- Email: [email protected]
oxygen mixtures in a rectangular tube
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Available online at www.sciencedirect.com
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Short Communication
Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube Zhang Yun a, Cheng Yang-Fan b,c,*, Su Jian c, Wang Wen-Tao c, Han Ti-Fei c, Tan Ying-Xin a, Cao Wei-Guo a,** a
School of Environmental and Safety Engineering, North University of China, Taiyuan, 030051, PR China CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei, 230027, PR China c School of Chemical Engineering, Anhui University of Science and Technology, Huainan, 232001, PR China b
highlights New cell size data on H2eC3H8eO2 is obtained. Detonation velocity deficits of H2eC3H8eO2 mixtures are calculated. Near detonation limit behaviors of H2eC3H8eO2 are analyzed.
article info
abstract
Article history:
In this paper, an experimental study on the near detonation limits for propane-hydrogen-
Received 11 August 2019
oxygen is performed. Three mixtures (i.e., 8H2eC3H8e9O2, 4H2eC3H8e7O2 and 12H2eC3H8
Received in revised form
e11O2) are tested in a rectangular tube (52 mm 32 mm). Photodiodes with regular in-
21 October 2019
tervals are mounted on the tube wall to measure the time of arrival of detonation waves,
Accepted 27 October 2019
from which the detonation velocity is determined. Smoked foils are inserted into the tube
Available online xxx
to obtain the detonation cell pattern. The results indicate that well within the detonation limits, the detonation can propagate at a steady velocity. By reducing the initial pressure,
Keywords:
the detonation velocity decreases gradually. Subsequently, the detonation fails as the
Detonation limit
initial pressure is below a critical pressure. The critical pressures for 8H2eC3H8e9O2, 4H2
Detonation velocity deficit
eC3H8e7O2 and 12H2eC3H8e11O2 mixtures are 4 kPa, 5 kPa and 6 kPa, and the corre-
Cellular detonation structure
sponding detonation velocity deficits are 10%, 9%, 10%, respectively. The cellular detonation structures show that the cell size decreases with the decrease of the hydrogen concentration, and the cell structures are very irregular near the detonation limits. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei, 230027, PR China. ** Corresponding author. E-mail addresses: [email protected] (C. Yang-Fan), [email protected] (C. Wei-Guo). https://doi.org/10.1016/j.ijhydene.2019.10.249 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
2
international journal of hydrogen energy xxx (xxxx) xxx
Introduction As an ideal fuel that has the potential to be used as a pollution-free fuel with reduced greenhouse gas emissions, hydrogen (H2) is a promising fuel which can replace the diminishing fossil fuel supply. However, hydrogen has some salient characteristics, such as wide flammable limit range and high reaction sensitivity, making the safety issues related to hydrogen to be a serious challenge [1e3]. Regarding hydrogen safety, some related studies [4e12] have been devoted to the determination of the detonation mechanism and description of the dynamic parameters, such as detonation limits, critical tube diameter, detonation cell size, critical energy and detonation velocity deficit. Previous researches have confirmed that the addition of some hydrocarbons (e.g., methane or propane) to hydrogen can decrease the sensitivity of the detonable mixture of hydrogen/oxygen [13,14]. On the other hand, the performances of the binary fuel blends of propane and hydrogen are improved, if hydrogen is added to propane, e.g., cleaner products and less unwanted pollutants, higher thermal efficiency. Tang et al. [15] studied the laminar burning velocities and the onset of cellular instabilities of hydrogen-propane-air mixtures. Law et al. [16] analyzed the critical conditions for the onset of instability of the fuel blends at evaluated pressures. Azatyan et al. [13] studied the inhibition effect of propane on hydrogen-air detonations. In industry, its application also can be wide, such as internal combustion engine and rocket booster. Detonation limit, referring to the conditions outside of which a self-sustained detonation wave is unable to propagate [17e19], is of significance for hazard assessment, as well as fundamental point of view. For detonation limit determination, Manson [20] used the instability of detonation velocity as a criterion. Meanwhile, the galloping detonation appeared as the limits are approached. The recognized criterion is the l= 3 rule [17,19]. Near the limit, the detonation velocity fluctuates and the lowest mode of single-head spin with l ¼ p, D, in which l and D represent the detonation cell size and the tube diameter, respectively. Hence, to determine the detonation limit of a given mixture, detonation velocity and cellular structure records are of importance. In recent years, some studies have been performed to explore the combustion characteristics of binary fuel blends, such as laminar burning velocity, DDT (deflagration to detonation transition), detonation limits and detonation cell size [21e25]. However, few literatures reported the detonation limits of propane/hydrogen mixtures. In this study, systematic investigations on the near detonation limits behavior of propane-hydrogen-oxygen mixtures in a rectangular tube were conducted. The detonation velocity was measured using
photodiodes mounted on the tube wall, which is used to determine detonation limits. The detonation velocity deficits are calculated, both experimentally measured and theoretical prediction using Fay’s model. In addition, the cellular detonation structure was obtained using smoked foils technique and analyzed.
Experimental setup and procedures In the present study, three explosive mixtures of propanehydrogen-oxygen, i.e., 8H2eC3H8e9O2, 4H2eC3H8e7O2 and 12H2eC3H8e11O2, are used to study their near detonation limits behavior, the details of which are tabulated in Table 1. It is noteworthy that 8H2eC3H8e9O2 is at stoichiometry both for C3H8eO2 and H2eO2, 4H2eC3H8e7O2 has higher content of propane while hydrogen is higher in 12H2eC3H8e11O2. Experiments are conducted in a 2000 mm long rectangular stainless steel driver section (40 mm 25 mm) followed by a test section (52 mm 32 mm) of detonation tube with 3000 mm in length, as shown schematically in Fig. 1(a). The explosive mixtures are prepared by the method of partial pressures in a mixing chamber and allowed to be mixed in the chamber for more than 20 h in order to ensure mixture homogeneity. Prior to an experiment, the detonation tube is evacuated to a pressure less than 100Pa. Subsequently, the mixture is introduced into the tube accompanying with the increase of the inner pressure to the desired initial pressure (r0 ) at room temperature (303 K), which can control the detonable mixture sensitivity and left 10 min till the mixture becomes perfectly quiescent. The initial pressure is monitored by an digital manometer (SXT-4A, 0e150 kPa) with the accuracy of ±0.1 kPa. Ignition is achieved by a high energy spark from a capacitor discharge, leading to the formation of detonation wave. At the location of 4000 mm downstream from the spark gap, four photodiodes are mounted on the wall of the tube with the interval distance of 200 mm. The detonation velocity can be determined by taking the slope of the trajectory of the photodiodes. Smoked foils are used to record the detonation cell structure. The smoked foil was made of a thin plastic sheet (400 mm 50 mm) covered with uniform soot and the inserted into the end of the tube. Each shot was repeated at least 3 times to achieve reproducibility.
Results and discussion Fig. 1(b) shows typical trajectories of detonation propagating in the tube for 8H2eC3H8e9O2. The x -axis is the TOA (time of arrive) of the detonation, while the y -axis represents the corresponding location of the photodiode. From the trajectory
Table 1 e C3H8eH2eO2 mixtures with various compositions used in this experiment. Mixtures 8H2eC3H8e9O2 4H2eC3H8e7O2 12H2eC3H8e11O2
C3H8(vol%)
H2 (vol%)
O2 (vol%)
Equivalence ratio
Note
5.56 8.33 4.17
44.44 33.33 50.00
50.00 58.34 45.83
1 1 1
Stoichiometry Higher propane Higher hydrogen
Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
international journal of hydrogen energy xxx (xxxx) xxx
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Fig. 1 e (a) Experimental setup; (b) Trajectories of self-sustained detonations and failing detonation for the 8H2eC3H8e9O2 mixture; (c) Oscillograms of optical and pressure sensors for an unsuccessful propagation detonation in 8H2eC3H8e9O2 at p0 ¼ 3 kPa.
Fig. 2 e Detonation velocity as a function of initial pressure for different mixtures. Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
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international journal of hydrogen energy xxx (xxxx) xxx
Table 2 e Detonation cell size correlations for three mixtures. Mixtures 8H2eC3H8e9O2 4H2eC3H8e7O2 12H2eC3H8e11O2
A
h
250.1 316.7 259.1
1.208 1.374 1.233
plots, the velocities for steady and unsteady detonation can be determined. For instance, the detonation velocities for 8H2eC3H8e9O2 are steady at the initial pressure p0 ¼ 20 kPa and p0 ¼ 12 kPa, since the slopes are invariable. However, when p0 ¼ 3 kPa, one can see the detonation velocity decreases gradually along the tube. As suggested in previous studies [26e29], the unsteady velocity can be considered as the detonation approaches the limits. This also can be observed by the comparison between the optical and pressure signals, which is shown in Fig. 1 (c). The optical signals (reflect the reaction zone) are slightly behind the corresponding pressure signals (reflect the shock), indicating the decoupling of the reaction zone-shock complex, i.e., the detonation fails. The experimentally measured detonation velocity in mixtures at various initial pressures is shown in Fig. 2, where the Chapman-Jouguet (CJ) detonation velocity is also available. It is worth noting that the CJ detonation velocities are computed using the ideal one-dimensional ZND model in Chemkin package [30]. Fig. 2 indicates that, well within the detonation limit, the detonation velocity considerably steady with a little
deficit because of the heat and momentum losses from the walls of the tube. Herein, the detonation velocity deficit is defined by Ref. [17]: DV VCJ V ¼ VCJ VCJ
(1)
In which VCJ and V denote the ideal CJ detonation velocity, the experimentally measured velocity respectively, and DV ¼ VCJ V. By reducing the initial pressure, the detonation velocity is decreased and the detonation limit is approached. Subsequently, the self-sustained detonation is unable to be achieved when the initial pressure is below a critical pressure (pc ), and the critical pressure is determined from the experiment (see Fig. 2). The experimental results indicate that pc ¼ 4 kPa for 8H2eC3H8e9O2, pc ¼ 5 kPa for 4H2eC3H8e7O2, and pc ¼ 6 kPa for 12H2eC3H8e11O2. When p0 < pc , the measured detonation velocity fluctuates significantly. This indicates that the detonation cannot sustain a steady velocity. The detonation velocity deficits are roughly 10% for the three mixtures. According to Fay’s theory [31], the detonation velocity deficit can be calculated based on the one-dimensional ZND structure. Thus, equation (1) can be replaced by: 12 DV ð1 nÞ2 ¼1 VCJ ð1 nÞ2 þ g2 ð2n n2 Þ
(2)
Fig. 3 e Experimentally measured detonation cell size in different mixtures. Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
international journal of hydrogen energy xxx (xxxx) xxx
Here, g is the specific heat ratio under the CJ condition, and n is written by: n¼
x ð1 þ gÞð1 þ xÞ
(3)
The area divergence x can be expressed in terms of the boundary layer displacement thickness d* as: x¼
A1 ða þ d* Þðb þ d* Þ 2d* 1z 1¼ ab A2 DH
(4)
where, DH is the hydraulic diameter of the rectangular tube, which can be expressed as: DH ¼
4ab 2ða þ bÞ
(5)
a and b denote the length and width of the cross-section of the rectangular tube, respectively. For smooth tubes, the boundary layer displacement thickness is: d* ¼ 0:22c0:8
me r0 V
0:2 (6)
c, me , r0 , V represent the reaction zone thickness, the viscosity of the hot gas at the post-shock state, the initial gas density and the detonation velocity, respectively. In this study, the viscosity of the hot gas at the post-shock state, the initial gas density and the specific heat ratio were calculated using NASA-CEA program [32]. To calculate the detonation velocity deficit, the reaction zone thickness (c) must be computed in advance. In some
5
related research [15,16,33], the reaction zone thickness (c) can be simplified to be equal to the detonation cell length (L), i.e., c ¼ L. Edwards [34] argued that the correlation between the detonation cell length (L) and the detonation cell size (l) is L ¼ 1:67 l, which is adopted in this study. The detonation cell size (l) is experimentally measured by means of the pattern on the smoked foils. Good agreement is found with the tendency in previous studies [18,35]. In this study, the detonation cell size is recorded using smoked foils and experimentally measured. For most hydrocarbons, the detonation cell size fitting correlations can be written as lðmmÞ ¼ Aðp0 ½kPaÞh [36,37]. It had been suggested by Jesuthasan [38] that the detonation structure is independent of the tube geometry. Thus, the expression also can be used to fit the cell sizes in the experiment, which are shown in Table 2. Fig. 3 shows the detonation cell sizes for the three mixtures, with the curve fit included. For each condition, ten measurements were made based on the smoked foil, from which the average cell size could be determined. Satisfactory agreement can be detected between the experiments and the curves. With the decreasing of the hydrogen concentration, the detonation cell size decreases. Fig. 4 shows the detonation velocities normalized with the CJ value versus different initial pressure, both theoretically predicted using Fay’s model and experimentally measured. It can be seen that the detonation velocity deficits increase with the decrease of the initial pressure for both experimental data and computed data. Generally, the measured detonation velocity deficits are in good agreement with the predicted
Fig. 4 e Variation of normalized detonation velocity versus initial pressure for different mixtures. Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
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international journal of hydrogen energy xxx (xxxx) xxx
Fig. 5 e The detonation cell pattern on smoked foils for in (a): 8H2eC3H8e9O2, (b): 4H2eC3H8e7O2 and (c): 12H2eC3H8e11O2. values. The mean errors between the experimental and theoretical values are less than 3%. Firstly, this can be ascribed to the measurement of the detonation cell size. The cellular structures are irregular; thus, the uncertainties cannot be avoided. Secondly, the detonation in hydrogen-propaneoxygen is dominated by the instability, which is not considered in Fay’s model. For most mixtures without dilution, the detonation is unstable with irregular cellular structures [20]. In the experiment, the cellular structures of propane-hydrogen-oxygen are irregular. And with the decrease of the initial pressure, the cellular structures are more erratic. Fig. 5 shows the detonation cellular structures in C3H8eH2eO2 mixtures at and near the critical pressures (pc ), respectively. For 8H2eC3H8e9O2, the cellular structure can be seen in Fig. 5 (a). When the initial pressure is 4 kPa, detonation in 8H2eC3H8e9O2 is singleheaded, thereafter the structure turns into a formation similar to “double-headed”. This is because the unstable gases are likely to form localized explosions, which facilitates the initiation of a detonation [17]. As the initial pressure declines (p0 ¼ 3 kPa) outside the detonation limit, no cell is formed and only slight trajectories are discernible. As for 4H2eC3H8e7O2 at p0 ¼ 5 kPa and p0 ¼ 4 kPa, some trace lines are detected at the forepart of the smoked foil, and then disappear. Heat and momentum loss from the wall is becoming more significant at the longer distance from the igniter. For 12H2eC3H8e11O2 at p0 ¼ 6 kPa and p0 ¼ 5 kPa, the trajectories of the triple point are more indiscernible.
Conclusion In this study, an investigation on the near detonation limits behavior of propane-hydrogen-oxygen mixtures (8H2eC3H8e9O2, 4H2eC3H8e7O2 and 12H2eC3H8e11O2) in a rectangular tube (52 mm 32 mm) is carried out. The detonation limits are determined via the measurement of
detonation velocity. The detonation velocity deficit is computed by experimental results and Fay’s theory. The detonation cell structure is recorded and analyzed. Generally, the detonation velocity decreases with the decrease of the initial pressure. Within the detonation limits, the detonation velocity is steady with a small velocity deficit. Outside the limits, large velocity fluctuations were observed, which indicates the failure of a detonation. The detonation limits for 8H2eC3H8e9O2, 4H2eC3H8e7O2 and 12H2eC3H8e11O2 are 4 kPa, 5 kPa and 6 kPa, respectively, and the corresponding detonation velocity deficits are all about 10%. The detonation velocity deficits were evaluated using Fay’s model with reasonable accuracy. Near the detonation limits, the recorded cellular patterns are relatively complicated. Below the limits, only some triple-point trajectories can be observed. However, only one smoked foil on the bottom wall was used in this study. The cellular structures on four walls will be further investigated to give more insight into the mechanisms near the limits.
Acknowledgement This work was supported by National Natural Science Foundation of China (Nos. 11602001, 11802272, 11972046 and 51674229), Open Project Foundation of CAS Key Laboratory of Mechanical Behavior and Design of Materials (No. lmbd201701) and China Postdoctoral Science Foundation (2017M610381 and 2019M651085), and the authors would like to thank these foundations for the financial support.
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international journal of hydrogen energy xxx (xxxx) xxx
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Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Short Communication
Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube Zhang Yun a, Cheng Yang-Fan b,c,*, Su Jian c, Wang Wen-Tao c, Han Ti-Fei c, Tan Ying-Xin a, Cao Wei-Guo a,** a
School of Environmental and Safety Engineering, North University of China, Taiyuan, 030051, PR China CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei, 230027, PR China c School of Chemical Engineering, Anhui University of Science and Technology, Huainan, 232001, PR China b
highlights New cell size data on H2eC3H8eO2 is obtained. Detonation velocity deficits of H2eC3H8eO2 mixtures are calculated. Near detonation limit behaviors of H2eC3H8eO2 are analyzed.
article info
abstract
Article history:
In this paper, an experimental study on the near detonation limits for propane-hydrogen-
Received 11 August 2019
oxygen is performed. Three mixtures (i.e., 8H2eC3H8e9O2, 4H2eC3H8e7O2 and 12H2eC3H8
Received in revised form
e11O2) are tested in a rectangular tube (52 mm 32 mm). Photodiodes with regular in-
21 October 2019
tervals are mounted on the tube wall to measure the time of arrival of detonation waves,
Accepted 27 October 2019
from which the detonation velocity is determined. Smoked foils are inserted into the tube
Available online xxx
to obtain the detonation cell pattern. The results indicate that well within the detonation limits, the detonation can propagate at a steady velocity. By reducing the initial pressure,
Keywords:
the detonation velocity decreases gradually. Subsequently, the detonation fails as the
Detonation limit
initial pressure is below a critical pressure. The critical pressures for 8H2eC3H8e9O2, 4H2
Detonation velocity deficit
eC3H8e7O2 and 12H2eC3H8e11O2 mixtures are 4 kPa, 5 kPa and 6 kPa, and the corre-
Cellular detonation structure
sponding detonation velocity deficits are 10%, 9%, 10%, respectively. The cellular detonation structures show that the cell size decreases with the decrease of the hydrogen concentration, and the cell structures are very irregular near the detonation limits. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei, 230027, PR China. ** Corresponding author. E-mail addresses: [email protected] (C. Yang-Fan), [email protected] (C. Wei-Guo). https://doi.org/10.1016/j.ijhydene.2019.10.249 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
2
international journal of hydrogen energy xxx (xxxx) xxx
Introduction As an ideal fuel that has the potential to be used as a pollution-free fuel with reduced greenhouse gas emissions, hydrogen (H2) is a promising fuel which can replace the diminishing fossil fuel supply. However, hydrogen has some salient characteristics, such as wide flammable limit range and high reaction sensitivity, making the safety issues related to hydrogen to be a serious challenge [1e3]. Regarding hydrogen safety, some related studies [4e12] have been devoted to the determination of the detonation mechanism and description of the dynamic parameters, such as detonation limits, critical tube diameter, detonation cell size, critical energy and detonation velocity deficit. Previous researches have confirmed that the addition of some hydrocarbons (e.g., methane or propane) to hydrogen can decrease the sensitivity of the detonable mixture of hydrogen/oxygen [13,14]. On the other hand, the performances of the binary fuel blends of propane and hydrogen are improved, if hydrogen is added to propane, e.g., cleaner products and less unwanted pollutants, higher thermal efficiency. Tang et al. [15] studied the laminar burning velocities and the onset of cellular instabilities of hydrogen-propane-air mixtures. Law et al. [16] analyzed the critical conditions for the onset of instability of the fuel blends at evaluated pressures. Azatyan et al. [13] studied the inhibition effect of propane on hydrogen-air detonations. In industry, its application also can be wide, such as internal combustion engine and rocket booster. Detonation limit, referring to the conditions outside of which a self-sustained detonation wave is unable to propagate [17e19], is of significance for hazard assessment, as well as fundamental point of view. For detonation limit determination, Manson [20] used the instability of detonation velocity as a criterion. Meanwhile, the galloping detonation appeared as the limits are approached. The recognized criterion is the l= 3 rule [17,19]. Near the limit, the detonation velocity fluctuates and the lowest mode of single-head spin with l ¼ p, D, in which l and D represent the detonation cell size and the tube diameter, respectively. Hence, to determine the detonation limit of a given mixture, detonation velocity and cellular structure records are of importance. In recent years, some studies have been performed to explore the combustion characteristics of binary fuel blends, such as laminar burning velocity, DDT (deflagration to detonation transition), detonation limits and detonation cell size [21e25]. However, few literatures reported the detonation limits of propane/hydrogen mixtures. In this study, systematic investigations on the near detonation limits behavior of propane-hydrogen-oxygen mixtures in a rectangular tube were conducted. The detonation velocity was measured using
photodiodes mounted on the tube wall, which is used to determine detonation limits. The detonation velocity deficits are calculated, both experimentally measured and theoretical prediction using Fay’s model. In addition, the cellular detonation structure was obtained using smoked foils technique and analyzed.
Experimental setup and procedures In the present study, three explosive mixtures of propanehydrogen-oxygen, i.e., 8H2eC3H8e9O2, 4H2eC3H8e7O2 and 12H2eC3H8e11O2, are used to study their near detonation limits behavior, the details of which are tabulated in Table 1. It is noteworthy that 8H2eC3H8e9O2 is at stoichiometry both for C3H8eO2 and H2eO2, 4H2eC3H8e7O2 has higher content of propane while hydrogen is higher in 12H2eC3H8e11O2. Experiments are conducted in a 2000 mm long rectangular stainless steel driver section (40 mm 25 mm) followed by a test section (52 mm 32 mm) of detonation tube with 3000 mm in length, as shown schematically in Fig. 1(a). The explosive mixtures are prepared by the method of partial pressures in a mixing chamber and allowed to be mixed in the chamber for more than 20 h in order to ensure mixture homogeneity. Prior to an experiment, the detonation tube is evacuated to a pressure less than 100Pa. Subsequently, the mixture is introduced into the tube accompanying with the increase of the inner pressure to the desired initial pressure (r0 ) at room temperature (303 K), which can control the detonable mixture sensitivity and left 10 min till the mixture becomes perfectly quiescent. The initial pressure is monitored by an digital manometer (SXT-4A, 0e150 kPa) with the accuracy of ±0.1 kPa. Ignition is achieved by a high energy spark from a capacitor discharge, leading to the formation of detonation wave. At the location of 4000 mm downstream from the spark gap, four photodiodes are mounted on the wall of the tube with the interval distance of 200 mm. The detonation velocity can be determined by taking the slope of the trajectory of the photodiodes. Smoked foils are used to record the detonation cell structure. The smoked foil was made of a thin plastic sheet (400 mm 50 mm) covered with uniform soot and the inserted into the end of the tube. Each shot was repeated at least 3 times to achieve reproducibility.
Results and discussion Fig. 1(b) shows typical trajectories of detonation propagating in the tube for 8H2eC3H8e9O2. The x -axis is the TOA (time of arrive) of the detonation, while the y -axis represents the corresponding location of the photodiode. From the trajectory
Table 1 e C3H8eH2eO2 mixtures with various compositions used in this experiment. Mixtures 8H2eC3H8e9O2 4H2eC3H8e7O2 12H2eC3H8e11O2
C3H8(vol%)
H2 (vol%)
O2 (vol%)
Equivalence ratio
Note
5.56 8.33 4.17
44.44 33.33 50.00
50.00 58.34 45.83
1 1 1
Stoichiometry Higher propane Higher hydrogen
Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
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Fig. 1 e (a) Experimental setup; (b) Trajectories of self-sustained detonations and failing detonation for the 8H2eC3H8e9O2 mixture; (c) Oscillograms of optical and pressure sensors for an unsuccessful propagation detonation in 8H2eC3H8e9O2 at p0 ¼ 3 kPa.
Fig. 2 e Detonation velocity as a function of initial pressure for different mixtures. Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
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Table 2 e Detonation cell size correlations for three mixtures. Mixtures 8H2eC3H8e9O2 4H2eC3H8e7O2 12H2eC3H8e11O2
A
h
250.1 316.7 259.1
1.208 1.374 1.233
plots, the velocities for steady and unsteady detonation can be determined. For instance, the detonation velocities for 8H2eC3H8e9O2 are steady at the initial pressure p0 ¼ 20 kPa and p0 ¼ 12 kPa, since the slopes are invariable. However, when p0 ¼ 3 kPa, one can see the detonation velocity decreases gradually along the tube. As suggested in previous studies [26e29], the unsteady velocity can be considered as the detonation approaches the limits. This also can be observed by the comparison between the optical and pressure signals, which is shown in Fig. 1 (c). The optical signals (reflect the reaction zone) are slightly behind the corresponding pressure signals (reflect the shock), indicating the decoupling of the reaction zone-shock complex, i.e., the detonation fails. The experimentally measured detonation velocity in mixtures at various initial pressures is shown in Fig. 2, where the Chapman-Jouguet (CJ) detonation velocity is also available. It is worth noting that the CJ detonation velocities are computed using the ideal one-dimensional ZND model in Chemkin package [30]. Fig. 2 indicates that, well within the detonation limit, the detonation velocity considerably steady with a little
deficit because of the heat and momentum losses from the walls of the tube. Herein, the detonation velocity deficit is defined by Ref. [17]: DV VCJ V ¼ VCJ VCJ
(1)
In which VCJ and V denote the ideal CJ detonation velocity, the experimentally measured velocity respectively, and DV ¼ VCJ V. By reducing the initial pressure, the detonation velocity is decreased and the detonation limit is approached. Subsequently, the self-sustained detonation is unable to be achieved when the initial pressure is below a critical pressure (pc ), and the critical pressure is determined from the experiment (see Fig. 2). The experimental results indicate that pc ¼ 4 kPa for 8H2eC3H8e9O2, pc ¼ 5 kPa for 4H2eC3H8e7O2, and pc ¼ 6 kPa for 12H2eC3H8e11O2. When p0 < pc , the measured detonation velocity fluctuates significantly. This indicates that the detonation cannot sustain a steady velocity. The detonation velocity deficits are roughly 10% for the three mixtures. According to Fay’s theory [31], the detonation velocity deficit can be calculated based on the one-dimensional ZND structure. Thus, equation (1) can be replaced by: 12 DV ð1 nÞ2 ¼1 VCJ ð1 nÞ2 þ g2 ð2n n2 Þ
(2)
Fig. 3 e Experimentally measured detonation cell size in different mixtures. Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
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Here, g is the specific heat ratio under the CJ condition, and n is written by: n¼
x ð1 þ gÞð1 þ xÞ
(3)
The area divergence x can be expressed in terms of the boundary layer displacement thickness d* as: x¼
A1 ða þ d* Þðb þ d* Þ 2d* 1z 1¼ ab A2 DH
(4)
where, DH is the hydraulic diameter of the rectangular tube, which can be expressed as: DH ¼
4ab 2ða þ bÞ
(5)
a and b denote the length and width of the cross-section of the rectangular tube, respectively. For smooth tubes, the boundary layer displacement thickness is: d* ¼ 0:22c0:8
me r0 V
0:2 (6)
c, me , r0 , V represent the reaction zone thickness, the viscosity of the hot gas at the post-shock state, the initial gas density and the detonation velocity, respectively. In this study, the viscosity of the hot gas at the post-shock state, the initial gas density and the specific heat ratio were calculated using NASA-CEA program [32]. To calculate the detonation velocity deficit, the reaction zone thickness (c) must be computed in advance. In some
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related research [15,16,33], the reaction zone thickness (c) can be simplified to be equal to the detonation cell length (L), i.e., c ¼ L. Edwards [34] argued that the correlation between the detonation cell length (L) and the detonation cell size (l) is L ¼ 1:67 l, which is adopted in this study. The detonation cell size (l) is experimentally measured by means of the pattern on the smoked foils. Good agreement is found with the tendency in previous studies [18,35]. In this study, the detonation cell size is recorded using smoked foils and experimentally measured. For most hydrocarbons, the detonation cell size fitting correlations can be written as lðmmÞ ¼ Aðp0 ½kPaÞh [36,37]. It had been suggested by Jesuthasan [38] that the detonation structure is independent of the tube geometry. Thus, the expression also can be used to fit the cell sizes in the experiment, which are shown in Table 2. Fig. 3 shows the detonation cell sizes for the three mixtures, with the curve fit included. For each condition, ten measurements were made based on the smoked foil, from which the average cell size could be determined. Satisfactory agreement can be detected between the experiments and the curves. With the decreasing of the hydrogen concentration, the detonation cell size decreases. Fig. 4 shows the detonation velocities normalized with the CJ value versus different initial pressure, both theoretically predicted using Fay’s model and experimentally measured. It can be seen that the detonation velocity deficits increase with the decrease of the initial pressure for both experimental data and computed data. Generally, the measured detonation velocity deficits are in good agreement with the predicted
Fig. 4 e Variation of normalized detonation velocity versus initial pressure for different mixtures. Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249
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Fig. 5 e The detonation cell pattern on smoked foils for in (a): 8H2eC3H8e9O2, (b): 4H2eC3H8e7O2 and (c): 12H2eC3H8e11O2. values. The mean errors between the experimental and theoretical values are less than 3%. Firstly, this can be ascribed to the measurement of the detonation cell size. The cellular structures are irregular; thus, the uncertainties cannot be avoided. Secondly, the detonation in hydrogen-propaneoxygen is dominated by the instability, which is not considered in Fay’s model. For most mixtures without dilution, the detonation is unstable with irregular cellular structures [20]. In the experiment, the cellular structures of propane-hydrogen-oxygen are irregular. And with the decrease of the initial pressure, the cellular structures are more erratic. Fig. 5 shows the detonation cellular structures in C3H8eH2eO2 mixtures at and near the critical pressures (pc ), respectively. For 8H2eC3H8e9O2, the cellular structure can be seen in Fig. 5 (a). When the initial pressure is 4 kPa, detonation in 8H2eC3H8e9O2 is singleheaded, thereafter the structure turns into a formation similar to “double-headed”. This is because the unstable gases are likely to form localized explosions, which facilitates the initiation of a detonation [17]. As the initial pressure declines (p0 ¼ 3 kPa) outside the detonation limit, no cell is formed and only slight trajectories are discernible. As for 4H2eC3H8e7O2 at p0 ¼ 5 kPa and p0 ¼ 4 kPa, some trace lines are detected at the forepart of the smoked foil, and then disappear. Heat and momentum loss from the wall is becoming more significant at the longer distance from the igniter. For 12H2eC3H8e11O2 at p0 ¼ 6 kPa and p0 ¼ 5 kPa, the trajectories of the triple point are more indiscernible.
Conclusion In this study, an investigation on the near detonation limits behavior of propane-hydrogen-oxygen mixtures (8H2eC3H8e9O2, 4H2eC3H8e7O2 and 12H2eC3H8e11O2) in a rectangular tube (52 mm 32 mm) is carried out. The detonation limits are determined via the measurement of
detonation velocity. The detonation velocity deficit is computed by experimental results and Fay’s theory. The detonation cell structure is recorded and analyzed. Generally, the detonation velocity decreases with the decrease of the initial pressure. Within the detonation limits, the detonation velocity is steady with a small velocity deficit. Outside the limits, large velocity fluctuations were observed, which indicates the failure of a detonation. The detonation limits for 8H2eC3H8e9O2, 4H2eC3H8e7O2 and 12H2eC3H8e11O2 are 4 kPa, 5 kPa and 6 kPa, respectively, and the corresponding detonation velocity deficits are all about 10%. The detonation velocity deficits were evaluated using Fay’s model with reasonable accuracy. Near the detonation limits, the recorded cellular patterns are relatively complicated. Below the limits, only some triple-point trajectories can be observed. However, only one smoked foil on the bottom wall was used in this study. The cellular structures on four walls will be further investigated to give more insight into the mechanisms near the limits.
Acknowledgement This work was supported by National Natural Science Foundation of China (Nos. 11602001, 11802272, 11972046 and 51674229), Open Project Foundation of CAS Key Laboratory of Mechanical Behavior and Design of Materials (No. lmbd201701) and China Postdoctoral Science Foundation (2017M610381 and 2019M651085), and the authors would like to thank these foundations for the financial support.
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Please cite this article as: Yun Z et al., Experimental investigation on the near detonation limits of propane/hydrogen/oxygen mixtures in a rectangular tube, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.10.249