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Flame propagation and combustion modes in end-gas region of confined space
Combustion and Flame 190 (2018) 216–223
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Flame propagation and combustion modes in end-gas region of confined space Lei Zhou, Lijia Zhong, Jianfu Zhao, Dongzhi Gao, Haiqiao Wei∗ State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China
a r t i c l e
i n f o
Article history: Received 15 August 2017 Revised 21 October 2017 Accepted 8 December 2017
Keywords: Flame propagation Combustion mode Confined space Shock wave
a b s t r a c t Flame propagation is investigated in a designed experimental apparatus equipped with a perforated plate in a constant volume chamber. The effect of the perforated plate is to generate a rapidly accelerating flame based on Bychkov work (Bychkov et al. 2008), in which the flame across the obstacle will becomes a strong jet flame. The experiment was conducted with a hydrogen–air mixture at different conditions. In this work, six different turbulent flame propagation and combustion modes were clearly observed at various conditions in our designed experiment. In the presence of perforated plate, the turbulent flame formed through the perforated plate may perform six types of turbulent propagations at the end gas regime. These types form through the interaction between the flame and the shock or acoustic wave and because of the limited effect of the wall in confined space. The six forms are as follows: (1) a normal flame propagation with a low flame front tip velocity and combustion rate; (2) a weak pulsation propagation with weak fluctuation due to the acoustic wave; (3) a pulsation propagation only with a visible reflected shock wave; (4) a strong pulsation propagation with a forward shock wave and shock reflection; (5) a continuously accelerating flame propagation due to auto-ignition of the unburned mixture between flame front and shock wave, which also leads to strong pressure oscillation; and (6) a violent pulsation propagation with a multi-shock wave leading to end gas auto-ignition with large pressure oscillation. © 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Background and introduction Turbulent flame is one of the most interesting parts of combustion physics and turbulence research as evidenced by analytical, experimental and computational studies in the past few decades [1–8]. Much detail can be found in comprehensive reviews on turbulent and other types of flames [9–12]. For example, some of these studies examined the turbulent premixed flame speed in a nearly constant-pressure apparatus with fans, which presented the self-similar propagation of a turbulent flame [6,13,14]. In other studies [15–19], they showed that turbulence corrugates the flame front by increasing the burning rate and facilitating flame acceleration, which boosts the process of deflagration to detonation transition (DDT). Of particular interest is turbulent flame acceleration and propagation in confined space. As turbulent combustion in confined space, i.e., confinement, occurs, flame acceleration and expanding propagation will generates a series of compression waves with considerable amplitude. In turn, confinement significantly influ-
∗
Corresponding author. E-mail address: [email protected] (H. Wei).
ences the turbulent flame brush and wrinkles it. Therefore, in flame propagation the flame–shock/acoustic interactions play a vital role and finally determine the turbulent flame development and combustion phenomena. Understanding the turbulent flame propagation mechanism involving flame–shock/acoustic interaction in confined space not only is of fundamental significance but also contributes to practical applications such as spark-ignition engines with knock phenomenon and explosion hazards in coal mine fields. There have been some attempts to explain flame acceleration and flame–shock/acoustic wave interactions. Of course, flame acceleration is strongly relevant to flame–shock/acoustic interactions. Based on previous explanations, there are four primary aspects to flame acceleration and flame-shock/acoustic interactions: 1) flame self-acceleration for expanding spherical flame, 2) flame acceleration mechanisms in DDT, and 3) flame–acoustic interaction, 4) flame–shock interaction. Law and co-workers [6] comprehensively investigated the turbulent flame acceleration mechanism for a spherical flame in a constant pressure vessel. They found the normalized turbulent flame speed as a function of length scale and transport property, which demonstrates flame self-similar propagation. After, they clarified the scaling of turbulent flame speed with Markstein diffusion consideration [16]. Kim et al. [20] also presented the
https://doi.org/10.1016/j.combustflame.2017.12.007 0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
L. Zhou et al. / Combustion and Flame 190 (2018) 216–223
self-similar propagation in large scale gas explosions. Bradley et al. [21] have also made much contributions for the turbulent flame burning velocity. In past decades, a great deal of effort [1,2,22–27] has also been spent on studying the turbulent flame acceleration mechanism for DDT in channels equipped with and without obstacles. Recently, Dorofeev [2] reviewed the underlying mechanism and physical phenomena of flame acceleration in different configurations. Compared to flame propagation in smooth tubes, flame in obstructed tubes with obstacles is easier to convert into a turbulent flame. They demonstrated different flame acceleration mechanisms, in which Shelkin mechanism [28] and Bychkov theory [29] are the most popular and well-known. When burning occurs in confined space, a flame will produce a series of acoustic waves. The study of flame–acoustic wave (pressure wave) interactions has made substantial contributions to understanding flame propagation and flame configuration [25,30–33], in which a more interesting topic is the flame-acoustic resonance in a tube. In a simple tube without obstacle, Petchenko et al. [30] presented flame propagation in a tube with a closed end by direct numerical simulation. As a result, acoustic oscillations produce an strongly corrugated flame front induced by strong Rayleigh–Taylor(RT) instability. Akkerman and Law [13] developed a quasi-1D model to study the effect of acoustic coupling on power-law flame acceleration in spherical confinement. The acoustic interact with the flame front finally affected the flame morphology and propagation speed. Xiao et al. [25] experimentally demonstrated the periodical interaction of the flame with the pressure wave because of the contact of the flame front with the lateral walls. When the acoustic or compression waves coalesce ahead of the flame to form a stronger compression wave, a leading shock wave is formed. Apart from the Kelvin–Helmholtz instability mechanism for the interface between the flame and the shock wave, flame–shock wave interactions distort the flame front and increases the energy release rate in the combustion system according to the Richtmyer–Meshkov (RM) instability [34], which plays a key role in the DDT. In fact, for flame propagation in tube, five stages of flame dynamics can be distinguished based on the classical tulip flame propagation [35–37]. However, the combustion modes of turbulent flame dynamics in confined space have not yet been clearly demonstrated in previous studies. Additionally, the effect of flameshock/acoustic interactions on the flame propagation and combustion modes with pressure oscillation has not yet been comprehensively studied. Therefore, the objective of this seminal work is to experimentally and clearly reveal the possibility modes of flame propagation and combustion phenomena in confined space for the first time. The experiment was carried out by our designed experimental apparatus equipped with a perforated plate. A hydrogen–air mixture was chosen as the test fuel because of its fast flame propagation velocity and its clean combustion character as a renewable fuel. In this work, the effect of the perforated plate is to generate a rapidly accelerating flame based on Bychkov work [29] and a wrinkled flame due to RT instability. The paper is organized as follows: the experimental setup and conditions are briefly discussed in Section 2; flame propagation and combustion modes are presented in Section 3; and finally, main findings from this work are drawn in the last section. 2. Experiment setup This experiment was carried out in a newly designed constant volume combustion bomb (CVCB) equipped with a highspeed Schlieren photography system, as shown in Fig. 1. The entire experimental system consisted of a constant volume combustion chamber, a high-speed Schlieren photography system, a pressure
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Fig. 1. Experimental apparatus.
recording system, an intake and exhaust system, a high-voltage ignition system, perforated plates with different aperture sizes and a synchronization controller. The combustion chamber was a closed cylindrical cavity with an inner diameter of 100 mm and length of 230 mm. The entire vessel was uniformly preheated by a set of electrical heating elements with a power rating of 2 kW. The interior air temperature was set to 353 K and controlled within 3 K using a closed-loop feedback controller. The pressure rise during the combustion process was recorded using a Kistler 6113B pressure transducer at 100 kHz. In this experiment, hydrogen is selected as a fuel. And according to the Dalton partial pressure law, the quantity of hydrogen and air was defined in terms of the pressure at different equivalence ratios. Prior ignition, the fuel and the air mixture were initially premixed for 5 min to realize homogeneous mixture without gas flow effect. The mixture was ignited using a slightly modified standard ignition plug with extended electrodes. The ignition system generated a spark with duration of 0.7 ms and the timing was synchronized with the interior pressure rise recording. For safety reasons, an 8 MPa pressure release valve was installed in the combustion vessel. Replaceable perforated plates with different aperture sizes of 1.5 mm, 2.5 mm, and 3 mm were installed at the middle (A) distance from the left wall to generate turbulent flames with different intensities. The perforated plate was made using a 3 mm thick stainless steel plate. There were several 2 mm diameter through-holes on it, distributed in rectangular form (18 rows, 14 columns) as shown in Fig. 1 and in this work the number of holes remains constant. The porosity (or void fraction) in present work indicates a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. At the end of the chamber, there is a heating rod with a diameter of 10 mm to heat the mixture at the end. However, in this work the heating rod was not used. Instead of the heating rod at the same position, the second spark plug was used to ignite the end mixture. The test conditions involving initial ambient temperature, ambient pressure, equivalence ratio, hole size and porosity are shown in Table 1. Because the focus of this work is to demonstrate the potential combustion modes in confined space, the present cases are chosen to represent all the possible combustion modes. A 240 W lamp is used as the light source. The light is focused onto a slit using a focusing lens to generate the spotlight for the Schlieren technique. Passing through a group of mirrors, the
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L. Zhou et al. / Combustion and Flame 190 (2018) 216–223 Table 1 Experiment conditions for different turbulent propagation modes. Combustion mode
Equivalence ratio
Initial pressure (bar)
Initial temperature (K)
Perforated plate standard: hole size (mm)
M1 M2 M3 M4 M5 M6
0.5 1.5 1 1 1 1
1 1 2 3 4 2
361 361 361 358 390 353
3 3 3 2.5 1.5 1.5
Perforated plate standard: porosity (%) 18 18 18 12 12 12
Fig. 2. Flame propagation schematic diagram.
light path was then cut by a knife-edge which is essential for the Schlieren method. The high speed camera is synchronized with the spark timing and the interior pressure transducer. In this study, the flame propagation velocity was calculated based on the time derivation of the flame tip position, distance from the ignition point. And this was called flame tip velocity in the text. It is noticeable that the present turbulent flame propagation or front tip velocity actually corresponds to the flame displacement velocity [38] in this work, which is generally used in most studies of flame propagation in DDT [39–41]. In our recent work [42], a detailed investigation regarding the definition of flame tip velocity was reviewed. Based on a framing rate of 90,0 0 0 frames per second and a resolution of 0.18 mm/pixel, the uncertainty is 16 m/s. 3. Flame propagation mechanisms To investigate the turbulent flame propagation in confined space, a newly experimental apparatus was designed for this work. Through the present experiment, the flame propagation schematic is summarized in Fig. 2. In Fig. 2, the Schlieren imaging used is to describe the flame propagation in general methodology, which is obtained at hole size of 3 mm, porosity of 12% and initial pressure of 4 bar. In the newly experimental apparatus, the perforated plate is used to generate a turbulent flame and effectively study
the flame acceleration mechanism and flame–shock/acoustic interactions. In [29], Bychkov pointed out that the flame acceleration is induced by the delayed burning combustion before the flame passes through the obstacles in a tube with obstacles, which could produce a powerful jet flow and subsequently lead to an extremely high flame tip velocity. Before this theory, the general explanation presented was that the KH/RT instabilities with shear effect are triggered when the flame suddenly passes through an obstacle or a vent [1], which promotes the flame surface to increase and wrinkle with faster flame burning. Note that, in Bychkov’s work [29], the flame acceleration mechanism is based on the laminar flame, and the theory was formulated based on the incompressible flow with an open end. Therefore, as a beneficial supplement, Akkerman et al. [43–46] analyzed the influence of gas compression on flame acceleration. They presented that gas compression moderates the flame acceleration noticeably and reduces the exponential acceleration rate with and without obstacles, which can be employed to partly explain the present experiment about the laminar flame and turbulent flame propagations. Besides, in the present experiment, two important factors are discovered at another side of the perforated plate before the flame passes through, i.e., turbulence and heating unburnt mixture with a certain velocity in disturbance region. These two factors take precedence over the limited effect of increasing the hole size of perforated plate. Overall, the present perforated
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plate performs that it could generate stronger turbulence, which increases the burning rate and facilitates flame acceleration. In Fig. 2, for the spherical flame propagation stage, the laminar spherical flame propagates with a gradually increasing due to expanding flame at first stage. After that, the smooth spherical flame spread outwardly with gradually decreasing velocity because of the confinement of the perforated plate before flame passing through perforated plate. Meanwhile, a flatted flame configuration with delayed burning combustion due to the gas compression based on the confinement is found. For jet flame stage, it is found that a rapid increase in jet flame tip velocity is generated as the flame passes through the perforated plate. Based on the Bychkov theory [29], in the flame propagation direction a powerful jet flow is produced, and the jet flow renders the flame tip to propagate faster, which produces appositive feedback between flame and the flow, leading to flame acceleration. Note that it is different from the configuration of Bychkov’ work that in present work, a spherical flame is divided into several jet flames by the perforated plate. Thus in this respect, KH/RT instability also plays an important role on increasing flame surface area and flame burning velocity. After that, the flame tip velocity naturally decreases due to the fluid dynamic mechanism. It is possible that the suddenly increased jet flame tip velocity is beyond actual burning velocity for the unburnt mixture. However, in terms of gas flow velocity, the gradually decreasing gas flow velocity away the perforated plate contributes to the main reason. Note that the detailed process of flame acceleration after perforated plate can be found in Appendix based on simulation and experiment. When the corrugated turbulent flame is formed, the velocity begins increasing again. In fact, turbulent flame propagation in end gas region of confined space is very complicated and not fully understood in previous works. Therefore, we divide the turbulent flame propagation process into two stages, an initial development stage and a propagation stage where in end gas region is in confined space. In initially developing stage of turbulent flame, the turbulent flame performs the self-similar and selfacceleration process, and the comprehensive mechanisms can be found in the works by Law and Akkerman [6,13,14]. Specially, in the initial stage of turbulent flame acceleration the KH/RT instability and flame-acoustic instability can promote the flame acceleration. However, importantly, the strong turbulent flame acceleration leads to a strong flow in the flame propagation direction and the flame surface increases for turbulent flame, which consequently promotes the flame tip velocity. This process resembles the “finger flame” acceleration mechanism that was quantitatively studied in [37,46]. As for the second stage that flame propagates into the end-gas region of confined space as shown in Fig. 2, there are some reflected waves and gas compression effects due to the confinement effect. The combustion process becomes complex. Therefore, turbulent flame propagation in the end gas region becomes the key point at which to determine propagation modes and finally combustion phenomena including complex physical phenomena and mechanisms. 4. Results and discussions The present work demonstrates the turbulent flame propagation process in the end gas region of confined space. Figure 3 shows the different flame tip velocities plotted against the distance into end gas under various conditions. Note that in this work, the experimental conditions are not the main topic, but the difference in observed flame velocities are the primary issue of concern. It can be found that there are approximately six different types of flame tip velocity induced by various combustion phenomena. Furthermore, Fig. 4 shows a series of Schlieren images for different turbulent flame propagation and combustion phenomena
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Fig. 3. Flame tip velocity at different conditions in end gas of confined space.
under various conditions. It can be concluded from both Figs. 3 and 4 the combustion phenomena can be drawn as flowing with and without the interaction between flame and shock wave or acoustic wave and being minimally affected by the wall in the confined space. There are (1) a normal flame propagation with low flame tip velocity and combustion rate(M1), (2) a weak pulsation propagation with weak fluctuation due to the acoustic wave(M2), (3) a pulsation propagation of turbulent flame but only with a visible reflected shock wave (M3), (4) a strong pulsation propagation of a turbulent flame with a strong forward shock wave and shock reflection (M4), (5) a continuously accelerating flame propagation due to the auto-ignition of unburned mixture appearing in front of the turbulent flame front (M5), and (6) fast flame with multi-shock wave leading to end gas auto-ignition with a very high combustion velocity (M6), In confined space, three major fundamental theories can contribute to the turbulent flame acceleration mechanism. First of all, the self-acceleration of a turbulent flame could be a selfsimilar propagation depending on the intensity of the hydrodynamic instability as well as that of the diffusional–thermal instability [6,16], which promotes an increasing flame tip velocity. Apart from this mechanism, when the turbulent flame front is going to pass through the unburned gas mixture where the pressure and temperature are enhanced by the compression waves including shock waves as well as the disturbance, the burning rate will increase. Consequently, the flame tip velocity increases. Actually this mechanism is usually neglected but becomes more important in confined space. This mechanism has contributed to all the turbulent developing stages, especially the initial turbulent formation stage. Overall, for the first combustion mode (M1), the turbulent flame is controlled by the self-acceleration mechanism and the compressed gas limited by flame movement to the wall. Meanwhile, the flame tip velocity is very low compared with others in Fig. 3. Because in the conditions of M1, for the equivalence ratio of 0.5 the laminar flame velocity is relatively low and combustion intensity is weak. The third mechanism involving Richtmyer– Meshkov (RM) instability [30] is discussed later. For the second combustion mode (M2) a weak oscillation of flame tip velocity is observed in Fig. 3 and the flame images are shown in Fig. 4. This combustion phenomenon is caused by flameacoustic/pressure wave interactions. Under the conditions of M2, compared to the case M1 the equivalence ratio of 1.5 is larger, and the combustion intensity becomes strong. Thus, the flame tip ve-
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Fig. 4. Schlieren images for different flame front propagation and combustion modes at different conditions in end gas region of confined space.
locity becomes greater around 160 m/s as shown in Fig. 3. But in this case, there is not obvious shock wave ahead of the flame as shown in Fig. 4. However, a weak pulsation propagation of flame with weak fluctuation is found in Fig. 3. The flame–acoustic interaction plays a vital role in flame configuration for the low speed flame with weak pulsation propagation. As shown in [30], the resonance of flame tip velocity with an acoustic wave or pressure wave in [25] produce a violent folding of the flame front, which forms a different flame configuration. Here, the present result shows the interaction effects of the weak turbulent flame, which alters the flame tip velocity. Third, an additional flame surface is increased by the reflected shock wave due to the Richtmyer–Meshkov (RM) instability [30]. Consequently the turbulent flame accelerates according to previous studies mostly concerned with the flame acceleration process. The present work demonstrates the effect of flame–shock interactions on flame propagation and combustion phenomena as shown in Figs. 3 and 4. It can be seen that for the third combustion mode (M3), a visible reflected shock wave is observed as shown in Fig. 4. This wave generates the flame tip velocity oscillation and slightly pushes the flame back. Compared to the conditions of case M2, the initial pressure of case M3 becomes larger. Thus, the turbulent flame velocity will increase in high pressure according to the theory of premixed flame explosion obtained by Law et al. [6]. In previous work, effect of initial pressure on turbulent flame propagation in confined space has been well investigated. However, in case M3 the turbulent flame intensity is not enough to produce obvious shock wave ahead of flame, thus only a visible reflected shock wave is observed in Fig. 4. Therefore, when the turbulent flame tip velocity increases, the accelerating flame is similar to a piston pushing the unburnt gas mixture compressed into a compressed state. Compression waves generate at the flame front and coalesce ahead of the flame to form a stronger compression wave until a leading shock wave is formed [15]. It can be seen that the shock wave (the strength of shock of around M = 1) ahead of turbulent flame and reflected shock wave can be clearly observed for case M4 as shown in Fig. 4. Meanwhile, a turbulent flame inversion is generated as seen in Fig. 4 due to the flame-reflected shock interaction, which is consistent with Markstein’s result [47] but more precisely demonstrated in the present work. Note that compared to above three cases, the case M4 has smaller hole size and porosity apart from the initial pressure. The intensity of flame tip velocity depends on the hole size and porosity of the perforated plate. Reducing both the hole size and porosity can increase the wrinkled flame surface at smaller scales and the turbulent intensity, which leads to a fast flame. In case M6, the turbulent flame is approximately 280 m/s.
Fig. 5. Profiles of pressure oscillations for different combustion modes.
Furthermore, as the hole size reduces to 1.5 mm, the turbulent flame tip velocity can further increases. The primary flame tip velocity reaches about 370 m/s. The temperature of the unburned gas increases transiently after the primary shock wave propagation induced by primary flame. Therefore, secondary flame is observed in Fig. 4. And the turbulent flame tip velocity increases to a velocity of approximately 780 m/s for the secondary flame, a very fast shock wave of approximately of 750 m/s (the secondary shock) is formed to cause a strong compression effect on the unburnt mixture of the end gas. As a result, the end-gas autoignition appears in a heated unburnt mixture induced by the shock wave, which is the sixth type of combustion modes (M6). A quasi-detonation wave is then generated and propagated reversely with a velocity of approximately 1700 m/s. In fact, in DDT, a general phenomenon is that the denotation occurs in front of the flame after the leading shock passes through the unburnt mixture. As the initial ambient temperature and pressure increase of case M5 compared to cases M6 and M4, the autoignition of unburnt mixture in front of flame easily occurs, which could leads to the flame acceleration continually as shown in Fig. 3. And it can be seen that the a shock wave ahead of the turbulent flame propagates and produces a preheated zone, which also contributes to the autoignition occurrence as shown in Fig. 4. The autoignition ahead of flame will generates a violent pressure oscillation as discussed in Fig. 5 later. Note that the combustion mode M6 appears at a particular condition according to the well-known SWACER (shock wave amplifica-
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tion by coherent energy release) or the Zeldovich mechanism. In our previous experiment [48], we employed a spark to ignite the hydrogen-air mixture in end gas, but it could not form the detonation. Similarly, the calculated result of Chen [49] also presented the combustion mode of end-gas auto ignition without detonation as develop in a closed chamber with the hydrogen-air mixture. Overall, the flame-shock interaction based on the RM instability mechanism [30] results in very different combustion phenomena from M3 to M6 in the present experiment. Note that the RT and RM instabilities are powerful instabilities that may strongly influence and dominate the flame accelerating propagation process. However, in initial turbulent formation and development the turbulent flame self-acceleration theory by Law and Akkerman [6,13,14] will control turbulent flame propagation. Once the compression wave induced by the accelerating flame become sufficiently strong the RT or RM instability will determine the whole flame acceleration and combustion phenomena. Of course, the different combustion modes are also relevant to local thermodynamic conditions. In confined space, combustion is always accompanied by the pressure oscillation. Therefore, the pressure oscillations for different combustion modes are shown in Fig. 5. It can be seen that following the increase of combustion intensity, the pressure oscillation intensifies and the peak amplitude of the pressure oscillation also increases. They almost have a linear relationship. The maximum amplitude is approximately 6 MPa for combustion mode M5 with autoignition in front of the flame. Meanwhile, the peak pressure is approximately 4.5 MPa for combustion mode M6 with end-gas autoignition obtained in the present work. In previous studies, the pressure oscillation is close to flame tip velocity oscillation, named resonance of flame–acoustic. For intense turbulent flame propagation in confined space, the obvious resonance is not obtained, because of the more complicated combustion pressure wave from every direction in confined space. However, several critical spikes of pressure oscillation are consistent with the turbulent flame and shock wave propagations that are not presented here. 5. Conclusions This experiment is carried out by our designed experimental apparatus equipped with a perforated plate. The effect of the perforated plate is to generate a rapidly accelerating flame and form a turbulent flame. This work experimentally reveals possible modes of flame propagation and combustion phenomena in confined space clearly. It is found that, in the presence of the perforated plate, the turbulent flame formed through the perforated plate may perform six types of flame propagations at the end gas regime owing to the interaction between flame and shock wave or acoustic wave and the limiting effect of the wall in the confined space. The different pressure oscillations depending on the different combustion modes are observed. Note that the present work cannot employ the mathematical method to quantitatively evaluate the turbulent flame propagation due to the complexity of the combustion phenomena. In the future, we will try to use the mathematical proof to analyze the combustion modes.
Fig. A1. Evolution of flame propagation when passing through the perforated plate (Up: experimental results, Below: numerical results).
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 91641203, 51606133). We also thank the reviewers for providing helpful comments and suggestions. Appendix A. Flame passing through the perforated plate The evolution of flame propagation when passing through the perforated plate by experiment and simulation is shown in Fig. A1.
Fig. A2. Evolution of flame propagation velocity when passing through the perforated plate (experimental and numerical results).
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Fig. A3. Variation of temperature and velocity in the centerline of the combustion chamber (Numerical results).
The case condition is carried out at an initial pressure of 4 bar and hole size of 3 mm. It is noted that constrained by the size of the optical window, only the region from 0 to 78 mm could be observed. Distinguished by the flame morphology and propagation velocity, three distinct stages were observed in the in the process of flame propagation over the orifice plate: laminar flame stage, jet flame stage and turbulent flame stage. During the laminar flame stage, the flame presented as a semi-spherical shape driven by the no-slip boundary condition on the wall and Darrieus–Landua instability. When the flame passed through the perforated plate, the flame front was split into several jet flames with an intense increase of the flame propagation velocity. As time went on, the jet flames coalesced with each other and a wrinkled turbulent flame was formed. Note that the present numerical method only can perform the simply process of flame passing through perforated plate, the entire process cannot be well carried out. Figure A2 shows the evolution of flame propagation velocity when passing through the perforated plate. Although the nu-
merical flame velocity was lower than the experimental velocity, the evolution trends of flame propagation velocity were consistent with the present experiment. During the laminar flame stage, the flame propagation velocity increased at first and then descended. When the flame approached the perforated plate, the flame decelerated due to the hindering effect of the obstacle. After passed through the perforated plate, the flame propagation velocity increased in an order of magnitude, from around 20 m/s to 110 m/s. The flame acceleration was induced by the delayed burning combustion before the flame passes through the perforated plate, which could produce a powerful jet flow and subsequently lead to an extremely high flame tip velocity. Additionally, the present perforated plate performed that it could generate stronger turbulence, which increased the burning rate and facilitated flame acceleration. With the departure of the flame front from the perforated, the flame propagation naturally performed a decline due to fluid-dynamic mechanisms. When the corrugated turbulent flame was formed, the turbulent flame performed a selfsimilar and self-acceleration process. The relevant theory explanations can be found in main text. The variation of the temperature and velocity in the centerline of the combustion chamber was investigated to demonstrate the interactions of flame and combustion-generated flow during the evolution of flame passing through the perforated plate, which is shown in Fig. A3. Five time points are selected, including 0.400, 0.700, 0.975, 1.225 and 1.400 ms. Before the flame passing through the perforated at 0.400 and 0.700 ms, a powerful jet flow was formed close to the perforated plate downstream, which made great contributions to the flame acceleration when passing through the perforated plate. After the flame passed through the perforated plate at 0.975, 1.225 and 1.400 ms, the velocity of unburned gas decreased as with the distance departing from the flame front, which means that the gas velocity was driven by the flame in this period. It also can be seen that the flame front surpasses the peak of flow velocity after flame passed through perforated plate. The results resembles the quantitatively studies in [37,46]. Appendix B. flame pulsation propagations of different combustion modes Figure A4 shows the evolutions of flame propagation velocity versus time after the perforated plate at different combustion modes. Overall, the flame propagation velocity experienced a decline trend after passing through the perforated plate at every combustion mode. In the end of the combustion chamber, the flame propagation velocity oscillated due to flame-acoustic/shock wave interaction. Depending on the intensity of the shock wave, the oscillating amplitude was different among different combustion modes. The oscillating amplitude was smallest at Mode 2, and biggest at Mode 4. And it is worth nothing that the flame back-
Fig. A4. Oscillating propagation of the flame at different combustion modes.
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Combustion and Flame journal homepage: www.elsevier.com/locate/combustflame
Flame propagation and combustion modes in end-gas region of confined space Lei Zhou, Lijia Zhong, Jianfu Zhao, Dongzhi Gao, Haiqiao Wei∗ State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China
a r t i c l e
i n f o
Article history: Received 15 August 2017 Revised 21 October 2017 Accepted 8 December 2017
Keywords: Flame propagation Combustion mode Confined space Shock wave
a b s t r a c t Flame propagation is investigated in a designed experimental apparatus equipped with a perforated plate in a constant volume chamber. The effect of the perforated plate is to generate a rapidly accelerating flame based on Bychkov work (Bychkov et al. 2008), in which the flame across the obstacle will becomes a strong jet flame. The experiment was conducted with a hydrogen–air mixture at different conditions. In this work, six different turbulent flame propagation and combustion modes were clearly observed at various conditions in our designed experiment. In the presence of perforated plate, the turbulent flame formed through the perforated plate may perform six types of turbulent propagations at the end gas regime. These types form through the interaction between the flame and the shock or acoustic wave and because of the limited effect of the wall in confined space. The six forms are as follows: (1) a normal flame propagation with a low flame front tip velocity and combustion rate; (2) a weak pulsation propagation with weak fluctuation due to the acoustic wave; (3) a pulsation propagation only with a visible reflected shock wave; (4) a strong pulsation propagation with a forward shock wave and shock reflection; (5) a continuously accelerating flame propagation due to auto-ignition of the unburned mixture between flame front and shock wave, which also leads to strong pressure oscillation; and (6) a violent pulsation propagation with a multi-shock wave leading to end gas auto-ignition with large pressure oscillation. © 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Background and introduction Turbulent flame is one of the most interesting parts of combustion physics and turbulence research as evidenced by analytical, experimental and computational studies in the past few decades [1–8]. Much detail can be found in comprehensive reviews on turbulent and other types of flames [9–12]. For example, some of these studies examined the turbulent premixed flame speed in a nearly constant-pressure apparatus with fans, which presented the self-similar propagation of a turbulent flame [6,13,14]. In other studies [15–19], they showed that turbulence corrugates the flame front by increasing the burning rate and facilitating flame acceleration, which boosts the process of deflagration to detonation transition (DDT). Of particular interest is turbulent flame acceleration and propagation in confined space. As turbulent combustion in confined space, i.e., confinement, occurs, flame acceleration and expanding propagation will generates a series of compression waves with considerable amplitude. In turn, confinement significantly influ-
∗
Corresponding author. E-mail address: [email protected] (H. Wei).
ences the turbulent flame brush and wrinkles it. Therefore, in flame propagation the flame–shock/acoustic interactions play a vital role and finally determine the turbulent flame development and combustion phenomena. Understanding the turbulent flame propagation mechanism involving flame–shock/acoustic interaction in confined space not only is of fundamental significance but also contributes to practical applications such as spark-ignition engines with knock phenomenon and explosion hazards in coal mine fields. There have been some attempts to explain flame acceleration and flame–shock/acoustic wave interactions. Of course, flame acceleration is strongly relevant to flame–shock/acoustic interactions. Based on previous explanations, there are four primary aspects to flame acceleration and flame-shock/acoustic interactions: 1) flame self-acceleration for expanding spherical flame, 2) flame acceleration mechanisms in DDT, and 3) flame–acoustic interaction, 4) flame–shock interaction. Law and co-workers [6] comprehensively investigated the turbulent flame acceleration mechanism for a spherical flame in a constant pressure vessel. They found the normalized turbulent flame speed as a function of length scale and transport property, which demonstrates flame self-similar propagation. After, they clarified the scaling of turbulent flame speed with Markstein diffusion consideration [16]. Kim et al. [20] also presented the
https://doi.org/10.1016/j.combustflame.2017.12.007 0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
L. Zhou et al. / Combustion and Flame 190 (2018) 216–223
self-similar propagation in large scale gas explosions. Bradley et al. [21] have also made much contributions for the turbulent flame burning velocity. In past decades, a great deal of effort [1,2,22–27] has also been spent on studying the turbulent flame acceleration mechanism for DDT in channels equipped with and without obstacles. Recently, Dorofeev [2] reviewed the underlying mechanism and physical phenomena of flame acceleration in different configurations. Compared to flame propagation in smooth tubes, flame in obstructed tubes with obstacles is easier to convert into a turbulent flame. They demonstrated different flame acceleration mechanisms, in which Shelkin mechanism [28] and Bychkov theory [29] are the most popular and well-known. When burning occurs in confined space, a flame will produce a series of acoustic waves. The study of flame–acoustic wave (pressure wave) interactions has made substantial contributions to understanding flame propagation and flame configuration [25,30–33], in which a more interesting topic is the flame-acoustic resonance in a tube. In a simple tube without obstacle, Petchenko et al. [30] presented flame propagation in a tube with a closed end by direct numerical simulation. As a result, acoustic oscillations produce an strongly corrugated flame front induced by strong Rayleigh–Taylor(RT) instability. Akkerman and Law [13] developed a quasi-1D model to study the effect of acoustic coupling on power-law flame acceleration in spherical confinement. The acoustic interact with the flame front finally affected the flame morphology and propagation speed. Xiao et al. [25] experimentally demonstrated the periodical interaction of the flame with the pressure wave because of the contact of the flame front with the lateral walls. When the acoustic or compression waves coalesce ahead of the flame to form a stronger compression wave, a leading shock wave is formed. Apart from the Kelvin–Helmholtz instability mechanism for the interface between the flame and the shock wave, flame–shock wave interactions distort the flame front and increases the energy release rate in the combustion system according to the Richtmyer–Meshkov (RM) instability [34], which plays a key role in the DDT. In fact, for flame propagation in tube, five stages of flame dynamics can be distinguished based on the classical tulip flame propagation [35–37]. However, the combustion modes of turbulent flame dynamics in confined space have not yet been clearly demonstrated in previous studies. Additionally, the effect of flameshock/acoustic interactions on the flame propagation and combustion modes with pressure oscillation has not yet been comprehensively studied. Therefore, the objective of this seminal work is to experimentally and clearly reveal the possibility modes of flame propagation and combustion phenomena in confined space for the first time. The experiment was carried out by our designed experimental apparatus equipped with a perforated plate. A hydrogen–air mixture was chosen as the test fuel because of its fast flame propagation velocity and its clean combustion character as a renewable fuel. In this work, the effect of the perforated plate is to generate a rapidly accelerating flame based on Bychkov work [29] and a wrinkled flame due to RT instability. The paper is organized as follows: the experimental setup and conditions are briefly discussed in Section 2; flame propagation and combustion modes are presented in Section 3; and finally, main findings from this work are drawn in the last section. 2. Experiment setup This experiment was carried out in a newly designed constant volume combustion bomb (CVCB) equipped with a highspeed Schlieren photography system, as shown in Fig. 1. The entire experimental system consisted of a constant volume combustion chamber, a high-speed Schlieren photography system, a pressure
217
Fig. 1. Experimental apparatus.
recording system, an intake and exhaust system, a high-voltage ignition system, perforated plates with different aperture sizes and a synchronization controller. The combustion chamber was a closed cylindrical cavity with an inner diameter of 100 mm and length of 230 mm. The entire vessel was uniformly preheated by a set of electrical heating elements with a power rating of 2 kW. The interior air temperature was set to 353 K and controlled within 3 K using a closed-loop feedback controller. The pressure rise during the combustion process was recorded using a Kistler 6113B pressure transducer at 100 kHz. In this experiment, hydrogen is selected as a fuel. And according to the Dalton partial pressure law, the quantity of hydrogen and air was defined in terms of the pressure at different equivalence ratios. Prior ignition, the fuel and the air mixture were initially premixed for 5 min to realize homogeneous mixture without gas flow effect. The mixture was ignited using a slightly modified standard ignition plug with extended electrodes. The ignition system generated a spark with duration of 0.7 ms and the timing was synchronized with the interior pressure rise recording. For safety reasons, an 8 MPa pressure release valve was installed in the combustion vessel. Replaceable perforated plates with different aperture sizes of 1.5 mm, 2.5 mm, and 3 mm were installed at the middle (A) distance from the left wall to generate turbulent flames with different intensities. The perforated plate was made using a 3 mm thick stainless steel plate. There were several 2 mm diameter through-holes on it, distributed in rectangular form (18 rows, 14 columns) as shown in Fig. 1 and in this work the number of holes remains constant. The porosity (or void fraction) in present work indicates a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. At the end of the chamber, there is a heating rod with a diameter of 10 mm to heat the mixture at the end. However, in this work the heating rod was not used. Instead of the heating rod at the same position, the second spark plug was used to ignite the end mixture. The test conditions involving initial ambient temperature, ambient pressure, equivalence ratio, hole size and porosity are shown in Table 1. Because the focus of this work is to demonstrate the potential combustion modes in confined space, the present cases are chosen to represent all the possible combustion modes. A 240 W lamp is used as the light source. The light is focused onto a slit using a focusing lens to generate the spotlight for the Schlieren technique. Passing through a group of mirrors, the
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L. Zhou et al. / Combustion and Flame 190 (2018) 216–223 Table 1 Experiment conditions for different turbulent propagation modes. Combustion mode
Equivalence ratio
Initial pressure (bar)
Initial temperature (K)
Perforated plate standard: hole size (mm)
M1 M2 M3 M4 M5 M6
0.5 1.5 1 1 1 1
1 1 2 3 4 2
361 361 361 358 390 353
3 3 3 2.5 1.5 1.5
Perforated plate standard: porosity (%) 18 18 18 12 12 12
Fig. 2. Flame propagation schematic diagram.
light path was then cut by a knife-edge which is essential for the Schlieren method. The high speed camera is synchronized with the spark timing and the interior pressure transducer. In this study, the flame propagation velocity was calculated based on the time derivation of the flame tip position, distance from the ignition point. And this was called flame tip velocity in the text. It is noticeable that the present turbulent flame propagation or front tip velocity actually corresponds to the flame displacement velocity [38] in this work, which is generally used in most studies of flame propagation in DDT [39–41]. In our recent work [42], a detailed investigation regarding the definition of flame tip velocity was reviewed. Based on a framing rate of 90,0 0 0 frames per second and a resolution of 0.18 mm/pixel, the uncertainty is 16 m/s. 3. Flame propagation mechanisms To investigate the turbulent flame propagation in confined space, a newly experimental apparatus was designed for this work. Through the present experiment, the flame propagation schematic is summarized in Fig. 2. In Fig. 2, the Schlieren imaging used is to describe the flame propagation in general methodology, which is obtained at hole size of 3 mm, porosity of 12% and initial pressure of 4 bar. In the newly experimental apparatus, the perforated plate is used to generate a turbulent flame and effectively study
the flame acceleration mechanism and flame–shock/acoustic interactions. In [29], Bychkov pointed out that the flame acceleration is induced by the delayed burning combustion before the flame passes through the obstacles in a tube with obstacles, which could produce a powerful jet flow and subsequently lead to an extremely high flame tip velocity. Before this theory, the general explanation presented was that the KH/RT instabilities with shear effect are triggered when the flame suddenly passes through an obstacle or a vent [1], which promotes the flame surface to increase and wrinkle with faster flame burning. Note that, in Bychkov’s work [29], the flame acceleration mechanism is based on the laminar flame, and the theory was formulated based on the incompressible flow with an open end. Therefore, as a beneficial supplement, Akkerman et al. [43–46] analyzed the influence of gas compression on flame acceleration. They presented that gas compression moderates the flame acceleration noticeably and reduces the exponential acceleration rate with and without obstacles, which can be employed to partly explain the present experiment about the laminar flame and turbulent flame propagations. Besides, in the present experiment, two important factors are discovered at another side of the perforated plate before the flame passes through, i.e., turbulence and heating unburnt mixture with a certain velocity in disturbance region. These two factors take precedence over the limited effect of increasing the hole size of perforated plate. Overall, the present perforated
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plate performs that it could generate stronger turbulence, which increases the burning rate and facilitates flame acceleration. In Fig. 2, for the spherical flame propagation stage, the laminar spherical flame propagates with a gradually increasing due to expanding flame at first stage. After that, the smooth spherical flame spread outwardly with gradually decreasing velocity because of the confinement of the perforated plate before flame passing through perforated plate. Meanwhile, a flatted flame configuration with delayed burning combustion due to the gas compression based on the confinement is found. For jet flame stage, it is found that a rapid increase in jet flame tip velocity is generated as the flame passes through the perforated plate. Based on the Bychkov theory [29], in the flame propagation direction a powerful jet flow is produced, and the jet flow renders the flame tip to propagate faster, which produces appositive feedback between flame and the flow, leading to flame acceleration. Note that it is different from the configuration of Bychkov’ work that in present work, a spherical flame is divided into several jet flames by the perforated plate. Thus in this respect, KH/RT instability also plays an important role on increasing flame surface area and flame burning velocity. After that, the flame tip velocity naturally decreases due to the fluid dynamic mechanism. It is possible that the suddenly increased jet flame tip velocity is beyond actual burning velocity for the unburnt mixture. However, in terms of gas flow velocity, the gradually decreasing gas flow velocity away the perforated plate contributes to the main reason. Note that the detailed process of flame acceleration after perforated plate can be found in Appendix based on simulation and experiment. When the corrugated turbulent flame is formed, the velocity begins increasing again. In fact, turbulent flame propagation in end gas region of confined space is very complicated and not fully understood in previous works. Therefore, we divide the turbulent flame propagation process into two stages, an initial development stage and a propagation stage where in end gas region is in confined space. In initially developing stage of turbulent flame, the turbulent flame performs the self-similar and selfacceleration process, and the comprehensive mechanisms can be found in the works by Law and Akkerman [6,13,14]. Specially, in the initial stage of turbulent flame acceleration the KH/RT instability and flame-acoustic instability can promote the flame acceleration. However, importantly, the strong turbulent flame acceleration leads to a strong flow in the flame propagation direction and the flame surface increases for turbulent flame, which consequently promotes the flame tip velocity. This process resembles the “finger flame” acceleration mechanism that was quantitatively studied in [37,46]. As for the second stage that flame propagates into the end-gas region of confined space as shown in Fig. 2, there are some reflected waves and gas compression effects due to the confinement effect. The combustion process becomes complex. Therefore, turbulent flame propagation in the end gas region becomes the key point at which to determine propagation modes and finally combustion phenomena including complex physical phenomena and mechanisms. 4. Results and discussions The present work demonstrates the turbulent flame propagation process in the end gas region of confined space. Figure 3 shows the different flame tip velocities plotted against the distance into end gas under various conditions. Note that in this work, the experimental conditions are not the main topic, but the difference in observed flame velocities are the primary issue of concern. It can be found that there are approximately six different types of flame tip velocity induced by various combustion phenomena. Furthermore, Fig. 4 shows a series of Schlieren images for different turbulent flame propagation and combustion phenomena
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Fig. 3. Flame tip velocity at different conditions in end gas of confined space.
under various conditions. It can be concluded from both Figs. 3 and 4 the combustion phenomena can be drawn as flowing with and without the interaction between flame and shock wave or acoustic wave and being minimally affected by the wall in the confined space. There are (1) a normal flame propagation with low flame tip velocity and combustion rate(M1), (2) a weak pulsation propagation with weak fluctuation due to the acoustic wave(M2), (3) a pulsation propagation of turbulent flame but only with a visible reflected shock wave (M3), (4) a strong pulsation propagation of a turbulent flame with a strong forward shock wave and shock reflection (M4), (5) a continuously accelerating flame propagation due to the auto-ignition of unburned mixture appearing in front of the turbulent flame front (M5), and (6) fast flame with multi-shock wave leading to end gas auto-ignition with a very high combustion velocity (M6), In confined space, three major fundamental theories can contribute to the turbulent flame acceleration mechanism. First of all, the self-acceleration of a turbulent flame could be a selfsimilar propagation depending on the intensity of the hydrodynamic instability as well as that of the diffusional–thermal instability [6,16], which promotes an increasing flame tip velocity. Apart from this mechanism, when the turbulent flame front is going to pass through the unburned gas mixture where the pressure and temperature are enhanced by the compression waves including shock waves as well as the disturbance, the burning rate will increase. Consequently, the flame tip velocity increases. Actually this mechanism is usually neglected but becomes more important in confined space. This mechanism has contributed to all the turbulent developing stages, especially the initial turbulent formation stage. Overall, for the first combustion mode (M1), the turbulent flame is controlled by the self-acceleration mechanism and the compressed gas limited by flame movement to the wall. Meanwhile, the flame tip velocity is very low compared with others in Fig. 3. Because in the conditions of M1, for the equivalence ratio of 0.5 the laminar flame velocity is relatively low and combustion intensity is weak. The third mechanism involving Richtmyer– Meshkov (RM) instability [30] is discussed later. For the second combustion mode (M2) a weak oscillation of flame tip velocity is observed in Fig. 3 and the flame images are shown in Fig. 4. This combustion phenomenon is caused by flameacoustic/pressure wave interactions. Under the conditions of M2, compared to the case M1 the equivalence ratio of 1.5 is larger, and the combustion intensity becomes strong. Thus, the flame tip ve-
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Fig. 4. Schlieren images for different flame front propagation and combustion modes at different conditions in end gas region of confined space.
locity becomes greater around 160 m/s as shown in Fig. 3. But in this case, there is not obvious shock wave ahead of the flame as shown in Fig. 4. However, a weak pulsation propagation of flame with weak fluctuation is found in Fig. 3. The flame–acoustic interaction plays a vital role in flame configuration for the low speed flame with weak pulsation propagation. As shown in [30], the resonance of flame tip velocity with an acoustic wave or pressure wave in [25] produce a violent folding of the flame front, which forms a different flame configuration. Here, the present result shows the interaction effects of the weak turbulent flame, which alters the flame tip velocity. Third, an additional flame surface is increased by the reflected shock wave due to the Richtmyer–Meshkov (RM) instability [30]. Consequently the turbulent flame accelerates according to previous studies mostly concerned with the flame acceleration process. The present work demonstrates the effect of flame–shock interactions on flame propagation and combustion phenomena as shown in Figs. 3 and 4. It can be seen that for the third combustion mode (M3), a visible reflected shock wave is observed as shown in Fig. 4. This wave generates the flame tip velocity oscillation and slightly pushes the flame back. Compared to the conditions of case M2, the initial pressure of case M3 becomes larger. Thus, the turbulent flame velocity will increase in high pressure according to the theory of premixed flame explosion obtained by Law et al. [6]. In previous work, effect of initial pressure on turbulent flame propagation in confined space has been well investigated. However, in case M3 the turbulent flame intensity is not enough to produce obvious shock wave ahead of flame, thus only a visible reflected shock wave is observed in Fig. 4. Therefore, when the turbulent flame tip velocity increases, the accelerating flame is similar to a piston pushing the unburnt gas mixture compressed into a compressed state. Compression waves generate at the flame front and coalesce ahead of the flame to form a stronger compression wave until a leading shock wave is formed [15]. It can be seen that the shock wave (the strength of shock of around M = 1) ahead of turbulent flame and reflected shock wave can be clearly observed for case M4 as shown in Fig. 4. Meanwhile, a turbulent flame inversion is generated as seen in Fig. 4 due to the flame-reflected shock interaction, which is consistent with Markstein’s result [47] but more precisely demonstrated in the present work. Note that compared to above three cases, the case M4 has smaller hole size and porosity apart from the initial pressure. The intensity of flame tip velocity depends on the hole size and porosity of the perforated plate. Reducing both the hole size and porosity can increase the wrinkled flame surface at smaller scales and the turbulent intensity, which leads to a fast flame. In case M6, the turbulent flame is approximately 280 m/s.
Fig. 5. Profiles of pressure oscillations for different combustion modes.
Furthermore, as the hole size reduces to 1.5 mm, the turbulent flame tip velocity can further increases. The primary flame tip velocity reaches about 370 m/s. The temperature of the unburned gas increases transiently after the primary shock wave propagation induced by primary flame. Therefore, secondary flame is observed in Fig. 4. And the turbulent flame tip velocity increases to a velocity of approximately 780 m/s for the secondary flame, a very fast shock wave of approximately of 750 m/s (the secondary shock) is formed to cause a strong compression effect on the unburnt mixture of the end gas. As a result, the end-gas autoignition appears in a heated unburnt mixture induced by the shock wave, which is the sixth type of combustion modes (M6). A quasi-detonation wave is then generated and propagated reversely with a velocity of approximately 1700 m/s. In fact, in DDT, a general phenomenon is that the denotation occurs in front of the flame after the leading shock passes through the unburnt mixture. As the initial ambient temperature and pressure increase of case M5 compared to cases M6 and M4, the autoignition of unburnt mixture in front of flame easily occurs, which could leads to the flame acceleration continually as shown in Fig. 3. And it can be seen that the a shock wave ahead of the turbulent flame propagates and produces a preheated zone, which also contributes to the autoignition occurrence as shown in Fig. 4. The autoignition ahead of flame will generates a violent pressure oscillation as discussed in Fig. 5 later. Note that the combustion mode M6 appears at a particular condition according to the well-known SWACER (shock wave amplifica-
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tion by coherent energy release) or the Zeldovich mechanism. In our previous experiment [48], we employed a spark to ignite the hydrogen-air mixture in end gas, but it could not form the detonation. Similarly, the calculated result of Chen [49] also presented the combustion mode of end-gas auto ignition without detonation as develop in a closed chamber with the hydrogen-air mixture. Overall, the flame-shock interaction based on the RM instability mechanism [30] results in very different combustion phenomena from M3 to M6 in the present experiment. Note that the RT and RM instabilities are powerful instabilities that may strongly influence and dominate the flame accelerating propagation process. However, in initial turbulent formation and development the turbulent flame self-acceleration theory by Law and Akkerman [6,13,14] will control turbulent flame propagation. Once the compression wave induced by the accelerating flame become sufficiently strong the RT or RM instability will determine the whole flame acceleration and combustion phenomena. Of course, the different combustion modes are also relevant to local thermodynamic conditions. In confined space, combustion is always accompanied by the pressure oscillation. Therefore, the pressure oscillations for different combustion modes are shown in Fig. 5. It can be seen that following the increase of combustion intensity, the pressure oscillation intensifies and the peak amplitude of the pressure oscillation also increases. They almost have a linear relationship. The maximum amplitude is approximately 6 MPa for combustion mode M5 with autoignition in front of the flame. Meanwhile, the peak pressure is approximately 4.5 MPa for combustion mode M6 with end-gas autoignition obtained in the present work. In previous studies, the pressure oscillation is close to flame tip velocity oscillation, named resonance of flame–acoustic. For intense turbulent flame propagation in confined space, the obvious resonance is not obtained, because of the more complicated combustion pressure wave from every direction in confined space. However, several critical spikes of pressure oscillation are consistent with the turbulent flame and shock wave propagations that are not presented here. 5. Conclusions This experiment is carried out by our designed experimental apparatus equipped with a perforated plate. The effect of the perforated plate is to generate a rapidly accelerating flame and form a turbulent flame. This work experimentally reveals possible modes of flame propagation and combustion phenomena in confined space clearly. It is found that, in the presence of the perforated plate, the turbulent flame formed through the perforated plate may perform six types of flame propagations at the end gas regime owing to the interaction between flame and shock wave or acoustic wave and the limiting effect of the wall in the confined space. The different pressure oscillations depending on the different combustion modes are observed. Note that the present work cannot employ the mathematical method to quantitatively evaluate the turbulent flame propagation due to the complexity of the combustion phenomena. In the future, we will try to use the mathematical proof to analyze the combustion modes.
Fig. A1. Evolution of flame propagation when passing through the perforated plate (Up: experimental results, Below: numerical results).
Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 91641203, 51606133). We also thank the reviewers for providing helpful comments and suggestions. Appendix A. Flame passing through the perforated plate The evolution of flame propagation when passing through the perforated plate by experiment and simulation is shown in Fig. A1.
Fig. A2. Evolution of flame propagation velocity when passing through the perforated plate (experimental and numerical results).
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Fig. A3. Variation of temperature and velocity in the centerline of the combustion chamber (Numerical results).
The case condition is carried out at an initial pressure of 4 bar and hole size of 3 mm. It is noted that constrained by the size of the optical window, only the region from 0 to 78 mm could be observed. Distinguished by the flame morphology and propagation velocity, three distinct stages were observed in the in the process of flame propagation over the orifice plate: laminar flame stage, jet flame stage and turbulent flame stage. During the laminar flame stage, the flame presented as a semi-spherical shape driven by the no-slip boundary condition on the wall and Darrieus–Landua instability. When the flame passed through the perforated plate, the flame front was split into several jet flames with an intense increase of the flame propagation velocity. As time went on, the jet flames coalesced with each other and a wrinkled turbulent flame was formed. Note that the present numerical method only can perform the simply process of flame passing through perforated plate, the entire process cannot be well carried out. Figure A2 shows the evolution of flame propagation velocity when passing through the perforated plate. Although the nu-
merical flame velocity was lower than the experimental velocity, the evolution trends of flame propagation velocity were consistent with the present experiment. During the laminar flame stage, the flame propagation velocity increased at first and then descended. When the flame approached the perforated plate, the flame decelerated due to the hindering effect of the obstacle. After passed through the perforated plate, the flame propagation velocity increased in an order of magnitude, from around 20 m/s to 110 m/s. The flame acceleration was induced by the delayed burning combustion before the flame passes through the perforated plate, which could produce a powerful jet flow and subsequently lead to an extremely high flame tip velocity. Additionally, the present perforated plate performed that it could generate stronger turbulence, which increased the burning rate and facilitated flame acceleration. With the departure of the flame front from the perforated, the flame propagation naturally performed a decline due to fluid-dynamic mechanisms. When the corrugated turbulent flame was formed, the turbulent flame performed a selfsimilar and self-acceleration process. The relevant theory explanations can be found in main text. The variation of the temperature and velocity in the centerline of the combustion chamber was investigated to demonstrate the interactions of flame and combustion-generated flow during the evolution of flame passing through the perforated plate, which is shown in Fig. A3. Five time points are selected, including 0.400, 0.700, 0.975, 1.225 and 1.400 ms. Before the flame passing through the perforated at 0.400 and 0.700 ms, a powerful jet flow was formed close to the perforated plate downstream, which made great contributions to the flame acceleration when passing through the perforated plate. After the flame passed through the perforated plate at 0.975, 1.225 and 1.400 ms, the velocity of unburned gas decreased as with the distance departing from the flame front, which means that the gas velocity was driven by the flame in this period. It also can be seen that the flame front surpasses the peak of flow velocity after flame passed through perforated plate. The results resembles the quantitatively studies in [37,46]. Appendix B. flame pulsation propagations of different combustion modes Figure A4 shows the evolutions of flame propagation velocity versus time after the perforated plate at different combustion modes. Overall, the flame propagation velocity experienced a decline trend after passing through the perforated plate at every combustion mode. In the end of the combustion chamber, the flame propagation velocity oscillated due to flame-acoustic/shock wave interaction. Depending on the intensity of the shock wave, the oscillating amplitude was different among different combustion modes. The oscillating amplitude was smallest at Mode 2, and biggest at Mode 4. And it is worth nothing that the flame back-
Fig. A4. Oscillating propagation of the flame at different combustion modes.
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