- Email: [email protected]
Reinitiation phenomenon in hydrogen-air rotating detonation engine
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Reinitiation phenomenon in hydrogen-air rotating detonation engine Songbai Yao, Zhuang Ma, Shujie Zhang, Mingyi Luan, Jianping Wang* Center for Combustion and Propulsion, CAPT & SKLTCS, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China
article info
abstract
Article history:
This article presents a numerical study on the rotating detonation engine (RDE). The
Received 10 July 2017
simulation explores the phenomenon of the reinitiation of detonations in the RDE with a
Received in revised form
cylindrical combustion chamber. The process is modelled by the three-dimensional reac-
29 August 2017
tive Euler equations with an Arrhenius form of the reaction rate for the premixed stoi-
Accepted 1 September 2017
chiometric hydrogen-air mixture. The detonation flow goes through three stages:
Available online xxx
initiation, quenching, and spontaneous reinitiation. The detonation fronts collide with each other and also have frequent collisions with the outer wall after initiation. While
Keywords:
there is a possibility of generating new detonation fronts from the explosion, it is also likely
Rotating detonation
that the explosion will burn out the surrounding reactive mixtures and snuff out the
Reinitiation
detonation waves. The simulation shows that a strong collision between two detonation
Simulation
wave fronts extinguishes the detonation flow and consequently renders the engine inop-
Detonation engine
erative for an extended period until a spontaneous reinitiation occurs in the flow. The reinitiation is found to be triggered by a rapid and sharp increase of pressure near the chamber wall. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction There are in general two modes of combustion for explosive mixtures: deflagration and detonation [1]. For the former, the propagation velocity of flame is of the order of 1 m/s with respect to the unburned mixtures, whereas for the latter, the detonation is a supersonic combustion wave with a strong leading shock which is sustained by the subsequent postshock heat release. The detonation wave propagates at the speed of the order of 2000 m/s. The possibility of these two modes of combustion was reported by Mallard and Le Chatelier [2] (1881) at the School of Mines in Paris. Most of the early research on detonation is aimed to explore the physical mechanism and chemical process of
detonation phenomena [1]. The enormous power of detonations can cause destructive consequences and hence the prevention of accidental detonation is a major branch of detonation research. In contrast, some researchers pay attention to the utilization of detonations for propulsion systems. In the 1950s, attempts at harnessing the power of detonations for propulsion systems have led to the concept of detonation engines. Nicholls et al. [3] examined the feasibility of a propulsion device operating on “intermittent gaseous detonation waves” at the University of Michigan, which was more frequently called “pulsed detonation engines (PDE)” afterwards. Meanwhile, Voitsekhovskii [4] from the Lavrent'ev Institute of Hydrodynamics (LIH) achieved rotating detonations in the combustion chamber with premixed acetylene-
* Corresponding author. E-mail addresses: [email protected], [email protected] (J. Wang). https://doi.org/10.1016/j.ijhydene.2017.09.015 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
2
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 1 e Voltage-time signal (hydrogen-air mixture). oxygen mixtures. The rotating detonation engine (RDE), which is also called the continuous detonation engine (CDE), has become another concept of a detonation-based propulsion system. Bykovskii et al. [5] from LIH have initiated a programme of research on the RDE with different geometries and various gaseous and liquid fuels since early 1970s. They have made remarkable achievements in testing the feasibility of the RDE. As Lu and Braun [6] suggested in their review article, the experimental research on the RDE over the past decades
has further demonstrated the feasibility of the RDE and attracted worldwide attention. Frolov et al. [7] carried out a large-scale RDE with a total mass flow rate of 7.5 kg/s. They obtained a maximum thrust of 6 kN and a fuel-based specific impulse of 3000 s. They recently achieved rotating detonations with the ternary “hydrogen-liquid propane-air” mixture [8].
Table 1 e Chemistry model parameters for stoichiometric hydrogen-air detonations [34]. Parameter
Value
g1 (reactants) g2 (products) R1 ðJ=kg$KÞ R2 ðJ=kg$KÞ QðMJ=kgÞ Ta ðKÞ Að1=sÞ
Fig. 2 e Schematic of RDE with a cylindrical chamber.
1.3961 1.1653 395.75 346.2 5.4704 15100 1.0 109
Fig. 3 e Schematic of initiation.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
3
Fig. 4 e Pressure distributions of the flow after initiation during the period of t ¼ 18e46 ms. The international research team led by Wolanski has entailed the application of the RDE to the gas turbine, GTD-350 [9]. The U. S. Air Force Research Laboratory conducted a series of experiments in an optically accessible RDE [10]. They also examined the performance of the RDE with different configurations in terms of thrust and specific impulse [11]. Also, substantial progress has been made by University of Cincinnati [12], MBDA [13], CNRS [14], Nagoya University [15], Nanjing University of Science and Technology [16], National University of Defense Technology [17], and Peking University [18,19], among others. In addition, a great many numerical simulations, e.g., the studies of [20e26], have been performed to analyse various aspects of rotating detonations since Zhdan et al. [27] carried out the first numerical study on the RDE. The initiation, propagation, and stabilization of rotating detonation waves require further investigation, as pointed out by Lu and Braun. In addition, the reinitiation of detonations has been observed in our experiments (Fig. 1). After ignition,
we observed the formation of continuously rotating detonations in the combustion chamber. And some time later, detonations were quenched and the RDE remained idle for a period of time. Detonations, however, were found to reinitiate spontaneously in the combustion chamber. In some other experiments [12], the failure and reinitiation of detonations in the RDE were also observed. Fundamental research on the reinitiation of detonations has been conducted, such as the work of Oran et al. [28] and Williams et al. [29]. Smirnov and Nikitin [30] developed three-dimensional codes which can be used for the simulations of onset, decay, and reinitiation of detonations, and they also analyzed these detonation-related phenomena in the tube with cavities by theoretical and experimental investigations [31]. The reinitiation of detonations in the RDE, however, has not been discussed in detail, especially by numerical simulation. In this study, we reproduced the reinitiation of detonations in a hydrogen-air RDE with a cylindrical chamber [32,33] (Fig. 2) through three-
Fig. 5 e Pressure distributions of the flow after initiation during the period of t ¼ 48e64 ms. Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
4
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 6 e Pressure distributions of the flow e collision between two detonation wave fronts.
Fig. 7 e Pressure distributions of the flow e the collision and the subsequent quenching of detonations.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
5
Fig. 8 e Pressure distributions of the flow e “in the doldrums”.
Fig. 9 e Variation of the average axial velocity along the length of the chamber (L). dimensional simulations. Moreover, the possible mechanism underlying this phenomenon was discussed.
Problem formulations and numerical methodology
rt þ V $ðruÞ ¼ 0;
(1)
ðruÞt þ V $ðruuÞ þ Vp ¼ 0;
(2)
ðreÞt þ V $ððre þ pÞuÞ ¼ 0;
(3)
_ ðrbÞt þ V $ðrubÞ ¼ u:
(4)
Governing equations and numerical methodology In this study, the cylindrical combustion chamber has a radius of 6.0 cm in and is 8.0 cm in length. The governing equations are the three-dimensional Euler equations:
The gaseous mixtures are assumed to be perfect. The total energy e is given by:
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
6
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 10 e Distribution of pressure over the cross section located at z ¼ 0.025 m. The colour scale shows the values of pressure. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
p 1 þ ui ui þ bQ; e¼ r$ðg 1Þ 2
(5)
where Q is the chemical energy, b the reaction progress variable, and g the ratio of specific heats. The simulations assume a one-step irreversible Arrhenius kinetics that converts reactive gaseous mixtures into products: Ta ; u_ ¼ Arbexp T
(6)
where Ta is the activation temperature and A is the preexponential constant. The chemical parameters [34] are summarized in Table 1. We avoid duplication of the materials that can be found in our previous research [33]. In order to make the paper self-contained, however, a certain amount of description of the computational methodology is given below. An embedded partition grid system is adopted to avoid the singularity problem at the central axis of the cylindrical coordinates. A computational grid size of 0.5 mm is used in the azimuthal (averaged), radial and axial directions. The flux terms are integrated by the fifth-order monotonicity-preserving weighted essentially non-oscillatory (MPWENO) scheme and are marched in time with the third-order total variation diminishing (TVD) Runge-Kutta method. Further details about the numerical methods and code validations can be found in Ref. [33]. The accumulation of errors in our simulations is estimated using the method suggested by Smirnov et al. [35] and it is found to be within acceptable limits. Lau-Chapdelaine [36] performed a series of simulations to explore the mechanisms responsible for the reinitiation of detonations diffracting over a cylindrical obstacle. On the basis of a comparison between solutions calculated by the one- and two-step chemistry models, he found that the onestep chemistry model is sufficient in replicating and predicting reinitiation of detonations, whereas the two-step chemistry model is capable of reproducing some of the finer details. The one-step Arrhenius chemistry model has some other limitations. For instance, due to the absence of a loss
mechanism, the one-step Arrhenius chemistry model cannot give the critical initiation energy, detonation limits, and the like [1].
Initiation and boundary conditions The pre-detonator connected tangentially to the combustion chamber emits a detonation wave into the annulus and starts the RDE in the experiment, which is one of the most frequently employed means of ignition. Similarly, a steady ChapmanJouguet (C-J) detonation wave obtained from one-dimensional simulations is mapped onto the head of the combustion chamber to simulate the pre-detonator. The entire combustion chamber is initially filled with reactive mixtures (Fig. 3). The injection stagnation pressure and temperature of the reactive gaseous mixtures are fixed at 3 MPa and 600 K, respectively, assuming a quiescent infinite reservoir of fuel supply. The injection conditions (p, T, w) are set assuming micro Laval nozzles inlet that is similar to the experimental set-up [37]. The injection conditions depend on the pressure on the head wall pw : (1) In the case of p0 pw , the reactive mixtures cannot be injected into the combustion chamber; (2) In the case of p1 pw < p0 , the flow downstream of the throat is subsonic and is given by the isentropic solutions; (3) In the case of p2 pw < p1 , a normal shock wave is formed downstream of the throat and the flow is given by the normal shock equations; (4) In the case of pw < p2 , the flow downstream of the throat is supersonic and the flow in the nozzle no longer communicates with the wall pressure pw . The critical pressure p1 is given by the isentropic solutions: gþ1 2ðg1Þ se 1 2 g1 2 M 1 þ ¼ ; ae 2 s Mae g þ 1
(7)
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
7
Fig. 11 e Contours of (a) reaction progress variable and (b) pressure of the flow field over the cross section located at z ¼ 0.025 m.
where se is the area at the exit and s* the area at the throat ðse =s* ¼ 10Þ. As a function of se =s , the exit Mae is doublevalued and p1 is the pressure corresponding to the case of subsonic flow ðMae < 1Þ at the exit of the injector. The normal shock stands precisely at the exit when p ¼ p2 and thus p2 can be obtained from the normal shock equations. Adiabatic, slip and non-catalytic boundary conditions are enforced at the outer wall. As for the outflow boundary conditions, they are
obtained by an extrapolation method suggested by Gamezo et al. [38]: Yb ¼ Y1 ð1 rÞ þ Y∞ r;
(8)
where r ¼ 0.05 is the relaxation rate coefficient, Y1 ðp1 ; r1 ; b1 Þ the values in the first cell near the boundary and Y∞ ðp∞ ; r∞ ; b∞ Þ the values of the ambient flow parameters. The ambient pressure p∞ is set to 0.05 MPa.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
8
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 12 e Pressure versus time at the point x ¼ 0.03 m, y ¼ ¡0.04 m, z ¼ 0.025 m.
Results and discussion Initial stage Fig. 4 shows the pressure distribution of the flow after initiation. The initial detonation wave is injected tangentially in a clockwise direction and the detonation front is pointed by arrow A. Apart from detonation front A, multiple shock waves begin to propagate throughout the entire region filled with reactive mixtures. There is strong likelihood that detonations or explosions will happen somewhere else due to the compression effect. At t ¼ 46 ms, a shock wave has developed into a strong detonation front which is on a collision course with the outer wall (arrow B in Fig. 4). The collision triggers an explosion which generates a new detonation front C (Fig. 5) that propagates on the opposite side of the detonation front B. In the meantime, a reflected shock has also developed into a new detonation front at t ¼ 62 ms (arrow D in Fig. 5). Meanwhile, a collision between the detonation fronts A and B is going to occur. The three-dimensional figures are reduced to two-dimensions by unwrapping the annulus ðR ¼ 0:06 mÞ along the azimuthal direction and mapping the flow field to a rectangular coordinate. The fuel injection area is located at the bottom of Fig. 6 and the exit area at the top. During the period of t ¼ 62 ms to t ¼ 64 ms, the detonation fronts A and B are moving toward each other and they collide head-on at t ¼ 64 ms. Unlike the previous collision between the detonation front B and the outer wall, this one does not generate new detonation waves. On the contrary, the reactive mixtures surrounding the detonation waves are burned out by the explosion and hence the detonation fronts A and B are extinguished. The detonation front C initiated previously continues to rotate on the periphery of the combustion chamber. During this initial period, the detonation flow is unstable and the interactions are intensive. However, the behaviour of detonation waves falls into four major categories that have been described above: propagation, collision (between each other and with the outer wall), generation, and quenching.
Reinitiation of quenched detonation During the period of t ¼ 1375 ms to t ¼ 1380 ms, a collision between two remaining detonation fronts snuffs out the detonation flow (Fig. 7). The flow maintains the status quo for a period of over 500 ms (Fig. 8). The characteristics of the flow during this period can be described by the average axial velocity of every cross section along the length of the combustion chamber (L), which is calculated by: Z wdS w¼
S
;
(9)
where w is the axial velocity of fluid particles and S the cross section area. Fig. 9 shows the variation of w along the length of the combustion chamber during the period of t ¼ 1400 ms to t ¼ 1900 ms. It demonstrates that the burned products in Fig. 8 accelerate toward the exit. In addition, since detonations are extinguished, the expansion process slows down gradually. It is therefore found in Fig. 9 that the curve descends successively from t ¼ 1400 ms to t ¼ 1900 ms. At t ¼ 1916 ms, shock waves are observed gathering in the area circled in Figs. 10 and 11b. And then at t ¼ 1918 ms a high pressure spot near the outer wall appears, which is captured in the cross section located at z ¼ 0:025 m. This high pressure spot sets off a reinitiation. It is worth noting that our results demonstrate some common features with other studies [39,40]. The reinitiation of detonations occurs at the spot surrounded by the hot reaction products (Fig. 11a). The unburned reactive mixtures are compressed and ignited by strong shock waves. Smirnov et al. [31] pointed out three possible scenarios in the analysis of detonation initiation; one of them is that a strong shock wave is formed due to a local energy release and, as a result of compression, reactions are activated in the gas at elevated temperatures. Lau-Chapdelaine [36] also summarized four possible mechanisms whereby a detonation can reinitiate and one of them is auto-ignition following shock compression. The reason why the high pressure spot appears near the chamber wall is probably due to the effect of concave wall curvature: the compression is most pronounced near the concave wall.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
9
Fig. 13 e Distribution of pressure and temperature of the flow e development of detonations after reinitiation. Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
10
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 14 e (a) Simulation: propagation of detonations at t ¼ 1932 ms and (b) experiment: natural luminosity image of autoignition of detonations [42].
Fig. 12 shows the pressure measurement at a fixed point near the reinitiation spot. The pressure signal presents a pressure rise of Dpz4MPa at t ¼ 1916 ms when the renitiation takes place. The development of detonations after the reinitiation is shown in Fig. 13. The reinitiation creates a new detonation front C2 which propagates into reactive mixtures and spreads over the entire cross section. The detonation front C2 will develop in the course of propagation, which can reach Uz1950 m/s, very close to the C-J detonation velocity. Meanwhile, the explosion triggered by the reinitiation collides with the outer wall and the reflected waves bounce back toward the reactive mixtures, resulting in the formation of the detonation fronts A2 and B2. This is consistent with the observations that strong shock reflection could initiate detonations in the experiment [41]. The detonation fronts A2 and B2 start to move along the periphery of the combustion chamber since the reactive mixtures surrounding the explosion position are already burned out due to the explosion. In Fig. 12, the oscillations of pressure after t ¼ 1916 ms are caused by those reflected shock waves propagating toward the center. It is interesting to find that the reinitiation process in the RDE bears some similarity to the auto-ignition of detonations in internal combustion engines, although it cannot directly extend to the case studied here. By varying the initial thermodynamic conditions of the combustion chamber, Qi et al. [42] observed in several cases that detonations were initiated. The incandescent zone in Fig. 14b is a detonation, which was the result of the explosion and the collision with the combustion chamber wall. They found that the detonation was initiated by the near-wall auto-ignition. This is also the case in the simulations, as shown earlier in Fig. 11. The detonation developed similarly in the experiment. The detonation front indicated by the black arrow in Fig. 14b was reported to be a self-sustained detonation wave propagating with a speed close to C-J detonation. Like detonation front A2 and B2 in Fig. 14a, the other two newly-initiated wave fronts in Fig. 14b move along the periphery of the chamber wall, depicted by the dotted yellow arrows.
Conclusions The present work discussed the phenomenon of the reinitiation of detonations in the RDE with a cylindrical combustion chamber. The reinitiation of detonations was observed in our experiments and investigated in detail by a three-dimensional simulation. Our simulation showed that detonation waves propagated in more than one direction in the flow after initiation. They collided with each other and with the outer wall, thus reconstructing the detonation flow intensively. The collision created explosions which were likely to generate new detonation fronts or, conversely, extinguish detonations. In the simulation, a strong head-on collision between two detonation fronts snuffed out the detonation flow. After a period of time, a spontaneous reinitiation was triggered by a high pressure spot near the outer wall of the combustion chamber. It was demonstrated that the reinitiation of detonations occurred due to the formation of strong shock waves at the spot where unburned mixtures were surrounded by reaction products.
Acknowledgments This research has been supported by the National Natural Science Foundation of China (Grant No. 91441110).
references
[1] Lee JHS. The detonation phenomenon. 1st ed. Cambridge, UK: Cambridge University Press; 2008. [2] Mallard E, Le Chatelier H. Sur les vitesses de propagation de langes gazeux explosifs. Comptes l’inflammation dans les me ances l’Acade mie Sci 1881;93:145e8. Rendus Hebd Se [3] Nicholls JA, Wilkinson HR, Morrison RB. Intermittent detonation as a thrust-producing mechanism. J Propul Power 1957;27:534e41. [4] Voitsekhovskii BV. Statsionarnaya Dyetonatsiya. Sov Dokl Fluid Mech 1959;129:1254e6.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
[5] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous spin detonations. J Propul Power 2006;22:1204e16. [6] Lu FK, Braun EM. Rotating detonation wave propulsion: experimental challenges, modeling, and engine concepts. J Propul Power 2014;30:1125e42. [7] Frolov SM, Aksenov VS, Ivanov VS, Shamshin IO. Large-scale hydrogen-air continuous detonation combustor. Int J Hydrogen Energy 2015;40:1616e23. [8] Frolov SM, Aksenov VS, Ivanov VS, Shamshin IO. Continuous detonation combustion of ternary “hydrogeneliquid propaneeair” mixture in annular combustor. Int J Hydrogen Energ 2017;42:16808e20. ski P. Detonative propulsion. Proc Combust Inst [9] Wolan 2013;34:125e58. [10] Rankin BA, Richardson DR, Caswell AW, Naples AG, Hoke JL, Schauer FR. Chemiluminescence imaging of an optically accessible non-premixed rotating detonation engine. Combust Flame 2017;176:12e22. [11] Fotia ML, Schauer F, Kaemming T, Hoke J. Experimental study of the performance of a rotating detonation engine with nozzle. J Propul Power 2016;32:674e81. [12] St George A, Driscoll R, Anand V, Gutmark EJ. Starting transients and detonation onset behavior in a rotating detonation combustor. In: 54th AIAA Aerospace Sciences Meeting, San Diego; 2016. [13] Le Naour B, Falempin F, Coulon K. MBDA R&T effort regarding continuous detonation wave engine for propulsion e status in 2016. In: International Space Planes and Hypersonic Systems and Technologies Conferences; 2017. [14] Zitoun R, Hansmetzger P, Vidal P, Chinnayya A, Rodriguez V, Virot F, et al. Detonation regimes in a small-scale RDE. In: International Constant Volume and Detonation Combustion Workshop 2017, Poitiers, France; 2017. [15] Nakagami S, Matsuoka K, Kasahara J, Matsuo A, Funaki I. Experimental study of the structure of forward-tilting rotating detonation waves and highly maintained combustion chamber pressure in a disk-shaped combustor. Proc Combust Inst 2017;36:2673e80. [16] Zhou S, Ma H, Liu D, Yan Y, Li S. Experimental study of a hydrogen-air rotating detonation combustor. Int J Hydrogen Energ 2017;42:14741e9. [17] Zhang H, Liu W, Liu S. Experimental investigations on H2/air rotating detonation wave in the hollow chamber with Laval nozzle. Int J Hydrogen Energ 2017;42:3363e70. [18] Liu Y, Wang Y, Li Y, Li Y, Wang J. Spectral analysis and selfadjusting mechanism for oscillation phenomenon in hydrogen-oxygen continuously rotating detonation engine. Chin J Aeronaut 2015;28:669e75. [19] Wang Y, Wang J, Li Y, Li Y. Induction for multiple rotating detonation waves in the hydrogeneoxygen mixture with tangential flow. Int J Hydrogen Energy 2014;39:11792e7. [20] Hishida M, Fujiwara T, Wolanski P. Fundamentals of rotating detonations. Shock Waves 2009;19:1e10. [21] Yi T, Lou J, Turangan C, Choi J, Wolanski P. Propulsive performance of a continuously rotating detonation engine. J Propul Power 2011;27:171e81. [22] Zhou R, Wang J. Numerical investigation of flow particle paths and thermodynamic performance of continuously rotating detonation engines. Combust Flame 2012;159:3632e45. [23] Schwer D, Kailasanath K. Fluid dynamics of rotating detonation engines with hydrogen and hydrocarbon fuels. Proc Combust Inst 2013;34:1991e8.
11
[24] Gaillard T, Davidenko D, Dupoirieux F. Numerical optimisation in non reacting conditions of the injector geometry for a continuous detonation wave rocket engine. Acta Astronaut 2015;111:334e44. [25] Tsuboi N, Watanabe Y, Kojima T, Hayashi AK. Numerical estimation of the thrust performance on a rotating detonation engine for a hydrogeneoxygen mixture. Proc Combust Inst 2015;35:2005e13. [26] Dubrovskii AV, Ivanov VS, Frolov SM. Three-dimensional numerical simulation of the operation process in a continuous detonation combustor with separate feeding of hydrogen and air. Russ J Phys Chem B 2015;9:104e19. [27] Zhdan SA, Bykovskii FA, Vedernikov EF. Mathematical modeling of a rotating detonation wave in a hydrogenoxygen mixture. Combust Explos Shock Waves 2007;43:449e59. [28] Oran ES, Jones DA, Sichel M. Numerical simulations of detonation transmission. Proc R Soc Lond A 1992;436:267e97. [29] Williams DN, Bauwens L, Oran ES. A numerical study of the mechanisms of self-reignition in low-overdrive detonations. Shock Waves 1996;6:93e110. [30] Smirnov NN, Nikitin VF. Modeling and simulation of hydrogen combustion in engines. Int J Hydrogen Energ 2014;39:1122e36. [31] Smirnov NN, Nikitin VF, Phylippov YG. Deflagration-todetonation transition in gases in tubes with cavities. J Eng Phys Thermophys 2010;83:1287e316. [32] Shao Y, Wang JP. Three dimensional simulation of rotating detonation engine without inner wall. In: 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems, Irvine; 2011. [33] Tang X, Wang J, Shao Y. Three-dimensional numerical investigations of the rotating detonation engine with a hollow combustor. Combust Flame 2015;162:997e1008. [34] Ma F, Choi J, Yang V. Propulsive performance of air breathing pulse detonation engines. J Propul Power 2006;22:1188e203. [35] Smirnov NN, Betelin VB, Nikitin VF, Stamov LI, Altoukhov DI. Accumulation of errors in numerical simulations of chemically reacting gas dynamics. Acta Astronaut 2015;117:338e55. [36] Lau-Chapdelaine SSM. Numerical simulations of detonation re-initiation behind an obstacle. Canada: University of Ottawa; 2013. [37] Lin W, Zhou J, Liu S, Lin Z. An experimental study on CH4/O2 continuously rotating detonation wave in a hollow combustion chamber. Exp Therm Fluid Sci 2015;62:122e30. [38] Gamezo VN, Desbordes D, Oran ES. Formation and evolution of two-dimensional cellular detonations. Combust Flame 1999;116:154e65. [39] Liberman MA, Ivanov MF, Kiverin AD, Kuznetsov MS, Chukalovsky AA, Rakhimova TV. Deflagration-to-detonation transition in highly reactive combustible mixtures. Acta Astronaut 2010;67:688e701. [40] Smirnov NN, Betelin VB, Nikitin VF, Phylippov YG, Koo J. Detonation engine fed by acetyleneeoxygen mixture. Acta Astronaut 2014;104:134e46. [41] Jones DA, Sichel M, Oran ES. Reignition of detonations by reflected shocks. Shock Waves 1995;5:47e57. [42] Qi Y, Wang Z, Wang J, He X. Effects of thermodynamic conditions on the end gas combustion mode associated with engine knock. Combust Flame 2015;162:4119e28.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Reinitiation phenomenon in hydrogen-air rotating detonation engine Songbai Yao, Zhuang Ma, Shujie Zhang, Mingyi Luan, Jianping Wang* Center for Combustion and Propulsion, CAPT & SKLTCS, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China
article info
abstract
Article history:
This article presents a numerical study on the rotating detonation engine (RDE). The
Received 10 July 2017
simulation explores the phenomenon of the reinitiation of detonations in the RDE with a
Received in revised form
cylindrical combustion chamber. The process is modelled by the three-dimensional reac-
29 August 2017
tive Euler equations with an Arrhenius form of the reaction rate for the premixed stoi-
Accepted 1 September 2017
chiometric hydrogen-air mixture. The detonation flow goes through three stages:
Available online xxx
initiation, quenching, and spontaneous reinitiation. The detonation fronts collide with each other and also have frequent collisions with the outer wall after initiation. While
Keywords:
there is a possibility of generating new detonation fronts from the explosion, it is also likely
Rotating detonation
that the explosion will burn out the surrounding reactive mixtures and snuff out the
Reinitiation
detonation waves. The simulation shows that a strong collision between two detonation
Simulation
wave fronts extinguishes the detonation flow and consequently renders the engine inop-
Detonation engine
erative for an extended period until a spontaneous reinitiation occurs in the flow. The reinitiation is found to be triggered by a rapid and sharp increase of pressure near the chamber wall. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction There are in general two modes of combustion for explosive mixtures: deflagration and detonation [1]. For the former, the propagation velocity of flame is of the order of 1 m/s with respect to the unburned mixtures, whereas for the latter, the detonation is a supersonic combustion wave with a strong leading shock which is sustained by the subsequent postshock heat release. The detonation wave propagates at the speed of the order of 2000 m/s. The possibility of these two modes of combustion was reported by Mallard and Le Chatelier [2] (1881) at the School of Mines in Paris. Most of the early research on detonation is aimed to explore the physical mechanism and chemical process of
detonation phenomena [1]. The enormous power of detonations can cause destructive consequences and hence the prevention of accidental detonation is a major branch of detonation research. In contrast, some researchers pay attention to the utilization of detonations for propulsion systems. In the 1950s, attempts at harnessing the power of detonations for propulsion systems have led to the concept of detonation engines. Nicholls et al. [3] examined the feasibility of a propulsion device operating on “intermittent gaseous detonation waves” at the University of Michigan, which was more frequently called “pulsed detonation engines (PDE)” afterwards. Meanwhile, Voitsekhovskii [4] from the Lavrent'ev Institute of Hydrodynamics (LIH) achieved rotating detonations in the combustion chamber with premixed acetylene-
* Corresponding author. E-mail addresses: [email protected], [email protected] (J. Wang). https://doi.org/10.1016/j.ijhydene.2017.09.015 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
2
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 1 e Voltage-time signal (hydrogen-air mixture). oxygen mixtures. The rotating detonation engine (RDE), which is also called the continuous detonation engine (CDE), has become another concept of a detonation-based propulsion system. Bykovskii et al. [5] from LIH have initiated a programme of research on the RDE with different geometries and various gaseous and liquid fuels since early 1970s. They have made remarkable achievements in testing the feasibility of the RDE. As Lu and Braun [6] suggested in their review article, the experimental research on the RDE over the past decades
has further demonstrated the feasibility of the RDE and attracted worldwide attention. Frolov et al. [7] carried out a large-scale RDE with a total mass flow rate of 7.5 kg/s. They obtained a maximum thrust of 6 kN and a fuel-based specific impulse of 3000 s. They recently achieved rotating detonations with the ternary “hydrogen-liquid propane-air” mixture [8].
Table 1 e Chemistry model parameters for stoichiometric hydrogen-air detonations [34]. Parameter
Value
g1 (reactants) g2 (products) R1 ðJ=kg$KÞ R2 ðJ=kg$KÞ QðMJ=kgÞ Ta ðKÞ Að1=sÞ
Fig. 2 e Schematic of RDE with a cylindrical chamber.
1.3961 1.1653 395.75 346.2 5.4704 15100 1.0 109
Fig. 3 e Schematic of initiation.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
3
Fig. 4 e Pressure distributions of the flow after initiation during the period of t ¼ 18e46 ms. The international research team led by Wolanski has entailed the application of the RDE to the gas turbine, GTD-350 [9]. The U. S. Air Force Research Laboratory conducted a series of experiments in an optically accessible RDE [10]. They also examined the performance of the RDE with different configurations in terms of thrust and specific impulse [11]. Also, substantial progress has been made by University of Cincinnati [12], MBDA [13], CNRS [14], Nagoya University [15], Nanjing University of Science and Technology [16], National University of Defense Technology [17], and Peking University [18,19], among others. In addition, a great many numerical simulations, e.g., the studies of [20e26], have been performed to analyse various aspects of rotating detonations since Zhdan et al. [27] carried out the first numerical study on the RDE. The initiation, propagation, and stabilization of rotating detonation waves require further investigation, as pointed out by Lu and Braun. In addition, the reinitiation of detonations has been observed in our experiments (Fig. 1). After ignition,
we observed the formation of continuously rotating detonations in the combustion chamber. And some time later, detonations were quenched and the RDE remained idle for a period of time. Detonations, however, were found to reinitiate spontaneously in the combustion chamber. In some other experiments [12], the failure and reinitiation of detonations in the RDE were also observed. Fundamental research on the reinitiation of detonations has been conducted, such as the work of Oran et al. [28] and Williams et al. [29]. Smirnov and Nikitin [30] developed three-dimensional codes which can be used for the simulations of onset, decay, and reinitiation of detonations, and they also analyzed these detonation-related phenomena in the tube with cavities by theoretical and experimental investigations [31]. The reinitiation of detonations in the RDE, however, has not been discussed in detail, especially by numerical simulation. In this study, we reproduced the reinitiation of detonations in a hydrogen-air RDE with a cylindrical chamber [32,33] (Fig. 2) through three-
Fig. 5 e Pressure distributions of the flow after initiation during the period of t ¼ 48e64 ms. Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
4
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 6 e Pressure distributions of the flow e collision between two detonation wave fronts.
Fig. 7 e Pressure distributions of the flow e the collision and the subsequent quenching of detonations.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
5
Fig. 8 e Pressure distributions of the flow e “in the doldrums”.
Fig. 9 e Variation of the average axial velocity along the length of the chamber (L). dimensional simulations. Moreover, the possible mechanism underlying this phenomenon was discussed.
Problem formulations and numerical methodology
rt þ V $ðruÞ ¼ 0;
(1)
ðruÞt þ V $ðruuÞ þ Vp ¼ 0;
(2)
ðreÞt þ V $ððre þ pÞuÞ ¼ 0;
(3)
_ ðrbÞt þ V $ðrubÞ ¼ u:
(4)
Governing equations and numerical methodology In this study, the cylindrical combustion chamber has a radius of 6.0 cm in and is 8.0 cm in length. The governing equations are the three-dimensional Euler equations:
The gaseous mixtures are assumed to be perfect. The total energy e is given by:
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
6
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 10 e Distribution of pressure over the cross section located at z ¼ 0.025 m. The colour scale shows the values of pressure. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
p 1 þ ui ui þ bQ; e¼ r$ðg 1Þ 2
(5)
where Q is the chemical energy, b the reaction progress variable, and g the ratio of specific heats. The simulations assume a one-step irreversible Arrhenius kinetics that converts reactive gaseous mixtures into products: Ta ; u_ ¼ Arbexp T
(6)
where Ta is the activation temperature and A is the preexponential constant. The chemical parameters [34] are summarized in Table 1. We avoid duplication of the materials that can be found in our previous research [33]. In order to make the paper self-contained, however, a certain amount of description of the computational methodology is given below. An embedded partition grid system is adopted to avoid the singularity problem at the central axis of the cylindrical coordinates. A computational grid size of 0.5 mm is used in the azimuthal (averaged), radial and axial directions. The flux terms are integrated by the fifth-order monotonicity-preserving weighted essentially non-oscillatory (MPWENO) scheme and are marched in time with the third-order total variation diminishing (TVD) Runge-Kutta method. Further details about the numerical methods and code validations can be found in Ref. [33]. The accumulation of errors in our simulations is estimated using the method suggested by Smirnov et al. [35] and it is found to be within acceptable limits. Lau-Chapdelaine [36] performed a series of simulations to explore the mechanisms responsible for the reinitiation of detonations diffracting over a cylindrical obstacle. On the basis of a comparison between solutions calculated by the one- and two-step chemistry models, he found that the onestep chemistry model is sufficient in replicating and predicting reinitiation of detonations, whereas the two-step chemistry model is capable of reproducing some of the finer details. The one-step Arrhenius chemistry model has some other limitations. For instance, due to the absence of a loss
mechanism, the one-step Arrhenius chemistry model cannot give the critical initiation energy, detonation limits, and the like [1].
Initiation and boundary conditions The pre-detonator connected tangentially to the combustion chamber emits a detonation wave into the annulus and starts the RDE in the experiment, which is one of the most frequently employed means of ignition. Similarly, a steady ChapmanJouguet (C-J) detonation wave obtained from one-dimensional simulations is mapped onto the head of the combustion chamber to simulate the pre-detonator. The entire combustion chamber is initially filled with reactive mixtures (Fig. 3). The injection stagnation pressure and temperature of the reactive gaseous mixtures are fixed at 3 MPa and 600 K, respectively, assuming a quiescent infinite reservoir of fuel supply. The injection conditions (p, T, w) are set assuming micro Laval nozzles inlet that is similar to the experimental set-up [37]. The injection conditions depend on the pressure on the head wall pw : (1) In the case of p0 pw , the reactive mixtures cannot be injected into the combustion chamber; (2) In the case of p1 pw < p0 , the flow downstream of the throat is subsonic and is given by the isentropic solutions; (3) In the case of p2 pw < p1 , a normal shock wave is formed downstream of the throat and the flow is given by the normal shock equations; (4) In the case of pw < p2 , the flow downstream of the throat is supersonic and the flow in the nozzle no longer communicates with the wall pressure pw . The critical pressure p1 is given by the isentropic solutions: gþ1 2ðg1Þ se 1 2 g1 2 M 1 þ ¼ ; ae 2 s Mae g þ 1
(7)
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
7
Fig. 11 e Contours of (a) reaction progress variable and (b) pressure of the flow field over the cross section located at z ¼ 0.025 m.
where se is the area at the exit and s* the area at the throat ðse =s* ¼ 10Þ. As a function of se =s , the exit Mae is doublevalued and p1 is the pressure corresponding to the case of subsonic flow ðMae < 1Þ at the exit of the injector. The normal shock stands precisely at the exit when p ¼ p2 and thus p2 can be obtained from the normal shock equations. Adiabatic, slip and non-catalytic boundary conditions are enforced at the outer wall. As for the outflow boundary conditions, they are
obtained by an extrapolation method suggested by Gamezo et al. [38]: Yb ¼ Y1 ð1 rÞ þ Y∞ r;
(8)
where r ¼ 0.05 is the relaxation rate coefficient, Y1 ðp1 ; r1 ; b1 Þ the values in the first cell near the boundary and Y∞ ðp∞ ; r∞ ; b∞ Þ the values of the ambient flow parameters. The ambient pressure p∞ is set to 0.05 MPa.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
8
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 12 e Pressure versus time at the point x ¼ 0.03 m, y ¼ ¡0.04 m, z ¼ 0.025 m.
Results and discussion Initial stage Fig. 4 shows the pressure distribution of the flow after initiation. The initial detonation wave is injected tangentially in a clockwise direction and the detonation front is pointed by arrow A. Apart from detonation front A, multiple shock waves begin to propagate throughout the entire region filled with reactive mixtures. There is strong likelihood that detonations or explosions will happen somewhere else due to the compression effect. At t ¼ 46 ms, a shock wave has developed into a strong detonation front which is on a collision course with the outer wall (arrow B in Fig. 4). The collision triggers an explosion which generates a new detonation front C (Fig. 5) that propagates on the opposite side of the detonation front B. In the meantime, a reflected shock has also developed into a new detonation front at t ¼ 62 ms (arrow D in Fig. 5). Meanwhile, a collision between the detonation fronts A and B is going to occur. The three-dimensional figures are reduced to two-dimensions by unwrapping the annulus ðR ¼ 0:06 mÞ along the azimuthal direction and mapping the flow field to a rectangular coordinate. The fuel injection area is located at the bottom of Fig. 6 and the exit area at the top. During the period of t ¼ 62 ms to t ¼ 64 ms, the detonation fronts A and B are moving toward each other and they collide head-on at t ¼ 64 ms. Unlike the previous collision between the detonation front B and the outer wall, this one does not generate new detonation waves. On the contrary, the reactive mixtures surrounding the detonation waves are burned out by the explosion and hence the detonation fronts A and B are extinguished. The detonation front C initiated previously continues to rotate on the periphery of the combustion chamber. During this initial period, the detonation flow is unstable and the interactions are intensive. However, the behaviour of detonation waves falls into four major categories that have been described above: propagation, collision (between each other and with the outer wall), generation, and quenching.
Reinitiation of quenched detonation During the period of t ¼ 1375 ms to t ¼ 1380 ms, a collision between two remaining detonation fronts snuffs out the detonation flow (Fig. 7). The flow maintains the status quo for a period of over 500 ms (Fig. 8). The characteristics of the flow during this period can be described by the average axial velocity of every cross section along the length of the combustion chamber (L), which is calculated by: Z wdS w¼
S
;
(9)
where w is the axial velocity of fluid particles and S the cross section area. Fig. 9 shows the variation of w along the length of the combustion chamber during the period of t ¼ 1400 ms to t ¼ 1900 ms. It demonstrates that the burned products in Fig. 8 accelerate toward the exit. In addition, since detonations are extinguished, the expansion process slows down gradually. It is therefore found in Fig. 9 that the curve descends successively from t ¼ 1400 ms to t ¼ 1900 ms. At t ¼ 1916 ms, shock waves are observed gathering in the area circled in Figs. 10 and 11b. And then at t ¼ 1918 ms a high pressure spot near the outer wall appears, which is captured in the cross section located at z ¼ 0:025 m. This high pressure spot sets off a reinitiation. It is worth noting that our results demonstrate some common features with other studies [39,40]. The reinitiation of detonations occurs at the spot surrounded by the hot reaction products (Fig. 11a). The unburned reactive mixtures are compressed and ignited by strong shock waves. Smirnov et al. [31] pointed out three possible scenarios in the analysis of detonation initiation; one of them is that a strong shock wave is formed due to a local energy release and, as a result of compression, reactions are activated in the gas at elevated temperatures. Lau-Chapdelaine [36] also summarized four possible mechanisms whereby a detonation can reinitiate and one of them is auto-ignition following shock compression. The reason why the high pressure spot appears near the chamber wall is probably due to the effect of concave wall curvature: the compression is most pronounced near the concave wall.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
9
Fig. 13 e Distribution of pressure and temperature of the flow e development of detonations after reinitiation. Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
10
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
Fig. 14 e (a) Simulation: propagation of detonations at t ¼ 1932 ms and (b) experiment: natural luminosity image of autoignition of detonations [42].
Fig. 12 shows the pressure measurement at a fixed point near the reinitiation spot. The pressure signal presents a pressure rise of Dpz4MPa at t ¼ 1916 ms when the renitiation takes place. The development of detonations after the reinitiation is shown in Fig. 13. The reinitiation creates a new detonation front C2 which propagates into reactive mixtures and spreads over the entire cross section. The detonation front C2 will develop in the course of propagation, which can reach Uz1950 m/s, very close to the C-J detonation velocity. Meanwhile, the explosion triggered by the reinitiation collides with the outer wall and the reflected waves bounce back toward the reactive mixtures, resulting in the formation of the detonation fronts A2 and B2. This is consistent with the observations that strong shock reflection could initiate detonations in the experiment [41]. The detonation fronts A2 and B2 start to move along the periphery of the combustion chamber since the reactive mixtures surrounding the explosion position are already burned out due to the explosion. In Fig. 12, the oscillations of pressure after t ¼ 1916 ms are caused by those reflected shock waves propagating toward the center. It is interesting to find that the reinitiation process in the RDE bears some similarity to the auto-ignition of detonations in internal combustion engines, although it cannot directly extend to the case studied here. By varying the initial thermodynamic conditions of the combustion chamber, Qi et al. [42] observed in several cases that detonations were initiated. The incandescent zone in Fig. 14b is a detonation, which was the result of the explosion and the collision with the combustion chamber wall. They found that the detonation was initiated by the near-wall auto-ignition. This is also the case in the simulations, as shown earlier in Fig. 11. The detonation developed similarly in the experiment. The detonation front indicated by the black arrow in Fig. 14b was reported to be a self-sustained detonation wave propagating with a speed close to C-J detonation. Like detonation front A2 and B2 in Fig. 14a, the other two newly-initiated wave fronts in Fig. 14b move along the periphery of the chamber wall, depicted by the dotted yellow arrows.
Conclusions The present work discussed the phenomenon of the reinitiation of detonations in the RDE with a cylindrical combustion chamber. The reinitiation of detonations was observed in our experiments and investigated in detail by a three-dimensional simulation. Our simulation showed that detonation waves propagated in more than one direction in the flow after initiation. They collided with each other and with the outer wall, thus reconstructing the detonation flow intensively. The collision created explosions which were likely to generate new detonation fronts or, conversely, extinguish detonations. In the simulation, a strong head-on collision between two detonation fronts snuffed out the detonation flow. After a period of time, a spontaneous reinitiation was triggered by a high pressure spot near the outer wall of the combustion chamber. It was demonstrated that the reinitiation of detonations occurred due to the formation of strong shock waves at the spot where unburned mixtures were surrounded by reaction products.
Acknowledgments This research has been supported by the National Natural Science Foundation of China (Grant No. 91441110).
references
[1] Lee JHS. The detonation phenomenon. 1st ed. Cambridge, UK: Cambridge University Press; 2008. [2] Mallard E, Le Chatelier H. Sur les vitesses de propagation de langes gazeux explosifs. Comptes l’inflammation dans les me ances l’Acade mie Sci 1881;93:145e8. Rendus Hebd Se [3] Nicholls JA, Wilkinson HR, Morrison RB. Intermittent detonation as a thrust-producing mechanism. J Propul Power 1957;27:534e41. [4] Voitsekhovskii BV. Statsionarnaya Dyetonatsiya. Sov Dokl Fluid Mech 1959;129:1254e6.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 1
[5] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous spin detonations. J Propul Power 2006;22:1204e16. [6] Lu FK, Braun EM. Rotating detonation wave propulsion: experimental challenges, modeling, and engine concepts. J Propul Power 2014;30:1125e42. [7] Frolov SM, Aksenov VS, Ivanov VS, Shamshin IO. Large-scale hydrogen-air continuous detonation combustor. Int J Hydrogen Energy 2015;40:1616e23. [8] Frolov SM, Aksenov VS, Ivanov VS, Shamshin IO. Continuous detonation combustion of ternary “hydrogeneliquid propaneeair” mixture in annular combustor. Int J Hydrogen Energ 2017;42:16808e20. ski P. Detonative propulsion. Proc Combust Inst [9] Wolan 2013;34:125e58. [10] Rankin BA, Richardson DR, Caswell AW, Naples AG, Hoke JL, Schauer FR. Chemiluminescence imaging of an optically accessible non-premixed rotating detonation engine. Combust Flame 2017;176:12e22. [11] Fotia ML, Schauer F, Kaemming T, Hoke J. Experimental study of the performance of a rotating detonation engine with nozzle. J Propul Power 2016;32:674e81. [12] St George A, Driscoll R, Anand V, Gutmark EJ. Starting transients and detonation onset behavior in a rotating detonation combustor. In: 54th AIAA Aerospace Sciences Meeting, San Diego; 2016. [13] Le Naour B, Falempin F, Coulon K. MBDA R&T effort regarding continuous detonation wave engine for propulsion e status in 2016. In: International Space Planes and Hypersonic Systems and Technologies Conferences; 2017. [14] Zitoun R, Hansmetzger P, Vidal P, Chinnayya A, Rodriguez V, Virot F, et al. Detonation regimes in a small-scale RDE. In: International Constant Volume and Detonation Combustion Workshop 2017, Poitiers, France; 2017. [15] Nakagami S, Matsuoka K, Kasahara J, Matsuo A, Funaki I. Experimental study of the structure of forward-tilting rotating detonation waves and highly maintained combustion chamber pressure in a disk-shaped combustor. Proc Combust Inst 2017;36:2673e80. [16] Zhou S, Ma H, Liu D, Yan Y, Li S. Experimental study of a hydrogen-air rotating detonation combustor. Int J Hydrogen Energ 2017;42:14741e9. [17] Zhang H, Liu W, Liu S. Experimental investigations on H2/air rotating detonation wave in the hollow chamber with Laval nozzle. Int J Hydrogen Energ 2017;42:3363e70. [18] Liu Y, Wang Y, Li Y, Li Y, Wang J. Spectral analysis and selfadjusting mechanism for oscillation phenomenon in hydrogen-oxygen continuously rotating detonation engine. Chin J Aeronaut 2015;28:669e75. [19] Wang Y, Wang J, Li Y, Li Y. Induction for multiple rotating detonation waves in the hydrogeneoxygen mixture with tangential flow. Int J Hydrogen Energy 2014;39:11792e7. [20] Hishida M, Fujiwara T, Wolanski P. Fundamentals of rotating detonations. Shock Waves 2009;19:1e10. [21] Yi T, Lou J, Turangan C, Choi J, Wolanski P. Propulsive performance of a continuously rotating detonation engine. J Propul Power 2011;27:171e81. [22] Zhou R, Wang J. Numerical investigation of flow particle paths and thermodynamic performance of continuously rotating detonation engines. Combust Flame 2012;159:3632e45. [23] Schwer D, Kailasanath K. Fluid dynamics of rotating detonation engines with hydrogen and hydrocarbon fuels. Proc Combust Inst 2013;34:1991e8.
11
[24] Gaillard T, Davidenko D, Dupoirieux F. Numerical optimisation in non reacting conditions of the injector geometry for a continuous detonation wave rocket engine. Acta Astronaut 2015;111:334e44. [25] Tsuboi N, Watanabe Y, Kojima T, Hayashi AK. Numerical estimation of the thrust performance on a rotating detonation engine for a hydrogeneoxygen mixture. Proc Combust Inst 2015;35:2005e13. [26] Dubrovskii AV, Ivanov VS, Frolov SM. Three-dimensional numerical simulation of the operation process in a continuous detonation combustor with separate feeding of hydrogen and air. Russ J Phys Chem B 2015;9:104e19. [27] Zhdan SA, Bykovskii FA, Vedernikov EF. Mathematical modeling of a rotating detonation wave in a hydrogenoxygen mixture. Combust Explos Shock Waves 2007;43:449e59. [28] Oran ES, Jones DA, Sichel M. Numerical simulations of detonation transmission. Proc R Soc Lond A 1992;436:267e97. [29] Williams DN, Bauwens L, Oran ES. A numerical study of the mechanisms of self-reignition in low-overdrive detonations. Shock Waves 1996;6:93e110. [30] Smirnov NN, Nikitin VF. Modeling and simulation of hydrogen combustion in engines. Int J Hydrogen Energ 2014;39:1122e36. [31] Smirnov NN, Nikitin VF, Phylippov YG. Deflagration-todetonation transition in gases in tubes with cavities. J Eng Phys Thermophys 2010;83:1287e316. [32] Shao Y, Wang JP. Three dimensional simulation of rotating detonation engine without inner wall. In: 23rd International Colloquium on the Dynamics of Explosions and Reactive Systems, Irvine; 2011. [33] Tang X, Wang J, Shao Y. Three-dimensional numerical investigations of the rotating detonation engine with a hollow combustor. Combust Flame 2015;162:997e1008. [34] Ma F, Choi J, Yang V. Propulsive performance of air breathing pulse detonation engines. J Propul Power 2006;22:1188e203. [35] Smirnov NN, Betelin VB, Nikitin VF, Stamov LI, Altoukhov DI. Accumulation of errors in numerical simulations of chemically reacting gas dynamics. Acta Astronaut 2015;117:338e55. [36] Lau-Chapdelaine SSM. Numerical simulations of detonation re-initiation behind an obstacle. Canada: University of Ottawa; 2013. [37] Lin W, Zhou J, Liu S, Lin Z. An experimental study on CH4/O2 continuously rotating detonation wave in a hollow combustion chamber. Exp Therm Fluid Sci 2015;62:122e30. [38] Gamezo VN, Desbordes D, Oran ES. Formation and evolution of two-dimensional cellular detonations. Combust Flame 1999;116:154e65. [39] Liberman MA, Ivanov MF, Kiverin AD, Kuznetsov MS, Chukalovsky AA, Rakhimova TV. Deflagration-to-detonation transition in highly reactive combustible mixtures. Acta Astronaut 2010;67:688e701. [40] Smirnov NN, Betelin VB, Nikitin VF, Phylippov YG, Koo J. Detonation engine fed by acetyleneeoxygen mixture. Acta Astronaut 2014;104:134e46. [41] Jones DA, Sichel M, Oran ES. Reignition of detonations by reflected shocks. Shock Waves 1995;5:47e57. [42] Qi Y, Wang Z, Wang J, He X. Effects of thermodynamic conditions on the end gas combustion mode associated with engine knock. Combust Flame 2015;162:4119e28.
Please cite this article in press as: Yao S, et al., Reinitiation phenomenon in hydrogen-air rotating detonation engine, International Journal of Hydrogen Energy (2017), https://doi.org/10.1016/j.ijhydene.2017.09.015