which means that the whole production of burned gases is used for acceleration of the flame front in axial direction. Indeed, as shown in Fig. 4, beginning from t  10 ms the flame speed and the chamber pressure increase exponentially. The two succeeding images of Fig. 5 (t = 21.3 ms and t = 26.7 ms) and the first two images of Fig. 6 (t = 28 ms) show the second phase of flame propagation with a classical fingershaped front. It is worth noticing that contrary to the suggestions of some authors, the convex flame front neither generates the velocity gradient in its vicinity nor deflects the streamlines. The burned and unburned gases in the near flame front field advance concertedly in axial direction. However, starting from t = 28 ms, a part of burned gases close to the rear end of the chamber is deflected back to this end. This zone of backwards deflected burned gases has nothing to do with the flame front. It appears simply because the production of burned gases had already stopped near the rear end (where the flame skirt is extinguished), so the burned gases produced in the last, still active part of the flame skirt can expand in the forward as well as in the backward direction. The process is initiated in the lower part of the chamber

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even if the upper flame skirt (as mentioned before) begins to vanish earlier. This is due to the convection of the burned gases produced at the bottom of the chamber (buoyancy effect), which

drives the gases produced in the upper flame skirt out from the rear end. However, when the flame skirt shortens, the zone of forward deflected gases moves away from the rear end and the backward flow becomes clearly established, the burned gases from the upper skirt are also driven back towards the rear end (see images for t = 29.3 ms and 30.3 ms). Obviously, as a part of burned gases produced in the flame skirts is now returned back to the rear end and does not more contribute to the forward motion of the flame, the flame front flattens and slows down (see curve Xc in Fig. 4). The image for t = 30.3 ms of Fig. 6 and both images for t = 30.7 ms of Fig. 7 are very important. They demonstrate that in this stage of the process the burned gases produced in the flame skirts are partially deflected forwards and partially backwards. This proves once again that the convex shape of the flame front has no influence on the backward flow created in the burning gases. Considering that the velocities of unburned gases before the flame front are clearly higher than the velocities of burned gases just behind the flame front (see images for t = 30.7 ms and 31 ms), and that they increase with the distance from the flame front, we can rather say that the accelerated earlier unburned gases try to drag the burned gases forwards and that there is a competition between the two (backward and forward) flows. The last image of Fig. 7 (t = 31 ms) and both images of Fig. 8 definitely confirm this hypothesis. (Note: Two juxtaposed images of Fig. 8 are from slightly different instants but approximately correspond to the same flow pattern in the chamber.) At t = 31 ms, in the zone ‘‘A’’, the burned gas coming from the upper wall are first deflected towards the rear end and then returned and dragged with the forward moving burned gases from the lower flame skirt. At t = 31.7 ms, in the same zone ‘‘A’’ the backward flow overcomes and the gases (also a part of those from the lower flame skirt) are now drawn out from the flame front, towards the rear end, which generates quite a complex flow structure just behind the flame front. Finally, one millisecond later (at t = 32.7 ms) almost all burned gases (except those near the walls) are deflected towards the rear chamber end (see first image in Fig. 9), while ahead the flame front all the unburned gases are still drawn forwards. Starting from this moment the flame front curvature begins to invert and the flame takes the tulip shape. We can notice that, together with the flame front, the unburned gases in the concave zone are also progressively drawn back by the reverse flow of burned gases (t P 35.7 ms). However, near the walls the influence of the reverse flow is less marked and the burned gases produced in the remaining part of flame skirt are still pushed perpendicularly towards the axis or even forwards, like before. This brings about an interesting effect already observed in Fig. 4: during some period the lateral parts of flame front advance, the central part moves back, the concave flame front is more and more slender but as a whole it stays practically at the same place indicated in Fig. 9 by the vertical ‘‘Y’’ line. It is clear from Figs. 7–9 that the process of flame front inversion is very dynamic. The streamlines change continuously their directions and the whole flow pattern varies significantly, first in the zone close to the flame front but progressively also in the rest of burned gases. Starting from t  44 ms we observe the formation of more stable vortexes behind the cusp of the flame front (the first image of Fig. 10 seems to indicate that they may be threedimensional). Later, similar complementary vortexes appear closer to the rear chamber end (Section S2 in Fig. 10). We can explain the formation of all these vortexes in the following manner. When the flame front advances, the space ‘‘offered’’ for the burned gases expanding into the reverse flow increases, so they can quietly slow down and stop, especially because only a part of burned gases is deflected backwards. However, starting from about 32 ms the flame stops but the amount of gases returned back with the reverse flow increases. The burned

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gas expanding with high velocity from the flame front and all directed backwards are not more able to rapidly slow down and stop in a fixed volume between the flame front and the rear chamber end. This brings inevitably about the formation of vortexes. Dunn-Rankin [13,14] supposed that these vortexes (visible also in Fig. 3) are generated by the convex shape of flame front and that they trigger the tulip inversion while, in fact, they are a consequence of this inversion. The presented PIV images show that in the examined chamber the flow structure behind the flame front, just before the inversion of the flame curvature, is very complex. This is probably due to the fact that the inversion takes place relatively far from the ignition point and the gas velocities reach quite high values before the inversion (more than 10 m/s for 21 ms < t < 28 ms). At the same time the lengths of the upper and lower flame skirts and the timings of their extinction are slightly different, which results in nonsymmetrical flow structure behind the flame front just before the inversion. Therefore it seemed interesting to verify the process of tulip formation in configuration with smaller aspect ratio (LC//C) where this asymmetry is less important. However, instead of choosing a shorter chamber we will examine the process in the same closed chamber but with central ignition. Figure 11 shows the images of the tulip flame formation obtained from direct visualization. (The contrast and luminosity of these images were treated to better expose the flame skirt, indicated in the images by the arrows ‘‘S’’). Figures 12 and 13 juxtapose, in turn, the PIV images taken from two windows S1–S2 and S2–S3 (see Fig. 11) of the right half part of the chamber. From the PIV images we can notice that the whole process is exactly the same as in the previously analyzed case with rear end ignition. However, as supposed, the flow structure is more symmetrical, the maximal reached flow velocities are clearly lower (especially in burning gases) and the inversion takes place closer to the ignition point, not far from the middle of each half chamber. Once again the images from t = 28.3 ms (Fig. 12) to t = 30.0 ms (Fig. 13) confirm without ambiguity that the flame front curvature has no influence on the backward deflection of burned gases. A virtual separation surface between the forward and backward deflected gases appears within the burned gases far from the flame front and then it approaches progressively the front. In two first images of Fig. 13 this virtual separation surface is very close to the flame front but

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Fig. 12. PIV images of flame propagation in closed chamber /C = 0.1 m, LC = 0.785 m with central ignition, up to the beginning of flame front flattening (3000 PIVim/s).

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Fig. 11. Tulip flame phenomenon in closed chamber /C = 0.1 m, LC = 0.785 m with central ignition (5000 im/s).

Fig. 13. PIV images of tulip flame formation in closed chamber /C = 0.1 m, LC = 0.785 m, with central ignition (3000 PIVim/s).

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still the burning gases just behind the flame front are drawn forwards by the unburned gases, while the burned gases farther from the flame front are drawn backwards by the reverse flow. The next image, for t = 32.0 ms, presents the flow pattern just before the beginning of the inversion. The center of the flame front becomes the surface of separation. After this moment the flame front is intercepted by the reverse flow and the inversion begins. The propagation of the flame in each half part of the chamber with central ignition is equivalent to the propagation in a twice shorter chamber with rear end ignition. Figure 14 shows indeed that the inversion of the flame front in such a chamber occurs at the same distance from the ignition point.

3.2. Tulip flame formation in a partially open chamber It is evident that if the process of tulip flame formation depends essentially on the competition between backward and forward flows, any change in confinement which modifies the flow conditions will influence this process. Figure 15 shows the phase of tulip inversion in the same chamber as examined in Section 3.1 but with an opening of diameter 36 mm at the end opposite to the ignition. One can notice that the inverted front is clearly less slender than that in the closed chamber but, above all, that the inversion begins farther from the ignition point (0.565 m, compared to 0.34 m for the closed chamber of Fig. 3) and later (38.4 ms, compared to 34 ms in Fig. 3). In fact, due to the opening, in the phase of finger-shaped front the unburned gases develop higher velocities and longer lateral skirt (in the case presented in Fig. 15 the maximal skirt length was about 0.4 m while it was only 0.28 m in the closed chamber of Fig. 3). Next, when the flame skirt begins to extinguish, the flame front slows down very little, so the zone of the reverse flow takes more time to reach the front. If the flame is strongly drawn forwards by unburned gases the backward flow just behind the flame front is not always necessary for the flame front inversion occurrence. Figure 16 a and b present PIV images from the Sections 5–6 and 7–8 (see Fig. 3) of the same chamber with an opening / = 36 mm but now connected to a duct of diameter 36 mm and length 1.6 m (a kind of a chamber with ducted vent). In this case, when the flame front flattens (t = 37.7 ms) the velocity of burning gases in the zone behind the front is reduced considerably but does not change its direction. (Actually, the reverse flow is observed farther from the flame front,

35.4 ms

37.9 ms

38.9 ms

43.7 ms

49.2 ms

Fig. 15. Flame propagation in partially open chamber (/C = 0.1 m, LC = 0.785 m, /opening = 36 mm) with rear end ignition (6300 im/s).

(a)

S5

31.7 ms

37.7 ms

40.3 ms

(b)

31.4 ms

S6

S8

S7

53.0 ms

34.9 ms

40.8 ms

45.4 ms

92.2 ms

Fig. 14. Tulip flame in closed chamber /C = 0.1 m, LC = 0.385 m with rear end ignition (6300 im/s).

Fig. 16. PIV images of tulip flame formation in partially open chamber (/C = 0.1 m, LC = 0.785 m, /opening = 36 mm) with rear end ignition and duct / = 36 mm, L = 1.6 m (3000 PIVim/s); (a) Sections 5–6; (b) Sections 7–8.

in Sections 4 and 3.) In the next image, for t = 40.3 ms, in the same zone appear weak local vortexes but, in general, the gas velocity is close to zero. On the contrary, the unburned gases move at high velocity towards the opening, sucked by the gas column in the duct. A high velocity of unburned gases and the decrease in speed of burned gases near the axis is enough to invert the flame front. Figure 16b shows that when the flame front approaches the opening (in Section 8) the acceleration of the unburned gases sucked into the duct deflects the streamlines and accentuates the concave shape but generally the inversion is not very deep.

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The PIV images of Fig. 16 demonstrate that likewise in this case the flame front itself does not generate the reverse flow and is not responsible for the tulip inversion. Figure 17 illustrates another interesting situation where the presence of an opening may promote the inversion of the flame front propagating in the direction opposite to the opening. The images presented in this figure were obtained from a partially open chamber but with smaller opening / = 16 mm (without duct) and central ignition. As in other partially open chambers, a privileged direction of gas movement is towards the opening, on the left. This increases the gas velocity directed to the opening and reduces that of opposite direction. Therefore, the flame propagating towards the opening flattens but, transported quickly by the unburned gases, has not enough time to invert. On the contrary, the flame propagating towards the closed end, on the right, slows down more quickly and undergoes the inversion slightly earlier and clearly closer to the ignition point than in the case of the closed chamber shown in Fig. 11. Finally, an example of some spectacular coupling between the flame front inversion and the gas movement resulting from the confinement is presented in Fig. 18 which corresponds to the shorter (0.32 m long), partially open chamber with duct (/ = 16 mm) and central ignition. Generally, with an aspect ratio of 1.6 for each half part of the chamber, such a chamber is too short for the tulip inversion occurrence (the value of 2 is considered as minimum) and indeed, before the left flame front reaches the opening (t  23.7 ms), there is no sign of tulip inversion or even flame front flattening. However, two milliseconds later, a secondary explosion in the duct (a phenomenon explained in Refs. [19,20]) generates a reverse flow of burned gases coming from the duct. This reverse flow folds the left flame front and pushes the right front (but mainly its central part) towards the rear end of the chamber. At t = 30 ms about, when the outward movement of the gases starts again, the right flame front is drawn back towards the duct, but now this backward movement affects mainly the gases in a zone closer to the lateral walls. The central part of the front still progresses towards the rear end. One might try to assimilate this specific inversion to Taylor instabilities but an analysis of gas movement in the chamber shows that the shape of the flame front results from a complex flow structure generated inside the chamber during this second outflow. Actually, due to a relatively small duct diameter (/duct = 16 mm compared to /C = 0.1 m), the reverse flow penetrates mainly near the chamber axis. When

IGN

IGN

19.5 ms

23.7 ms

25.7 ms

28.8 ms

30.3 ms

36.5 ms

47.8 ms

56.8 ms

Fig. 18. Flame propagation in partially open chamber (/C = 0.1 m, LC = 0.32 m, /opening = 16 mm) with central ignition and duct / = 16 mm, L = 1.6 m (6000 im/s).

the outward movement of the gases starts again the gas in this reverse flow slows down and stops but does not return in bulk to the opening. Only its outer layer is drawn back, as indicated by the arrows in image t = 30.3 ms of Fig. 18. On the other hand, the burned gases from the flame skirt near the walls first expand towards the axis and then are deflected towards the opening. Therefore, the gases expelled from the chamber (or rather sucked by the gas column in the duct) come essentially from an intermediate zone between the walls and the chamber axis, generating in this way new streamlines directed towards the duct, which bend in such a spectacular manner the flame front.

22.6 ms

3.3. Tulip flame formation in long tubes 26.8 ms

30.0 ms

36.2 ms

44.2 ms

Fig. 17. Flame propagation in partially open chamber (/C = 0.1 m, LC = 0.785 m, /opening = 16 mm) with central ignition (5000 im/s).

In all, up to now examined cases, acoustic waves had negligible influence on the process of tulip flame formation. They eventually manifested themselves on the pressure diagrams as perturbations of very small amplitudes. This was due to the relatively short chamber. Even in a partially open chamber, where the Helmholtz oscillations are usually present, the flame left the chamber before such oscillations start. In a long chamber however, a kind of tube, acoustic oscillations may dominate the process. The pressure measured at the closed end may change from positive to negative values many times (see Fig. 19), and consequently should change the gas velocity. As the inversion of the flame front is related to the backward movement of the gases, it is obvious that acoustic oscillations of sufficiently high amplitude may eventually bring about several

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(a)

2

0.25 0.2

33.0 ms

0.15

1.6 P199

0.1

33.7 ms

1.2

X (m)

P (bar)

0.05 0

34.7 ms

0.8

-0.05

34.7 ms

-0.1 -0.15

-0.25

0.4

P300

-0.2

XF199 0

10

36.3 ms

Ls199 20

30

40

50

60

0 70

38.7 ms

t (ms) 40.3 ms

Fig. 19. Pressure evolution and flame front progress in open tubes /T = 0.07 m. P199, pressure curves from three runs in tube LT = 1.99 m; XF199, flame front position in tube LT = 1.99 m (one of three runs); Ls199, length of the flame skirt in tube LT = 1.99 m (that of XF), P300, pressure variations in tube LT = 3.00 m. Thick short vertical lines indicate the beginning of flame front inversions in tube 1.99 m and the asterisk on pressure curve P300 indicates the beginning of the first inversion in tube 3.00 m.

inversions (the phenomenon which was noticed by many researchers). Figure 19 shows the evolution of essential parameters of flame propagation in an open tube /T = 0.07 m, LT = 1.99 m. Three pressure curves P199 correspond to the runs discussed later and shown in Figs. 20 and 21 but all the runs were quite well reproducible. The flame front positions (XF199) and the length of flame skirt (Ls199) in tube LT = 1.99 m were obtained from one of the three runs above mentioned. Mainly, the results from tube LT = 1.99 m will be discussed in the paper but one pressure curve from a run in tube /T = 0.07 m, LT = 3.00 m is also plotted in Fig. 19 in order to provide some supplementary arguments. In both examined tubes two flame front inversions take place (they are marked in P199 and XF199 curves by thick short vertical lines and by an asterisk on pressure curve P300) but the second inversion in tube LT = 3.00 m takes place beyond the limits of the diagram in Fig. 19. As can be seen, the beginning of the first inversion in tube LT = 1.99 m occurs just before the first pressure minimum of an evident standing wave generated in the chamber. Therefore, the next pressure increase indicates that the backward movement of all the gases (burned and unburned) is installed. This backward movement pushes the flame back towards the closed end. It should be stressed that the curve XF corresponds to the most advanced point of the flame front, which means that the whole flame moves backwards. (In the diagram of Fig. 4 from the closed chamber LC = 0.785 m we also observed the backward movement but only of the central point of the flame front, while the mean position of the flame front was constant.) The backward movement of unburned gases is probably responsible for a kind of indentation in the previously formed tulip flame, which can be seen in images for t = 38.7 ms and t = 40.3 ms of Fig. 20a. It is interesting to notice that, contrary to the usually observed cusped or slightly rounded tip of the tulip flame front, this indentation is accompanied with a flat, truncated end, alike in Markstein’s experiments with a shock wave interaction [4,5]. When the backward movement stops, and the outflow from the chamber starts again, the flame front is disrupted and accelerated towards the open end (see two last images in Fig. 20a). Between x = 1.6 m and x = 1.7 m a second inversion takes place but, as the images in Fig. 20b demonstrate, it has little to do with a thin sharp shape of the laminar flame front in the first tulip flame.

46.3 ms 52.3 ms 1.0 m

0.6 m

(b)

60.0 ms

62.7 ms

64.3 ms 1.5 m Fig. 20. Flame propagation in open tube (/T = 0.07 m, LT = 1.99 m): (a) first flame front inversion; (b) second flame front inversion. (3000 im/s).

If the second inversion is undeniably due to the backflow imposed by the acoustic standing wave (starting from that moment the pressure in the tube increases which mean that the gases return to the closed end), the question remains, whether the acoustic waves are also responsible for the onset of the first inversion or only for the above described indentation in the tulip flame. Once again we tried to provide an answer with help of PIV images but this time the problem was more complicated. First, the flame front inversion takes place farther, about 0.9 m from the ignition, so the synchronization of the events occurring in distant sections of the tube is delicate, especially when the investigated windows had to be reduced to 15 cm (because of smaller tube diameter). Second, in a long tube a correct and uniform powder screen is more difficult to obtain and the unburned gases of high velocity sweep the powder away from the tube. A slightly better result was obtained by putting more powder on the tube ground, not turning the tube upside down before the ignition, and allowing the powder to be progressively lifted up by the gas, but this produced a clearly non-uniform stratified powder concentration, thus the obtained PIV images were not very conclusive. Nevertheless, three images of Fig. 21 which present the flow pattern behind the already formed tulip flame are quite interesting. They show a zone of backward movement (visible mainly at the bottom of the tube) which advances from the closed end towards the flame front. On the other hand, an analysis of images from direct visualization indicates that up to t  35 ms (thus,

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the outflow from the tube (the pressure decreases) so the standing wave cannot be responsible for the flame front inversion. When the same long tube /T = 0.07 m, LT = 1.99 m is closed at both ends the flame undergoes multiple, repeated inversions indicated by the curve XF in Fig. 22. These inversions, except the first one which is similar to that described in the case of the open tube, are forced by the standing acoustic wave clearly evidenced by the pressure variations at the beginning (Pign) and the end of the tube (Pend). The frequency of these inversions increases as the flame advances in the tube. In the lapse of time shown in Fig. 22 this frequency changes from 85 Hz to 126 Hz, which corresponds to a change in mean speed of sound from 340 m/s to 502 m/s. Of course, as in the open tubes, the second and further inversions are different from the first inversion of a smooth laminar flame front. They occur in a disrupted or, later, turbulent flame in which the front surface becomes more and more difficult to define.

35.3 ms

35.7 ms

4. Conclusions 36.3 ms

0.91 m

0.76 m

Fig. 21. PIV images of tulip flame in open tube /T = 0.07 m, LT = 1.99 m (3000 PIVim/s).

already after the inversion) all the gases in the tube move towards the open end. Therefore, it seems that the process of flame front inversion begins, alike in partially open chamber presented in Figs. 15 and 16, by a deceleration in burned gases due to the extinction of the flame skirt. This deceleration generates a rarefaction wave (pressure decrease in Fig. 19) which progressively stops the outflow from the tube. As the velocity of unburned gases decreases, the burned gases are less drawn forwards and the backward movements becomes visible. (Note: If an acoustic wave was directly responsible for the flame front inversion we would observed in PIV images of Fig. 21 the backward movement in the whole tube at the same time, or coming from the open end.) The experiment with tube 3.0 m corroborates this hypothesis. The tulip phenomenon (asterisk on curve P300) clearly occurs in the phase of

1.2

1

P (bar), XF (m)

XF 0.8 s0

T

Pend

0.6 Pign

0.4

0.2

0 0

10

20

30

40

50

60

70

80

90

100

temps (ms) Fig. 22. Pressure evolution and flame front progress in closed tube /T = 0.07 m, LT = 1.99 m. Pign, pressure at the ignition end; Pend, pressure at the end opposite to the ignition; XF, flame front position; s0, beginning of the flame skirt extinction; T, beginning of flame front inversion.

All the presented experimental results demonstrate that the inversion of the flame front observed in the tulip flame phenomenon results from a simple hydrodynamic process. When the fundamental burning velocity is low (as in the case of the propane–air mixture) the flame is virtually transported by the gas and its shape depends on the flow structure. This structure is generated by the expansion of burned gases and especially the gases burned in the lateral flame skirt near the wall, which constitutes a major part of the flame front surface area. Initially, all burned gases expanding from the lateral skirt are deflected downstream, and push forwards the flame front together with the unburned mixture. When the flame at the walls begins to extinguish, its skirt shortens and the reaction zone moves away from the rear end of the chamber, the expanding gases can also be deflected backwards. The backward directed burned gases do not contribute to the forward movement of the flame front. Therefore the flame front slows down and flattens. At the same time the zone of reverse flow, which first appears near the rear end, enlarges quickly and approaches the flame front. A crucial situation takes place when the flame front becomes directly exposed to the action of two opposed flows: the reverse flow of burned gases and the forward directed flow of unburned, previously accelerated gases. The reverse flow (as deflected from radial direction) acts essentially near the axis, drawing back the central part of the flame front, while at the walls the flame is drawn forward by the unburned gases. In this way the tulip flame is formed. (It may be reminded that the reverse flow in burned gases was observed in experiments of Dunn-Rankin et al. (Refs. [13,17]) but, as mentioned in Introduction, they misinterpreted its origin and relationship with the flame front inversion.) The above conclusions are strictly validated (by PIV images) for the chambers of small and moderate aspect ratio. The results obtained with long tubes seem to indicate however that the same mechanism is also present in those configurations, but, in addition, the wave phenomena ought to be taken into account. Simply, the gas movement generated by the acoustic waves is superposed on the backflow of burned gases deflected from the flame skirt. (A partially open chamber of small and moderate aspect ratio can be considered as an intermediate case between the two mentioned configurations.) Finally, one may say that the tulip flame is an effect of superposition (in the zone close to the flame front) of three gas movement components: backward movement of deflected burned gases (present in every configuration but acting mainly near the axis), forward movement of unburned and burned gases (accelerated in the phase of finger-shaped flame front) and general movement imposed by the confinement (which includes a preferential movement due to an opening, acoustic wave phenomena, but also, for

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example, a reverse flow resulting from the secondary explosion in ducted venting). It should be stressed once again that the intrinsic instabilities of the flame front (Rayleigh–Taylor, Richtmyer–Meshkov or Darrieus–Landau) are not involved in this process. Indeed, the reverse flow which is responsible for the flame front inversion always starts in the zone close to the ignition point and not at the flame front. The convex flame front has no influence on the phenomenon. Only the lateral parts of the flame front with radial expansion of burned gases are necessary. Gonzales et al. [14] believed that the Darrieus–Landau instability is always present in tulip flame formation but the characteristic time scale of this instability is longer than the characteristic time scale related to the flow field effect, so this instability affects the flattened front less rapidly than the confined flow field. We suppose that even if both time scales were comparable a possible effect produced by the Darrieus–Landau instability would be much weaker than that resulting from the action of the reverse flow in burned gases. Dold and Joulin [15], on the basis of their theoretical model, emphasizes the role of Darrieus–Landau instability but their model completely neglects the structure of the far-field burned gas (the burned gases come to rest behind the flame). Note All the above conclusions are restricted to the flame front inversion occurring spontaneously during the flame propagation in

horizontal chambers closed at the ignition end. We do not consider vertical chambers in which the effect of buoyancy force may be important, or some cases of inversion forced by artificial, external factors (shock wave [4,5], multiple ignition points [14], etc.). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

[18] [19] [20]

O.C. Ellis, J. Fuel Sci. 7 (1928) 502–508. O.C. Ellis, H. Robinson, J. Chem. Soc. 127 (1925) 760–767. O.C. Ellis, R.V. Wheeler, J. Chem. Soc. 3215–3218 (1928). G.H. Markstein (Ed.), Nonsteady Flame Propagation, Pergamon Press, New York, 1964. G.H. Markstein, Proc. Combust. Inst. 6 (1956) 387–398. L. Ehret, U. Neubert, H. Hannemann, Z. Angew. Phys. 4 (1952) 126. J.C. Leyer, Rev. Inst. Fr. Pétrole 27 (2) (1972) 279–316. J.C. Leyer, N. Manson, Proc. Combust. Inst. 13 (1971) 551–558. R. Starke, P. Roth, Combust. Flame 66 (1986) 249–259. C. Clanet, G. Searby, Combust. Flame 105 (1996) 225–238. S. Kerampran, D. Desbordes, B. Veyssiere, Combust. Sci. Technol. 158 (2000) 71–91. S. Kerampran, Ph.D. thesis, Université de Poitiers, 2000. D. Dunn-Rankin, P.K. Barr, R.F. Sawyer, Combust. Inst. 21 (1986) 1291–1301. M. Gonzalez, R. Borghi, A. Saouab, Combust. Flame 88 (1992) 201–220. J.W. Dold, G. Joulin, Proc. Combust. Inst. 25 (1994) 450–456. V. Bychkov, V. Akkerman, G. Fru, A. Petchenko, L.E. Eriksson, Combust. Flame 150 (2007) 263–276. D. Dunn-Rankin, in: J. Jarosinski, B. Veyssiere (Eds.), Combustion Phenomena, Selected Mechanisms of Flame Formation, Propagation, and Extinction, CRC Press, 2008. F. Marra, G. Continillo, Proc. Combust. Inst. 26 (1996) 907–913. B. Ponizy, J.C. Leyer, Combust. Flame 116 (1999). 259–271 and 272–289. B. Ponizy, N. Henneton, A. Claverie, B. Veyssiere, Combust. Flame 161 (2014) 1348–1364.