Experimental and Numerical Study of Laminar Burning Velocity of

Article pubs.acs.org/EF

Experimental and Numerical Study of Laminar Burning Velocity of Ethane−Air Mixtures of Variable Initial Composition, Temperature and Pressure Maria Mitu,† Domnina Razus,*,† Venera Giurcan,† and Dumitru Oancea‡ †

“Ilie Murgulescu” Institute of Physical Chemistry, Romanian Academy, Splaiul Independenţei 202, 060021 Bucharest, Romania Department of Physical Chemistry, University of Bucharest, Bulevardul Regina Elisabeta 4-12, 030018 Bucharest, Romania

‡

ABSTRACT: Pressure−time records of ethane−air centrally ignited explosions in a spherical closed vessel have been used to study the flame propagation in mixtures with various initial concentrations, pressures and temperatures ([C2H6] = 3.40−7.60 vol %, p0 = 30−130 kPa, T0 = 298−433 K). The normal burning velocities have been calculated from pressure−time records for an extended duration of spherical propagation by means of an improved equation for the burnt mass fraction, recently discussed. For the stoichiometric ethane−air mixture, Su,st = (43.5 ± 1.0) cm/s was obtained, within the range of reported literature data from the spherical bomb technique. The normal burning velocities were examined in correlation with the temperature and pressure reached during flame propagation, in single experiments. A power law has been used to describe the dependency of burning velocities on pressure and temperature. The thermal exponents of burning velocities range between 1.40 and 2.20, revealing the influence of the initial pressure of the flammable mixture. The baric coefficient exponents of burning velocities range within −0.48 and −0.32 (at T0 = 298 K) and within −0.52 and −0.29 (at T0 = 425 K) with minimum values at the most reactive composition. The experimental normal burning velocities of ethane−air mixtures are compared with the normal burning velocities of laminar premixed flames measured by other experimental techniques and with normal burning velocities computed by numerical simulations performed with a detailed mechanism (GRI-Mech version 3.0) by means of COSILAB package, under the assumption of adiabatic propagation. The computed normal burning velocities depend on initial pressure and temperature in a similar way to the experimental burning velocities but underestimate them in the range of stoichiometric and ethane-rich mixtures. technique have been recently examined36 in connection to other available techniques based on the use of nonstationary flames. In the present paper, the technique of constant volume combustion is used for determining the normal burning velocities of ethane−air gaseous mixtures from transient pressure−time records using the burnt mass fraction (BMF) evaluated by means of a simple model.34 The model has previously been used for determination of burning velocities of propylene−air, propylene−air−inert35 and propane−air mixtures;36 the reported NBVs ranging well within literature data resulted from other experimental techniques. Ethane (in concentrations below 6 vol %) is one of the main components of natural gas used nowadays as an alternative, eco-friendly fuel in the power generation industry, materials synthesis and automotive propulsion. The occurrence of variable ethane concentrations in natural gas may change the combustion characteristics of the composite fuel, which is important when the use of natural gas from completely different sources is inevitable. Ethane−air combustion characteristics have been investigated for the analysis of various engines and/or combustors’ performances for developing better combustion devices. Explosion pressures of ethane−air mixtures measured in various closed vessels have been

1. INTRODUCTION Normal burning velocity (NBV) is a basic property characteristic for flame propagation in gaseous fuel−air mixtures, dependent on the fuel type, fuel-to-oxygen ratio, pressure, temperature and dilution by inert gases. NBV is used to validate kinetic mechanisms used for flame modeling, for predicting the performance and emission of combustion engines and for design of explosion suppressing devices. Experimental NBVs are also used to calculate the overall reaction orders and the apparent activation energies, required in CFD (computational fluid dynamics) modeling of explosions propagating in enclosures. Various techniques have been developed for determining the NBV of flammable mixtures based on the study of stationary or nonstationary flames. The first group includes flames stabilized on conical or flat flame burners1−10 and stagnation flow flames;4,6,11−15 the nonstationary techniques use outwardly propagating spherical flames.9,10,16−36 Among these last methods, constant volume combustion is one of the most suitable, because it allows measurement to be made within wide ranges of pressure and temperature. Therefore, flame propagation at pressures and temperatures different from ambient, where normal burners cannot be used, can be more easily studied. An additional feature is the possibility to determine the NBV from data of a single experiment, using adequate corrections for flame stretch and curvature in the early stage of flame propagation and for heat losses in the late stage of propagation. The advantages and drawbacks of this © 2014 American Chemical Society

Received: November 6, 2013 Revised: February 13, 2014 Published: February 17, 2014 2179

dx.doi.org/10.1021/ef402197y | Energy Fuels 2014, 28, 2179−2188

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measured at ambient initial pressure and temperature by Bartknecht (5 L sphere),37 Senecal et al. (22 L cylindrical vessel),38 Holtappels et al. (20 L sphere)39 and van den Schoor et al. (4.2 L sphere).40 Other data, measured at various initial pressures and initial temperatures higher than ambient, have been reported by Maisey et al. (65 °C; 10 L sphere),41 Holtappels et al. (100 and 200 °C, 20 L sphere)39 and Mitu et al. (298 to 423 K; 0.52 L sphere).42 Combustion of ethane−air mixtures has also been subject of many numerical studies,4−15,17−22,43−46 because ethane is intermediate during the oxidation of many hydrocarbons like methane, propane and higher alkanes and its oxidation is the main pathway for C2 intermediate species generation. Various detailed kinetic models have been tested by extensive temperature and chemical species concentrations measurements within the flame front (the main reaction zone) of flames stabilized in various burner configurations and have been used to predict the system behavior under extensive variation of the state parameters. The present data consist in the NBVs of ethane−air mixtures with variable initial concentration ([C2H6 ] = 3.40−7.60 vol %), from experiments at variable initial pressure and temperature (within the range from 30 to 130 kPa and from 298 to 433 K). The NBVs of ethane−air mixtures from experimental data are compared with NBVs obtained from the numerical modeling of one-dimensional ethane−air laminar flames propagating at identical initial concentrations, pressures and temperatures.

Figure 1. Pressure−time records of explosions for the stoichiometric ethane−air mixture at p0 = 101.3 kPa and various initial temperatures.

unburned gas; π is the relative pressure, defined as π = p/p0 with p as the transient pressure (at time t) and p0 as the initial pressure. For BMF, the relationship derived by O’Donovan50 has been used: n=

θ=

Tf,p

, with Tf,p as the average transient

⎛ πe ⎞1 − 1/ γ * ⎜ ⎟ ⎝π⎠

(4)

The initial dimensionless temperature of the burned gas is θ0 = (Tf,V/Tf,p) and the end dimensionless temperature of the burned gas is θe = 1; Tf,p is the adiabatic flame temperature of isobaric combustion at p = p0 and Tf,V is the adiabatic flame temperature of isochoric combustion at p = p0. The parameter γ* is a composite parameter, determined as: γ* = lnπe/ln(πe/ θ0). The initial dimensionless temperature θ0 and the end dimensionless pressure πe are readily obtained from equilibrium calculations. The measurements from the early stage of explosion propagation (from p0 to 1.5 p0) have been left aside, to avoid the influence of flame stretch and curvature on NBV during this stage. Data evaluation was performed up to the inflection point of p(t) curves, when usually the heat lost toward the vessel becomes significant. The complete algorithm used to extract NBV from p(t) data has been previously given.36

3. DATA EVALUATION The basic equations for calculating the burning velocities from transient pressure−time records in a spherical vessel have been taken from Fiock48 and Manton and Lewis and von Elbe:49 (1)

and rb = R c[1 − (1 − n)π −1/ γu]1/3

(3) Tf,e

burned gas temperature and Tf,e as the average end burned gas temperature. Throughout derivation of these equations, the basic assumptions used for modeling spherical flames have been maintained: the ignition source is quasi punctiform; the flame propagates as a sphere during the whole process; the flame front thickness can be neglected in comparison with the flame radius; the heat transferred between the flame front and the electrodes and the vessel’s wall is negligible; both the unburned and burned gases are ideal. The main problem in using eqs 1−3 is the accurate calculation of temperature profile within the burned gas, in various moments of unsteady combustion process and at its end. In previous studies34,36 it was shown that θ, the dimensionless burned gas temperature, varies as a function of transient dimensionless pressure π, following a power law similar to the adiabatic compression law:

Measurements on spherical expanding flames of ethane−air mixtures were performed in a closed spherical vessel (R = 5 cm) with a central ignition rated to 4 MPa. The vessel was fitted with ports, for filling and evacuating the flammable mixture, electrodes and an ionization probe. The vessel was thermostatted by ±1 °C using an AEM IRT96 controller. Other details concerning the explosion vessel and the preparation of flammable mixtures have been given in previous publications.36,47 The pressure−time records of explosions were captured by a piezoelectric pressure transducer (Kistler 601A) connected to a charge amplifier (Kistler 5001SN). The signal from the ionization probe amplifier and from the charge amplifier were acquired at 5 × 103−104 signals per second by a TestLab Tektronix 2505 acquisition data system. The studied mixtures had an equivalence ratio φ = 0.77−1.93 ([C2H6] = 3.4−7.6 vol %), variable initial pressures within 30−130 kPa and variable initial temperatures within 298−433 K. Ethane (99.9%) (SIAD, Italy) was used without further purification. Typical pressure−time records obtained during combustion of the stoichiometric ethane−air mixture at p0 = 101.3 kPa and various initial temperatures are shown in Figure 1.

Rc 3 ⎛ 1 ⎞1/ γu dn ⎜ ⎟ 3rb 2 ⎝ π ⎠ dt

πe − θπ 1 − 1/ γu

where πe = pe/p0 and θ =

2. EXPERIMENTAL SECTION

Su =

θ(π − π 1 − 1/ γu)

(2)

Here, rb is the transient flame radius (at pressure p), Rc is the radius of the explosion vessel, n is the burnt mass fraction (BMF), γu is the adiabatic compression coefficient of the 2180


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4. COMPUTING PROCEDURE The adiabatic flame temperatures of ethane−air in the constantpressure and constant-volume combustion at variable initial temperatures from 298 to 450 K and variable initial pressures from 50 to 200 kPa have been obtained from equilibrium computations made with the 0-D COSILAB package. The program uses the thermodynamic criteria of chemical equilibrium: the minimum of free Gibbs energy, at constant temperature and pressure or the minimum of free Helmholtz energy, at constant temperature and volume, to find the equilibrium composition of burned gas for gaseous fuel− oxidizer mixtures. Fifty-three compounds were considered as combustion products. The kinetic modeling of one-dimensional, premixed, laminar, free ethane−air flames was made with the 1-D COSILAB package (version 3.0.3)51 using the GRI mechanism, version 3.0 (53 chemical species and 325 elementary reactions). The runs were performed for isobaric combustion of ethane−air mixtures at variable initial pressures from 50 to 150 kPa and variable initial temperatures from 300 to 450 K. The thermodynamic and molecular databases of Sandia National Laboratories, USA (CHEMKIN format) have been used. Premixed 1D laminar adiabatic free flames have been considered.

Figure 3. NBVs versus pressure during the explosion of the stoichiometric ethane−air mixture at T0 = 298 K and various initial pressures.

flames of fuel−air mixtures propagating in centrally ignited explosions in a closed spherical vessel. They have cut, to a large extent, the data obtained in the early stage of propagation by leaving aside the results influenced by noise; this was beneficial for the statistical analysis of data. In addition, the remaining p(t) results delivered a normal burning velocity less influenced by the stretch rate, because stretch is sufficiently small over the remaining period and it can be ignored.33 At the same time, they used an improved method to establish the end point of p(t) curves able to be examined based on schlieren photographs of flames that enabled the determination of the onset point of cellular flames32,33 unusable for normal burning velocity determination. In the present case, data of each single experiment have been used to model the dependency of NBV on pressure by a power law:

5. RESULTS AND DISCUSSION 5.1. Experimental Normal Burning Velocities. Relevant results computed from data of single experiments performed with stoichiometric ethane−air mixtures at an initial pressure of 101.3 kPa and variable initial temperatures are shown in Figure 2, where plots of burning velocities versus transient pressure are

Su = Su,0π ε

(5)

where Su,0 is the NBV at the initial moment of combustion (p0 and T0) and ε is a composite parameter named “thermokinetic coefficient”.26 All data referring to ethane−air mixtures in various conditions (initial concentration, pressure and temperature) have been examined according to eq 5 by a nonlinear regression analysis obtaining good coefficients of determination, rn2. The statistical analysis of results revealed that NBVs at the initial moment of combustion, Su,0, are obtained with standard deviations between 0.3 and 1.5%, and the thermokinetic coefficients, ε, are obtained with standard deviations between 0.3 and 1.2%. Representative values of Su,0 and ε for C2H6−air mixtures in different initial conditions are given in Table 1. Within the examined ranges, ε increases with temperature and decreases with pressure. According to previous literature studies,23,47 the burning velocities determined in different runs can be examined together if the conditions of chosen experiments match an unique isentrope (Tu; p). Indeed, measurements have been made at initial pressures and temperatures matching the isentropes starting at 40 kPa and 298 K. Following this procedure, NBV could be obtained for a pressure range between 40 and 800 kPa and a temperature range between 298 and 650 K. Any plot Su(p) shown in Figure 2 or 3 could be extended, according to this protocol, toward higher pressures and/or temperatures by choosing adequate data sets among

Figure 2. NBVs versus pressure during the explosion of the stoichiometric ethane−air mixture at p0 = 101.3 kPa and various initial temperatures.

given. Similar diagrams have been obtained for all ethane−air mixtures with variable initial composition, temperature and pressure. In the early stage of propagation (1.5 p0 ≤ p ≤ 2.0 p0), the data are scattered in all the curves from Figure 2; at later stages, NBVs have a monotonous variation versus p. Other data are plotted in Figure 3, where the NBVs computed from single experiments at T0 = 298 K and variable initial pressures are given. As the law of adiabatic compression is considered valid in the unburned gas zone, the data can be alternatively plotted against unburned gas temperature Tu; the observed trend remains the same for all results. Hinton and Stone32,33 performed a similar analysis of pressure−time data obtained during single experiments on 2181


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Table 1. Best fit Parameters for NBVs Correlation with Pressure during Single Explosions of Ethane−Air Mixtures in a Spherical Vessel [C2H6] (vol %)

p0 (kPa)

T0 (K)

Su,0 (cm s−1)

4.04

60

298 363 423 298 363 423 298 363 423 298 363 423

31.50 45.57 62.33 21.77 30.35 40.51 58.79 78.05 99.87 42.50 58.15 73.92

120

5.71

60

120

± ± ± ± ± ± ± ± ± ± ± ±

0.02 0.03 0.06 0.02 0.03 0.04 0.04 0.06 0.14 0.06 0.09 0.12

ε 0.1326 0.1722 0.1854 0.1332 0.1845 0.2113 0.0806 0.1311 0.1469 0.1136 0.1250 0.1439

± ± ± ± ± ± ± ± ± ± ± ±

frequently used to indicate the initial pressure and temperature influence on NBV by power laws: ⎛ 1⎞ ε = ν + μ⎜⎜1 − ⎟⎟ γu ⎠ ⎝

rn2 0.0009 0.0013 0.0027 0.0005 0.0009 0.0013 0.0010 0.0013 0.0028 0.0010 0.0012 0.0014

0.9741 0.9759 0.9440 0.9885 0.9891 0.9836 0.9731 0.9847 0.9600 0.9817 0.9836 0.9878

⎛ T ⎞ μ⎛ p ⎞ Su = Su,0⎜ ⎟ ⎜⎜ ⎟⎟ ⎝ Tref ⎠ ⎝ pref ⎠

(6) γ

(7)

In the present case, the thermal and baric coefficients μ and ν have been calculated from correlations of experimental Su,0 (NBV extrapolated at the initial moment of explosion) with initial temperature (at constant initial pressure) and with initial pressure (at constant initial temperature) by means of a nonlinear regression analysis. Typical diagrams plotting NBV of a lean mixture versus the initial pressure are given in Figure 5. The variation of NBV with the initial temperature is shown in Figures 6 and 7 where the lines correspond to the best-fit correlations of data.

measurements. A representative diagram is shown in Figure 4, where four partly overlapping data sets are plotted. A good

Figure 5. NBVs of a lean ethane−air mixture ([C2H6] = 4.04 vol %; φ = 0.70) at various initial pressures and temperatures.

Figure 4. NBVs of the stoichiometric ethane−air mixture during explosions at various initial pressures and temperatures, along several isentropes.

The corresponding thermal and baric coefficients of ethane− air mixtures with variable composition are listed in Tables 3 and 4. The thermal and baric coefficients of NBV for ethane−air have values within the range characteristic for alkane−air flames. For instance, the thermal coefficients of propane−air lie

overlapping reveals the correctness of the proposed model. This possibility to determine the NBV of a fuel−air mixture over extended ranges of pressure and temperature is a useful feature of the model to be used together with pressure measurements in closed vessels with central ignition. For the individual runs selected in Figure 4, the thermokinetic coefficients are listed in Table 2. By assuming that all data fit the same unique adiabate, which starts from p0 = 40 kPa and T0 = 298 K and is extended up to 540 kPa and 500 K, we found ε = 0.135. The thermokinetic coefficient ε can be expressed as a function of ν and μ, the baric and thermal exponents of NBV, Table 2. Thermokinetic Coefficients of Burning Velocity Dependence on Pressure during Single Experiments p0 (kPa)

T0 (K)

ε

40 60 80 110

298 333 363 393

0.119 0.132 0.139 0.140

Figure 6. NBVs of various ethane−air mixtures at atmospheric pressure and variable initial temperatures. 2182


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drawn in Figure 8 to mark this. Our data are quite close to those reported by Tseng, obtained by optical observation of flames during the early stage of propagation in a spherical vessel18 and Farrell, obtained from p(t) records in a spherical vessel27 but systematically higher as compared to results of Farrell, obtained from optical observation of the same flames during the same propagation stage in a spherical vessel.27 The peak NBV, Su,max = (46.5 ± 1.0) cm/s was obtained at the same composition ([C2H6] = 6.0−6.2 vol %; φ = 1.1−1.2) by other techniques, using stationary flames stabilized on a Bunsen burner2 and spherical flames propagating in a closed vessel18 and by the present measurements. Other measurements, performed by heat flux method, indicate, however, lower values of the peak NBV: Su,max = (42 ± 0.5) cm/s.5,7,22 For the stoichiometric ethane−air mixture, we obtained Su,st = (43.5 ± 1.0) cm/s, within the range of reported literature data obtained by the spherical bomb technique, extended from 37.510 to 44.0 cm/s.11 The results seem more scattered on the side of rich ethane−air mixtures as compared to lean mixtures. The present model affords the determination of NBV during a longer period of flame propagation, which is a great advantage over other models restricted just to the constant-pressure period of outwardly propagating flames. Using this feature, one can determine the NBV at higher pressures and/or temperatures than those used as initial conditions for experiments. Two alternative procedures can be used. (a) The first procedure consists in examining the transient values of NBV under isobaric or isothermal conditions versus transient temperature Tu or transient pressure p, using data sets obtained at variable initial pressures and/or temperatures. Typical results are given in Tables 5 and 6. (b) The second procedure is based on the use of thermokinetic coefficients, related to the baric and thermal exponents by eq 6. In this case, a preliminary determination of the baric coefficient ν and of adiabatic compression coefficient γu is necessary for calculation of any thermal coefficient μ. Alternatively, a preliminary determination of the thermal coefficient μ and of adiabatic compression coefficient γu is necessary for calculation of any baric coefficient ν. The baric and thermal exponents calculated by this procedure have quite close values to those computed by procedure a. From the reference NBVs and their baric and thermal coefficients, computed for various initial temperatures and/or pressures according to one of these procedures, the NBVs of ethane−air at elevated temperatures and/or pressures can be calculated. Examples are given in Figures 9 and 10, where data are plotted as Su versus ethane concentration at various temperatures and various pressures, respectively; the graphs include also the lines representing the best-fit correlations of data.

Figure 7. NBVs of preheated ethane−air mixtures at 101.3 kPa as a function of mixture composition.

between 1.70 and 2.20, as reported from closed vessel measurements.16,23,26,52 Typical values of baric coefficients are −0.30 for stoichiometric methane−air;53 between −0.26 and −0.12 for propane−air;16,23,28,52 −0.11 for stoichiometric butane−air mixtures.54 For the stoichiometric ethane−air mixture, the thermal coefficient μ = 1.55 was reported.16 For this mixture, baric coefficients between −0.27 and −0.12 were found, referring to burning velocities at ambient initial temperature.10,11,16,20 In the present case, the thermal coefficients range between 1.40 and 2.20, revealing the influence of the total initial pressure of the flammable mixture. In all cases, ethane−air mixtures characterized by the lowest NBV (mixtures far from stoichiometry) are influenced in a higher degree by preheating and have the largest thermal coefficients. The baric coefficients range within −0.48 and −0.32 (at T0 = 298 K) and within −0.52 and −0.29 (at T0 = 425 K) with minimum values at the most reactive composition (corresponding to [C2H6] = 6.33 vol %, with φ = 1.13). Examination of our results on atmospheric laminar C2H6−air flames in comparison with literature data reveals a satisfactory agreement of NBVs obtained by the closed vessel and by other experimental techniques.2−16,18−22,27 The NBVs obtained by the closed vessel technique during our measurements and extracted from literature18,21,27 have been plotted in Figure 8 against the equivalence ratio φ (the equivalence ratio φ is defined as φ = ([C2H6]/[O2])/([C2H6]/[O2])stoich, where the subscript “stoich” refers to the stoichiometric ethane−air mixture) of the ethane−air mixture. As shown in a previous paper,55 the average standard error in measurements of the explosion pressure was 2% and the average standard error in the corresponding NBV was under 3.5%, using the same methodology for NBV determination. Error bars have been

Table 3. Thermal Coefficients (μ) of NBVs at Various Initial Pressures p0 (kPa) [C2H6] (vol %) 3.42 4.04 4.80 5.71 6.33 6.96 7.58

40 2.066 1.826 1.541 1.494 1.402 1.692

± ± ± ± ± ±

60 0.031 0.017 0.017 0.110 0.009 0.056

2.110 1.869 1.703 1.447 1.393 1.470 1.542

± ± ± ± ± ± ±

80 0.106 0.059 0.018 0.043 0.043 0.019 0.041

2.222 1.832 1.705 1.435 1.502 1.379 1.553 2183

± ± ± ± ± ± ±

100 0.035 0.089 0.032 0.065 0.111 0.055 0.055

2.159 1.868 1.712 1.584 1.499 1.518 1.591

± ± ± ± ± ± ±

0.043 0.078 0.035 0.041 0.040 0.036 0.042

120 2.174 1.807 1.658 1.642 1.646 1.486 1.617

± ± ± ± ± ± ±

0.034 0.043 0.014 0.108 0.015 0.077 0.061


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Table 4. Baric Coefficients (−ν) of NBVs at Various Initial Temperatures T0 (K) [C2H6] (vol %)

298

3.42 4.04 4.80 5.71 6.33 6.96 7.58

0.423 0.422 0.483 0.320 0.327 0.341 0.423

± ± ± ± ± ± ±

333

0.003 0.014 0.009 0.031 0.010 0.024 0.003

0.432 0.404 0.496 0.321 0.320 0.364 0.432

± ± ± ± ± ± ±

363

0.040 0.008 0.016 0.005 0.013 0.011 0.040

0.441 0.459 0.512 0.311 0.248 0.353 0.441

± ± ± ± ± ± ±

393

0.018 0.026 0.015 0.013 0.017 0.017 0.018

0.513 0.485 0.526 0.282 0.291 0.339 0.513

± ± ± ± ± ± ±

0.045 0.025 0.019 0.024 0.027 0.014 0.045

423 0.516 0.482 0.531 0.308 0.286 0.330 0.516

± ± ± ± ± ± ±

0.021 0.023 0.020 0.010 0.027 0.022 0.021

Figure 9. Correlations between Su and [C2H6] for ethane−air mixtures at p0 = 200 kPa and various temperatures.

Figure 8. NBVs of ethane−air mixtures at ambient initial conditions against equivalence ratio, from present measurements and several literature sources.

Table 5. Thermal Coefficients (μ) of NBVs at Various Initial Pressures, Computed from Data Evaluated in Experiments at Variable Initial Temperatures p0 (kPa) [C2H6] (vol %)

100

200

300

400

500

4.80 5.71 6.33

1.712 1.584 1.500

1.816 1.668 1.637

1.932 1.756 1.756

1.651 1.809 1.839

2.116 1.182 1.921

Table 6. Baric Coefficients (−ν) of NBVs at Various Initial Temperatures, Computed from Data Evaluated in Experiments at Variable Initial Pressures Figure 10. Correlations between Su and [C2H6] for ethane−air mixtures at T0 = 500 K and various pressures.

T0 (K) [C2H6] (vol %)

300

400

500

600

4.80 5.71 6.33

0.483 0.320 0.327

0.520 0.310 0.276

0.337 0.304 0.289

0.302 0.295 0.299

Table 7. NBVs of the Stoichiometric Ethane−Air at Various Initial Conditions from Our Measurements and from Various Literature Sources

The NBVs predicted by this procedure and literature data referring to ethane−air at elevated pressures or/and temperatures are listed in Table 7. Our results agree to a fair extent with literature data, especially those accurately obtained from pressure−time records by making the necessary corrections for stretch in the early stage of flame propagation, as given by Kochar et al.,10 Hassan et al.20 and Jomaas et al.21 5.2. Computed NBVs. The NBVs of preheated ethane−air computed by kinetic modeling with GRI-Mech version 3.0 are plotted in Figure 11 in comparison with experimental NBVs and with NBVs predicted by other kinetic models. The experimental NBVs match well the computed results only in 2184

p0 (kPa)

T0 (K)

Su (cm s−1), from our measurements

200 200 400 500 1000 506 100

298 298 298 298 298 325 343

37.9 37.9 30.7 28.7 23.2 32.6 58.0

Su (cm s−1) , from literature 37.0 34.0 31.0 27.0 23.0 28.0 53.0

measuring technique spherically expanding flames in a closed vessel, extrapolation to zero stretch counterflow twin flames

reference 20 21 20 21 10 10 14


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Table 8. Reference Values of Computed NBVs of Ethane− Air and Thermal and Baric Coefficients (μ and −ν) [C2H6] (vol %)

Su,ref (cm s−1)

μ

−ν

3.42 4.04 4.80 5.71 6.33 6.96 7.58

14.31 24.02 33.37 41.00 42.55 37.93 29.43

2.04 1.72 1.69 1.58 1.47 1.62 1.74

0.297 0.370 0.298 0.245 0.178 0.227 0.237

NBVs (mixtures far from stoichiometry) are influenced in a higher degree by preheating and have larger thermal coefficients. 5.3. Overall Kinetic Parameters of Ethane Oxidation in Air, Under Flame Conditions. The thermal and baric coefficients of NBVs are mainly used to predict their variation within and, sometimes, beyond the usual range of temperature and pressure variation. Additional alternative information, related to the kinetics of the overall process, can be extracted from these parameters: the overall reaction orders nr can be determined from the baric coefficients56 and the overall activation energies of flame propagation can be determined from the thermal coefficients (in fact, from the NBVs at variable temperatures) according to the following equations:

Figure 11. Measured and calculated NBVs of ethane−air flames against equivalence ratio at various initial temperatures and p0 = 101.3 kPa.

the lean region of the flammability range; for the stoichiometric and rich ethane−air mixtures, the computed NBVs underestimate the experimental NBVs at all examined temperatures. Both NBVs predicted by Egolfopoulos et al., using their own kinetic scheme11 and by Dyakov et al., using the kinetic model of Konnov7 are close to NBVs predicted by GRI 3.0 mechanism, but differ from experimental NBVs in the region of the most reactive ethane−air flames (1.00 ≤ φ ≤ 1.25). The results obtained at variable initial pressures show a satisfactory agreement between experimental and computed NBVs, especially at temperatures above ambient, as seen from Figure 12 where data characteristic for a lean ethane−air mixture ([C2H6] = 4.80 vol %) are plotted.

nr = 2(ν + 1)

(8)

Su = cte−Ea /2RTf

(9)

where Tf is the average flame front temperature, computed by means of adiabatic flame temperatures Tf according to the following equation:57 Tf = T0 + 0.74(Tf − T0)

(10)

Typical results referring to the studied systems are given in Tables 9 and 10. For comparison, Ea = 365 kJ/mol was found for the stoichiometric propane−air mixture at 101.3 kPa, from similar data.58 Table 9. Overall Reaction Orders (n) Computed from NBVs Determined in Experiments at Variable Initial Pressures T0 (K)

Figure 12. Measured and calculated NBVs propagating in a lean ethane−air flame against initial pressure, at various initial temperatures.

The examination of the baric and thermal coefficients of NBVs reveals, however, a similar variation of experimental and computed burning velocities. Typical values of these coefficients and of reference NBVs (Su at Tref = 298 K and pref = 101.3 kPa) obtained from chemical modeling are given in Table 8. The baric and thermal coefficients of computed NBVs match well the results determined from experimental NBVs, whose reference values have been indicated in section 5.1: μ = 1.55 for the stoichiometric ethane−air mixture16 and ν = −0.27 to −0.12.10,11,16,20 ethane−air mixtures characterized by lower

[C2H6] (vol %)

298

333

363

393

423

3.42 4.04 4.80 5.71 6.33 6.96 7.58

1.154 1.157 1.035 1.361 1.345 1.318 1.160

1.136 1.192 1.007 1.359 1.360 1.272 1.140

1.119 1.083 0.976 1.378 1.504 1.293 1.196

0.974 1.031 0.948 1.436 1.417 1.334 1.129

0.967 1.036 0.938 1.384 1.427 1.340 1.104

The overall reaction orders and activation energies are useful input parameters in CFD modeling of flame propagation in enclosures in various conditions. Therefore, the present data referring to ethane−air mixtures at temperatures and pressures different from ambient represent valuable information for flame modeling. 2185


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Table 10. Activation Energies (Ea) of Ethane Oxidation, Computed from Burning Velocities Determined in Experiments at Variable Initial Temperatures [C2H6] (vol %)

φ

Ea (kJ/mol)

coefficient of determination, rn2

3.42 4.04 4.80 5.71 6.33 6.96 7.58

0.592 0.703 0.842 1.012 1.129 1.250 1.370

239 244 314 383 325 284 313

0.998 0.991 0.991 0.999 0.997 0.997 0.977

NOMENCLATURE E = energy (J) n = burnt mass fraction (−); overall reaction order p = pressure (kPa) r, R = radius (cm) Rg = universal gas constant (8.31 J mol−1 K−1) S = normal burning velocity (cm s−1) t = time (s) T = temperature (K)

Greek

γ = adiabatic compression coefficient (−) ε = thermokinetic coefficient (−) θ = relative temperature (−) μ = thermal coefficient of burning velocities (−) ν = baric coefficient of burning velocities (−) π = relative pressure (−) φ = equivalence ratio (−)

6. CONCLUSIONS Examination of p(t) records obtained during explosions in a spherical vessel makes it possible the calculation of transient values of several deflagration parameters: the burned mass fraction (BMF), the flame radius, rb, and the normal burning velocity, NBV. In the present paper, ethane−air mixtures with variable initial concentration, pressure and temperature have been studied. Data evaluation has been made with an improved model for BMF valid for an extended duration of flame propagation, restricted to the stage when energy losses are negligible. The NBV obtained with this method agree with NBV obtained by other authors from pressure−time measurements in centrally ignited explosions; the agreement with data obtained by experimental techniques is just satisfactory. The NBVs of ethane−air obtained either in a single experiment or in several experiments (when NBVs extrapolated to initial conditions were acquired) have been analyzed and discussed, taking into account their pressure and temperature dependence. The correlation of NBV with pressure and temperature was conveniently described by a power law, which allowed the comparison with other reported data. The thermal and baric exponents of NBVs for ethane−air fall within the common variation range, characteristic for hydrocarbon−air mixtures. From the reference NBVs and their baric and thermal coefficients, the NBVs of ethane−air at temperatures and/or pressures different form ambient can be evaluated. The agreement between the evaluated NBVs and literature data validates both the experimental procedure and calculation model. The computed NBVs depend on pressure and temperature in a similar way as the NBVs from experiments, but underestimate the NBVs from the present measurements. On the other hand, the baric and thermal coefficients of computed burning velocities match better the values determined from experimental NBVs.

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Article

Subscripts

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a = activation b = burned gas c = combustion vessel e = end (final) state of the burned gas f = flame p = isobaric process r = reaction ref = reference state u = unburned gas V = isochoric process

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AUTHOR INFORMATION

Corresponding Author

*D. Razus. E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS − UEFISCDI, project PN-II-RU-PD-2011-3-0053. 2186


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Experimental and Numerical Study of Laminar Burning Velocity of

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