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Reduced methanol kinetic mechanisms for combustion applications
Combustion and Flame 142 (2005) 258–265 www.elsevier.com/locate/combustflame
Reduced methanol kinetic mechanisms for combustion applications S. Yalamanchili a , W.A. Sirignano a,∗ , R. Seiser b , K. Seshadri b a Mechanical and Aerospace Engineering, University of California, Irvine, Irvine, CA 92697, USA b Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA
Received 24 June 2004; received in revised form 4 November 2004; accepted 2 January 2005 Available online 3 May 2005
Abstract Reduced chemical kinetic mechanisms for methanol combustion were investigated by evaluating ignition delay magnitudes and combustion in a continuously stirred reactor. Unsteady computations were made to study the characteristics of the kinetic mechanisms proposed in the literature and to compare the dependence of various parameters on methanol combustion. All computations were done under isobaric conditions, and, to capture the influence of all the reactions involved in the mechanism, a very small time step was used. Finite-difference methods were used to solve the coupled differential equations. The five-step mechanism developed by C.M. Mueller and N. Peters [in: N. Peters, B. Rogg (Eds.), Reduced Kinetic Mechanisms for Applications in Combustion Systems, SpringerVerlag, New York, 1993, pp. 143–155] for premixed flames and both the five-step mechanism and the four-step mechanisms developed by C.M. Mueller, K. Seshadri, J.Y. Chen [ibid, pp. 284–307] for non-premixed flames were considered. It was found that the Mueller et al. five-step mechanism, with some modifications, best supported the spontaneous ignition and continuous stirred reactor combustion. The results were validated by comparing calculated ignition delays with available experimental data of C.T. Bowman [Combust. Flame 25 (1975) 343–354], and calculated final steady-state concentrations with chemical equilibrium calculations [J.-Y. Chen, Combust. Sci. Technol. 78 (1991) 127]. Initial temperature and concentration and the operating pressure of the system have a major effect on the delay of methanol ignition. The residence time of the continuous stirred reactor affects ignition delay and also changes the transient characteristic of chemical composition of the fuel–vapor mixture. The computations are intended to guide and explain many combustion studies that require a methanol kinetic mechanism. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Methanol kinetics; Ignition; Stirred reactor
1. Introduction Reduced mechanisms are useful for practical computations in which many complexities exist and more than one independent variable is used. Three well-
* Corresponding author. Fax: +1 949 824 3773.
E-mail address: [email protected] (W.A. Sirignano).
known four- and five-step methanol oxidation reduced kinetic schemes have been advanced by Mueller and Peters [1] for established premixed flames (MP5) and by Mueller et al. [2] for established diffusion flames (MSC4 and MSC5). The formulation of the five-step mechanism (MSC5) introduced steady-state approximations to the following species: CH2 OH, CHO, OH, O, HO2 , and H2 O2 [2]. This work extends the methanol reduced kinetic model to be valid for ig-
0010-2180/$ – see front matter 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2005.01.018
S. Yalamanchili et al. / Combustion and Flame 142 (2005) 258–265
nition, developing flames, and established steady or unsteady flames. It also improves the ability of the model to predict the equilibrium composition and temperature downstream of a premixed flame, using a modified MSC5 mechanism built on an understanding of all of the known important elementary reactions. Some more recent mechanisms might have updated kinetic constants for the elementary reactions, but the structure of the mechanism is not different. Other articles on methanol reduced kinetics either address only the steady state [3], postulate a mechanism [4], or require at least 14 steps for the unsteady initiation process [5]. For one portion of our modified model development, spontaneous ignition and homogeneous oxidation were considered. We studied temporal behavior in a constant-pressure, adiabatic, spatially uniform situation: volume changed with time. A second unsteady configuration was also studied wherein the fresh premixed combustible gas was continuously introduced into a high-temperature environment with available chemical radicals. An ideal, continuous, stirred reactor achieves perfect mixing of reactants and products inside the control volume. The continuous stirred reactor (CSR) case was chosen to test the accuracy of the kinetic model when solving a combusting-flow process with a residence time. Under the infinite mixing rate assumption, the outflow temperature and concentrations are taken to be identical to those inside the control volume. On exiting the volume after a finite residence time, the mixture is assumed to cease reacting; combustion need not be complete and chemical equilibrium need not exist in the exit flow. Both inflow properties and initial properties within the volume are prescribed, and then properties within the volume (and equivalently in the exit flow) are determined as functions of time. The mass inflow rate is held constant throughout the operation. The implication of a constant pressure, a constant volume, and a constant mass inflow rate with temporally varying temperature and concentration is that the outflow rate must change with time in a controlled manner. Variable exit area can be used to maintain the desired constant pressure. The constant ratio of the chamber volume to the volumetric inflow rate is called the “residence time,” although differences between inflow density and chamber density and/or unsteadiness cause this ratio to differ somewhat from a true time-dependent travel time.
2. Kinetic models Our computations showed that the MSC4, MSC5, and MP5 kinetic models did not support the ignition delay characteristics. This was not surprising as the
259
models were designed to describe established flame structures after the ignition delay period. Hence, these mechanisms had to be modified by the addition of Reaction 96, an initiation reaction. So, we created modified mechanisms MMSC96 4, MMSC96 5, and MMP96 5 (see Appendix A). The rate of Reaction 96 was high prior to ignition and approximately zero after ignition; therefore, it is very important to model ignition delay characteristics. However, the modified five-step mechanism (MMP5) still did not support the ignition delay characteristics, even though it was sufficient to describe premixed flames. MMP5 predicted negative values for the mass fraction of the hydrogen molecule. Further, the mechanism did not predict the correct characteristic temporal curves for all of the major species. It was concluded that MMP5 was not robust enough to predict ignition delay. Furthermore, MMSC96 5 overestimated the final adiabatic temperature (calculated following Ref. [9]) by almost 600 K. Because of the absence of a backward reaction for Reaction 17, CO2 , CO, and O2 were not at equilibrium after complete combustion. Hence, it overestimated the final concentration of CO2 and underestimated the final O2 and CO concentrations. So, MMSC96 5 was further modified by the addition of a backward reaction for Reaction 17. See Appendix A; Reactions 1 and 18 [1] produce the equilibrium balance for CO2 , CO, and O2 . In our calculations, CH2 O did not reach steady state, and, hence, MMSC96 4, which assumes steady state for CH2 O, should not be used. MMP5 implicitly contains a backward reaction for Reaction 17 (Appendix A). As this model also includes the steady-state balance for the intermediate species CH, CH2 , and CH3 , combinations of a few reactions (Reactions 1, 2, 19, and 20 from Ref. [1]) provide the backward reaction for Reaction 17. However, due to the problems mentioned earlier, the model was still not robust enough to predict spontaneous ignition characteristics. MMSC5, MMSC4, and MMP5 predict the same final adiabatic temperature when the above-mentioned modifications are made.
3. Governing equations and numerical method The independent variables considered are the major species mass fractions and the temperature of the system. A system of quasi-linear ordinary differential equations is developed to govern the mass fractions of the eight major species CH3 OH, O2 , H2 O, CO2 , CO, H2 , H, and CH2 O, and temperature T . The intermediate species were assumed to be at steady state, and simple algebraic equations were developed. For both spontaneous ignition and CSR computations, constant pressure and perfect gases were con-
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sidered. Also, for the CSR calculations, continuous flow was considered. All elementary reactions involved are assumed to be first order in terms of the reactants (products) for forward (backward) reactions. Hence, the rate of production of species i due to a reaction between species j and k is Yj Yk 2 n Ej k Rj k = Aj k (1) . ρ T j k exp − Wj Wk RT Wj and Wk are molecular weights, and Yj and Yk are mass fractions. 3.1. Spontaneous ignition 3.1.1. Species mass balance dYi ρ Rj k . = Wi Ri = Wi dt
(2)
j,k
3.1.2. Energy balance dT Wi Hi Ri ≡ Q. ρCp = dt
(3)
i
3.2. Continuous stirred reactor 3.2.1. Total mass balance d(ρV ) ˙ out . = ρinlet f0 − m dt
ρ f dYi = inlet 0 (Yi−inlet − Yi ) + Ri . dt V
5. Comparison with ignition experiments
(5)
3.2.3. Energy balance ρinlet Cp f0 dT (6) = (Tinlet − T ) + Q. dt V Here, m ˙ out is the outlet mass flow rate; Wj and Wk are molecular weights; Yi , Yj , and Yk are mass fractions; Hi is the heat of formation of species i; f0 is the volumetric inflow rate; and V is the volume of the fluid in the CSR. The integer index i indicates one of the eight major species. The integer indices j and k can indicate major or steady-state species. Of course, only for certain combinations of the integer values will Aij k be nonzero [1,2]. With the use of steady-state approximations for the intermediate species and the conservation of C, H, and O atoms, each overall species reaction rate Ri can be expressed, following standard practice [1,2], as a linear combination of the five basic reduced reaction rates defined in Appendix A. A perfect gas is assumed. The data for specific heats and heats of formation were obtained from Refs. [6–8]. A second-order-accurate finite-difference method was used to solve the coupled equations. ρCp
In the CSR calculations, the results of only the complete combustion cases were validated against the equilibrium code [9], because, in only these cases, the system reached chemical equilibrium. Extreme cases were chosen to be validated. The results matched to a certain order of accuracy. There were still small errors (less than 2.6%) in the final equilibrium concentrations because the kinetic model does not consider the mass of steady-state species for mass balances. Unlike the chemical equilibrium code, they were assumed to be negligible. The resulting OH and O equilibrium concentrations are comparable to the H and H2 equilibrium concentrations. As the steadystate species are not considered in the mass and mole balances for the reduced kinetics, there are some differences between the results of a full equilibrium calculation and the final state of the reduced kinetic calculation. This particular modified five-step kinetic model (MMSC5) is robust and can be used for modeling ignition and flame-spread problems to determine flame propagation and spontaneous ignition characteristics.
(4)
3.2.2. Species mass balance ρ
4. Chemical equilibrium
The ignition delays, which are found experimentally by Bowman [10] for high initial temperatures, can be used to validate the kinetic model. He used argon as the inert gas. As seen in Table 1, the ignition delays predicted by the derived kinetic model MMSC5 matched very well the experimental results. For validation, fuel–oxidizer mixtures were considered in both fuel-rich and lean regions. The experimental correlation [10] relates species concentration, initial temperature, and ignition-delay time: E −0.5 C −0.1 Coxygen τmax = A exp (7) methanol . RT Here, τmax is the ignition delay; Coxygen and Cmethanol are molecular oxygen and methanol concentrations; T is the initial temperature; R is the universal gas constant; and A and E are kinetic constants. The correlation was compared with the calculated ignition delays. From the log plot, the calculated values were found to be A = 3.1E–13 s(mol/cm3 )0.6 and E = 143.83 kJ/mol. The experimental values are A = 2.1E–13 s(mol/cm3 )0.6 and E = 151.5 kJ/mol.
6. Effect of parameters on spontaneous ignition Fig. 1 is a general transient plot of the concentrations of major species (CH3 OH, O2 , H2 O, CO2 , CO,
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261
Table 1 Ignition delays of different cases Case no.
Equivalence ratio
Mole fractions
Initial temp. (K)
XCH3 OH
X O2
Xargon
Ignition delay (µs) Experimental (Bowman [10])
Theoretical
1
0.75
0.02
0.04
0.94
1570 1790 1925
190 45 18
164 36 14
2
0.75
0.01
0.02
0.97
1545 1800 2125
225 40 9
180 47 7
3
1.5
0.01
0.01
0.98
1575 1870 2090
242 34 15
241 22 12
4
0.375
0.01
0.04
0.95
1555 1710 2030
140 36 9
130 49 7
5
3
0.02
0.01
0.97
1555 1860 1975
260 36 20
200 34 20
Fig. 1. Transient plots of the major species and temperature for the reduced MMSC5 mechanism shown between 0.4 and 0.5 s.
H2 , H, and CH2 O) versus temperature. The computations were done for wide parameter ranges to show the robustness of the model. These parameters include initial temperature, initial stoichiometric composition, operating pressure, and equivalence ratio.
Fig. 2 shows that the reaction rates increase with increasing initial temperatures and the ignition delay decreases. In all computations, the initial total mass of the mixture was kept constant. Hence, the mass frac-
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Fig. 2. Plots of temperature for Condition 6 in Table 2 at various initial temperatures.
Fig. 3. Plots of temperature at various initial compositions with initial temperature 900 K. Numbers on graph indicate the condition from Table 2. Table 2 Various stoichiometric mixtures studied Condition
YCH3 OH
Y O2
1 2 3 4 5 6
0.06725 0.0807 0.09415 0.1076 0.12105 0.1345
0.1009 0.12108 0.14126 0.16144 0.18162 0.2018
tion of the inert component was different for different initial fuel–oxidizer compositions. Table 2 indicates the six different stoichiometric conditions considered. The amount of inert component varies from case to case here. Even though complete combustion occurred, the temporal characteristics of some of the product species (CO, H2 , and H) were observed to differ between weaker (i.e., more inert mass) and stronger (i.e., less inert mass) stoichiometric compositions and between fuel-rich and fuel-lean mixtures. Fig. 3 shows that the adiabatic temperature is higher and the ignition delay is shorter for stronger stoichio-
metric concentrations of fuel and oxygen. Fig. 4 indicates how the equivalence ratio can affect both the adiabatic temperature and the ignition delay. As the total density of the system increases at higher pressures, the reaction rates of all the elementary reactions involved increase with increasing pressure. Therefore, as the total pressure of the system increases, the ignition delay decreases. The final equilibrium concentrations of the major products, H2 O and CO2 , are very weakly dependent on pressure. 7. Effect of parameters on continuous stirred reactor The computations for the well-stirred reactor were performed until the steady state was attained. Different parameters were considered not only to test the robustness of the reduced kinetic mechanism developed, but also to understand when there exist situations of incomplete combustion after the reactor has reached a steady state. The parameters studied include inlet fuel–oxidizer composition, operating pres-
S. Yalamanchili et al. / Combustion and Flame 142 (2005) 258–265
263
Fig. 4. Plots of temperature at various equivalence ratios with initial temperature 900 K.
Fig. 5. Transient plots of mass fractions of CH3 OH and H2 O for both complete and incomplete combustion shown between 0.2 and 1 s.
sure of the reactor, initial temperature, and residence time of the reactor. Fig. 5 shows the transient plots for both complete and incomplete combustion cases at steady state. Both cases have the same operating conditions with respect to atmospheric pressure, residence time (1 s), initial and inlet temperatures of the fuel–oxidizer mixture (900 K), and initial stoichiometric mixture (methanol and oxygen mass fractions of 0.135 and 0.202, respectively). The only difference is in the stoichiometric inlet concentrations, with complete combustion having larger concentrations equal to the initial concentrations and incomplete
combustion having one-half the amounts of methanol and oxygen. If, at any time less than the residence time, the difference between influx and efflux equals the total reaction rate for each major species, then steady state has been attained but chemical equilibrium may not have been reached. If complete combustion occurs, the ignition delay decreases for stronger inlet (less inert) stoichiometric concentrations of methanol and oxygen, in complete agreement with the spontaneous ignition solution. However, slight differences would occur in the calculations for ignition delay and final adiabatic tem-
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peratures between the spontaneous ignition problem and CSR, because the species mass balance (Eq. (4)) and energy balance (Eq. (6)) of CSR are exactly the same as for the ignition delay problem (Eqs. (2) and (5), respectively) only when the residence time, V /f0 , tends to infinity. The residence times considered thus far are not large enough. To check the above-mentioned result, a large residence time (15 times greater than the original residence time) was considered. Then, the ignition delays of the CSR and spontaneous ignition problem matched. The reaction rate depends on the initial composition of the fuel– oxidizer mixture. For lower concentrations (more inert) of the stoichiometric mixture, the reaction time for the mixture is long and, hence, can be longer than the residence time of the reactor if the residence time is small. Therefore, in these cases, the steady state is not the equilibrium state. Also, the temporal plots of the species are different from that of complete combustion. The final adiabatic flame temperature, as mentioned previously, is a function of the inlet concentration of the fuel–oxygen mixture. Therefore, the adiabatic temperature increases with stronger inlet concentrations. As a result, a greater percentage of the oxygen is consumed for weaker inlet concentrations, as the dissociation of CO2 to CO is predominant at higher temperatures. Thus, other species are present in scarce concentrations even after complete combustion of fuel. For a residence time of 1 s, only fuel-rich mixtures achieve equilibrium. However, for fuel-lean mixtures, equilibrium does not occur owing to the fact that less fuel is present. Therefore, the chemical reaction time becomes longer than the residence time, and the fuel does not remain in the reactor long enough to react completely. The behavior characteristic of fuel-rich mixtures is the same as that observed for the spontaneous ignition problem. However, there is a slight difference in the oxygen-versus-time profile for the fuelrich case because of the difference in the inlet and initial concentrations of oxygen. An inflection point is observed in the time profile of oxygen. This inflection point corresponds to the time at which the inlet concentration of oxygen equals the reactor concentration. This particular phenomenon is not observed in the fuel-lean case due to incomplete combustion, even though there is a difference between the initial and inlet concentrations of the fuel. A residence time of 1 s was used to analyze the effects of different operating pressures. As was the case for the spontaneous ignition problem, the ignition delay decreased at higher reactor pressures. The ignition delay was shorter than the residence time and exactly the same predicted in the spontaneous ignition problem. For lower operating pressures, the residence time was not sufficiently long. The final adiabatic temper-
ature increased as the total pressure of the reactor increased. As an increase in the pressure results in an increase in the total reaction rate, the amount of final products formed is greater. The initial temperature of the system affects only the ignition delay. Further, the ignition delay increases with decreasing initial temperature. The lower the initial temperature, the longer the time needed to heat the fuel mixture for ignition. These cases cannot be compared with any of the cases in the spontaneous ignition problem because the initial conditions of a spontaneous ignition problem are equivalent to the inlet conditions of the CSR but not to the initial conditions. Unlike the inlet temperature, the initial temperature of the fuel mixture does not affect the eventual reaction rates of the system. Hence, the final concentrations and the final adiabatic temperature remain the same for all cases. The inlet composition and the operating pressure of the reactor affect primarily the eventual reaction rates of the system.
8. Conclusions A modified five-step methanol kinetic model (MMSC5) was developed based on existing models [2]. This new kinetic model supports both spontaneous ignition and CSR combustion. A detailed computational study was made of the effects of different parameters on spontaneous ignition characteristics and CSR combustion. These parametric studies include the effects of temperature, pressure, and fuel– oxidizer composition. In the CSR, a steady state condition could be achieved before complete combustion of fuel. An understanding of this phenomenon will assist in many combustion studies. The final concentrations obtained in the computations were validated by the chemical equilibrium code [9]. The results matched with a good level of accuracy. MMSC5 was generated by addition of Reaction 96 and by addition of the reverse reaction for elementary Reaction 17 (Appendix A). Addition of Reaction 96 permitted the kinetic model to support spontaneous ignition characteristics, and addition of reverse Reaction 17 achieved the expected final chemical equilibrium for CO2 and CO. Thus, we can conclude that step MMSC5 is a robust model that can predict spontaneous ignition [10] and CSR combustion and, hence, can be used effectively for many combustion studies involving methanol kinetic mechanisms.
Acknowledgment A portion of the UCI effort was supported by the NASA Microgravity Program.
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Appendix A. Kinetic model A.1. Reduced five-step mechanism of Mueller et al. CH3 OH + 2H 2H2 + CH2 O, CH2 O CO + H2 ,
(I)
ArT n e−Ea /RT , where i is the equation number and T is the temperature of the system. The subscript f implies a forward reaction and b implies a backward reaction.
(II)
CO + H2 O CO2 + H2 ,
(III)
H + H + M H2 + M,
(IV)
3H2 + O2 2H + 2H2 O.
265
(V)
A.2. Overall reaction rates WI = w86 + w87 + w96 , WII = w29 + w30 + w31 + w32 , WIII = w18 , WIV = w5 + w12 + w15 + w16 + w17 + w21 + w22 + w23 − w32 − w85 , WV = w1 + w6 + w9 − w12 + w13 − w17 . A.3. Elementary reactions added Reaction numbers are identical to those in Refs. [1,2] except for these additions: 17: O2 + M → O + O + M (backward reaction), 96: CH3 OH + O2 → CH2 OH + HO2 . See Refs. [1,2] for rate constants of the elementary reactions. The rate constants are given by Ki =
References [1] C.M. Mueller, N. Peters, in: N. Peters, B. Rogg (Eds.), Reduced Kinetic Mechanisms for Applications in Combustion Systems, Springer-Verlag, New York, 1993, pp. 143–155. [2] C.M. Mueller, K. Seshadri, J.Y. Chen, in: N. Peters, B. Rogg (Eds.), Reduced Kinetic Mechanisms for Applications in Combustion Systems, Springer-Verlag, New York, 1993, pp. 284–307. [3] J.-Y. Chen, Combust. Sci. Technol. 78 (1991) 127. [4] D. Aronowitz, R.J. Santoro, F.L. Dryer, I. Glassman, Proc. Combust. Inst. 17 (1979) 633–644. [5] R.P. Lindstedt, M.P. Meyer, Proc. Combust. Inst. 29 (2002) 1395–1402. [6] N.B. Vargaftik, Tables on the Thermophysical Properties of Liquids and Gases, second ed., Hemisphere, Washington, DC, 1975. [7] Y. Touloukian, Thermophysical Properties of Matter, vol. 11, Plenum, New York, 1970. [8] C.L. Yaws, Physical Properties: A Guide to Physical, Thermodynamic, and Transport Property Data of Industrially Important Chemical Compounds, Chemical Engineering, New York, 1977. [9] W.C. Reynolds, STANJAN Chemical Thermodynamic Equilibrium Code, available at: http://grashof.engr. colostate.edu/tools/equil.html. [10] C.T. Bowman, Combust. Flame 25 (1975) 343–354.
Reduced methanol kinetic mechanisms for combustion applications S. Yalamanchili a , W.A. Sirignano a,∗ , R. Seiser b , K. Seshadri b a Mechanical and Aerospace Engineering, University of California, Irvine, Irvine, CA 92697, USA b Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA
Received 24 June 2004; received in revised form 4 November 2004; accepted 2 January 2005 Available online 3 May 2005
Abstract Reduced chemical kinetic mechanisms for methanol combustion were investigated by evaluating ignition delay magnitudes and combustion in a continuously stirred reactor. Unsteady computations were made to study the characteristics of the kinetic mechanisms proposed in the literature and to compare the dependence of various parameters on methanol combustion. All computations were done under isobaric conditions, and, to capture the influence of all the reactions involved in the mechanism, a very small time step was used. Finite-difference methods were used to solve the coupled differential equations. The five-step mechanism developed by C.M. Mueller and N. Peters [in: N. Peters, B. Rogg (Eds.), Reduced Kinetic Mechanisms for Applications in Combustion Systems, SpringerVerlag, New York, 1993, pp. 143–155] for premixed flames and both the five-step mechanism and the four-step mechanisms developed by C.M. Mueller, K. Seshadri, J.Y. Chen [ibid, pp. 284–307] for non-premixed flames were considered. It was found that the Mueller et al. five-step mechanism, with some modifications, best supported the spontaneous ignition and continuous stirred reactor combustion. The results were validated by comparing calculated ignition delays with available experimental data of C.T. Bowman [Combust. Flame 25 (1975) 343–354], and calculated final steady-state concentrations with chemical equilibrium calculations [J.-Y. Chen, Combust. Sci. Technol. 78 (1991) 127]. Initial temperature and concentration and the operating pressure of the system have a major effect on the delay of methanol ignition. The residence time of the continuous stirred reactor affects ignition delay and also changes the transient characteristic of chemical composition of the fuel–vapor mixture. The computations are intended to guide and explain many combustion studies that require a methanol kinetic mechanism. 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Methanol kinetics; Ignition; Stirred reactor
1. Introduction Reduced mechanisms are useful for practical computations in which many complexities exist and more than one independent variable is used. Three well-
* Corresponding author. Fax: +1 949 824 3773.
E-mail address: [email protected] (W.A. Sirignano).
known four- and five-step methanol oxidation reduced kinetic schemes have been advanced by Mueller and Peters [1] for established premixed flames (MP5) and by Mueller et al. [2] for established diffusion flames (MSC4 and MSC5). The formulation of the five-step mechanism (MSC5) introduced steady-state approximations to the following species: CH2 OH, CHO, OH, O, HO2 , and H2 O2 [2]. This work extends the methanol reduced kinetic model to be valid for ig-
0010-2180/$ – see front matter 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:10.1016/j.combustflame.2005.01.018
S. Yalamanchili et al. / Combustion and Flame 142 (2005) 258–265
nition, developing flames, and established steady or unsteady flames. It also improves the ability of the model to predict the equilibrium composition and temperature downstream of a premixed flame, using a modified MSC5 mechanism built on an understanding of all of the known important elementary reactions. Some more recent mechanisms might have updated kinetic constants for the elementary reactions, but the structure of the mechanism is not different. Other articles on methanol reduced kinetics either address only the steady state [3], postulate a mechanism [4], or require at least 14 steps for the unsteady initiation process [5]. For one portion of our modified model development, spontaneous ignition and homogeneous oxidation were considered. We studied temporal behavior in a constant-pressure, adiabatic, spatially uniform situation: volume changed with time. A second unsteady configuration was also studied wherein the fresh premixed combustible gas was continuously introduced into a high-temperature environment with available chemical radicals. An ideal, continuous, stirred reactor achieves perfect mixing of reactants and products inside the control volume. The continuous stirred reactor (CSR) case was chosen to test the accuracy of the kinetic model when solving a combusting-flow process with a residence time. Under the infinite mixing rate assumption, the outflow temperature and concentrations are taken to be identical to those inside the control volume. On exiting the volume after a finite residence time, the mixture is assumed to cease reacting; combustion need not be complete and chemical equilibrium need not exist in the exit flow. Both inflow properties and initial properties within the volume are prescribed, and then properties within the volume (and equivalently in the exit flow) are determined as functions of time. The mass inflow rate is held constant throughout the operation. The implication of a constant pressure, a constant volume, and a constant mass inflow rate with temporally varying temperature and concentration is that the outflow rate must change with time in a controlled manner. Variable exit area can be used to maintain the desired constant pressure. The constant ratio of the chamber volume to the volumetric inflow rate is called the “residence time,” although differences between inflow density and chamber density and/or unsteadiness cause this ratio to differ somewhat from a true time-dependent travel time.
2. Kinetic models Our computations showed that the MSC4, MSC5, and MP5 kinetic models did not support the ignition delay characteristics. This was not surprising as the
259
models were designed to describe established flame structures after the ignition delay period. Hence, these mechanisms had to be modified by the addition of Reaction 96, an initiation reaction. So, we created modified mechanisms MMSC96 4, MMSC96 5, and MMP96 5 (see Appendix A). The rate of Reaction 96 was high prior to ignition and approximately zero after ignition; therefore, it is very important to model ignition delay characteristics. However, the modified five-step mechanism (MMP5) still did not support the ignition delay characteristics, even though it was sufficient to describe premixed flames. MMP5 predicted negative values for the mass fraction of the hydrogen molecule. Further, the mechanism did not predict the correct characteristic temporal curves for all of the major species. It was concluded that MMP5 was not robust enough to predict ignition delay. Furthermore, MMSC96 5 overestimated the final adiabatic temperature (calculated following Ref. [9]) by almost 600 K. Because of the absence of a backward reaction for Reaction 17, CO2 , CO, and O2 were not at equilibrium after complete combustion. Hence, it overestimated the final concentration of CO2 and underestimated the final O2 and CO concentrations. So, MMSC96 5 was further modified by the addition of a backward reaction for Reaction 17. See Appendix A; Reactions 1 and 18 [1] produce the equilibrium balance for CO2 , CO, and O2 . In our calculations, CH2 O did not reach steady state, and, hence, MMSC96 4, which assumes steady state for CH2 O, should not be used. MMP5 implicitly contains a backward reaction for Reaction 17 (Appendix A). As this model also includes the steady-state balance for the intermediate species CH, CH2 , and CH3 , combinations of a few reactions (Reactions 1, 2, 19, and 20 from Ref. [1]) provide the backward reaction for Reaction 17. However, due to the problems mentioned earlier, the model was still not robust enough to predict spontaneous ignition characteristics. MMSC5, MMSC4, and MMP5 predict the same final adiabatic temperature when the above-mentioned modifications are made.
3. Governing equations and numerical method The independent variables considered are the major species mass fractions and the temperature of the system. A system of quasi-linear ordinary differential equations is developed to govern the mass fractions of the eight major species CH3 OH, O2 , H2 O, CO2 , CO, H2 , H, and CH2 O, and temperature T . The intermediate species were assumed to be at steady state, and simple algebraic equations were developed. For both spontaneous ignition and CSR computations, constant pressure and perfect gases were con-
260
S. Yalamanchili et al. / Combustion and Flame 142 (2005) 258–265
sidered. Also, for the CSR calculations, continuous flow was considered. All elementary reactions involved are assumed to be first order in terms of the reactants (products) for forward (backward) reactions. Hence, the rate of production of species i due to a reaction between species j and k is Yj Yk 2 n Ej k Rj k = Aj k (1) . ρ T j k exp − Wj Wk RT Wj and Wk are molecular weights, and Yj and Yk are mass fractions. 3.1. Spontaneous ignition 3.1.1. Species mass balance dYi ρ Rj k . = Wi Ri = Wi dt
(2)
j,k
3.1.2. Energy balance dT Wi Hi Ri ≡ Q. ρCp = dt
(3)
i
3.2. Continuous stirred reactor 3.2.1. Total mass balance d(ρV ) ˙ out . = ρinlet f0 − m dt
ρ f dYi = inlet 0 (Yi−inlet − Yi ) + Ri . dt V
5. Comparison with ignition experiments
(5)
3.2.3. Energy balance ρinlet Cp f0 dT (6) = (Tinlet − T ) + Q. dt V Here, m ˙ out is the outlet mass flow rate; Wj and Wk are molecular weights; Yi , Yj , and Yk are mass fractions; Hi is the heat of formation of species i; f0 is the volumetric inflow rate; and V is the volume of the fluid in the CSR. The integer index i indicates one of the eight major species. The integer indices j and k can indicate major or steady-state species. Of course, only for certain combinations of the integer values will Aij k be nonzero [1,2]. With the use of steady-state approximations for the intermediate species and the conservation of C, H, and O atoms, each overall species reaction rate Ri can be expressed, following standard practice [1,2], as a linear combination of the five basic reduced reaction rates defined in Appendix A. A perfect gas is assumed. The data for specific heats and heats of formation were obtained from Refs. [6–8]. A second-order-accurate finite-difference method was used to solve the coupled equations. ρCp
In the CSR calculations, the results of only the complete combustion cases were validated against the equilibrium code [9], because, in only these cases, the system reached chemical equilibrium. Extreme cases were chosen to be validated. The results matched to a certain order of accuracy. There were still small errors (less than 2.6%) in the final equilibrium concentrations because the kinetic model does not consider the mass of steady-state species for mass balances. Unlike the chemical equilibrium code, they were assumed to be negligible. The resulting OH and O equilibrium concentrations are comparable to the H and H2 equilibrium concentrations. As the steadystate species are not considered in the mass and mole balances for the reduced kinetics, there are some differences between the results of a full equilibrium calculation and the final state of the reduced kinetic calculation. This particular modified five-step kinetic model (MMSC5) is robust and can be used for modeling ignition and flame-spread problems to determine flame propagation and spontaneous ignition characteristics.
(4)
3.2.2. Species mass balance ρ
4. Chemical equilibrium
The ignition delays, which are found experimentally by Bowman [10] for high initial temperatures, can be used to validate the kinetic model. He used argon as the inert gas. As seen in Table 1, the ignition delays predicted by the derived kinetic model MMSC5 matched very well the experimental results. For validation, fuel–oxidizer mixtures were considered in both fuel-rich and lean regions. The experimental correlation [10] relates species concentration, initial temperature, and ignition-delay time: E −0.5 C −0.1 Coxygen τmax = A exp (7) methanol . RT Here, τmax is the ignition delay; Coxygen and Cmethanol are molecular oxygen and methanol concentrations; T is the initial temperature; R is the universal gas constant; and A and E are kinetic constants. The correlation was compared with the calculated ignition delays. From the log plot, the calculated values were found to be A = 3.1E–13 s(mol/cm3 )0.6 and E = 143.83 kJ/mol. The experimental values are A = 2.1E–13 s(mol/cm3 )0.6 and E = 151.5 kJ/mol.
6. Effect of parameters on spontaneous ignition Fig. 1 is a general transient plot of the concentrations of major species (CH3 OH, O2 , H2 O, CO2 , CO,
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261
Table 1 Ignition delays of different cases Case no.
Equivalence ratio
Mole fractions
Initial temp. (K)
XCH3 OH
X O2
Xargon
Ignition delay (µs) Experimental (Bowman [10])
Theoretical
1
0.75
0.02
0.04
0.94
1570 1790 1925
190 45 18
164 36 14
2
0.75
0.01
0.02
0.97
1545 1800 2125
225 40 9
180 47 7
3
1.5
0.01
0.01
0.98
1575 1870 2090
242 34 15
241 22 12
4
0.375
0.01
0.04
0.95
1555 1710 2030
140 36 9
130 49 7
5
3
0.02
0.01
0.97
1555 1860 1975
260 36 20
200 34 20
Fig. 1. Transient plots of the major species and temperature for the reduced MMSC5 mechanism shown between 0.4 and 0.5 s.
H2 , H, and CH2 O) versus temperature. The computations were done for wide parameter ranges to show the robustness of the model. These parameters include initial temperature, initial stoichiometric composition, operating pressure, and equivalence ratio.
Fig. 2 shows that the reaction rates increase with increasing initial temperatures and the ignition delay decreases. In all computations, the initial total mass of the mixture was kept constant. Hence, the mass frac-
262
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Fig. 2. Plots of temperature for Condition 6 in Table 2 at various initial temperatures.
Fig. 3. Plots of temperature at various initial compositions with initial temperature 900 K. Numbers on graph indicate the condition from Table 2. Table 2 Various stoichiometric mixtures studied Condition
YCH3 OH
Y O2
1 2 3 4 5 6
0.06725 0.0807 0.09415 0.1076 0.12105 0.1345
0.1009 0.12108 0.14126 0.16144 0.18162 0.2018
tion of the inert component was different for different initial fuel–oxidizer compositions. Table 2 indicates the six different stoichiometric conditions considered. The amount of inert component varies from case to case here. Even though complete combustion occurred, the temporal characteristics of some of the product species (CO, H2 , and H) were observed to differ between weaker (i.e., more inert mass) and stronger (i.e., less inert mass) stoichiometric compositions and between fuel-rich and fuel-lean mixtures. Fig. 3 shows that the adiabatic temperature is higher and the ignition delay is shorter for stronger stoichio-
metric concentrations of fuel and oxygen. Fig. 4 indicates how the equivalence ratio can affect both the adiabatic temperature and the ignition delay. As the total density of the system increases at higher pressures, the reaction rates of all the elementary reactions involved increase with increasing pressure. Therefore, as the total pressure of the system increases, the ignition delay decreases. The final equilibrium concentrations of the major products, H2 O and CO2 , are very weakly dependent on pressure. 7. Effect of parameters on continuous stirred reactor The computations for the well-stirred reactor were performed until the steady state was attained. Different parameters were considered not only to test the robustness of the reduced kinetic mechanism developed, but also to understand when there exist situations of incomplete combustion after the reactor has reached a steady state. The parameters studied include inlet fuel–oxidizer composition, operating pres-
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263
Fig. 4. Plots of temperature at various equivalence ratios with initial temperature 900 K.
Fig. 5. Transient plots of mass fractions of CH3 OH and H2 O for both complete and incomplete combustion shown between 0.2 and 1 s.
sure of the reactor, initial temperature, and residence time of the reactor. Fig. 5 shows the transient plots for both complete and incomplete combustion cases at steady state. Both cases have the same operating conditions with respect to atmospheric pressure, residence time (1 s), initial and inlet temperatures of the fuel–oxidizer mixture (900 K), and initial stoichiometric mixture (methanol and oxygen mass fractions of 0.135 and 0.202, respectively). The only difference is in the stoichiometric inlet concentrations, with complete combustion having larger concentrations equal to the initial concentrations and incomplete
combustion having one-half the amounts of methanol and oxygen. If, at any time less than the residence time, the difference between influx and efflux equals the total reaction rate for each major species, then steady state has been attained but chemical equilibrium may not have been reached. If complete combustion occurs, the ignition delay decreases for stronger inlet (less inert) stoichiometric concentrations of methanol and oxygen, in complete agreement with the spontaneous ignition solution. However, slight differences would occur in the calculations for ignition delay and final adiabatic tem-
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peratures between the spontaneous ignition problem and CSR, because the species mass balance (Eq. (4)) and energy balance (Eq. (6)) of CSR are exactly the same as for the ignition delay problem (Eqs. (2) and (5), respectively) only when the residence time, V /f0 , tends to infinity. The residence times considered thus far are not large enough. To check the above-mentioned result, a large residence time (15 times greater than the original residence time) was considered. Then, the ignition delays of the CSR and spontaneous ignition problem matched. The reaction rate depends on the initial composition of the fuel– oxidizer mixture. For lower concentrations (more inert) of the stoichiometric mixture, the reaction time for the mixture is long and, hence, can be longer than the residence time of the reactor if the residence time is small. Therefore, in these cases, the steady state is not the equilibrium state. Also, the temporal plots of the species are different from that of complete combustion. The final adiabatic flame temperature, as mentioned previously, is a function of the inlet concentration of the fuel–oxygen mixture. Therefore, the adiabatic temperature increases with stronger inlet concentrations. As a result, a greater percentage of the oxygen is consumed for weaker inlet concentrations, as the dissociation of CO2 to CO is predominant at higher temperatures. Thus, other species are present in scarce concentrations even after complete combustion of fuel. For a residence time of 1 s, only fuel-rich mixtures achieve equilibrium. However, for fuel-lean mixtures, equilibrium does not occur owing to the fact that less fuel is present. Therefore, the chemical reaction time becomes longer than the residence time, and the fuel does not remain in the reactor long enough to react completely. The behavior characteristic of fuel-rich mixtures is the same as that observed for the spontaneous ignition problem. However, there is a slight difference in the oxygen-versus-time profile for the fuelrich case because of the difference in the inlet and initial concentrations of oxygen. An inflection point is observed in the time profile of oxygen. This inflection point corresponds to the time at which the inlet concentration of oxygen equals the reactor concentration. This particular phenomenon is not observed in the fuel-lean case due to incomplete combustion, even though there is a difference between the initial and inlet concentrations of the fuel. A residence time of 1 s was used to analyze the effects of different operating pressures. As was the case for the spontaneous ignition problem, the ignition delay decreased at higher reactor pressures. The ignition delay was shorter than the residence time and exactly the same predicted in the spontaneous ignition problem. For lower operating pressures, the residence time was not sufficiently long. The final adiabatic temper-
ature increased as the total pressure of the reactor increased. As an increase in the pressure results in an increase in the total reaction rate, the amount of final products formed is greater. The initial temperature of the system affects only the ignition delay. Further, the ignition delay increases with decreasing initial temperature. The lower the initial temperature, the longer the time needed to heat the fuel mixture for ignition. These cases cannot be compared with any of the cases in the spontaneous ignition problem because the initial conditions of a spontaneous ignition problem are equivalent to the inlet conditions of the CSR but not to the initial conditions. Unlike the inlet temperature, the initial temperature of the fuel mixture does not affect the eventual reaction rates of the system. Hence, the final concentrations and the final adiabatic temperature remain the same for all cases. The inlet composition and the operating pressure of the reactor affect primarily the eventual reaction rates of the system.
8. Conclusions A modified five-step methanol kinetic model (MMSC5) was developed based on existing models [2]. This new kinetic model supports both spontaneous ignition and CSR combustion. A detailed computational study was made of the effects of different parameters on spontaneous ignition characteristics and CSR combustion. These parametric studies include the effects of temperature, pressure, and fuel– oxidizer composition. In the CSR, a steady state condition could be achieved before complete combustion of fuel. An understanding of this phenomenon will assist in many combustion studies. The final concentrations obtained in the computations were validated by the chemical equilibrium code [9]. The results matched with a good level of accuracy. MMSC5 was generated by addition of Reaction 96 and by addition of the reverse reaction for elementary Reaction 17 (Appendix A). Addition of Reaction 96 permitted the kinetic model to support spontaneous ignition characteristics, and addition of reverse Reaction 17 achieved the expected final chemical equilibrium for CO2 and CO. Thus, we can conclude that step MMSC5 is a robust model that can predict spontaneous ignition [10] and CSR combustion and, hence, can be used effectively for many combustion studies involving methanol kinetic mechanisms.
Acknowledgment A portion of the UCI effort was supported by the NASA Microgravity Program.
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Appendix A. Kinetic model A.1. Reduced five-step mechanism of Mueller et al. CH3 OH + 2H 2H2 + CH2 O, CH2 O CO + H2 ,
(I)
ArT n e−Ea /RT , where i is the equation number and T is the temperature of the system. The subscript f implies a forward reaction and b implies a backward reaction.
(II)
CO + H2 O CO2 + H2 ,
(III)
H + H + M H2 + M,
(IV)
3H2 + O2 2H + 2H2 O.
265
(V)
A.2. Overall reaction rates WI = w86 + w87 + w96 , WII = w29 + w30 + w31 + w32 , WIII = w18 , WIV = w5 + w12 + w15 + w16 + w17 + w21 + w22 + w23 − w32 − w85 , WV = w1 + w6 + w9 − w12 + w13 − w17 . A.3. Elementary reactions added Reaction numbers are identical to those in Refs. [1,2] except for these additions: 17: O2 + M → O + O + M (backward reaction), 96: CH3 OH + O2 → CH2 OH + HO2 . See Refs. [1,2] for rate constants of the elementary reactions. The rate constants are given by Ki =
References [1] C.M. Mueller, N. Peters, in: N. Peters, B. Rogg (Eds.), Reduced Kinetic Mechanisms for Applications in Combustion Systems, Springer-Verlag, New York, 1993, pp. 143–155. [2] C.M. Mueller, K. Seshadri, J.Y. Chen, in: N. Peters, B. Rogg (Eds.), Reduced Kinetic Mechanisms for Applications in Combustion Systems, Springer-Verlag, New York, 1993, pp. 284–307. [3] J.-Y. Chen, Combust. Sci. Technol. 78 (1991) 127. [4] D. Aronowitz, R.J. Santoro, F.L. Dryer, I. Glassman, Proc. Combust. Inst. 17 (1979) 633–644. [5] R.P. Lindstedt, M.P. Meyer, Proc. Combust. Inst. 29 (2002) 1395–1402. [6] N.B. Vargaftik, Tables on the Thermophysical Properties of Liquids and Gases, second ed., Hemisphere, Washington, DC, 1975. [7] Y. Touloukian, Thermophysical Properties of Matter, vol. 11, Plenum, New York, 1970. [8] C.L. Yaws, Physical Properties: A Guide to Physical, Thermodynamic, and Transport Property Data of Industrially Important Chemical Compounds, Chemical Engineering, New York, 1977. [9] W.C. Reynolds, STANJAN Chemical Thermodynamic Equilibrium Code, available at: http://grashof.engr. colostate.edu/tools/equil.html. [10] C.T. Bowman, Combust. Flame 25 (1975) 343–354.