On the Estimation and Validation of Global Single-Step Kinetics Parameters of Ethanol-Air Oxidation Using Diffusion Flame Extinction Data
Accepted for publication as short communication in
Combustion Science and Technology
Rishi Dubey Under-Graduate Student Department of Mechanical Engineering Indian Institute of Technology Madras, Chennai, Tamilnadu, INDIA 600036 Karnam Bhadraiah Graduate Student Thermodynamics and Combustion Engineering Laboratory Department of Mechanical Engineering Indian Institute of Technology Madras, Chennai, Tamilnadu, INDIA 600036 and Vasudevan Raghavan Assistant Professor and Corresponding Author Thermodynamics and Combustion Engineering Laboratory Department of Mechanical Engineering Indian Institute of Technology Madras, Chennai, Tamilnadu, INDIA 600036 Phone: 91-44-22574712 Email:
[email protected]
Abstract In this study, based on the extinction characteristics of non-premixed flames, global single-step kinetics parameters are estimated for ethanol oxidation in air. Using a quasi-steady heterogeneous experimental setup, the air velocity at which an envelope flame surrounding the sphere transits to a wake flame that burns in the rear region of the sphere, termed as the transition or the extinction velocity, are obtained in a previous study. These extinction velocities for different sphere sizes are employed in this study to estimate the single-step kinetics parameters. The estimated global single-step kinetics has been employed in a numerical model and extinction characteristics of opposed-flow ethanol-air diffusion flames have been predicted and validated against the available experimental results in literature.
Keywords: Ethanol; Global single-step kinetics; Diffusion Flame; Flame extinction; Porous-sphere experiments
Introduction Ethanol is a renewable bio-fuel. It can be produced from agricultural feed-stocks such as sugarcane. Ethanol can be employed as a transportation fuel even in its original form and can also be easily blended with fuels such as gasoline (Agarwal, 2007). Since bio-fuels are new and evolving, fundamental studies have to be carried out to determine their burning characteristics under several ambient conditions. The rate at which a bio-fuel will burn should be understood to study the combustion systems employing that fuel. For the numerical simulation of several practical combustion systems including engine applications, a global single-step kinetics mechanism for gas-phase oxidation of that fuel in an air environment would be necessary. The chemical kinetics of gas-phase oxidation of ethanol has been reported over the last five decades. Data have been reported from non-flow (static) reactors, flow reactors, diffusion flames, and laminar premixed flame experiments by several researchers (Natarajan and Bhaskaran (1981), Dunphy et al. (1991), Egolfopoulos et al. (1992), Norton and Dryer (1992), Marinov (1999), Li et al. (2001), Saxena and Williams (2007) and Seiser et al., 2007). Detailed chemical kinetics models to describe the gas-phase oxidation of ethanol in air are available (Norton and Dryer (1992), Marinov (1999), Saxena and Williams (2007) and Seiser et al., 2007). A global single-step mechanism for ethanol-air oxidation has also been reported by Westbrook and Dryer (1982).
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In this study, based on the results obtained from the porous sphere technique, single-step kinetics parameters are estimated for ethanol oxidation in air. Details of the porous sphere technique are available in detail in literature (Sami and Ogasawara (1970), Balakrishnan et al. (2001), Raghavan et al. (2005) and Parag and Raghavan, 2009). In this technique, ethanol is supplied to the surface of a constant diameter inert porous sphere at a rate equal to the rate of its combustion, which depends on the sphere diameter, air velocity and ambient conditions (Parag and Raghavan, 2009). The air velocity at which an envelope flame surrounding the sphere transits to a wake flame, which burns in the rear region of the sphere, is termed as the transition or the extinction velocity. The extinction velocities for several cases with different sphere diameters are reported in detail in an earlier work (Parag and Raghavan, 2009). These extinction velocities are employed in this study to estimate the single-step kinetics parameters and the global single-step kinetics has been validated against the available experimental results reported in literature (Seiser et al., 2007).
Formulation Extinction conditions are generally characterized in terms of the Damköhler number, which is the ratio of characteristic flow (residence) time to chemical reaction time. Characteristic flow time is given as the ratio of sphere radius (R) and air velocity (U∞), (τflow = R/U∞). Chemical time is estimated as the ratio of fuel vapor density (ρF) to mass based reaction rate ( ω& ), ( τ chem = ρ F ω& ). For a global single-step reaction, the reaction rate can be estimated using the expression ω& = κ [F ] n1 [O ] n2 M F , where ω& is the mass based reaction rate in kg/m3s, [F] and [O] are the concentrations of fuel and oxygen in kmol/m3, MF is the molecular mass of the fuel in kg/kmol, n1 and n2 are the rate exponents, and κ is the rate coefficient. The rate coefficient is given by the Arrhenius type of equation as κ = A exp(− Ea RuT ) , where A is the pre-exponential factor, Ea is the activation energy (J/kmol), Ru is universal gas constant (8314.3 J/kmol.K) and T is the temperature in Kelvin. By expressing the concentrations of fuel and oxygen as the respective ratios of the density to the molecular mass, the Damköhler number (Da) can be written as follows:
Da =
ρ R A exp(− Ea RuT ) F U∞ MF
n1 −1
ρO MO
n2
(1)
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Employing the flame extinction data of n-heptane, a similar form of the Damköhler number at extinction (DaM,e, where subscript M indicates properties calculated at a mean temperature and e denotes extinction) was correlated with the Reynolds number at extinction (2RU∞,e/νM) through the use of the transfer number and appropriate dimensionless activation and adiabatic flame temperatures by Pope and Gogos (2005) (refer equation (23) in Pope and Gogos (2005)). This correlation can be employed to calculate the extinction velocities iteratively, if the global single-step kinetics is well known. It can also be employed to arrive at the single-step kinetics parameters, if the extinction velocities for different spheres are measured. Therefore, in this study, the DaM,e correlation from Pope and Gogos (2005) is employed to arrive at the global single-step kinetics parameters of ethanol-air oxidation using the extinction velocities reported in literature (Parag and Raghavan, 2009).
Results and Discussion First of all, the DaM,e correlation has been checked and validated to see whether it predicts the extinction velocities of a different fuel for which global single-step kinetics is available. Methanol oxidation in air is well understood. The single-step kinetics mechanism reported by Westbrook and Dryer (1981) for methanol-air oxidation has been employed successfully in different numerical models (Raghavan et al., 2005, 2006) to predict the extinction velocities close to those obtained from the experiments. Therefore, the DaM,e correlation with the single-step kinetics parameters for methanol oxidation reported by Westbrook and Dryer (1981), is used to calculate the methanol extinction velocities for different sphere sizes. Thermo-physical properties and other required quantities have been estimated using the procedure given in Pope and Gogos (2005). Table 1 presents the agreement between the extinction velocity values predicted by the correlation with the experimentally measured values (Sami and Ogasawara (1970), Raghavan et al., 2005). It is seen from Table 1 that except for a couple of data points, the overall agreement between the theoretical prediction and the experimental value is quite reasonable with a maximum error around 12%. However, unlike the methanol case, it was observed that the single-step kinetics parameters for ethanol-air, reported in Westbrook and Dryer (1981), were unable to predict the experimental values of extinction velocities of ethanol-air diffusion flames (Table 2). Therefore, the global single-step chemistry parameters for ethanol-air reaction have been estimated using DaM,e correlation. The activation energy (Ea) and
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the rate exponent values (n1 and n2) of ethanol-air single-step kinetics were adopted from Westbrook and Dryer (1981). The pre-exponential factor (A) has been iteratively calculated by employing the extinction velocities for different sphere sizes, measured from porous sphere experiments (Parag and Raghavan, 2009), and using the DaM,e correlation. Table 3 presents the pre-exponential factor calculated using the DaM,e correlation and it can be observed that the maximum deviation in these values for each case against the average value is only around 7%. Therefore, employing the average pre-exponential value, the mole based global single-step reaction rate ( ω& ) for ethanol-air oxidation is estimated as
− 1.256 × 108 kmol [ F ] 0.15 [O ] 1.6 m3s 8314 .3 × T
ω& = 1.55 × 1010 exp
(2)
The above single-step kinetics has been validated against the experimental results. For this purpose, a numerical model which solves the mass, momentum, species and energy conservation equations in axisymmetric cylindrical polar coordinates (r, z) was employed. Simulation of opposed flow diffusion flames have been carried out. A commercially available CFD software called FLUENT (Fluent user guide), is used to solve the governing equations. An optically thin approximation based radiation sub-model (Barlow et al., 1999) is also employed in the numerical model using a User Defined Function (UDF) in FLUENT. Other features of the numerical model include the incorporation of temperature and species-concentration dependent thermophysical properties (from McBride et al., 1993) and second order accurate discretization schemes. Seiser et al. (2007) have reported experimentally measured extinction data for ethanol-air diffusion flames in terms of the strain rate at which flame extinction occurs for a given mass fraction of ethanol vapor in the fuel-stream. Initially, the numerical model itself has been validated to note if it could predict the opposed flow diffusion flame properly. For this purpose, a case has been simulated to predict the structure of methanol-air diffusion flame, as reported in Seiser et al. (2007). Methanol is chosen because its single-step kinetics is well established as discussed earlier. A computational domain as shown in Fig. 1 has been used to simulate axisymmetric opposed flow diffusion flames. The boundary conditions are also indicated in Fig. 1. Grid independence study has been carried out with uniform cell sizes of 0.05 mm, 0.1 mm and 0.2 mm in each direction and the cell sizes in both directions have been fixed as 0.1 mm. The structure of the opposed flow diffusion flame predicted by the present numerical model in terms of the profiles of the temperature (Fig. 2a) and the mass fractions of oxygen
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(Fig. 2b) and carbon-dioxide (Fig. 2c), is shown in Fig. 2. Also shown in Fig. 2 are the experimental measurements and the numerical predictions employing a detailed kinetics mechanism, reported in Seiser et al. (2007). It can be observed from Fig. 2 that the present numerical model with single-step chemistry and optically thin radiation sub-model is able to predict the opposed flow diffusion flames quite accurately. After validating the numerical model with known chemistry sub-model, the estimated single-step kinetics for ethanol-air oxidation has been incorporated in the model. Simulations were carried out to predict the extinction characteristics of opposed flow ethanol-air diffusion flames. Figure 3 shows the predicted extinction data in terms of the strain rate at which flame extinction occurs for a given mass fraction of ethanol vapor in the fuelstream along with the experimental values reported by Seiser et al. (2007). It is clear from Fig. 3 that the estimated single-step kinetics is able to predict the extinction characteristics quite accurately and therefore can be employed in a numerical or a theoretical model to simulate ethanol-air diffusion flames.
Summary In the above study, a validated global single-step kinetics mechanism for ethanol has been proposed. This mechanism can be employed in the numerical or theoretical modeling of diffusion flames and also in direct engine applications, where a similar combustion process occurs.
References Agarwal, A.K., 2007. Biofuels (alcohols and biodiesel) applications as fuels for internal combustion engines. Prog. Energy Comb. Sci. 33, 233-271. Balakrishnan, P., Sundararajan, T., Natarajan, R., 2001. Combustion of a fuel droplet in a mixed convective environment. Combustion Science and Technology. 163, 77-106. Barlow R. S., Smith N. S. A., Chen J. Y. and Bilger R. W., 1999. Nitric Oxide formation in dilute hydrogen jet flames: Isolation of the effects of Radiation and Turbulence-Chemistry submodels. Combustion and Flame. 117, 4-31. Dunphy, M. P., P.M. Patterson and J. M. Simmie, 1991. High temperature oxidation of ethanol. Part 2- Kinetic modeling. Journal of Chemical Society. Faraday Transactions. 87, 2549-2560. Egolfopoulos, F. N., D. X. Du and C. K. Law, 1992. A study on ethanol oxidation kinetics in laminar premixed flames, flow reactors and shock tubes. Proceedings of Combustion Institute. 24, 833-841. Fluent User Guide, Fluent 6.3.26, 2005 and http://www.fluent.com. Li, J., A. Kazakov and F.L. Dryer, 2001. Ethanol pyrolysis experiments in a variable pressure flow reactor. International Journal of Chemical Kinetics. 133, 859-867.
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Marinov, N. M. 1999. A detailed chemical kinetic model for high temperature ethanol oxidation. International Journal of Chemical Kinetics. 31, 183-220. McBride, B.J., Sanford, G. and Reno, M.A. (1993) Coefficients for calculating thermodynamic and transport properties of individual species. NASA Tech. Memorandum 4513. Natarajan, K. and K. A. Bhaskaran, 1981. An experimental and analytical study of methanol ignition behind shock waves. Combustion and Flame. 43, 35-49. Norton, T. S. and F. L. Dryer, 1992. An experimental and modeling study of ethanol oxidation kinetics in an atmospheric pressure flow reactor. International Journal of Chemical Kinetics. 24, 319-344. Parag, S. and V. Raghavan, 2009. Experimental Investigation of Burning Rates of Pure Ethanol and Ethanol Blended Fuels. Combustion and Flame. 156, 997-1005. Pope, D. N., Gogos, G., 2005. Numerical simulation of fuel droplet extinction due to forced convection. Combustion and Flame. 142, 89–106. Raghavan, V., Babu, V., Sundararajan, T., Natarajan, R., 2005. Flame shapes and burning rates of spherical fuel particles in a mixed convective environment. Int. J. Heat Mass Transfer. 48, 5354-5370. Raghavan, V., D. N. Pope, D. Howard and G. Gogos, 2006. Surface tension effects during low Reynolds number methanol droplet combustion. Combustion and Flame. 145, 791-801. Sami, H., Ogasawara, M., 1970. Study on the burning of a fuel droplet in heated and pressurized air stream: 1st report, experiment. JSME. Bulletin. 13, 395-404. Saxena, P. and F. A. Williams, 2007. Numerical and experimental studies of ethanol flames. Proceedings of Combustion Institute. 31, 1149-1156. Seiser, R., S. Humer, K. Seshadri and E. Pucher, 2007. Experimental investigation of methanol and ethanol flames in non-uniform flows. Proceedings of Combustion Institute. 31, 1173-1180. Westbrook, C. H. and F. L. Dryer, 1981. Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames. Combustion Science and Technology. 27, 31-43.
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Table 1: Calculation of extinction velocities for methanol spheres using the DaM,e correlation and singlestep methanol-air kinetics of Westbrook and Dryer (1981) at an ambient pressure of 1 bar Extinction velocity
Sphere
Ambient
diameter
temperature
d (mm)
T∞ (K)
By Correlation Pope and Gogos (2005)
Experimental
8.4
300
1.12
1.10
Raghavan et al. (2005)
10.8
300
1.28
1.27
Raghavan et al. (2005)
12.2
300
1.37
1.30
Raghavan et al. (2005)
14
300
1.47
1.39
Raghavan et al. (2005)
16.4
300
1.61
1.44
Raghavan et al. (2005)
18.6
300
1.69
1.53
Raghavan et al. (2005)
5.0
423
1.41
1.79
Sami and Ogasawara (1970)
5.0
573
2.62
2.32
Sami and Ogasawara (1970)
10.0
300
1.26
1.49
Sami and Ogasawara (1970)
10.0
423
2.04
2.19
Sami and Ogasawara (1970)
10.0
573
3.68
3.15
Sami and Ogasawara (1970)
References for experimental
U∞,c (m/s)
data
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Table 2: Calculation of extinction velocities for ethanol spheres using the DaM,e correlation and singlestep ethanol-air kinetics reported by Westbrook and Dryer (1981) at the ambient conditions of 300 K and 1 bar
Extinction velocity U∞,e (m/s)
Sphere diameter d (mm)
By correlation Pope and Gogos (2005)
Experiments (Parag and Raghavan, 2009)
8
0.57
0.95
9.5
0.62
0.99
10
0.64
1.03
10.6
0.66
1.06
11.2
0.68
1.09
12
0.70
1.10
12.6
0.72
1.13
13.6
0.75
1.15
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Table 3: Calculation of pre-exponential factor for ethanol-air single-step kinetics using the DaM,e correlation; activation energy and rate exponents values taken from Westbrook and Dryer (1981)
Sphere U∞,e (m/s)
A (m3/kmol)1-n1-n2(1/s)
8
0.95
1.65 x 1010
9.5
0.99
1.55 x 1010
10
1.03
1.57 x 1010
10.6
1.06
1.57 x 1010
11.2
1.09
1.56 x 1010
12
1.10
1.51 x 1010
12.6
1.13
1.51 x 1010
13.6
1.15
1.47 x 1010
diameter d (mm)
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Figure 1: Computational Domain; L, the length between the ducts is 10 mm and the inner diameter of each duct is 25 mm
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Figure 2: Validation of the present numerical model against the experimental and numerical results of Seiser et al. (2007) in terms of (a) temperature profile, (b) oxygen mass fraction profile and (c) carbondioxide mass fraction profiles
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Figure 3: Validation of the proposed single-step kinetics for ethanol-air oxidation against the experimental and numerical results of Seiser et al. (2007) in terms of prediction of extinction strain rate
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