Air Mixtures on

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Influence of Vapor−Liquid Two-Phase n‑Hexane/Air Mixtures on Flammability Limit and Minimum Ignition Energy Xueling Liu,* Qi Zhang, and Yue Wang State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China ABSTRACT: The aim of this work was to provide new experimental data on the influence of vapor−liquid two-phase n-hexane/ air mixtures on the lower flammability limit (LFL) and minimum ignition energy (MIE). A series of experiments was carried out as follows: (1) A set of vapor−liquid two-phase n-hexane/air mixtures of various concentrations was obtained at the mean Sauter mean diameter (SMD) of 10.63 μm and the 80-ms ignition moment in the vessel. The errors were analyzed. (2) Experiments were implemented on vapor−liquid two-phase n-hexane/air mixtures of various concentrations at an ignition energy of 28 J and the initial room temperature and pressure of 21 °C and 0.10 MPa, respectively. The effects of the concentration of n-hexane on the explosion pressure, explosion temperature, and LFL were analyzed, and the results are discussed. (3) A series of experiments was implemented on vapor−liquid two-phase n-hexane/air mixtures of various concentrations at various ignition energies. The MIE of the vapor−liquid two-phase n-hexane/air mixture was 0.5 mJ in this work, and the results are discussed.

1. INTRODUCTION n-Hexane from hydrocarbon fuel is an energetic material with a wide variety of applications, including as a liquid explosive, a solvent for chemical processing and analysis, and a highperformance fuel additive for internal-combustion (IC) engines.1 A number of studies have been performed on the spray and combustion characteristics in IC engines in the past few years.2 One study investigated better ways of controlling the combustion process, thus ensuring optimum performance and minimum emission levels during the combustion process.3 However, the key challenges facing the possible future widespread use of this fuel as an energy carrier are safetyrelated issues that must be addressed before social acceptance of this fuel can be achieved. Explosion hazards associated with the production, handling, transportation, and storage of this fuel must be resolved with a sufficient level of confidence . From broken pipelines or containers, fuel spray can result in serious accidents including fires and explosions, and even the deflagration to detonation transition (DDT).4,5 It is different with the spray and combustion in IC engines. Because of the ignition time and energy are unpredictable and the environmental temperature is commonly room temperature, the evaporation rate of fuel droplets is low. Once ignition occurs, vapor-phase premixed explosion and liquid-phase diffusive combustion coexist. Measuring the lower flammability limit (LFL) and minimum ignition energy (MIE) of vapor−liquid two-phase fuel/air mixtures is very complicated. In addition to the fuel physicochemical properties, such as surface tension and viscosity, one must also conside the droplet size, the fuel concentrations of the liquid and vapor phases, the environmental temperature and pressure, the evaporation rate, the ignition time and energy, and so on. The physicochemical properties and flammability characteristics of n-hexane are listed in Table 1. The flammability limits of gaseous n-hexane in air are 1.2−7.5% at atmospheric pressure and standard temperature.6,7 Unfortunately, few researchers have paid attention to the variation of the © 2014 American Chemical Society

Table 1. Physicochemical Properties and Flammability Characteristics of n-Hexane liquid hydrocarbon fuel density (water = 1 g/cm3) boiling point (°C) flash point (°C) saturated vapor pressure (kPa) explosion limits (%) (v/v) dynamic viscosity (Pa·s) surface tension (mN·m−1) minimum ignition energy (mJ) autoignition temperature (°C) critical temperature (°C) heat of combustion (kJ/mol)

n-hexane 0.692 at 20 °C 68.74 −23 13.33 at 15.8 °C 1.2−7.2 at 26 °C 0.00033 at 20 °C 18.40 at 20 °C 0.248 244 234.8 4159.1

flammability limits of vapor−liquid two-phase n-hexane/air mixtures. Further, the effect of ignition energy on the flammability limits is another important issue in the safe use of n-hexane/air mixtures related to the practical operating case. It has been reported8,9 that the MIE of gaseous n-hexane/air mixtures is 0.248 mJ. However, the influence of vapor−liquid two-phase n-hexane/air mixtures on the MIE was not reported in the previous literature. More importantly, some storage and transportation pipeline environments in China require flammability limits and MIE measurements related to the practical case. To acknowledge the flammability limits and MIE of vapor−liquid two-phase n-hexane/air mixtures related to the operating case, relevant experiments need to be carried out.

2. EXPERIMENTAL APPARATUS AND PROCEDURES 2.1. General. The experimental setup used in this work consisted of a 20-L cylindrical vessel with three pairs of Received: Revised: Accepted: Published: 12856

June 11, 2014 July 18, 2014 July 21, 2014 July 21, 2014 dx.doi.org/10.1021/ie5023496 | Ind. Eng. Chem. Res. 2014, 53, 12856−12865

Industrial & Engineering Chemistry Research

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Figure 1. Experimental setup: (a) plane sketch, (b) 3D sketch. (1) Ignition source, (2) pressure gauge, (3) liquid storage chamber, (4) nonreturn valve, (5) solenoid valve, (6) connection synchronized trigger system, (7) air compression chamber, (8) pressure data recorder, (9) temperature data recorder, (10) connection to high-pressure pump, (11) laser, (12) light sensor cable.

transparent observation windows, coupled with a double-nozzle pneumatic atomization system, an electric ignition system, and a data-acquisition system with pressure and temperature. It is shown in Figure 1. Experiments were performed in the cylinder explosion vessel with central ignition. The height (h) of the vessel was 312 mm, the inner diameter (2R) was 300 mm, and the thickness of the vessel walls was 10 mm. In the experimental vessel, ignition was achieved by means of an

inductive-capacitive spark produced between tungsten electrodes with rounded tips, separated by a spark gap of 3 mm. The electrode diameter used in the experiments was 5 mm. The device of spark ignition energy can be found in previous references.10−18 In three transparent windows, the Mie extinction detection system was placed at the positions 1/5, 1/2, and 4/5 of the vessel. The double-nozzle pneumatic atomization system, the optical particle size and concentration 12857

dx.doi.org/10.1021/ie5023496 | Ind. Eng. Chem. Res. 2014, 53, 12856−12865


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Figure 2. High-speed photographs of the atomization process in the transparent vessel.

the first category, no a priori information about the sought SDF is available, whereas in the second category, some a priori information is available (for example, the SDF can be described by an empirical distribution function). When the sought SDF can be described by a known function, f(D), eq 1 can be modified to

detection system, and the electric ignition system were controlled by a central control system and set to different trigger times in each experiment. The frequency response of each system was above 20 kHz. A description of the dataacquisition system with the pressure and temperature can be found in previous references.10−18 The measurement of n-hexane size distribution functions (SDFs) and concentrations was based on Mie extinction in this work.19,20 This remains an attractive approach owing to its relative simplicity in implementation, capability to provide continuous measurements with high temporal resolution, and very limited requirements for optical access. The governing equations for the measurement of SDFs by Mie extinction are as follows ⎛I ⎞ π ln⎜ 0 ⎟ = Cn ⎝I⎠ 4

∫0

∞

i = 1, 2, 3, ..., n

R ij =

Q̅ (λi , D32) Q̅ (λj , D32)

(2)

where Rij is the ratio between the measured extinctions at wavelengths λi and λj. Q̅ and D32 are the mean extinction coefficient and the Sauter mean diameter, defined as ∞

Q̅ (λi , D32) =

f (D) Q (πD/λi , m)D2 dD ,

∫0 f (D) Q (πD/λi , m)D2 dD ∞

∫0 f (D)D2 dD

(3)

∞

(1)

D32 =

where ln(I0/I) represents the extinction by n-hexane at wavelength λi; I0 and I are the intensities of incident and transmitted light, respectively, at wavelength λi; Cn is the number density of n-hexane; L is the path length; Q(πD/λi,m) is the extinction coefficient of n-hexane with diameter D at wavelength λi; m is the complex refractive index of the n-hexane at wavelength λi; f(D) is the n-hexane size distribution function defined such that ∫ ∞ 0 f(D) dD = 1, and f(D) dD represents the probability that n-hexane has a diameter between D and D + dD. The determination of the SDFs then reduces to the solution of eq 1 for f(D) based on extinction measurements performed at selected wavelengths. However, eq 1 is ill-conditioned, and the development of a stable algorithm to invert the extinction measurements to SDFs has long been a subject of research effort. These algorithms can be divided into two categories. In

∫0 f (D)D3 dD ∞

∫0 f (D)D2 dD

(4)

The log-normal function, defined by f (D) =

⎡ ⎤ 1 1 exp⎢ − (ln D − ln D̅ )2 ⎥ ⎣ 2(ln σ ) ⎦ 2π D ln σ

(5)

where σ characterizes the distribution width and D̅ is the mean size of the distribution, is one of the most commonly used SDFs and will be used as an example distribution function to introduce the measurement concept. The method of using multiwavelength light extinction is proposed in this work. The wavelengths used are 447, 543, and 638 nm. The measured intensities of incident and transmitted light, or the ratio of I0 and I; the wavelength λ of the incident light, the optical path L; the complex refractive index of the liquid m; and 12858



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the size distribution of particles can be functions of f(D) and concentration. If so, then the number density of n-hexane (Cn, also the volume concentration) can be expressed as Cn =

π 6

∫0

∞

f (D)D3 dD

(6)

The weight concentration can then be obtained by multiplying by the density of the particles Cm = ρCn

(7)

2.2. Ignition Delay Time. In this work, the ignition delay time (IDT) is defined as the time interval between the ITOS (initiation time of spray) and the ITOI (initiation time of ignition). Determination of the IDT must be performed using a premixed homogeneous vapor−liquid two-phase n-hexane/air mixture in the vessel. Therefore, the methods of image collection and Mie extinction detection were used for the pneumatic spray process in the following experiments. The experiments in this work were consistently performed under the following conditions: room temperature; duration of solenoid valve opening, 50 ms; pneumatic atomization pressure with high-pressure pumps, 0.8 MPa; design spray dose (DSD), 500 g/m3 n-hexane. A high-speed camera was used to collect images of the pneumatic spray process at a sampling frequency of 2000 fps (frames per second). The conditions that we designed and employed were consistent with the experimental volume of the transparent vessel. Backlighting was used in the acquisition of high-speed camera images of the pneumatic spray process. The light position was 1/2 of the transparent vessel (center ignition location of the vessel) in Figure 2. From the duration of the solenoid valve opening to the moment when the nozzle spray occurred was 9 ms (i.e., the atomization delay was 9 ms). Because of the 50-ms duration of solenoid valve opening, the whole spray process was completed in 60 ms. The maximum concentration of atomization was reached at 80 ms. After 100 ms, it can be seen that the concentration of liquid-phase nhexane atomization gradually weakened. The changes in the particle size distribution and concentration were recorded by Mie extinction, measured at 1/2 of the vessel. The Mie extinction detection system and the atomization system were triggered by a synchronous trigger, recording the particle size and concentration trend data of the spray process at a sampling frequency of 20 kHz. Data collection was set to a 10-ms sampling interval time. The changes in the Sauter mean diameter (SMD) and concentration for a design spray dose (DSD) of 500 g/m3 n-hexane in the spray process are shown in Figure 3. The SMD of liquid nhexane decreased from 50.47 to 11.74 μm, and the concentration of liquid n-hexane increased from 24.53 to 165.32 g/m3 as the duration of the pneumatic spray increased from 10 to 50 ms. After a duration of 50 ms, the solenoid valve was closed, at which point the SMD became relatively stable at 11.61 μm and the concentration fluctuations were weak between 202.35 and 204.35 g/m3 from 60 to 100 ms. The SMD gradually decreased from 11.61 to 11.09 μm, and the concentration gradually decreased from 204.35 g/m3 to 32.87 g/m3, for durations of 110−500 ms. The trend data of the SMD of liquid n-hexane and the real-time concentrations are listed in Table 2. According to the image collection data and the optical detection data of the pneumatic spray process, the ignition delay time (IDT) of 80 ms was confirmed.

Figure 3. SMD and concentration change trends during the spray process.

2.3. Vapor−Liquid Two-Phase n-Hexane Concentration Measurements. In this work, the design spray dose (DSD) and loss spray dose (LSD) were introduced as parameters for the concentration of liquid n-hexane in two liquid storage chambers in preparation for the experiments and the concentration of residual liquid in the two liquid storage chambers, respectively. By changing pneumatic atomization pressure with highpressure pumps and the design spray dose (DSD) of liquid nhexane, a sampling time of 80 ms was attained. A series of experiments was conducted, and the results are shown in Figure 4 and Table 3. For optical detection through the transparent window, using the Mie extinction system, measurements were made at positions 1−3 at 1/5, 1/2, and 4/5 of the vessel, respectively. The particle size distributions obtained at the three positions are shown in Figure 5. The mean SMD of liquid n-hexane from all experiments was 10.63 μm. 2.4. Experimental Ignition Procedure. In these experiments, the environmental conditions were as follows: The initial room temperature and pressure of the n-hexane/air mixture were 21 °C and 0.10 MPa, respectively. High-pressure gas was stored in two air chambers. Liquid n-hexane at the DSD was placed in the two storage chambers. The central control system was initialized, the duration of solenoid valve opening was 50 ms, and the IDT was 80 ms. Subsequently, the central control system was started, and the n-hexane/air mixture was ignited by an electric spark generated by a spark generator. After ignition had occurred within the vapor−liquid two-phase n-hexane/air mixture, a combustion wave formed and propagated from the position of ignition to the wall of the vessel. The histories of pressure and temperature resulting from the explosion of the n-hexane/air mixture were recorded at different points in the vessel by pressure gauges and temperature transducers connected to the data-acquisition system.

3. EXPERIMENTAL RESULTS AND DISCUSSION 3.1. Flame Temperatures and Explosion Pressures. The ignition energy (CU2/2) of 28 J was constant throughout all experiments. The experiments were carried out with mass concentrations of n-hexane in air of 36.3−198.66 g/m3 in the liquid phase and 0.69−3.42% in the vapor phase. For the measured SMD and concentration of n-hexane, the pressure 12859



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Table 2. Trend Data of SMD and Real-Time Concentration of Liquid n-Hexane time (ms)

SMD (D32, μm)

real-time concentration (g·m−3)

time (ms)

SMD (D32, μm)

real-time concentration (g·m−3)

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

50.47 20.28 13.54 12.04 11.71 11.63 11.61 11.61 11.61 11.61 11.61 11.96 12.07 12.36 12.07 12.21 11.49 12.16 12.00 12.36 12.33 11.70 12.13 11.91 11.57

24.53 66.35 96.58 132.70 165.23 202.35 204.35 202.35 203.35 203.35 204.35 189.78 180.27 168.78 146.62 117.71 94.90 66.74 54.15 47.64 42.83 36.62 39.90 32.56 36.28

260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500

11.58 12.28 11.56 12.05 11.69 12.24 11.56 11.57 11.67 11.54 11.58 11.51 11.23 11.18 11.97 11.19 11.58 12.05 11.31 11.96 11.86 11.91 11.72 11.55 11.09

34.68 38.88 36.03 38.30 33.68 31.68 36.47 37.07 38.07 37.77 31.47 39.57 40.77 31.27 35.47 36.87 35.37 37.67 37.77 40.77 32.27 34.87 40.77 34.57 32.87

and temperature changed with time and reached their peak values after the fronts of the pressure and temperature waves had passed. The peak values are defined as the peak pressure and the peak temperature. The peak pressure and peak temperature varied with the concentration of n-hexane. The results of all experiments at an ignition energy of 28 J are summarized in Table 4. The peak pressure and peak temperature included seven measured results: At vapor and liquid two-phase n-hexane concentrations of 1.15% and 48.00 g/m3, the overpressure and temperature were 0.51 MPa and 544 °C. At 1.23% and 78.01 g/ m3, the overpressure and temperature were 0.60 MPa and 643 °C. At 1.55% and 118.54 g/m3, the overpressure and temperature were 1.00 MPa and 816 °C. At 1.80% and 168.56 g/m3, the overpressure and temperature were 1.21 MPa and 788 °C. At 2.43% and 183.61 g/m3, the overpressure and temperature were 1.24 MPa and 751 °C. Finally, at 3.42% and 198.66 g/m3, the overpressure and temperature were 1.04 MPa

Figure 4. Concentrations of vapor and liquid in two-phase n-hexane/ air mixtures. [The flammability limits of n-hexane/air mixtures are 1.2−7.2% (v/v).6,7]

Table 3. Experimental Data on SMD and Concentration of Vapor-Liquid Two-Phase n-Hexane/Air Mixtures mean value pneumatic pressure (MPa)

duration of spray (ms)

design spray dose (DSD, g/m3)

loss spray dose (LSD, g/m3)

total actual concentration of n-hexane (g/m3)

pressure of 80-ms time node in the vessel (MPa)

mean SMD (μm)

actual concentration of liquid (g/m3)

0.80 0.75 0.70 0.65 0.60 0.55 0.50

50 50 50 50 50 50 50

462.00 396.00 330.00 264.00 198.00 132.00 99.00

132.00 118.80 92.00 86.00 72.60 39.60 36.00

330.00 277.20 238.00 178.00 125.40 92.40 63.00

0.104 0.104 0.103 0.103 0.102 0.102 0.102

11.06 11.61 10.51 10.20 10.19 10.34 10.48

198.66 183.61 168.56 118.54 78.01 48 36.3

12860

actual concentration of vapor (g/m3)

actual concentration of vapor (% v/v)

131.34 93.59 69.44 59.46 47.39 44.4 23.1

3.42 2.43 1.80 1.55 1.23 1.15 0.69



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S denote failure (the mixture in the vessel was not initiated in the experiment) and success (the explosion of the mixture was initiated), respectively. The energy input to mixtures with vapor and liquid two-phase n-hexane concentrations of 0.69% and 36.30 g/m3 and 1.15% and 48.00 g/m3 resulted in “3F” (failed ignition) and “1S, 2F” (successful ignition), respectively. Therefore, the low flammability limit of vapor−liquid twophase n-hexane/air mixture was confirmed at 1.15% and 48.00 g/m3, that is, a total concentration of 92.40 g/m3. The flammability limits of a pure vapor-phase n-hexane/air mixture are from 1.2% to 7.2% (v/v)6,7 at atmospheric pressure and standard temperature. In the current experiments, the concentration range of vapor-phase hexane is 0.69−3.42%. In the meantime, the flammability range of 1.15−3.42% was measured. The LFL of the vapor−liquid two-phase n-hexane/ air mixture was confirmed at 1.15%, which is close to the lower flammability limits in refs 6 and 7. It can therefore be concluded that the LFL of vapor−liquid two-phase n-hexane/air mixtures will be subject to the concentration of the pure vapor-phase nhexane/air mixture. The chemical reaction of a pure vapor-phase n-hexane/air mixture with a stoichiometric volume fraction is 19 ⎛⎜ 79 ⎞⎟ O2 + N2 ⎝ 2 21 ⎠ 19 79 = 7H 2O + 6CO2 + × N2 2 21

C6H14 +

(8)

The stoichiometric volume fraction of the pure vapor-phase n-hexane/air mixture is Cst =

1 1+

19 2

(1 + 7921 )

≈ 2.16% (9)

Equation 9 illustrates that the peak explosion pressure of a pure vapor-phase n-hexane/air mixture reaches its maximum value at a volume fraction of 2.16%, in theory. In actual chemical reactions, it is impossible that all of the C and H atoms in the mixture can be oxidized into CO2 and H2O. In fact, when the chemical reaction reaches a balanced state, CO, H 2 , and OH are always contained in the products. Consequently, the volume fraction at which the peak explosion pressure of a combustible gas/air mixture reaches its maximum value is always slightly greater than that in the stoichiometric state.16−19 In this work, the peak explosion pressure of the vapor−liquid two-phase n-hexane/air mixture reached its maximum value at a vapor-phase n-hexane volume fraction of 2.43%. This indicates that the peak explosion pressure trend of vapor−liquid two-phase n-hexane/air mixtures is similar to that of pure vapor-phase n-hexane/air mixtures. From previous works,16,17 the trends in the peak explosion pressure and peak explosion temperature of pure vapor-phase fuel/air mixtures have the characteristic of synchronicity. However, in this experiment, from Figure 4, the maximum peak temperature was at the vapor and liquid two-phase nhexane concentrations of 1.55% and 118.54 g/m3, respectively (i.e., a total concentration of 178.00 g/m3), and the maximum peak pressure was at the vapor and liquid two-phase n-hexane concentrations of 2.43% and 183.61 g/m3, respectively (i.e., a total concentration of 277.20 g/m3). The concentration of the maximum peak pressure was greater than the concentration of the maximum peak explosion temperature. Furthermore, in the previous literature,6,7 the peak temperature of a pure vaporphase n-hexane/air mixture was higher than that measured in

Figure 5. Particle size distributions of n-hexane at different locations at a sampling time of 80 ms: (a) position 1 at 1/5 of the vessel, (b) position 2 at 1/2 of the vessel, and (c) position 3 at 4/5 of the vessel.

and 663 °C. The trends of the peak pressure and peak temperature at various concentrations are shown in Figure 6. In Table 4, the column labeled “experiment times” represents the number of times an experiment was repeated, where F and 12861



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Table 4. Experimental Results in Vapor−Liquid Two-Phase n-Hexane/Air Mixtures at an Ignition Energy of 28 J capacitance (μF)

voltage (V)

ignition energy (0.5CU2, J)

total actual concentration of n-hexane (g/m3)

n-hexane liquid-phase concentration (g/m3)

n-hexane vapor-phase concentration (% v/v)

experiment timesa (S/F)

maximum pressure (MPa)

maximum temperature (°C)

14 14 14 14 14 14 14

2000 2000 2000 2000 2000 2000 2000

28 28 28 28 28 28 28

330.00 277.20 238.00 178.00 125.40 92.40 63.00

198.66 183.61 168.56 118.54 78.01 48.00 36.30

3.42 2.43 1.80 1.55 1.23 1.15 0.69

1S 1S 1S 1S 1S 1S, 2F 3F

1.04 1.24 1.21 1 0.6 0.51 −

663 751 788 816 643 544 −

a

S and F denote success and failure, respectively.

that the effects of turbulent flow on the dynamic vapor−liquid two-phase n-hexane/air mixture can be ignored at the 80-ms ignition moment used in this work. 3.2. Minimum Ignition Energy of Vapor−Liquid TwoPhase n-Hexane. By means of a traditional ignition test, one can easily determine the ignition energy based on the given capacitance and applied voltage through a simple calculation.13,14 The traditional test, referred to as the simple method, follows the general relationship

E=

1 CU 2 2

(10)

where C is the capacitance of the capacitor; U is the voltage of the capacitor discharge; and E is the energy stored in the capacitor, which is traditionally regarded as the ignition energy. The results of all experiments at various ignition energies in this work are summarized in Table 5. The variation of the MIE with the concentration of gaseous n-hexane is shown in Figure 7. The lowest affirmative value among the MIEs determined for all investigated mixtures at various concentrations in this work was 0.5 mJ. From the previous literature,8,9 the MIE of a pure vaporphase n-hexane/air mixture is 0.248 mJ. In this experimental process, at a mean particle size of the liquid phase of SMD = 10.60 μm, an MIE of 0.5 mJ was found for vapor and liquid two-phase n-hexane concentrations of 2.43% and 183.61 g/m3, respectively. In the previous and current works, the concentrations of the MIE of vapor-phase n-hexane were close to equivalent concentration conditions. However, the MIE of a vapor−liquid two-phase n-hexane/air mixture is larger than the MIE of a pure vapor hexane. It can therefore be

Figure 6. Trends of the peak pressure and peak temperature at various concentrations of the vapor−liquid two-phase n-hexane/air mixture.

this work. These results suggest that the vapor−liquid twophase fuel/air mixture is involved in a particle group diffusion− combustion process in evaporation on regularity of the influence of temperature. The LFL of the vapor−liquid two-phase n-hexane/air mixture was confirmed to be 1.15%, which is close to the LFLs in refs 6 and 7. Moreover, the maximum peak pressure of the vapor−liquid two-phase n-hexane/air mixture was at the vapor-phase n-hexane volume fraction of 2.43%, which is close to the maximum peak pressure of the pure vapor-phase nhexane/air mixture at 2.16%. Therefore, it can be concluded

Table 5. Experimental Results in Vapor−Liquid Two-Phase n-Hexane/Air Mixtures at Various Ignition Energies capacitance (μF)

voltage (V)

ignition energy (0.5CU2, mJ)



0.1 0.0003 0.1 0.0003 0.1 0.0003 0.1 0.0003 0.1 0.1 0.1 0.1

100 1600 100 1600 100 1600 100 1600 200 100 300 200

0.5 0.384 0.5 0.384 0.5 0.384 0.5 0.384 2 0.5 4.5 2

198.66 198.66 183.61 183.61 168.56 168.56 118.54 118.54 78.01 78.01 48.00 48.00

3.42 3.42 2.43 2.43 1.80 1.80 1.55 1.55 1.23 1.23 1.15 1.15

a

experiment timesa (S/F) 1S, 3F 1S, 3F 1S, 3F 1S, 3F 1S, 3F 1S, 3F

2F 2F 2F 2F 2F 2F

maximum pressure (MPa)

maximum temperature (°C)

0.475 − 0.55 − 0.505 − 0.405 − 0.265 − 0.205 −

474 − 537 − 564 − 584 − 460 − 389 −

S and F denote success and failure, respectively. 12862



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experiments, 10.63 μm, to examine the influence of various concentrations on the explosion parameters in this work. However, in fact, the experimental results and the SMD value of 10.63 μm contain an error. The actual SMDs of n-hexane/air mixtures and relative errors are listed in Table 6. From Figure 8, it can be observed that the maximum relative error of the SMD was 9.22%, as the mean concentration of the n-hexane/air mixture was 183.61%.

Figure 7. MIEs of the vapor−liquid two-phase n-hexane/air mixture at an initial pressure of 1 atm and an initial temperature of 21 °C and comparison to a previously reported MIE8,9 (0.248 mJ).

concluded that the MIE of a vapor−liquid two-phase n-hexane/ air mixture can be significantly affected by the evaporation of transient liquid droplets. 3.3. Error Estimation. To obtain accurate real-time concentration and SMD data of liquid-phase n-hexane at the ignition moment, the Mie extinction detection system was employed throughout this work. However, we noticed that, in addition to the fact that the real-time concentration and SMD of n-hexane change over time, the concentrations at different positions in the vessel were also not constant. The error in the actual concentration of n-hexane should thus be considered. Therefore, the average of the concentrations at positions 1 and 2 of the vessel was defined as the lower limit of the error, and the average of the concentrations at positions 2 and 3 was defined as the upper limit of the error, because the actual concentration of vapor-phase n-hexane was obtained from the total actual concentration of n-hexane and the actual concentration of liquid-phase n-hexane by subtracting. At the same time, a wall loss of 10% was considered. Therefore, the error in the actual concentration of vapor-phase n-hexane can be given. The concentration and the error value for the vapor− liquid two-phase n-hexane/air mixture are shown in Figure 4. The SMD is an important reference in this work. The fluctuations in the SMD are relatively narrow, so the SMD was identified as approximately close to a constant. This has significance in a comparison of the influence of concentration on the explosion parameters of n-hexane/air mixtures. The SMD was identified as as a constant with the average value in all

Figure 8. Actual SMD of liquid-phase n-hexane and relative error (position 1 at 1/5, position 2 at 1/2, and position 3 at 4/5 of the vessel).

The results of all MIEs are summarized in Table 5. Examination of the energies corresponding to situations involving failure (F) and success (S) shows that they are quite far apart. In fact, energy values between the energy input for a failed ignition and a successful ignition can also initiate combustion of the mixture. Therefore, the lowest energy corresponding to situations denoted as “1S, 2F” is defined as the affirmative value of the MIE, and the uncertainties in the ignition energy between the energy input in a “3F” (failed ignition) and “1S, 2F” (successful ignition) is defined as the uncertain region of the MIE in this work. The affirmative values of “1S, 2F” and “3F” and the uncertain region of the MIE are listed in Table 7. It is worth noting that the affirmative value of the MIE was employed only to clearly describe the experimental results. It is not a universal term in the safety engineering community.

Table 6. Actual SMDs of Liquid-Phase n-Hexane/Air Mixtures and Relative Errors SMD (μm) n-hexane liquid-phase concentration (g/m3)

position 1

position 2

position 3

mean value

mean value of all experimental data

relative error (%)

198.66 183.61 168.56 118.54 78.01 48.00 36.30

9.86 10.34 9.37 8.55 9.06 9.89 10.72

10.97 11.28 10.66 10.72 11.13 10.61 10.08

12.35 13.20 11.49 11.33 10.39 10.52 10.65

11.06 11.61 10.51 10.20 10.19 10.34 10.48

10.63 10.63 10.63 10.63 10.63 10.63 10.63

4.05 9.22 1.13 4.05 4.14 2.73 1.41

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Table 7. Actual MIEs of Vapor−Liquid Two-Phase n-Hexane/Air Mixtures and Their Uncertainties 1S, 2F

a




198.66 183.61 168.56 118.54 78.01 48.00

3.42 2.43 1.80 1.55 1.23 1.15

0.5 0.5 0.5 0.5 2 4.5

3F

experiment timesa (S/F) 1S, 1S, 1S, 1S, 1S, 1S,


experiment timesa (S/F)

uncertainty in ignition energy (J)

relative error in Ignition energy (%)

0.384 0.384 0.384 0.384 0.5 2

3F 3F 3F 3F 3F 3F

0.116 0.116 0.116 0.116 1.5 2.5

23.20 23.20 23.20 23.20 75.00 55.56

2F 2F 2F 2F 2F 2F

S and F denote success and failure, respectively.

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4. CONCLUSIONS In this work, liquid n-hexane was evaporated synchronously during the time of the spray. Vapor−liquid two-phase nhexane/air mixtures were formed. In fact, vapor-phase nhexane/air premixed explosion and liquid-phase diffusion combustion have taken place after ignition. More detailed conclusions are as follows: (1) At the SMD of n-hexane (10.63 μm), the concentration of the LFL associated with the vapor concentration in vapor− liquid two-phase n-hexane is similar to that reported in the literature,6 which is the concentration of the LFL of pure gasphase n-hexane. The classic study from the past, on monodisperse tetralin aerosols, 10 μm in diameter, by Burgoyne and Cohen,21 obtained a similar concentration for the LFL of pure gas-phase n-hexane, but did not mention the vapor-phase concentration at ignition timing. Both studies reached the same conclusion, but essential differences exist. This work found that the total concentration of the gas−liquid two-phase hexane/air mixture was greater than concentrations of the LFL6 under the condition of pure vapor n-hexane. However, because of the ignition timing, the concentration of the LFL of the gas-phase n-hexane played a decisive role in the law. In this work, the following quantitative conclusion was obtained: The LFL of the vapor−liquid two-phase n-hexane/air mixture is confirmed at the vapor-phase n-hexane concentration of 1.15% (v/v) and the liquid-phase n-hexane concentration of 48.00 g/m3, among the values determined for all investigated vapor−liquid two-phase n-hexane/air mixtures. (2) At the SMD of n-hexane (10.63 μm), the concentration of the maximum peak explosion pressure of vapor−liquid twophase n-hexane/air mixture is larger than the concentration of the maximum peak explosion temperature of the vapor−liquid two-phase n-hexane/air mixture. The peak pressure trend of the vapor−liquid two-phase n-hexane/air mixture is similar to the trend for a pure gaseous n-hexane/air mixture. The peak pressure of the vapor−liquid two-phase n-hexane/air mixture reached its maximum value at a vapor-phase n-hexane volume fraction of 2.43% (v/v). This is close to the value for gaseous nhexane/air mixtures with a stoichiometric volume fraction of 2.16% (v/v). (3) The MIE of a vapor−liquid two-phase n-hexane/air mixture is larger than the MIE under the conditions of pure vapor-phase n-hexane. At the SMD of liquid-phase n-hexane (10.63 μm), the MIE of the vapor−liquid two-phase n-hexane/ air mixture is 0.5 mJ, with corresponding vapor and liquid twophase n-hexane concentrations of 2.43% (v/v) and 183.61 g/ m3, respectively.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 10 68914252. Fax: +86 10 68914252. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research presented in this paper was supported by the National Science Foundation of China (11372044).

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