Methane–oxygen detonation characteristics near their propagation limits in ducts

Fuel 177 (2016) 1–7

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Methane–oxygen detonation characteristics near their propagation limits in ducts Bo Zhang a,b,⇑, Xiaobo Shen c, Lei Pang d, Yuan Gao e a

East China University of Science and Technology, Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, Shanghai 200237, China Beijing Institute of Technology, State Key Laboratory of Explosion Science and Technology, Beijing 100081, China c East China University of Science and Technology, State Environmental Protection Key Laboratory of Environmental Risk Assessment and Control on Chemical Process, Shanghai 200237, China d Beijing Institute of Petrochemical Technology, Beijing 102617, China e Peking University, College of Engineering, Department of Mechanics and Engineering Science, SKLTCS, Beijing 100871, China b

h i g h l i g h t s  New detonation cellular structures of CH4–O2 mixtures near the limits are reported.  Detonation cell sizes for CH4–O2 mixtures are experimentally measured.  Pressure range for the occurrence of single-headed spinning detonation is explored.  Detonation velocity deficits in different channels are determined.

a r t i c l e

i n f o

Article history: Received 29 December 2015 Received in revised form 17 February 2016 Accepted 29 February 2016 Available online 5 March 2016 Keywords: Detonation limits Methane–oxygen Velocity deficit Cellular structure

a b s t r a c t In this study, the near-limit behavior of gaseous detonations in three methane–oxygen mixtures (CH4–2O2, CH4–1.5O2 and CH4–4O2) is investigated experimentally. A 36-mm diameter circular tube and three annular channel gaps (w = 2 mm, 4.5 mm and 7 mm) were used to look at the effect of different geometries on the detonation limits phenomenon. Photodiodes and smoked foils were employed to measure the time-of-arrival of the detonation wave and record the cellular detonation structure, respectively. As the detonation propagates within the limits, the velocity is steady with only a few percent deficit. By decreasing the initial pressure and, hence, reducing the sensitivity of the mixture, the detonation velocity deficit increases gradually. When the initial pressure is approaching the detonation limits, no steady detonation velocity can be realized, and failure occurs. With decreasing initial pressure, the smoked foil records indicate clearly that the cellular detonation evolves from a multi-headed to double-headed and eventually to a single-head spin as the limits approaches. The single-headed spinning detonations for CH4–2O2, CH4–1.5O2 and CH4–4O2 mixtures in the 36-mm round tube occurs from p0 = 3–7 kPa, 4–10 kPa and 7–16 kPa, respectively. Using different annular channel widths, it is observed that the detonation velocity decreases as the channel gap is reduced. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Methane (CH4), is the main component of Natural Gas and produces less carbon dioxide for each unit of heat released, but more heat per mass unit than other complex hydrocarbons, it is thus considered as an environmental-friendly fuel [1]. However, the explosion and detonation accidents regarding methane mixture ⇑ Corresponding author at: East China University of Science and Technology, Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, Shanghai 200237, China. Tel.: +86 21 64253132; fax: +86 21 64253404. E-mail address: [email protected] (B. Zhang). http://dx.doi.org/10.1016/j.fuel.2016.02.089 0016-2361/Ó 2016 Elsevier Ltd. All rights reserved.

often occur and result in casualty and severe loss of property at industrial facilities, it received considerable attention in recent years in connection with the safety aspects of large-scale transport and underground coal mines, numerous previous researchers have contributed in discovering the phenomena and the mechanism of explosions and detonations [2–9]. A detonation wave is a supersonic combustion wave across which the thermodynamic states (e.g., pressure and temperature) increase sharply. It can be considered as a reacting shock wave where reactants transform into products, accompanied by an energy release across it [10]. Detonation limits refer to the conditions outside of which a self-sustained detonation wave can no

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longer propagate [10]. For a given explosive mixture, the detonation limits are approached by adding amounts of inert diluent, changing the composition of fuel/oxidizer, lowering initial pressure, or reducing the tube diameter. Well within the limits, the detonation propagates at a steady velocity close to the theoretical Chapman–Jouguet (CJ) value. Near the limits, the propagation phenomenon is generally unsteady and complex [11], and the detonation velocity fluctuates from 40 to 150% of the CJ value [12,13]. Haloua et al. [14] proposed four propagation modes to describe the near-limit phenomena, i.e., stable detonation, stuttering mode, galloping mode, and fast flame. The study of the propagation limits behavior in narrow gaps is important from the aspect of safety assessment for methane–oxygen mixtures, because the maximum safe gap determined from experiment is an important parameter for deflagration or detonation hazard assessments [15]. Therefore, near limits behavior of detonation has been investigated in recent years. For example, Gao et al. [16], and Fischer et al. [17] measured the minimum tube diameter for steady detonation propagation in various hydrocarbon fuel–oxygen combustible mixtures and in different diameter tubes. The results they obtained confirm the criterion that the minimum tube diameter before detonation failure (i.e., critical condition of detonation limits) equals k/3 (k is the detonation cell size). This criterion was first proposed by Lee [18]. Toward the limits, some general features were also explored. For instance, as the velocity progressively decreases, there exists a maximum deficit when an eigenvalue detonation velocity can no longer be found, considered as the onset of the detonability limits [19]. The investigations of velocity deficit and detonation structure were performed by Gao et al. [12,13], and Lee et al. [9]. Ishii et al. [20–22] studied the propagation behavior of detonation waves for hydrogen/oxygen/argon mixtures in narrow gaps and at low pressures. Near the limits, galloping detonations were observed for unstable mixtures in small diameter tubes, but not for highly argon diluted, stable mixtures. The authors concluded that a strong reaction sensitivity or instability of the combustible mixture is one of the key factors for the existence of the galloping detonations [13]. Although velocity deficit have been extensively investigated near the limits, a quantitative criterion or theory is lacking for predicting the limits. Therefore, more experimental investigations need to be carried out to focus on the detonation near-limit behavior. Furthermore, it has been established that the failure of detonations is due to the suppression of cellular instability and the wall loss, both causing velocity deficits and eventually failure [19]. Evidence that cellular instability is essential for the self-sustained propagation of detonations is available from experimental [23– 27] and numerical investigations [28–36]. Instabilities thus play an important role in the detonation limits. In this study, systematic investigations on the near detonation limits behavior of methane– oxygen mixtures are carried out, typical unstable mixtures with irregular cell pattern, CH4–2O2, CH4–1.5O2 and CH4–4O2, are used, corresponding to equivalence ratios of 1, 1.33 and 0.5, respectively. The propagation of detonations are investigated in a round tube with a 36-mm inner diameter, and also in thin annular channels with different scales (w = 2 mm, 4.5 mm and 7 mm). The heights of the channel are small compared to the radius of the annulus so that radial curvature effects are negligible and it can be considered as a two-dimensional geometry.

2. Experimental section The experimental apparatus consists of a 1.2-m long, 68-mm inner diameter steel driver section followed by a steel test section L = 2.5 m in length and an inner diameter of d = 36 mm, shown in Fig. 1(a), which is the same one that used in our previous studies

[37,38]. Note that in this setup L/d = 69.4, too short to observe the galloping or stuttering propagation modes near the detonation limits, and we therefore only focus on whether detonations can sustain a steady velocity over this distance. The annular channel test section is created by inserting smaller diameter tubes supported by fins into the end of the detonation test section. Smaller tubes are used to create three annular channel gaps: w = 2 mm, 4.5 mm and 7 mm, shown schematically in Fig. 1(b) and (c). Experiments are also conducted in the 36-mm diameter circular tube without an inserted tube for comparison. Fiber optics 2.2-mm in diameter and connected to a photodiode (IF-95OC) were spaced periodically along the entire length of the driver and test section. Three optical probes with interval distances of 20 cm were located in the driver section to verify that a CJ detonation was created prior to its transmission to the test section. Twenty optical probes spaced 10 cm apart were mounted on the test section to measure the time-of-arrival of the combustion wave. Typical optical probe traces are shown in Fig. 2. These diagnostics provide the time-of-arrival of the combustion wave determining the trajectory of the detonation. The detonation velocity is obtained by taking the slope of the trajectory. Three explosive mixtures of methane–oxygen, i.e., CH4–2O2, CH4–1.5O2 and CH4–4O2, with different equivalence ratio were used, the mixtures are ‘‘unstable” with highly irregular cell patterns. The reason that those three mixtures were chosen is because we try to find out the different detonation near-limit behavior at fuel-lean, stoichiometric and fuel-rich conditions for CH4–O2 mixtures and furthermore, it is attempted to investigate the influence of the equivalence ratio on the detonation limits behavior. The mixtures were allowed to mix in a 20-L bottle by diffusion for at least 24 h in order to ensure homogeneity prior to being used. For any given experiment, the detonation tube was evacuated to at least 100 Pa. The tube was then filled to the desired initial pressure. The initial pressure was monitored by an accurate digital manometer model OMEGA HHP242-030A (0–30 psi) with an accuracy of ±0.10% full scale (i.e., ±0.2 kPa). Smoked foils were also used to obtain the structure of the detonation in the 36-mm diameter circular tubes. The smoked foils were made of a thin (0.2 mm) plastic sheet uniformly covered with soot and carefully inserted into the test circular tube before each shot. 3. Results and discussions 3.1. Steady and unsteady velocity determination Fig. 3 shows typical trajectories of the detonation wave at different initial pressures in a 36-mm diameter round tube. The xaxis is the position of the combustion wave at the various optical probes, and the y-axis is the time-of-arrival of the wave. At an initial pressure of p0 = 10 kPa, the detonation velocity is found to be 2189 m/s, 98% CJ value. The CJ detonation velocity is calculated using the one-dimension ideal ZND model and CHEMKIN package. As the initial pressure decreased to p0 = 4.6 kPa, the detonation still can propagate at a steady velocity, but the value is of 0.90 VCJ. Whereas, with the initial pressure further decreases to a lower value, i.e., p0 = 2.5 kPa, there is no steady velocity can be realized, thus, at this initial pressure, detonation fails due to outside its limits. Therefore, the unsteady velocity can be considered as the detonation approaches its limits. 3.2. Round tube Fig. 4 shows the variation of the steady detonation velocity normalized with CJ value as a function of initial pressure in 36-mm

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B. Zhang et al. / Fuel 177 (2016) 1–7

L=2.5m, D=36mm

(a)

L=1.2m, D=68mm

Smaller tube 36mm

Smaller tube

1.35m (b)

Fig. 1. Sketch of experimental apparatus. (a) Experimental setup, (b) sketch of smaller tube, (c) sketch of annular gap, DW = detonation wave.

5 0 -5 driver section test section

Voltage/V

-10 -15 -20 -25 -30 -35 -40 -45

0

0.5

1

1.5

2

Time/s

2.5 -3 x 10

Fig. 2. Sample signals from the optical detectors (CH4–2O2, p0 = 10 kPa).

no steady velocity 1.00

2.5 kPa 4.6 kPa, 0.90 CJ 10.0 kPa,0.98 CJ

1.6x10-3

0.95

36-mm (this study) 36-mm curve fit From Jesuthasan: 65-mm 44-mm 13-mm

0.90

1.2x10-3

V/VCJ

Time of arrival / s

2.0x10-3

8.0x10-4

0.85

4.0x10-4

0.80

CH4-2O2 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Position / m Fig. 3. Typical trajectories of a self-propagating detonation and detonation failure in the 36 mm diameter tube for CH4–2O2 mixture.

round tube for CH4–2O2 (u = 1), and compared with the results from Jesuthasan [39] for the same mixture but in 65-mm, 44mm and 13-mm round tubes. It can be seen that, well within the detonation limits, the detonation velocity deficit is within a few percent of CJ values. As the limits are approached by reducing

0.75 0

10

20

30

40

50

Initial Pressure / kPa Fig. 4. Variation of normalized detonation velocity as a function of initial pressure in 36-mm round diameter tube and compared with previous results.

the initial pressure, the detonation velocity progressively decreases and deviates from the CJ value. Below the limits, detonation can not sustain a steady propagation velocity. It is noteworthy that the results do not indicate a significant difference in detonation velocity between a 65, 44 and 36 mm diameter tubes, but

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1.05

single-headed spin,4 kPa~10 kPa

1.00 0.95

V/VCJ

0.90 0.85 0.80

within the limit p0>10 kPa

0.75

CH4-1.5O2 36mm round tube

0.70 0

5

10

15

20

25

30

35

40

45

Initial Pressure / kPa

(a) 1.00

0.95

V/VCJ

single-headed spin,7 kPa~16 kPa 0.90

within the limit p0>16 kPa

0.85

CH4-4O2 36mm round tube

0.80 5

10

15

20

25

30

35

40

45

Initial Pressure / kPa

(b) Fig. 5. Variation of normalized detonation velocity as a function of initial pressure in 36-mm round diameter tube. (a): CH4–1.5O2, (b): CH4–4O2.

the velocity decrease is more abrupt in 13-mm round tube, which is due to the boundary layer exerts a greater effect in smaller tube. A similar plot for CH4–1.5O2 (u = 1.33) and CH4–4O2 (u = 0.5) mixtures are shown in Fig. 5. As the detonation limits approached, an abrupt drop of velocity deficit can be observed. Below the limits, detonation wave fails after entering the round tube, and a selfsustained detonation cannot be obtained. As can be seen from Figs. 4 and 5 that, the minimum values of normalized detonation velocity V/VCJ are approximately 0.80, 0.89 and 0.88 for CH4–2O2, CH4–1.5O2 and CH4–4O2 mixtures, respectively, below which the

stable self-sustained propagation detonation can no longer be observed. No obvious difference in velocity deficit is observed for fuel-lean (CH4–4O2) and fuel-rich (CH4–1.5O2) mixtures, but the deficit is larger for the stoichiometric case (i.e., CH4–2O2). Smoked foils are inserted into the 36-mm round tube to register the cellular detonation structure near the limits. As the detonation propagates past a foil covered with soot, the triple point displaces the soot and leaves trajectory of its passage. Fig. 6 shows the cellular detonation structure in the CH4–2O2 mixture near (3–7 kPa) and well within limits (8 kPa). It should be noted that the smoked foils are 1000 mm (2700–3700 mm from the igniter) in length and 100 mm in width. The foils are inserted into the tube from the end before each shot. The x-axis represents the distance from the igniter and the detonation propagates in the direction from left to right. One can see that at initial pressures of p0 = 8 kPa, doulbeheaded detonation structures are observed. As the initial pressure gradually decreases, the detonation changes to single-headed spin as the limits are approached. The single-headed spin structure can be observed in a range of initial pressure, i.e., p0 = 3–7 kPa. No cellular structure was observed at the pressure lower than 3 kPa. As the condition changes to fuel-lean or fuel-rich, the pressure range for the occurrence of single-headed spinning detonation is much wider. For example, for CH4–1.5O2 mixture, the pressure range for the existence of single-head spin is from 4 to 10 kPa (Fig. 7), whereas, the result is 7–16 kPa for CH4–4O2 mixture (Fig. 8). We define P⁄0 for the onset of spinning detonation and Plim as the spinning structure is missing, exactly the same method used by Wu and Lee [40], the results are tabulated in Table 1 for CH4–O2 mixtures. Wu and Lee [40] reported the pressure range for spinning detonation in CH4–2O2 is 4.3–6.0 kPa using d = 50.8 mm round tube. If we take into the consideration of the difference of the tube inner diameter, their result agrees with this study. At the initial pressure higher than the P⁄0, multi-headed and doubleheaded structure can be observed. Detonation cell size provides important information for the characterization of the explosion properties and is a useful parameter for detonation hazard assessments. The present experimentally measued cell size for CH4–2O2 is compared with the results obtained by Jesuthasan [39] and from the CALTECH detonation database [41], shown in Fig. 9. It is found that these sets of data are within satisfactory agreement if the measurement error is considered. The experimentally measured cell size for CH4–1.5O2 and CH4–4O2 mixtures are plotted with initial pressure, and shown in Fig. 10. 3.3. Annular channel As the detonation transitions from a round tube to an annular channel, due to the wall loss it can be observed that the steady detonation velocity further decreases. The detonation velocity for the CH4–2O2 mixture is around 0.97–0.98 VCJ at p0 = 10 kPa in the

Fig. 6. Typical smoked foils records for CH4–2O2 mixtures at different initial pressure.

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B. Zhang et al. / Fuel 177 (2016) 1–7

Fig. 7. Typical smoked foils records for CH4–1.5O2 mixtures at different initial pressure.

p0=7 kPa

p0=16 kPa

p0=17 kPa

mm Fig. 8. Typical smoked foils records for CH4–4O2 mixtures at different initial pressure.

150

Table 1 Pressure range for spinning detonation in CH4–O2 mixtures. CH4–2O2

CH4–1.5O2

CH4–4O2

3 ± 0.2 7 ± 0.2

4 ± 0.2 10 ± 0.2

7 ± 0.2 16 ± 0.2

CH4-1.5O2

200

This study Previous experiment

CH4-4O2

100

Cell Size / mm

Plim/kPa P⁄0/kPa

50

Cell Size / mm

150

0

100

0

10

20

30

40

50

Initial Pressure / kPa 50

Fig. 10. Detonation cell size for CH4–1.5O2 and CH4–4O2 mixtures.

CH4-2O2

0 0

10

20

30

40

50

Initial Pressure / kPa Fig. 9. Cell size as a function of initial pressure for CH4–2O2.

36-mm diameter round tube before the detonation enters into the annular channels. The velocity decreases to 0.83 VCJ, 0.77 VCJ and 0.60 VCJ in 7-mm, 4.5-mm and 2-mm channel gaps, respectively, as shown in Fig. 11. The critical pressure and the minimum velocity (Vmin) near the detonation limits in different channel gaps for all mixtures are summarized in Table 2. The results indicate that even well within

the limits the annular channel geometry has an effect of reducing the detonation velocity. As the limits are approached by decreasing the initial pressure, the detonation is subjected to more losses, which renders the detonation velocity decreases progressively and deviates from the CJ values. For a given initial pressure, the detonation velocity decreases with decreasing annular channel gap. As the channel gap is reduced, more wall losses causing larger velocity deficit. For example, it can be observed that the maximum velocity deficits (Vdef) for CH4–2O2 are about 27.0%, 30.8% and 41.8% of the CJ value in the 7-mm, 4.5-mm and 2-mm channel gaps, respectively. On the other hand, for the same channel gap, e.g., 2-mm annular channel, the velocity deficit is more prominent for the mixtures near the stoichiometric condition (i.e., CH4–2O2, CH4–1.5O2), with deficit of 41%. The deficit is less for the fuellean mixture (CH4–4O2), in which the deficit is 31.5%.

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B. Zhang et al. / Fuel 177 (2016) 1–7

2.1x10 -3

1373 m/s,0.70 VCJ

1.8x10 -3

Tiem of arrival / s

1759 m/s,0.77 VCJ

Channel gap: 2.0 mm 4.5 mm 7.0 mm

1.5x10 -3

1908 m/s,0.83 VCJ

1.2x10 -3 9.0x10 -4

annular channel

6.0x10 -4

2218~2244 m/s, 0.97~0.98 VCJ

3.0x10 -4 0.0

0.5

1.0

1.5

2.0

2.5

p0=10 kPa 3.0

3.5

Position / m Fig. 11. Typical trajectories of a self-propagating detonation in different channel gaps for CH4–2O2 mixture.

Table 2 Critical pressure and minimum velocity near the detonation limits in different channel gaps. Mixtures

Channel gaps/mm

CH4–2O2

7.0 4.5 2.0

CH4–1.5O2

7.0 4.5 2.0

CH4–4O2

7.0 4.5 2.0

Plim/kPa

Vmin/VCJ %

Vdef/VCJ %

73.0 69.2 58.2

27.0 30.8 41.8

4 8 12

74.0 69.6 59.0

26.0 30.4 41.0

8 11 19

79.1 76.5 68.5

20.9 23.5 31.5

5.5 6.5 9.5

4. Conclusions In this study, a detailed investigation on the near detonation limits behavior of methane–oxygen mixtures (CH4–2O2, CH4– 1.5O2 and CH4–4O2) in ducts (i.e., a 36-mm round tube and three annular channel gaps) is performed. The detonation velocity deficit and cellular structure are systematically obtained and analyzed. Some conclusions are made as follows: (1) Well within the limits, the detonation propagates at a relatively steady velocity with small deficit. As the limits are approached, the velocity gradually decreases and no steady detonation velocity can be realized. (2) Cellular detonation structure is recorded by inserting smoked foils. The result indicates that detonations show double- and multi-headed structure for conditions within the limits. Single-head spin structure is observed when the limits are approached. The onset of single-headed spinning detonation of CH4–2O2, CH4–1.5O2 and CH4–4O2 in the 36mm round tube occurs from p0 = 3–7 kPa, 4–10 kPa and 7– 16 kPa, respectively. (3) As the detonation transitions from a round tube to an annular channel, due to the wall loss the detonation velocity further decreases. As the channel gap is reduced, the detonation is subjected to more losses causing larger velocity deficit.

Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No.: 11402092) – China, and the project of State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology (Grant No.: KFJJ15-03M) – China.

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