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air fuels
Energy 159 (2018) 252e263
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Explosion hazard evaluation of renewable hydrogen/ammonia/air fuels Yanchao Li, Mingshu Bi, Bei Li, Yonghao Zhou, Lei Huang, Wei Gao* School of Chemical Machinery and Safety Engineering, Dalian University of Technology, Dalian, Liaoning 116024, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 December 2017 Received in revised form 19 June 2018 Accepted 24 June 2018 Available online 26 June 2018
Due to low ignition energy and wide range of flammability limit, explosion hazard of hydrogen/ammonia fuel must be evaluated to ensure safety application. In this work, effects of equivalence ratio, ammonia addition and initial pressure on the flame morphology and explosion pressure are revealed. The results demonstrate that effects of three factors on explosion hazard are ranked from the most important to the least important as initial pressure, equivalence ratio and ammonia hydrogen. The cellular flame formation by varying the equivalence ratio could be mainly attributed to the diffusional-thermal instability. The expanding flame of F ¼ 0.8, 1.0 and 1.5 tends to be stable with ammonia addition. As initial pressure increases, there exists a joint and competitive effect of the diffusional-thermal instability and hydrodynamic instability. Maximum explosion pressure of F ¼ 0.8, 1.0 and 1.5 decreases monotonously with ammonia addition and increases linearly with initial pressure. The explosion pressure prediction is underestimated using the smooth flame model and reproduced satisfactorily using the wrinkled flame model. By varying equivalence ratio, ammonia addition and initial pressure, the most elementary reaction that enhances laminar flame velocity is R9 and the first two inhibiting reactions to laminar burning velocity are R10 and R168. © 2018 Elsevier Ltd. All rights reserved.
Keywords: Explosion hazard Ammonia addition Cellular flame Explosion pressure prediction
1. Introduction Hydrogen energy is one of most promising solutions to the environmental issues as a carbon-free fuel, which could eliminate the environmental pollution and reduce the greenhouse gas emissions [1]. Hydrogen has attractive characteristics as an energy carrier [2]: (1) conversion to electricity with relatively high efficiency; (2) water is main material for production and is available in abundance; (3) storage in liquid form and transportation over long distances by gas pipe and tankers. Ammonia, as a potential hydrogen-carrier, exhibits the following attributes [3]: (1) ammonia contains large amounts of hydrogen component (17.7% by weight); (2) ammonia is easily stored and transported in the liquid phase (around 8 bar); (3) ammonia can be widely synthesized from renewable energy and fossil fuels. But there are considerable technological challenges using pure hydrogen and pure ammonia fuel. Pure hydrogen fuel has an extremely low ignition energy and very wide range of flammability limits. The combustion intensity of
* Corresponding author. E-mail address: [email protected] (W. Gao). https://doi.org/10.1016/j.energy.2018.06.174 0360-5442/© 2018 Elsevier Ltd. All rights reserved.
pure ammonia fuel is very low and pure ammonia fuel is susceptible to substantial NOx emission. Since ammonia-addition into hydrogen could overcome some drawbacks in pure hydrogen and pure ammonia fuel, hydrogen/ammonia fuel is attracting substantial attention and has been extensively extended in the internal combustion engine and gas turbine [4,5]. In order to establish safety precautions and ensure energy utilization, it is indispensable to evaluate the explosion hazard of hydrogen/ammonia fuel. In the published works, the attention about hydrogen/ammonia fuel is mainly focused on laminar burning velocity measurement, emission characteristics and the development of its chemical reaction mechanism. Ichikawa [6] found that unstretched laminar burning velocity of ammonia/air mixture increases nonmonotonically with hydrogen substitution, which is consistent with the results of Li [7], and Ichikawa concluded that Markstein length changes non-monotonically with hydrogen addition. Lee [8] pointed out that NOx and N2O formation could be enhanced by ammonia substitution on hydrogen/air flame, and the amount of NOx emissions on rich side increases and then decreases with ammonia substitution, which is much lower than that on lean side. Besides, there is limited data on hydrogen/ammonia oxidation mechanism due to the fact that ammonia is not conventional fuel.
Y. Li et al. / Energy 159 (2018) 252e263
b
Nomenclature xNH3 VH2 Yk
volume fraction of ammonia hydrogen volume mass fraction of kth species unburnt mixture density, kg/m3 flame thickness, mm specific heat, J/kg/K effective Lewis number Lewis number of hydrogen wrinkling ratio flame radius of equivalent flame surface area, m time, s the chamber radius, m laminar burning velocity at reference temperature and reference pressure, m/s initial pressure, kPa
ru d
cp Leeff LeH2
XD
Rs t r SL0 p0
Tian [9] established a detailed chemical kinetic mechanism for methane/ammonia flame, which consists of 84 species and 703 elementary reactions. Konnov [10] revised detailed reaction mechanism for hydrocarbon combustion with implementation of the NCN pathway of prompt-NO formation. Lindstedt [11] also constructed a chemical kinetic mechanism for ammonia oxidation, which includes 21 species and 95 elementary reactions. In order to safety utilization of hydrogen/ammonia fuel, the related equipment must be designed by considering the explosion pressure behavior. However, the data on the explosion pressure of hydrogen/ammonia fuel is very scarce. Especially due to the flame instabilities, the burning rate will be increased and this makes the explosion pressure prediction difficult. Nevertheless, many models are still established to predict the explosion pressure. Dohoe [12] developed a differential equation and assumed that the expanding flame is still smooth during gas explosion:
" #2=3 1=g dp 3ðpmax p0 Þ p 1=g p0 pmax p ¼ $ $ 1 $ $SL dt r p0 pmax p0 p (1) Based on the assumption that the compression of unburnt mixture is isothermal and adiabatic coefficient of unburnt gas is equal to unity, Bradley [13] simplified Equation (1) and pointed out that accurate values of laminar burning velocity is significantly important to predict the explosion pressure evolution:
dp 3 2=3 p p 2=3 ¼ $pmax $ $ðpmax p0 Þ1=3 $ 1 0 $SL dt r p0 p
(2)
Equation (2) is integrated by Lautkaski [14] and the cubic law is obtained, which correlates the explosion pressure and time from ignition:
S3L $t 3 V
Dp ¼ k$p0 $
(3)
It should be noted that the explosion pressure could not be predicted accurately using equation (1)e(3) and the reason is that the above equations neglect the effects of flame instabilities on the burning rate [15]. Amount of factors affect the pressure behaviors in gas explosions, such as initial temperature, initial pressure, ignition energy, equivalence ratio and gas component. Orthogonal experimental
VNH3 ki
s rb l SL xH2 LeNH3 Rp p pmax
g T0
a
253
pressure index, 0.32943 ammonia volume pre-exponential factor thermal expansion ratio burnt product density, kg/m3 thermal conductivity, J/m/K/s laminar burning velocity, m/s volume fraction of hydrogen Lewis number of ammonia flame radius of equivalent perimeter, m explosion pressure, MPa maximum explosion pressure in the adiabatic condition, MPa adiabatic coefficient of unburnt mixture, 1.385 initial temperature, K temperature index, 1.89209
design and fuzzy grey relational analysis are usually adopted to evaluate the importance of each factor in a system, which have been proved their effectiveness in energy conservation and thermal management system. Zuo [16] evaluated the effects of equivalence ratio, flow rate, wall thermal conductivity and wall emissivity on emitter efficiency of the micro-cylindrical combustor using orthogonal experimental design and fuzzy grey relational analysis. The results show that the fuzzy grey relational grades of the four factors are 0.7817, 0.5317, 0.7042 and 0.7018. The same analysis is adopted to reveal the cooling effect of a liquid-cooled battery thermal management system, E [17] pointed out that the pipe number has a most obvious effect on the average temperature of the cooling plate, and coolant flow velocity is second, pipe height has the minimum effect. Hydrogen/ammonia fuel has a good application prospect, and the data about explosion pressure must be obtained to prevent explosion accidents. Especially, the physicochemical properties of ammonia/air mixture, including laminar burning velocity, Lewis number and flame thickness etc., are quite different from that of hydrogen/air mixture, the flame morphology and explosion pressure of hydrogen/air mixture are destined to change significantly with ammonia addition. Thus the present work is aimed at evaluating the explosion hazard using the fuzzy grey relational analysis. The effect of equivalence ratio, ammonia addition and initial pressure on flame morphology and explosion pressure is revealed. Finally a new method of predicting the explosion pressure is developed by considering the flame instabilities. 2. Experimental 2.1. Experimental apparatus The experimental apparatus is schematically shown in Fig. 1, which consists of a 14 L spherical combustion chamber, a highspeed schlieren photography system, a gas supplying system, a transient pressure measurement system, a data acquistition system，a high-voltage ignition system, and a time controller system. To allow optical flame visualization, the parallel side walls of spherical chamber are equipped with two excellent quartz glasses, which have a diameter of 130 mm and a thickness of 90 mm. The flame shape changes are captured by a FASTCAM SA4 high-speed camera with operating speed 10000 frame/s. After evacuation, hydrogen, ammonia and dry air are fed into the chamber in sequence and the mixture composition is calculated using partial
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The comparison matrix is a matrix which consists of all factors affecting the system characteristics. If the factor number is m and these factors are investigated using n condition, the comparison matrix is as follows:
3 2 x1 ð1Þ x1 6 x2 7 6 x2 ð1Þ 7 6 x¼6 4 « 5¼4 « xm xm ð1Þ 2
Fig. 1. Schematic of experimental apparatus: (1) hydrogen; (2) ammonia; (3) air; (4) needle valve; (5) pressure gage; (6) flame arrester; (7) vacuum pump; (8) point light source; (9) focusing lens; (10) pressure transducer; (11) signal conditioner; (12) schlieren mirror; (13) optical window; (14) knife edge; (15) data recorder; (16) highvoltage igniter; (17) high-speed camera; (18) programmable logic controller; (19) computer.
pressure. The volume fraction of ammonia (ammonia addition) is defined as:
xNH3 ¼
xi ðkÞ0 ¼
xi ðkÞ min xi ðkÞ max xi ðkÞ min xi ðkÞ
xi ðkÞ ¼
Dmin þ l,Dmax DðkÞ þ l$Dmax
(8)
Grey relational analysis (GRA) is developed by Deng [19] and could be used to measure the approximation degree among the sequences using a grey relational grade. The steps of grey relational analysis are as follows: Step 1: Determine reference matrix and comparison matrix. The reference matrix could reflect the system characteristics, which is expressed:
,,,
c¼
½c; 1:5c ð1:5c; 2c
c < 1=3 c 1=3
D Dmax
D¼
(9)
(10)
m X n 1 X yt ðkÞ xtj ðkÞ m$n j¼1
(11)
k¼1
rij ¼
n 1X xtj ðkÞ n
(12)
k¼1
Step 5: Rank the effects of investigated factors based on the magnitude of the fuzzy grey grade.
2.4. Typical explosion pressure and pressure rise rate
2.3. Fuzzy grey relational analysis
yðnÞ
Fig. 2 shows the typical explosion pressure and pressure rise rate. The pressure rise rate is obtained by the time derivation of explosion pressure. It could be observed that the explosion pressure
(5)
Table 1 Orthogonal factor and level value.
1 2 3 4 5
(7)
Step 4: Calculate the fuzzy grey grade. Based on the grey relational coefficient, the fuzzy greedy grade is obtained:
The orthogonal experimental design is a popular method of designing the experiment with multiple factors and levels. This method is aimed to select the representative experiment for reducing the experiment number [18]. Table 1 shows the orthogonal factor and level value. In this work, the factor number is three and they both have five levels, which reduce the experiment number from 125 to 25.
Level
(6)
Step 3: Calculate the grey relational coefficient:
l2
2.2. Orthogonal experimental design
yð3Þ
3 x1 ðnÞ x2 ðnÞ 7 7 « 5 xm ðnÞ
Step 2: Nondimensionalize comparison matrix using the following equation:
(4)
Before ignition, about 10 min is required to ensure the mixture to become quiescent and homogeneous. The transient pressure dynamics in the chamber is measured using a PCB piezoelectric pressure transducer (model 113B24) and is recorded using data acquisition YOKOGAWA DL850E of sampling rate 100 kS/s. The ignition electrode, data acquistition device and high-speed camera are controlled by an OMRON CPM1A programmable logic controller.
yð2Þ
,,, ,,, « ,,,
where l is the resolution coefficient, which is calculated as follows:
VNH3 VNH3 þ VH2
y ¼ ½ yð1Þ
x1 ð2Þ x2 ð2Þ « xm ð2Þ
Factors Equivalence ratio F
Initial pressure p0/kPa
Ammonia addition xNH3
0.6 0.8 1.0 1.5 2.0
50 100 150 200 250
0.1 0.3 0.5 0.7 0.9
Fig. 2. Explosion pressure and pressure rise rate.
Y. Li et al. / Energy 159 (2018) 252e263
evolution could be divided into two stages: (Ⅰ) the constantpressure stage, the transient pressure in the spherical chamber maintains in an initial state; (Ⅱ) the pressure-buildup stage, the pressure buildup is caused by the combustion heat release and the fractional pressure rise is proportional to the fractional mass burnt. Besides, the pressure rise rate increases firstly and then decreases significantly with time.
255
and ammonia addition are taken to be comparison matrix. Based on the description of calculating fuzzy grey grade in Section 2.3, the factor order is displayed in Fig. 3. It is found that the fuzzy grey relational grades of equivalence ratio, initial pressure and ammonia addition are 0.6375, 0.6759 and 0.5252, respectively. This means that the effects of three factors on explosion hazard are ranked from the most important to the least important as initial pressure, equivalence ratio and ammonia addition.
3. Numerical method 4.2. Effects of equivalence ratio on explosion characteristics A freely propagating adiabatic, premixed, planar flame is computed using PREMIX in ANSYS CHEMKIN 17.0. PREMIX could solve the steady-state mass, species and energy conservation equation using a hybrid time-integration/Newton-iteration technique. In this work, the Konnov mechanism [10] is selected to calculate the sensitivity coefficient of elementary reaction to laminar burning velocity. Maximum number of grid point in the numerical calculation is 2500. The solution gradient and curvature are both set as 0.01 to obtain sufficiently accurate results. Besides, in order to evaluate the major step affecting laminar burning velocity, the sensitivity analysis is also conducted and the sensitivity coefficient is obtained as follows:
SFi ¼
ki vYk $ Yk vki
(13)
4. Results 4.1. Determination of factor order Table 2 shows the orthogonal designed table and its results. Since the explosion pressure behavior is determined by the flame propagation velocity, the average flame propagation velocity is regarded as evaluation index to evaluate the explosion hazard intuitively. The average flame propagation velocity is obtained using the time derivation of flame radius within the optical window. The average flame propagation velocity under various conditions is considered as reference matrix. Equivalence ratio, initial pressure
Table 2 Orthogonal designed table and its results. Case
Equivalence ratio
Initial pressure/kPa
Ammonia addition
Average flame propagation velocity/m$s1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
0.6 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 0.8 1 1 1 1 1 1.5 1.5 1.5 1.5 1.5 2 2 2 2 2
50 100 150 200 250 50 100 150 200 250 50 100 150 200 250 50 100 150 200 250 50 100 150 200 250
0.1 0.3 0.5 0.7 0.9 0.3 0.5 0.7 0.9 0.1 0.5 0.7 0.9 0.1 0.3 0.7 0.9 0.1 0.3 0.5 0.9 0.1 0.3 0.5 0.7
5.00 3.29 1.38 0.51 No ignition 5.61 3.53 1.06 0.46 12.04 5.51 2.49 0.97 15.47 16.82 0.84 0.83 17.56 4.08 2.76 No ignition 8.82 2.00 0.60 No ignition
Fig. 4 shows effects of equivalence ratio on flame morphology in the constant-pressure stage (p0 ¼ 100 kPa, xNH3 ¼ 0.5), and the flame radius of various equivalence ratios is almost equal to 50 mm. It is observed that the cellular structure could be only formed on the lean and stoichiometric side. As equivalence ratio increases, the cell size becomes larger and larger. A smooth flame structure could be observed at F ¼ 1.5 and 2.0. As expected, the time to reach the same flame radius decreases firstly until F ¼ 1.0 and then increases with equivalence ratio. Fig. 5 shows effects of equivalence ratio on flame morphology in the pressure-buildup stage. The fully developed cellular flame is observed on the lean and stoichiometric side. As the explosion pressure rises in the confined chamber, cracks are formed on the flame surface at F ¼ 1.5, but the expanding flame of F ¼ 2.0 still maintains a smooth structure. It should be widely accepted that the onset of cellular flame could be attributed to the hydrodynamic instability and diffusionalthermal instability in absence of body forces. Hydrodynamic instability is caused by the expansion across the flame surface, which is characterized by thermal expansion ratio and flame thickness [20,21]:
s¼
ru rb
(14)
d¼
l ru cp SL
(15)
Diffusional-thermal instability is caused by the preferential diffusion of mass and heat inside the flame front, which is only present for Lewis number less than unity. When Lewis number is larger than unity, the expanding flame will become stable under the diffusional-thermal instability. In this paper, there are two fuels (hydrogen and ammonia) in the mixture, thus Lewis number of the
Fig. 3. Fuzzy grey relational grade.
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Fig. 4. Effects of equivalence ratio on flame morphology in the constant-pressure stage.
Fig. 5. Effects of equivalence ratio on flame morphology in the pressure-buildup stage.
reactant mixture could be calculated using a volumetric fractionweighted average of Lewis number of hydrogen and ammonia [22]:
Leeff ¼ xH2 $LeH2 þ xNH3 $LeNH3
(16)
Fig. 6 shows effects of equivalence ratio on effective Lewis number, thermal expansion ratio and flame thickness. It is obvious that effective Lewis number is less than unity on the lean and stoichiometric side, but larger than unity on the rich side. This indicates that the diffusional-thermal instability could destabilize the flame surface on the lean and stoichiometric side and stabilize the flame surface on the rich side. Thermal expansion ratio increases firstly until F ¼ 1.0 and then decreases with equivalence ratio, which trend is opposite to that of flame thickness. This means that the effects of hydrodynamic instability on flame destabilization continues to enhance until F ¼ 1.0 and then attenuates. Despite the hydrodynamic instability is the intrinsic instability for the expanding flame, the most wrinkled flame could not be observed at F ¼ 1.0. In combination with Fig. 4, it could be inferred that the cellular flame formation by varying the equivalence ratio could be mainly attributed to the diffusional-thermal instability rather than the hydrodynamic instability. Fig. 7 shows effects of equivalence ratio on maximum explosion pressure and maximum pressure rise rate. The maximum error in maximum explosion pressure and maximum pressure rise rate is 0.0065 MPa and 0.00168MPa/ms1. In fact, the experimental uncertainty is strongly dependent on the resolution of pressure gage and pressure transducer, which least count is 10Pa and 35Pa, respectively. Both maximum explosion pressure and maximum pressure rise rate increase significantly until F ¼ 1.0 and then decrease monotonously with equivalence ratio.
in the pressure-buildup stage. The cellular flame of F ¼ 0.8, 1.0 and 1.5 could be observed until xNH3 ¼ 0.7, 0.7 and 0.3, respectively. The cell size of cellular flame increases significantly with ammonia addition. Especially, the cracks of F ¼ 1.5 decrease from xNH3 ¼ 0.5 to xNH3 ¼ 0.7, and smooth flame is formed at xNH3 ¼ 0.9. To quantitatively characterize the wrinkling level of cellular flame, the wrinkling ratio is adopted in this work and is calculated as follows [23]:
XD ¼
R2p R2S
(17)
It should be noted that this method of calculating the wrinkling ratio must detect the flame edge accurately. Here the flame contour is detected using Canny edge detection in Matlab. Fig. 10 illustrates effects of ammonia addition on the wrinkling ratio. It is observed that the troughs and cusps on the flame surface could be tracked accurately using Canny edge detection. The wrinkling ratio of F ¼ 0.8 and 1.0 continues to decrease and is almost equal to unity at xNH3 ¼ 0.9. The wrinkling ratio of F ¼ 1.5 decreases gradually until xNH3 ¼ 0.5 and then the wrinkling ratio is almost equal to unity. In combination with Fig. 8, it is found that wrinkling ratio XD ¼ 1 corresponds to smooth flame. Besides, when the ammonia addition
4.3. Effects of ammonia addition on explosion characteristics Fig. 8 shows effects of ammonia addition on flame morphology in the constant-pressure stage (p0 ¼ 100 kPa). As ammonia addition increases, the cellular flame of F ¼ 0.8 and 1.0 tends to be stable, the cracks on the flame surface of F ¼ 1.5 decrease obviously. And the smooth flame of F ¼ 0.8, 1.0 and 1.5 starts to be observed at xNH3 ¼ 0.9, 0.9 and 0.5. Besides, the time to reach the same flame radius continues to increase significantly with ammonia addition. Fig. 9 shows effects of ammonia addition on flame morphology
Fig. 6. Effects of equivalence ratio on effective Lewis number, thermal expansion ratio and flame thickness.
Y. Li et al. / Energy 159 (2018) 252e263
Fig. 7. Effects of equivalence ratio on maximum explosion pressure and maximum pressure rise rate.
257
1.0. Due to the fact that thinner flame will lead to stronger destabilizing propensity [24], the effect of the hydrodynamic instability on cellular flame formation continues to attenuate with ammonia addition. In a word, on the lean and stoichiometric side, the effects of both diffusional-thermal and hydrodynamic instability on the flame destabilization will attenuate with ammonia addition. On the rich side, the effects of diffusional-thermal instability on flame stabilization attenuate and the effects of hydrodynamic instability on flame destabilization also attenuate with ammonia addition. Fig. 12 shows effects of ammonia addition on maximum explosion pressure and maximum pressure rise rate. As ammonia addition increases, maximum explosion pressure of F ¼ 0.8, 1.0 and 1.5 decreases slowly until xNH3 ¼ 0.7, and then maximum explosion pressure decreases significantly. Besides, maximum pressure rise rate of F ¼ 0.8, 1.0 and 1.5 decreases monotonously with ammonia addition. 4.4. Effects of initial pressure on explosion characteristics
is fixed, the wrinkling ratio of F ¼ 0.8 is largest, following by that of F ¼ 0.8 and F ¼ 1.0. Fig. 11 shows effects of ammonia addition on effective Lewis number, thermal expansion ratio and flame thickness. As ammonia addition increases, effective Lewis number of F ¼ 0.8 and 1.0 increases continuously and effective Lewis number of F ¼ 0.8 and 1.0 is still less than unity, effective Lewis number of F ¼ 1.5 decreases monotonously but effective Lewis number of F ¼ 1.5 is still larger than unity. The above results indicate that the cellular flame of F ¼ 0.8 and 1.0 could be still triggered by the diffusional-thermal instability, but the effect of the diffusionalthermal instability on flame destabilization is attenuating gradually. Thermal expansion ratio of F ¼ 0.8, 1.0 and 1.5 increases slowly with ammonia addition. And when the ammonia addition is fixed, thermal expansion ratio from large to small is as follows: F ¼ 1.0, F ¼ 1.5 and F ¼ 0.8. Besides, the flame thickness of F ¼ 0.8, 1.0 and 1.5 increases significantly with ammonia addition and flame thickness of the decreasing order is at F ¼ 0.8, 1.5 and
Fig. 13 shows effects of initial pressure on flame morphology (xNH3 ¼ 0.5). For F ¼ 0.8 and 1.0, the cellular flame could be not fully developed at p0 ¼ 50 kPa and the cellular flame starts to be formed at p0 ¼ 100 kPa, then the cellular flame of F ¼ 0.8 and 1.0 becomes more unstable and the cell size continues to decrease with initial pressure. In addition, the expanding flame of F ¼ 1.5 exhibits a smooth structure until p0 ¼ 200 kPa and more cracks are formed along the long crack as initial pressure increases. Note that the time to arrive the same radius is prolonged slightly with increasing initial pressure. Fig. 14 shows effects of initial pressure on flame morphology in the pressure-buildup stage. For F ¼ 0.8 and 1.0, the developed cellular flame becomes more unstable and the cell size decrease significantly with initial pressure. The smooth flame is only observed at F ¼ 1.5 and xNH3 ¼ 0.1. For F ¼ 1.5, the cracks emerge at xNH3 ¼ 0.3 and the cellular flame starts to be formed at xNH3 ¼ 0.5. Similarly, the cell size also decreases with increasing initial pressure.
Fig. 8. Effects of ammonia addition on flame morphology in the constant-pressure stage.
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Fig. 9. Effects of ammonia addition on flame morphology in the pressure-buildup stage.
Fig. 15 shows the effect of initial pressure on the wrinkling ratio. As initial pressure increases, the wrinkling ratio of F ¼ 0.8 and 1.0 increases monotonously and the wrinkling ratio of F ¼ 1.5 is almost equal to unity. And when the initial pressure is fixed, the wrinkling ratio of F ¼ 0.8 is largest, following by that of F ¼ 1.0 and F ¼ 1.5. Table 3 shows effects of initial pressure on effective Lewis number. With increasing initial pressure, effective Lewis number of F ¼ 0.8, 1.0 and 1.5 almost remains constant, and effective Lewis number of F ¼ 0.8 and 1.0 is less than unity and effective Lewis number of F ¼ 1.5 is larger than unity. This means that the diffusional-thermal instability could trigger the flame destabilization at F ¼ 0.8 and 1.0, but this destabilization effect is not enhanced or suppressed with increasing initial pressure. Similarly, the diffusional-thermal instability could stabilize the expanding flame at F ¼ 1.5 and the variation in this stabilization effect is very limited. Table 4 shows effects of initial pressure on thermal expansion ratio. As the initial pressure increases, thermal expansion ratio of F ¼ 0.8, 1.0 and 1.5 almost remains constant and thermal expansion ratio of F ¼ 1.0 is largest, following by that of F ¼ 1.5 and F ¼ 0.8. Fig. 11. Effects of ammonia addition on effective Lewis number, thermal expansion ratio and flame thickness.
Fig. 16 shows effects of initial pressure on the flame thickness. As initial pressure increases, the flame thickness of F ¼ 0.8, 1.0 and 1.5 decreases monotonously. Except for p0 ¼ 50 kPa, the flame thickness from large to small is: F ¼ 0.8, 1.5 and 1.0. In combination with
Fig. 10. Effect of ammonia addition on the wrinkling ratio.
Fig. 12. Effects of ammonia addition on maximum explosion pressure and maximum pressure rise rate.
Y. Li et al. / Energy 159 (2018) 252e263
259
Fig. 13. Effects of initial pressure on flame morphology in the constant-pressure stage.
Table 4, it could be concluded that the flame destabilization of F ¼ 0.8 and 1.0 could be attributed to the joint effect of the diffusional-thermal instability and hydrodynamic instability, the crack emergence of F ¼ 1.5 is due to the competitive effect of the diffusional-thermal instability and hydrodynamic instability. Fig. 17 shows effects of initial pressure on maximum explosion pressure and maximum pressure rise rate. Maximum explosion pressure of F ¼ 0.8, 1.0 and 1.5 increases linearly with increasing initial pressure. It could be inferred that the mixture density increases significantly in the confined chamber as initial pressure increases, which will generate more combustion heat and thus enhance the explosion pressure. Besides, maximum pressure rise rate of F ¼ 0.8, 1.0 and 1.5 increases monotonously with increasing initial pressure.
5. Discussions 5.1. Explosion pressure prediction considering flame instabilities Fig. 18 shows the explosion pressure prediction considering flame instabilities, the experimental pressure is obtained from the condition with F ¼ 1.0, p0 ¼ 100 kPa and xNH3 ¼ 0.5. In the theoretical prediction, the smooth flame and wrinkled flame are assumed in the theoretical calculation. Assuming that the expanding flame is still smooth, the explosion pressure is calculated using the equation (1). Besides, the expanding flame is difficult to maintain a smooth structure under the flame instabilities. The wrinkled flame will increase the flame surface area and hence the combustion intensity. Thus an improved model is established by introducing the wrinkling ratio:
Fig. 14. Effects of initial pressure on flame morphology in the pressure-buildup stage.
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Fig. 15. Effect of initial pressure on the wrinkling ratio.
Fig. 16. Effects of initial pressure on the flame thickness.
Table 3 Effects of initial pressure on effective Lewis number. Initial pressure/kPa
Effective Lewis number
F ¼ 0.8
F ¼ 1.0
F ¼ 1.5
50 100 150 200 250
0.83264 0.83264 0.83264 0.83264 0.83264
0.86041 0.86041 0.86041 0.86041 0.86041
1.328 1.328 1.328 1.328 1.328
" #2=3 1=g dp 3ðpmax p0 Þ p 1=g p0 pmax p ¼ $ $ 1 $ $ðXD $SL Þ dt r p0 pmax p0 p (18) The static wrinkling ratio and dynamic wrinkling ratio are adopted in the improved model of predicting explosion pressure. The static wrinkling ratio is assumed to be still equal to 1.42 during gas explosion process, and the dynamic wrinkling ratio is adopted based on the following assumption: (1) when the expanding flame is smooth, the wrinkling ratio is equal to unity; (2) when the expanding flame starts to become unstable, the wrinkling ratio increases linearly with time. It should be noted that the unburnt mixture temperature and pressure ahead of expanding flame in the confined chamber will rise due to adiabatic compression, which affect laminar burning velocity significantly. Thus the dependence of laminar burning velocity in equations (1) and (18) on temperature and pressure during gas explosion needs to be considered as follows:
a b T p SL ¼ SL0 $ $ T0 p0
As shown in Fig. 18, the explosion pressure in the pressurebuildup stage is obviously underestimated using the smooth flame model. When the static wrinkling ratio is adopted in the theoretical calculation, the explosion pressure prediction could be improved significantly, but the explosion pressure before t ¼ 34 ms and after t ¼ 34 ms is slightly overpredicted and underestimated, respectively. This is because wrinkling ratio of the expanding flame with XD ¼ 1.42 is overpredicted before t ¼ 34 ms and underestimated after t ¼ 34 ms with respect to the value in the experiment. When the dynamic wrinkling ratio is assumed, it is obvious that the explosion pressure could be reproduced relatively satisfactorily. The above results also indicate that the explosion pressure could be predicted using the product of laminar burning velocity and dynamic wrinkling ratio. In order to reveal the flame destabilization in the pressurebuildup stage, effective Lewis number, thermal expansion ratio and flame thickness are calculated based on the accurate explosion pressure prediction. Fig. 19 shows effective Lewis number, thermal expansion ratio and flame thickness in the pressure-buildup stage (F ¼ 1.0, p0 ¼ 100 kPa and xNH3 ¼ 0.5). As the explosion pressure starts to rise, effective Lewis number decrease slowly, which indicates that the effect of diffusional-thermal instability on the flame stabilization enhances. Despite thermal expansion ratio and flame thickness decrease monotonously, but the ratio of thermal expansion ratio to flame thickness increases significantly, which demonstrates that the effect of hydrodynamic instability on flame destabilization enhances. In a word, under the joint effect of diffusional-thermal and hydrodynamic instability, the expanding flame becomes more wrinkled in the pressure-buildup stage.
(19)
Table 4 Effects of initial pressure on thermal expansion ratio. Initial pressure/kPa
Thermal expansion ratio
F ¼ 0.8
F ¼ 1.0
F ¼ 1.5
50 100 150 200 250
6.4371 6.4445 6.4488 6.4508 6.4524
7.11387 7.14757 7.16569 7.17679 7.18545
6.67352 6.67646 6.67859 6.67928 6.67991
Fig. 17. Effects of initial pressure on maximum explosion pressure and maximum pressure rise rate.
Y. Li et al. / Energy 159 (2018) 252e263
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increase with ammonia addition, which promotes chemical reactivity of R9 and R168. Fig. 22 shows sensitivity coefficient of elementary reactions to laminar burning velocity at various initial pressures. The most elementary reactions of enhancing or suppressing chemical reactivity are R9 and R10, respectively. And the sensitivity coefficient of both R9 and R10 increases monotonously with increasing initial pressure, which could be attributed to the fact that the molecules collision rate increases significantly with increasing initial pressure.
6. Conclusions
Fig. 18. Explosion pressure prediction considering flame instabilities.
5.2. Sensitivity analysis
The present work is aimed at evaluating the explosion hazard by varying equivalence ratio, ammonia addition and initial pressure. In the experiment, the high-speed schlieren photography and pressure transducer are used to record the flame morphology and pressure dynamics. In the theoretical prediction, the explosion pressure is calculated using the smooth flame model and wrinkled flame model. In the numerical simulation, the contributions of elementary reaction to laminar burning velocity are conducted using the sensitivity analysis. The results demonstrate that:
As discussed in Section 5.1, laminar burning velocity could be regarded as a characteristic parameter to predict the explosion pressure evolution. In order to reveal the contributions of elementary reaction to laminar burning velocity, the sensitivity analysis is conducted in the following content. Fig. 20 shows sensitivity coefficient of elementary reaction to laminar burning velocity at various equivalence ratios. The most elementary reaction of enhancing laminar burning velocity is R9. The elementary reaction and the corresponding step numbers are listed in Table 5. The sensitivity coefficient of R9 decreases firstly until F ¼ 1.0 and then increases with equivalence ratio. Since laminar burning velocity of hydrogen/ammonia/air mixture is linearly correlated with H, OH and NH2 radical [25], despite H radical is consumed, OH and O radicals are formed through R9, which enhance the chemical reactivity significantly. The first two inhibiting reactions are R10 and R168. Through R10 and R168, H and NH2 radicals are consumed in large quantities and thus the chemical reactivity decreases. Fig. 21 shows sensitivity coefficient of elementary reactions to laminar burning velocity at various ammonia additions. R8 and R9 exhibit higher positive sensitivity coefficient. More O and OH radicals are generated in R9, which is the dominant chain branching reaction. R168 is the main path for consumption of NH2 and O radicals, in which active radicals could be reduced significantly. And sensitivity coefficient of R168 increases monotonously with ammonia addition, this is because H and NH2 free radicals will
(1) Based on the orthogonal experimental design, the explosion hazard is evaluated by the fuzzy grey relational analysis and the fuzzy grey relational grade of decreasing order is initial pressure, equivalence ratio and ammonia addition. (2) By varying equivalence ratio, the cellular flame formation on the lean and stoichiometric side could be mainly attributed to the diffusional-thermal instability rather than the hydrodynamic instability. As ammonia addition increases, the expanding flame of F ¼ 0.8, 1.0 and 1.5 tends to be more stable. With increasing initial pressure, the flame destabilization of F ¼ 0.8 and 1.0 could be attributed to the joint effect of the diffusional-thermal instability and hydrodynamic instability, the crack emergence of F ¼ 1.5 is due to the competitive effect of the diffusional-thermal instability and hydrodynamic instability. (3) Both maximum explosion pressure and maximum pressure rise rate increase until F ¼ 1.0 and then decrease monotonously with equivalence ratio. As ammonia addition increases, maximum explosion pressure and maximum pressure rise rate decrease monotonously. With increasing initial pressure, maximum explosion pressure of F ¼ 0.8, 1.0 and 1.5 increases linearly and maximum pressure rise rate increases nonlinearly.
Fig. 19. Effective Lewis number, thermal expansion ratio and flame thickness in the pressure-buildup stage.
Fig. 20. Sensitivity coefficient of elementary reaction to laminar burning velocity at various equivalence ratios.
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Table 5 Step number and elementary reaction. Step Number
Elementary Reaction
Step Number
Elementary Reaction
R8 R9 R10 R12 R13 R17 R62
O þ H2 ¼ OH þ H H þ O2 ¼ OH þ O H þ O2 (þM) ¼ HO2(þM) H þ OH þ M ¼ H2O þ M H2þOH ¼ H2O þ H H þ H2O ¼ H2 þ O2 NH þ H2 ¼ NH2 þ H
R64 R71 R80 R136 R168 R176 R181
NH2þNH ¼ N2H2 þ H NH3þH ¼ NH2 þ H2 N2H2þM ¼ NNH þ H þ M HNO þ H ¼ NO þ H2 NH2 þ O ¼ HNO þ H NH2þNO ¼ NNH þ OH NH þ O ¼ NO þ H
coefficient of R9 increases monotonously with ammonia addition and initial pressure. Based on the above results, two suggestions are proposed to mitigate the explosion hazard: (1) higher initial pressure should be avoided firstly in the industrial container. Once the initial pressure is relatively higher, the static activation pressure must be as small as possible in the explosion venting; (2) the explosion suppression could be achieved by reducing laminar burning velocity. Considering the chemical kinetics, the inhibitor should be selected by suppressing the dominant chain branching reaction R9 or enhancing the inhibiting reaction R10. Acknowledgment
Fig. 21. Sensitivity coefficient of elementary reaction to laminar burning velocity at various ammonia additions.
(4) Due to the joint effect of diffusional-thermal instability and hydrodynamic instability, the expanding flame will become more wrinkled in the pressure-buildup stage, which certainly increases the flame surface area and hence the burning rate. In the theoretical calculation, the explosion pressure is underestimated significantly using the smooth flame model and could be reproduced very satisfactorily using the product of laminar burning velocity and dynamic wrinkling ratio. (5) By varying equivalence ratio, ammonia addition and initial pressure, the most elementary reaction that enhances laminar flame velocity is R9, the first two inhibiting reactions to laminar burning velocity are R10 and R168. And the sensitivity coefficient of R9 decreases firstly until F ¼ 1.0 and then increases with equivalence ratio. Besides, the sensitivity
Fig. 22. Sensitivity coefficient of elementary reaction to laminar burning velocity at various initial pressures.
The authors appreciate the financial supported by the National Key R&D Program of China (No. 2017YFC0804705), National Natural Science Foundation of China (No. 51406023 and No. 51674059) and China Postdoctoral Science Foundation Funded Project (No. 2017T100177). References [1] Hanley ES, Deane JP, Gallachoir BP. The role of hydrogen in low carbon energy futures-A review of existing perspectives. Renew Sustain Energy Rev 2018;82: 3027e45. [2] Sacramento EM, Carvalho P, Lima LC, Veziroglu TN. Feasibility study for the transition towards a hydrogen economy: a case study in Brazil. Energy Pol 2013;62:3e9. [3] Zamfirescu C, Dincer I. Ammonia as a green fuel and hydrogen source for vehicular applications. Fuel Process Technol 2009;90:729e37. [4] Frigo S, Gentili R. Analysis of the behaviour of a 4-stroke Si engine fuelled with ammonia and hydrogen. Int J Hydrogen Energy 2013;38:1607e15. [5] Medina AV, Pugh DG, Marsh P, Bulat G, Bowen P. Preliminary study on lean premixed combustion of ammonia-hydrogen for swirling gas turbine combustors. Int J Hydrogen Energy 2017;42:24495e503. [6] Ichikawa A, Hayakawa A, Kitagawa Y, Somarathne KD, Kudo T, Kobayashi H. Laminar burning velocity and Markstein length of ammonia/hydrogen/air premixed flames at elevated pressures. Int J Hydrogen Energy 2015;40: 9570e8. [7] Li J, Huang H, Kobayashi N, He Z, Osaka Y, Zeng T. Numerical study on effect of oxygen content in combustion air on ammonia combustion. Energy 2015;93: 2053e68. [8] Lee JH, Lee SI, Kwon OC. Effects of ammonia substitution on hydrogen/air flame propagation and emissions. Int J Hydrogen Energy 2010;35:11332e41. [9] Tian Z, Li Y, Zhang L, Glarborg P, Qi F. An experimental and kinetic modeling study of premixed NH3/CH4/O2/Ar flames at low pressure. Combust Flame 2009;156:1413e26. [10] Konnov AA. Implementation of the NCN pathway of prompt-NO formation in the detailed reaction mechanism. Combust Flame 2009;156:2093e105. [11] Lindstedt RP, Lockwood FC, Selim MA. Detailed kinetic modelling of chemistry and temperature effects on ammonia oxidation. Combust Sci Technol 1994;99:253e76. [12] Dahoe AE, Zevenbergen JF, Lemkowitz SM, Scarlett B. Dust explosion in spherical vessels: the role of flame thickness in the validity of the ‘cube-root law’. J Loss Prevent Proc 1996;9:33e44. [13] Bradley D, Mitcheson A. Mathematical solutions for explosions in spherical vessels. Combust Flame 1976;26:201e17. [14] Lautkaski R. Pressure rise in confined gas explosions. 2005. Project Report. [15] Dobashi R. Experimental study on gas explosion behavior in enclosure. J Loss Prevent Proc 1997;10:83e9. [16] Zuo W, E J, Liu X, Peng Q, Deng Y, Zhu H. Orthogonal experimental design and fuzzy grey relational analysis for emitter efficiency of the micro-cylindrical
Y. Li et al. / Energy 159 (2018) 252e263 combustor with a step. Appl Therm Eng 2016;103:945e51. [17] E J, Han D, Qiu A, Zhu H, Deng Y, Chen J, Zhao X, Zuo W, Wang H, Chen J, Peng Q. Orthogonal experimental design of liquid-cooling structure on the cooling effect of a liquid-cooled battery thermal management system. Appl Therm Eng 2018;132:508e20. [18] Zhao P, Ge S, Yoshikawa K. An orthogonal experimental study on solid fuel production from sewage sludge by employing steam explosion. Appl Energy 2013;112:1213e21. [19] Deng JL. Introduction to grey system theory. J Grey Syst 1989;1:1e24. [20] Vu TM, Park J, Kwon OB, Kim JS. Effects of hydrocarbon addition on cellular instabilities in expanding syngas-air spherical premixed flames. Int J Hydrogen Energy 2009;34:6961e9. [21] Wang J, Xie Y, Cai X, Nie Y, Peng C, Huang Z. Effect of H2O addition on the flame front evolution of syngas spherical propagation flames. Combust Sci
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Explosion hazard evaluation of renewable hydrogen/ammonia/air fuels Yanchao Li, Mingshu Bi, Bei Li, Yonghao Zhou, Lei Huang, Wei Gao* School of Chemical Machinery and Safety Engineering, Dalian University of Technology, Dalian, Liaoning 116024, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 December 2017 Received in revised form 19 June 2018 Accepted 24 June 2018 Available online 26 June 2018
Due to low ignition energy and wide range of flammability limit, explosion hazard of hydrogen/ammonia fuel must be evaluated to ensure safety application. In this work, effects of equivalence ratio, ammonia addition and initial pressure on the flame morphology and explosion pressure are revealed. The results demonstrate that effects of three factors on explosion hazard are ranked from the most important to the least important as initial pressure, equivalence ratio and ammonia hydrogen. The cellular flame formation by varying the equivalence ratio could be mainly attributed to the diffusional-thermal instability. The expanding flame of F ¼ 0.8, 1.0 and 1.5 tends to be stable with ammonia addition. As initial pressure increases, there exists a joint and competitive effect of the diffusional-thermal instability and hydrodynamic instability. Maximum explosion pressure of F ¼ 0.8, 1.0 and 1.5 decreases monotonously with ammonia addition and increases linearly with initial pressure. The explosion pressure prediction is underestimated using the smooth flame model and reproduced satisfactorily using the wrinkled flame model. By varying equivalence ratio, ammonia addition and initial pressure, the most elementary reaction that enhances laminar flame velocity is R9 and the first two inhibiting reactions to laminar burning velocity are R10 and R168. © 2018 Elsevier Ltd. All rights reserved.
Keywords: Explosion hazard Ammonia addition Cellular flame Explosion pressure prediction
1. Introduction Hydrogen energy is one of most promising solutions to the environmental issues as a carbon-free fuel, which could eliminate the environmental pollution and reduce the greenhouse gas emissions [1]. Hydrogen has attractive characteristics as an energy carrier [2]: (1) conversion to electricity with relatively high efficiency; (2) water is main material for production and is available in abundance; (3) storage in liquid form and transportation over long distances by gas pipe and tankers. Ammonia, as a potential hydrogen-carrier, exhibits the following attributes [3]: (1) ammonia contains large amounts of hydrogen component (17.7% by weight); (2) ammonia is easily stored and transported in the liquid phase (around 8 bar); (3) ammonia can be widely synthesized from renewable energy and fossil fuels. But there are considerable technological challenges using pure hydrogen and pure ammonia fuel. Pure hydrogen fuel has an extremely low ignition energy and very wide range of flammability limits. The combustion intensity of
* Corresponding author. E-mail address: [email protected] (W. Gao). https://doi.org/10.1016/j.energy.2018.06.174 0360-5442/© 2018 Elsevier Ltd. All rights reserved.
pure ammonia fuel is very low and pure ammonia fuel is susceptible to substantial NOx emission. Since ammonia-addition into hydrogen could overcome some drawbacks in pure hydrogen and pure ammonia fuel, hydrogen/ammonia fuel is attracting substantial attention and has been extensively extended in the internal combustion engine and gas turbine [4,5]. In order to establish safety precautions and ensure energy utilization, it is indispensable to evaluate the explosion hazard of hydrogen/ammonia fuel. In the published works, the attention about hydrogen/ammonia fuel is mainly focused on laminar burning velocity measurement, emission characteristics and the development of its chemical reaction mechanism. Ichikawa [6] found that unstretched laminar burning velocity of ammonia/air mixture increases nonmonotonically with hydrogen substitution, which is consistent with the results of Li [7], and Ichikawa concluded that Markstein length changes non-monotonically with hydrogen addition. Lee [8] pointed out that NOx and N2O formation could be enhanced by ammonia substitution on hydrogen/air flame, and the amount of NOx emissions on rich side increases and then decreases with ammonia substitution, which is much lower than that on lean side. Besides, there is limited data on hydrogen/ammonia oxidation mechanism due to the fact that ammonia is not conventional fuel.
Y. Li et al. / Energy 159 (2018) 252e263
b
Nomenclature xNH3 VH2 Yk
volume fraction of ammonia hydrogen volume mass fraction of kth species unburnt mixture density, kg/m3 flame thickness, mm specific heat, J/kg/K effective Lewis number Lewis number of hydrogen wrinkling ratio flame radius of equivalent flame surface area, m time, s the chamber radius, m laminar burning velocity at reference temperature and reference pressure, m/s initial pressure, kPa
ru d
cp Leeff LeH2
XD
Rs t r SL0 p0
Tian [9] established a detailed chemical kinetic mechanism for methane/ammonia flame, which consists of 84 species and 703 elementary reactions. Konnov [10] revised detailed reaction mechanism for hydrocarbon combustion with implementation of the NCN pathway of prompt-NO formation. Lindstedt [11] also constructed a chemical kinetic mechanism for ammonia oxidation, which includes 21 species and 95 elementary reactions. In order to safety utilization of hydrogen/ammonia fuel, the related equipment must be designed by considering the explosion pressure behavior. However, the data on the explosion pressure of hydrogen/ammonia fuel is very scarce. Especially due to the flame instabilities, the burning rate will be increased and this makes the explosion pressure prediction difficult. Nevertheless, many models are still established to predict the explosion pressure. Dohoe [12] developed a differential equation and assumed that the expanding flame is still smooth during gas explosion:
" #2=3 1=g dp 3ðpmax p0 Þ p 1=g p0 pmax p ¼ $ $ 1 $ $SL dt r p0 pmax p0 p (1) Based on the assumption that the compression of unburnt mixture is isothermal and adiabatic coefficient of unburnt gas is equal to unity, Bradley [13] simplified Equation (1) and pointed out that accurate values of laminar burning velocity is significantly important to predict the explosion pressure evolution:
dp 3 2=3 p p 2=3 ¼ $pmax $ $ðpmax p0 Þ1=3 $ 1 0 $SL dt r p0 p
(2)
Equation (2) is integrated by Lautkaski [14] and the cubic law is obtained, which correlates the explosion pressure and time from ignition:
S3L $t 3 V
Dp ¼ k$p0 $
(3)
It should be noted that the explosion pressure could not be predicted accurately using equation (1)e(3) and the reason is that the above equations neglect the effects of flame instabilities on the burning rate [15]. Amount of factors affect the pressure behaviors in gas explosions, such as initial temperature, initial pressure, ignition energy, equivalence ratio and gas component. Orthogonal experimental
VNH3 ki
s rb l SL xH2 LeNH3 Rp p pmax
g T0
a
253
pressure index, 0.32943 ammonia volume pre-exponential factor thermal expansion ratio burnt product density, kg/m3 thermal conductivity, J/m/K/s laminar burning velocity, m/s volume fraction of hydrogen Lewis number of ammonia flame radius of equivalent perimeter, m explosion pressure, MPa maximum explosion pressure in the adiabatic condition, MPa adiabatic coefficient of unburnt mixture, 1.385 initial temperature, K temperature index, 1.89209
design and fuzzy grey relational analysis are usually adopted to evaluate the importance of each factor in a system, which have been proved their effectiveness in energy conservation and thermal management system. Zuo [16] evaluated the effects of equivalence ratio, flow rate, wall thermal conductivity and wall emissivity on emitter efficiency of the micro-cylindrical combustor using orthogonal experimental design and fuzzy grey relational analysis. The results show that the fuzzy grey relational grades of the four factors are 0.7817, 0.5317, 0.7042 and 0.7018. The same analysis is adopted to reveal the cooling effect of a liquid-cooled battery thermal management system, E [17] pointed out that the pipe number has a most obvious effect on the average temperature of the cooling plate, and coolant flow velocity is second, pipe height has the minimum effect. Hydrogen/ammonia fuel has a good application prospect, and the data about explosion pressure must be obtained to prevent explosion accidents. Especially, the physicochemical properties of ammonia/air mixture, including laminar burning velocity, Lewis number and flame thickness etc., are quite different from that of hydrogen/air mixture, the flame morphology and explosion pressure of hydrogen/air mixture are destined to change significantly with ammonia addition. Thus the present work is aimed at evaluating the explosion hazard using the fuzzy grey relational analysis. The effect of equivalence ratio, ammonia addition and initial pressure on flame morphology and explosion pressure is revealed. Finally a new method of predicting the explosion pressure is developed by considering the flame instabilities. 2. Experimental 2.1. Experimental apparatus The experimental apparatus is schematically shown in Fig. 1, which consists of a 14 L spherical combustion chamber, a highspeed schlieren photography system, a gas supplying system, a transient pressure measurement system, a data acquistition system，a high-voltage ignition system, and a time controller system. To allow optical flame visualization, the parallel side walls of spherical chamber are equipped with two excellent quartz glasses, which have a diameter of 130 mm and a thickness of 90 mm. The flame shape changes are captured by a FASTCAM SA4 high-speed camera with operating speed 10000 frame/s. After evacuation, hydrogen, ammonia and dry air are fed into the chamber in sequence and the mixture composition is calculated using partial
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Y. Li et al. / Energy 159 (2018) 252e263
The comparison matrix is a matrix which consists of all factors affecting the system characteristics. If the factor number is m and these factors are investigated using n condition, the comparison matrix is as follows:
3 2 x1 ð1Þ x1 6 x2 7 6 x2 ð1Þ 7 6 x¼6 4 « 5¼4 « xm xm ð1Þ 2
Fig. 1. Schematic of experimental apparatus: (1) hydrogen; (2) ammonia; (3) air; (4) needle valve; (5) pressure gage; (6) flame arrester; (7) vacuum pump; (8) point light source; (9) focusing lens; (10) pressure transducer; (11) signal conditioner; (12) schlieren mirror; (13) optical window; (14) knife edge; (15) data recorder; (16) highvoltage igniter; (17) high-speed camera; (18) programmable logic controller; (19) computer.
pressure. The volume fraction of ammonia (ammonia addition) is defined as:
xNH3 ¼
xi ðkÞ0 ¼
xi ðkÞ min xi ðkÞ max xi ðkÞ min xi ðkÞ
xi ðkÞ ¼
Dmin þ l,Dmax DðkÞ þ l$Dmax
(8)
Grey relational analysis (GRA) is developed by Deng [19] and could be used to measure the approximation degree among the sequences using a grey relational grade. The steps of grey relational analysis are as follows: Step 1: Determine reference matrix and comparison matrix. The reference matrix could reflect the system characteristics, which is expressed:
,,,
c¼
½c; 1:5c ð1:5c; 2c
c < 1=3 c 1=3
D Dmax
D¼
(9)
(10)
m X n 1 X yt ðkÞ xtj ðkÞ m$n j¼1
(11)
k¼1
rij ¼
n 1X xtj ðkÞ n
(12)
k¼1
Step 5: Rank the effects of investigated factors based on the magnitude of the fuzzy grey grade.
2.4. Typical explosion pressure and pressure rise rate
2.3. Fuzzy grey relational analysis
yðnÞ
Fig. 2 shows the typical explosion pressure and pressure rise rate. The pressure rise rate is obtained by the time derivation of explosion pressure. It could be observed that the explosion pressure
(5)
Table 1 Orthogonal factor and level value.
1 2 3 4 5
(7)
Step 4: Calculate the fuzzy grey grade. Based on the grey relational coefficient, the fuzzy greedy grade is obtained:
The orthogonal experimental design is a popular method of designing the experiment with multiple factors and levels. This method is aimed to select the representative experiment for reducing the experiment number [18]. Table 1 shows the orthogonal factor and level value. In this work, the factor number is three and they both have five levels, which reduce the experiment number from 125 to 25.
Level
(6)
Step 3: Calculate the grey relational coefficient:
l2
2.2. Orthogonal experimental design
yð3Þ
3 x1 ðnÞ x2 ðnÞ 7 7 « 5 xm ðnÞ
Step 2: Nondimensionalize comparison matrix using the following equation:
(4)
Before ignition, about 10 min is required to ensure the mixture to become quiescent and homogeneous. The transient pressure dynamics in the chamber is measured using a PCB piezoelectric pressure transducer (model 113B24) and is recorded using data acquisition YOKOGAWA DL850E of sampling rate 100 kS/s. The ignition electrode, data acquistition device and high-speed camera are controlled by an OMRON CPM1A programmable logic controller.
yð2Þ
,,, ,,, « ,,,
where l is the resolution coefficient, which is calculated as follows:
VNH3 VNH3 þ VH2
y ¼ ½ yð1Þ
x1 ð2Þ x2 ð2Þ « xm ð2Þ
Factors Equivalence ratio F
Initial pressure p0/kPa
Ammonia addition xNH3
0.6 0.8 1.0 1.5 2.0
50 100 150 200 250
0.1 0.3 0.5 0.7 0.9
Fig. 2. Explosion pressure and pressure rise rate.
Y. Li et al. / Energy 159 (2018) 252e263
evolution could be divided into two stages: (Ⅰ) the constantpressure stage, the transient pressure in the spherical chamber maintains in an initial state; (Ⅱ) the pressure-buildup stage, the pressure buildup is caused by the combustion heat release and the fractional pressure rise is proportional to the fractional mass burnt. Besides, the pressure rise rate increases firstly and then decreases significantly with time.
255
and ammonia addition are taken to be comparison matrix. Based on the description of calculating fuzzy grey grade in Section 2.3, the factor order is displayed in Fig. 3. It is found that the fuzzy grey relational grades of equivalence ratio, initial pressure and ammonia addition are 0.6375, 0.6759 and 0.5252, respectively. This means that the effects of three factors on explosion hazard are ranked from the most important to the least important as initial pressure, equivalence ratio and ammonia addition.
3. Numerical method 4.2. Effects of equivalence ratio on explosion characteristics A freely propagating adiabatic, premixed, planar flame is computed using PREMIX in ANSYS CHEMKIN 17.0. PREMIX could solve the steady-state mass, species and energy conservation equation using a hybrid time-integration/Newton-iteration technique. In this work, the Konnov mechanism [10] is selected to calculate the sensitivity coefficient of elementary reaction to laminar burning velocity. Maximum number of grid point in the numerical calculation is 2500. The solution gradient and curvature are both set as 0.01 to obtain sufficiently accurate results. Besides, in order to evaluate the major step affecting laminar burning velocity, the sensitivity analysis is also conducted and the sensitivity coefficient is obtained as follows:
SFi ¼
ki vYk $ Yk vki
(13)
4. Results 4.1. Determination of factor order Table 2 shows the orthogonal designed table and its results. Since the explosion pressure behavior is determined by the flame propagation velocity, the average flame propagation velocity is regarded as evaluation index to evaluate the explosion hazard intuitively. The average flame propagation velocity is obtained using the time derivation of flame radius within the optical window. The average flame propagation velocity under various conditions is considered as reference matrix. Equivalence ratio, initial pressure
Table 2 Orthogonal designed table and its results. Case
Equivalence ratio
Initial pressure/kPa
Ammonia addition
Average flame propagation velocity/m$s1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
0.6 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 0.8 1 1 1 1 1 1.5 1.5 1.5 1.5 1.5 2 2 2 2 2
50 100 150 200 250 50 100 150 200 250 50 100 150 200 250 50 100 150 200 250 50 100 150 200 250
0.1 0.3 0.5 0.7 0.9 0.3 0.5 0.7 0.9 0.1 0.5 0.7 0.9 0.1 0.3 0.7 0.9 0.1 0.3 0.5 0.9 0.1 0.3 0.5 0.7
5.00 3.29 1.38 0.51 No ignition 5.61 3.53 1.06 0.46 12.04 5.51 2.49 0.97 15.47 16.82 0.84 0.83 17.56 4.08 2.76 No ignition 8.82 2.00 0.60 No ignition
Fig. 4 shows effects of equivalence ratio on flame morphology in the constant-pressure stage (p0 ¼ 100 kPa, xNH3 ¼ 0.5), and the flame radius of various equivalence ratios is almost equal to 50 mm. It is observed that the cellular structure could be only formed on the lean and stoichiometric side. As equivalence ratio increases, the cell size becomes larger and larger. A smooth flame structure could be observed at F ¼ 1.5 and 2.0. As expected, the time to reach the same flame radius decreases firstly until F ¼ 1.0 and then increases with equivalence ratio. Fig. 5 shows effects of equivalence ratio on flame morphology in the pressure-buildup stage. The fully developed cellular flame is observed on the lean and stoichiometric side. As the explosion pressure rises in the confined chamber, cracks are formed on the flame surface at F ¼ 1.5, but the expanding flame of F ¼ 2.0 still maintains a smooth structure. It should be widely accepted that the onset of cellular flame could be attributed to the hydrodynamic instability and diffusionalthermal instability in absence of body forces. Hydrodynamic instability is caused by the expansion across the flame surface, which is characterized by thermal expansion ratio and flame thickness [20,21]:
s¼
ru rb
(14)
d¼
l ru cp SL
(15)
Diffusional-thermal instability is caused by the preferential diffusion of mass and heat inside the flame front, which is only present for Lewis number less than unity. When Lewis number is larger than unity, the expanding flame will become stable under the diffusional-thermal instability. In this paper, there are two fuels (hydrogen and ammonia) in the mixture, thus Lewis number of the
Fig. 3. Fuzzy grey relational grade.
256
Y. Li et al. / Energy 159 (2018) 252e263
Fig. 4. Effects of equivalence ratio on flame morphology in the constant-pressure stage.
Fig. 5. Effects of equivalence ratio on flame morphology in the pressure-buildup stage.
reactant mixture could be calculated using a volumetric fractionweighted average of Lewis number of hydrogen and ammonia [22]:
Leeff ¼ xH2 $LeH2 þ xNH3 $LeNH3
(16)
Fig. 6 shows effects of equivalence ratio on effective Lewis number, thermal expansion ratio and flame thickness. It is obvious that effective Lewis number is less than unity on the lean and stoichiometric side, but larger than unity on the rich side. This indicates that the diffusional-thermal instability could destabilize the flame surface on the lean and stoichiometric side and stabilize the flame surface on the rich side. Thermal expansion ratio increases firstly until F ¼ 1.0 and then decreases with equivalence ratio, which trend is opposite to that of flame thickness. This means that the effects of hydrodynamic instability on flame destabilization continues to enhance until F ¼ 1.0 and then attenuates. Despite the hydrodynamic instability is the intrinsic instability for the expanding flame, the most wrinkled flame could not be observed at F ¼ 1.0. In combination with Fig. 4, it could be inferred that the cellular flame formation by varying the equivalence ratio could be mainly attributed to the diffusional-thermal instability rather than the hydrodynamic instability. Fig. 7 shows effects of equivalence ratio on maximum explosion pressure and maximum pressure rise rate. The maximum error in maximum explosion pressure and maximum pressure rise rate is 0.0065 MPa and 0.00168MPa/ms1. In fact, the experimental uncertainty is strongly dependent on the resolution of pressure gage and pressure transducer, which least count is 10Pa and 35Pa, respectively. Both maximum explosion pressure and maximum pressure rise rate increase significantly until F ¼ 1.0 and then decrease monotonously with equivalence ratio.
in the pressure-buildup stage. The cellular flame of F ¼ 0.8, 1.0 and 1.5 could be observed until xNH3 ¼ 0.7, 0.7 and 0.3, respectively. The cell size of cellular flame increases significantly with ammonia addition. Especially, the cracks of F ¼ 1.5 decrease from xNH3 ¼ 0.5 to xNH3 ¼ 0.7, and smooth flame is formed at xNH3 ¼ 0.9. To quantitatively characterize the wrinkling level of cellular flame, the wrinkling ratio is adopted in this work and is calculated as follows [23]:
XD ¼
R2p R2S
(17)
It should be noted that this method of calculating the wrinkling ratio must detect the flame edge accurately. Here the flame contour is detected using Canny edge detection in Matlab. Fig. 10 illustrates effects of ammonia addition on the wrinkling ratio. It is observed that the troughs and cusps on the flame surface could be tracked accurately using Canny edge detection. The wrinkling ratio of F ¼ 0.8 and 1.0 continues to decrease and is almost equal to unity at xNH3 ¼ 0.9. The wrinkling ratio of F ¼ 1.5 decreases gradually until xNH3 ¼ 0.5 and then the wrinkling ratio is almost equal to unity. In combination with Fig. 8, it is found that wrinkling ratio XD ¼ 1 corresponds to smooth flame. Besides, when the ammonia addition
4.3. Effects of ammonia addition on explosion characteristics Fig. 8 shows effects of ammonia addition on flame morphology in the constant-pressure stage (p0 ¼ 100 kPa). As ammonia addition increases, the cellular flame of F ¼ 0.8 and 1.0 tends to be stable, the cracks on the flame surface of F ¼ 1.5 decrease obviously. And the smooth flame of F ¼ 0.8, 1.0 and 1.5 starts to be observed at xNH3 ¼ 0.9, 0.9 and 0.5. Besides, the time to reach the same flame radius continues to increase significantly with ammonia addition. Fig. 9 shows effects of ammonia addition on flame morphology
Fig. 6. Effects of equivalence ratio on effective Lewis number, thermal expansion ratio and flame thickness.
Y. Li et al. / Energy 159 (2018) 252e263
Fig. 7. Effects of equivalence ratio on maximum explosion pressure and maximum pressure rise rate.
257
1.0. Due to the fact that thinner flame will lead to stronger destabilizing propensity [24], the effect of the hydrodynamic instability on cellular flame formation continues to attenuate with ammonia addition. In a word, on the lean and stoichiometric side, the effects of both diffusional-thermal and hydrodynamic instability on the flame destabilization will attenuate with ammonia addition. On the rich side, the effects of diffusional-thermal instability on flame stabilization attenuate and the effects of hydrodynamic instability on flame destabilization also attenuate with ammonia addition. Fig. 12 shows effects of ammonia addition on maximum explosion pressure and maximum pressure rise rate. As ammonia addition increases, maximum explosion pressure of F ¼ 0.8, 1.0 and 1.5 decreases slowly until xNH3 ¼ 0.7, and then maximum explosion pressure decreases significantly. Besides, maximum pressure rise rate of F ¼ 0.8, 1.0 and 1.5 decreases monotonously with ammonia addition. 4.4. Effects of initial pressure on explosion characteristics
is fixed, the wrinkling ratio of F ¼ 0.8 is largest, following by that of F ¼ 0.8 and F ¼ 1.0. Fig. 11 shows effects of ammonia addition on effective Lewis number, thermal expansion ratio and flame thickness. As ammonia addition increases, effective Lewis number of F ¼ 0.8 and 1.0 increases continuously and effective Lewis number of F ¼ 0.8 and 1.0 is still less than unity, effective Lewis number of F ¼ 1.5 decreases monotonously but effective Lewis number of F ¼ 1.5 is still larger than unity. The above results indicate that the cellular flame of F ¼ 0.8 and 1.0 could be still triggered by the diffusional-thermal instability, but the effect of the diffusionalthermal instability on flame destabilization is attenuating gradually. Thermal expansion ratio of F ¼ 0.8, 1.0 and 1.5 increases slowly with ammonia addition. And when the ammonia addition is fixed, thermal expansion ratio from large to small is as follows: F ¼ 1.0, F ¼ 1.5 and F ¼ 0.8. Besides, the flame thickness of F ¼ 0.8, 1.0 and 1.5 increases significantly with ammonia addition and flame thickness of the decreasing order is at F ¼ 0.8, 1.5 and
Fig. 13 shows effects of initial pressure on flame morphology (xNH3 ¼ 0.5). For F ¼ 0.8 and 1.0, the cellular flame could be not fully developed at p0 ¼ 50 kPa and the cellular flame starts to be formed at p0 ¼ 100 kPa, then the cellular flame of F ¼ 0.8 and 1.0 becomes more unstable and the cell size continues to decrease with initial pressure. In addition, the expanding flame of F ¼ 1.5 exhibits a smooth structure until p0 ¼ 200 kPa and more cracks are formed along the long crack as initial pressure increases. Note that the time to arrive the same radius is prolonged slightly with increasing initial pressure. Fig. 14 shows effects of initial pressure on flame morphology in the pressure-buildup stage. For F ¼ 0.8 and 1.0, the developed cellular flame becomes more unstable and the cell size decrease significantly with initial pressure. The smooth flame is only observed at F ¼ 1.5 and xNH3 ¼ 0.1. For F ¼ 1.5, the cracks emerge at xNH3 ¼ 0.3 and the cellular flame starts to be formed at xNH3 ¼ 0.5. Similarly, the cell size also decreases with increasing initial pressure.
Fig. 8. Effects of ammonia addition on flame morphology in the constant-pressure stage.
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Fig. 9. Effects of ammonia addition on flame morphology in the pressure-buildup stage.
Fig. 15 shows the effect of initial pressure on the wrinkling ratio. As initial pressure increases, the wrinkling ratio of F ¼ 0.8 and 1.0 increases monotonously and the wrinkling ratio of F ¼ 1.5 is almost equal to unity. And when the initial pressure is fixed, the wrinkling ratio of F ¼ 0.8 is largest, following by that of F ¼ 1.0 and F ¼ 1.5. Table 3 shows effects of initial pressure on effective Lewis number. With increasing initial pressure, effective Lewis number of F ¼ 0.8, 1.0 and 1.5 almost remains constant, and effective Lewis number of F ¼ 0.8 and 1.0 is less than unity and effective Lewis number of F ¼ 1.5 is larger than unity. This means that the diffusional-thermal instability could trigger the flame destabilization at F ¼ 0.8 and 1.0, but this destabilization effect is not enhanced or suppressed with increasing initial pressure. Similarly, the diffusional-thermal instability could stabilize the expanding flame at F ¼ 1.5 and the variation in this stabilization effect is very limited. Table 4 shows effects of initial pressure on thermal expansion ratio. As the initial pressure increases, thermal expansion ratio of F ¼ 0.8, 1.0 and 1.5 almost remains constant and thermal expansion ratio of F ¼ 1.0 is largest, following by that of F ¼ 1.5 and F ¼ 0.8. Fig. 11. Effects of ammonia addition on effective Lewis number, thermal expansion ratio and flame thickness.
Fig. 16 shows effects of initial pressure on the flame thickness. As initial pressure increases, the flame thickness of F ¼ 0.8, 1.0 and 1.5 decreases monotonously. Except for p0 ¼ 50 kPa, the flame thickness from large to small is: F ¼ 0.8, 1.5 and 1.0. In combination with
Fig. 10. Effect of ammonia addition on the wrinkling ratio.
Fig. 12. Effects of ammonia addition on maximum explosion pressure and maximum pressure rise rate.
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Fig. 13. Effects of initial pressure on flame morphology in the constant-pressure stage.
Table 4, it could be concluded that the flame destabilization of F ¼ 0.8 and 1.0 could be attributed to the joint effect of the diffusional-thermal instability and hydrodynamic instability, the crack emergence of F ¼ 1.5 is due to the competitive effect of the diffusional-thermal instability and hydrodynamic instability. Fig. 17 shows effects of initial pressure on maximum explosion pressure and maximum pressure rise rate. Maximum explosion pressure of F ¼ 0.8, 1.0 and 1.5 increases linearly with increasing initial pressure. It could be inferred that the mixture density increases significantly in the confined chamber as initial pressure increases, which will generate more combustion heat and thus enhance the explosion pressure. Besides, maximum pressure rise rate of F ¼ 0.8, 1.0 and 1.5 increases monotonously with increasing initial pressure.
5. Discussions 5.1. Explosion pressure prediction considering flame instabilities Fig. 18 shows the explosion pressure prediction considering flame instabilities, the experimental pressure is obtained from the condition with F ¼ 1.0, p0 ¼ 100 kPa and xNH3 ¼ 0.5. In the theoretical prediction, the smooth flame and wrinkled flame are assumed in the theoretical calculation. Assuming that the expanding flame is still smooth, the explosion pressure is calculated using the equation (1). Besides, the expanding flame is difficult to maintain a smooth structure under the flame instabilities. The wrinkled flame will increase the flame surface area and hence the combustion intensity. Thus an improved model is established by introducing the wrinkling ratio:
Fig. 14. Effects of initial pressure on flame morphology in the pressure-buildup stage.
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Fig. 15. Effect of initial pressure on the wrinkling ratio.
Fig. 16. Effects of initial pressure on the flame thickness.
Table 3 Effects of initial pressure on effective Lewis number. Initial pressure/kPa
Effective Lewis number
F ¼ 0.8
F ¼ 1.0
F ¼ 1.5
50 100 150 200 250
0.83264 0.83264 0.83264 0.83264 0.83264
0.86041 0.86041 0.86041 0.86041 0.86041
1.328 1.328 1.328 1.328 1.328
" #2=3 1=g dp 3ðpmax p0 Þ p 1=g p0 pmax p ¼ $ $ 1 $ $ðXD $SL Þ dt r p0 pmax p0 p (18) The static wrinkling ratio and dynamic wrinkling ratio are adopted in the improved model of predicting explosion pressure. The static wrinkling ratio is assumed to be still equal to 1.42 during gas explosion process, and the dynamic wrinkling ratio is adopted based on the following assumption: (1) when the expanding flame is smooth, the wrinkling ratio is equal to unity; (2) when the expanding flame starts to become unstable, the wrinkling ratio increases linearly with time. It should be noted that the unburnt mixture temperature and pressure ahead of expanding flame in the confined chamber will rise due to adiabatic compression, which affect laminar burning velocity significantly. Thus the dependence of laminar burning velocity in equations (1) and (18) on temperature and pressure during gas explosion needs to be considered as follows:
a b T p SL ¼ SL0 $ $ T0 p0
As shown in Fig. 18, the explosion pressure in the pressurebuildup stage is obviously underestimated using the smooth flame model. When the static wrinkling ratio is adopted in the theoretical calculation, the explosion pressure prediction could be improved significantly, but the explosion pressure before t ¼ 34 ms and after t ¼ 34 ms is slightly overpredicted and underestimated, respectively. This is because wrinkling ratio of the expanding flame with XD ¼ 1.42 is overpredicted before t ¼ 34 ms and underestimated after t ¼ 34 ms with respect to the value in the experiment. When the dynamic wrinkling ratio is assumed, it is obvious that the explosion pressure could be reproduced relatively satisfactorily. The above results also indicate that the explosion pressure could be predicted using the product of laminar burning velocity and dynamic wrinkling ratio. In order to reveal the flame destabilization in the pressurebuildup stage, effective Lewis number, thermal expansion ratio and flame thickness are calculated based on the accurate explosion pressure prediction. Fig. 19 shows effective Lewis number, thermal expansion ratio and flame thickness in the pressure-buildup stage (F ¼ 1.0, p0 ¼ 100 kPa and xNH3 ¼ 0.5). As the explosion pressure starts to rise, effective Lewis number decrease slowly, which indicates that the effect of diffusional-thermal instability on the flame stabilization enhances. Despite thermal expansion ratio and flame thickness decrease monotonously, but the ratio of thermal expansion ratio to flame thickness increases significantly, which demonstrates that the effect of hydrodynamic instability on flame destabilization enhances. In a word, under the joint effect of diffusional-thermal and hydrodynamic instability, the expanding flame becomes more wrinkled in the pressure-buildup stage.
(19)
Table 4 Effects of initial pressure on thermal expansion ratio. Initial pressure/kPa
Thermal expansion ratio
F ¼ 0.8
F ¼ 1.0
F ¼ 1.5
50 100 150 200 250
6.4371 6.4445 6.4488 6.4508 6.4524
7.11387 7.14757 7.16569 7.17679 7.18545
6.67352 6.67646 6.67859 6.67928 6.67991
Fig. 17. Effects of initial pressure on maximum explosion pressure and maximum pressure rise rate.
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increase with ammonia addition, which promotes chemical reactivity of R9 and R168. Fig. 22 shows sensitivity coefficient of elementary reactions to laminar burning velocity at various initial pressures. The most elementary reactions of enhancing or suppressing chemical reactivity are R9 and R10, respectively. And the sensitivity coefficient of both R9 and R10 increases monotonously with increasing initial pressure, which could be attributed to the fact that the molecules collision rate increases significantly with increasing initial pressure.
6. Conclusions
Fig. 18. Explosion pressure prediction considering flame instabilities.
5.2. Sensitivity analysis
The present work is aimed at evaluating the explosion hazard by varying equivalence ratio, ammonia addition and initial pressure. In the experiment, the high-speed schlieren photography and pressure transducer are used to record the flame morphology and pressure dynamics. In the theoretical prediction, the explosion pressure is calculated using the smooth flame model and wrinkled flame model. In the numerical simulation, the contributions of elementary reaction to laminar burning velocity are conducted using the sensitivity analysis. The results demonstrate that:
As discussed in Section 5.1, laminar burning velocity could be regarded as a characteristic parameter to predict the explosion pressure evolution. In order to reveal the contributions of elementary reaction to laminar burning velocity, the sensitivity analysis is conducted in the following content. Fig. 20 shows sensitivity coefficient of elementary reaction to laminar burning velocity at various equivalence ratios. The most elementary reaction of enhancing laminar burning velocity is R9. The elementary reaction and the corresponding step numbers are listed in Table 5. The sensitivity coefficient of R9 decreases firstly until F ¼ 1.0 and then increases with equivalence ratio. Since laminar burning velocity of hydrogen/ammonia/air mixture is linearly correlated with H, OH and NH2 radical [25], despite H radical is consumed, OH and O radicals are formed through R9, which enhance the chemical reactivity significantly. The first two inhibiting reactions are R10 and R168. Through R10 and R168, H and NH2 radicals are consumed in large quantities and thus the chemical reactivity decreases. Fig. 21 shows sensitivity coefficient of elementary reactions to laminar burning velocity at various ammonia additions. R8 and R9 exhibit higher positive sensitivity coefficient. More O and OH radicals are generated in R9, which is the dominant chain branching reaction. R168 is the main path for consumption of NH2 and O radicals, in which active radicals could be reduced significantly. And sensitivity coefficient of R168 increases monotonously with ammonia addition, this is because H and NH2 free radicals will
(1) Based on the orthogonal experimental design, the explosion hazard is evaluated by the fuzzy grey relational analysis and the fuzzy grey relational grade of decreasing order is initial pressure, equivalence ratio and ammonia addition. (2) By varying equivalence ratio, the cellular flame formation on the lean and stoichiometric side could be mainly attributed to the diffusional-thermal instability rather than the hydrodynamic instability. As ammonia addition increases, the expanding flame of F ¼ 0.8, 1.0 and 1.5 tends to be more stable. With increasing initial pressure, the flame destabilization of F ¼ 0.8 and 1.0 could be attributed to the joint effect of the diffusional-thermal instability and hydrodynamic instability, the crack emergence of F ¼ 1.5 is due to the competitive effect of the diffusional-thermal instability and hydrodynamic instability. (3) Both maximum explosion pressure and maximum pressure rise rate increase until F ¼ 1.0 and then decrease monotonously with equivalence ratio. As ammonia addition increases, maximum explosion pressure and maximum pressure rise rate decrease monotonously. With increasing initial pressure, maximum explosion pressure of F ¼ 0.8, 1.0 and 1.5 increases linearly and maximum pressure rise rate increases nonlinearly.
Fig. 19. Effective Lewis number, thermal expansion ratio and flame thickness in the pressure-buildup stage.
Fig. 20. Sensitivity coefficient of elementary reaction to laminar burning velocity at various equivalence ratios.
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Table 5 Step number and elementary reaction. Step Number
Elementary Reaction
Step Number
Elementary Reaction
R8 R9 R10 R12 R13 R17 R62
O þ H2 ¼ OH þ H H þ O2 ¼ OH þ O H þ O2 (þM) ¼ HO2(þM) H þ OH þ M ¼ H2O þ M H2þOH ¼ H2O þ H H þ H2O ¼ H2 þ O2 NH þ H2 ¼ NH2 þ H
R64 R71 R80 R136 R168 R176 R181
NH2þNH ¼ N2H2 þ H NH3þH ¼ NH2 þ H2 N2H2þM ¼ NNH þ H þ M HNO þ H ¼ NO þ H2 NH2 þ O ¼ HNO þ H NH2þNO ¼ NNH þ OH NH þ O ¼ NO þ H
coefficient of R9 increases monotonously with ammonia addition and initial pressure. Based on the above results, two suggestions are proposed to mitigate the explosion hazard: (1) higher initial pressure should be avoided firstly in the industrial container. Once the initial pressure is relatively higher, the static activation pressure must be as small as possible in the explosion venting; (2) the explosion suppression could be achieved by reducing laminar burning velocity. Considering the chemical kinetics, the inhibitor should be selected by suppressing the dominant chain branching reaction R9 or enhancing the inhibiting reaction R10. Acknowledgment
Fig. 21. Sensitivity coefficient of elementary reaction to laminar burning velocity at various ammonia additions.
(4) Due to the joint effect of diffusional-thermal instability and hydrodynamic instability, the expanding flame will become more wrinkled in the pressure-buildup stage, which certainly increases the flame surface area and hence the burning rate. In the theoretical calculation, the explosion pressure is underestimated significantly using the smooth flame model and could be reproduced very satisfactorily using the product of laminar burning velocity and dynamic wrinkling ratio. (5) By varying equivalence ratio, ammonia addition and initial pressure, the most elementary reaction that enhances laminar flame velocity is R9, the first two inhibiting reactions to laminar burning velocity are R10 and R168. And the sensitivity coefficient of R9 decreases firstly until F ¼ 1.0 and then increases with equivalence ratio. Besides, the sensitivity
Fig. 22. Sensitivity coefficient of elementary reaction to laminar burning velocity at various initial pressures.
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