2014 The 4th International Workshop on Computer Science and Engineering
Modeling the Fuel Rich Combustion of Liquid Ethanol and Liquid Oxygen Leonardo Henrique Marin Kist1,a and Luizildo Pitol-Filho1,b 1
Centro Universitário Católica de Santa Catarina, Rua dos Imigrantes 500, 89.254-430 Jaraguá do Sul, Santa Catarina, Brazil. a
[email protected],
[email protected]
Keywords: Combustion, dissociation, ethanol, liquid oxygen.
Abstract. In aerospace engineering, combustion requires optimization, in order to get the maximal advantage of the energy of reagents and products. Adiabatic flame temperature and composition of combustion products may be calculated by a combination of enthalpy and species balances, by considering the combustion and dissociation reactions. The present paper reports the combustion process between the liquid ethanol and liquid oxygen (LOX), in a fuel rich mixture. It considers the calculation of adiabatic flame temperature and dissociation using a simplified method, and finally compare results to those obtained by a complete dissociation model simulated by using a freeware numerical code. For adiabatic flame temperatures, the more significant discrepancies appeared at low oxygen to fuel ratios, where dissociation reactions are more expected to happen. Introduction Combustion is a chemical process where a fuel is oxidized, producing a significant amount of energy [1]. A source of heat ignites such reaction, which involves two reagents: a fuel and an oxidizer. The combustion will generate hot gases at high temperature called products of combustion. In order to model the combustion, it is necessary to determine the maximum temperature the combustion chamber will achieve and the composition of the gases produced by this reaction. In the combustion calculation is widely used the mixture ratio, which can be classified as stoichiometric mixture, fuel rich mixture and oxidizer rich mixture, according to the proportions of the fuel and oxidizer. The stoichiometric mixture has the minimum amount of oxidizer to do the combustion reaction. On the other hand, the fuel rich mixture has excess of fuel, while the oxidizer rich mixture has excess of oxidizer in the mixture. Fuel rich mixtures are used in rocket engines because the average molecular mass of combustion gases is low, what increases the specific impulse of rocket engine [2]. This paper reports the modeling of the combustion where two liquid propellants, namely ethanol and liquid oxygen (LOX), by using a fuel rich mixture and a simplified method to solve the dissociation problem. The results of adiabatic flame temperature and combustion products are then compared to those obtained by using a freeware developed by the National Aeronautics and Space Administration (NASA). Methods This combustion problem considers an ideal situation, where the flow is adiabatic and isentropic. This reaction will operate with a fuel rich mixture, where the more abundant species found in the combustion products are H2O, CO2, CO e H2 [3], according to the following chemical reaction: ݔ ܥଶ ܪହ ܱ ܪ ݔ ܱଶ ՜ ܰுమ ை ܪଶ ܱ ܰைమ ܱܥଶ ܰை ܱܥ ܰுమ ܪଶ
Where xa and xb are the molar fraction of ethanol an LOX respectively, and N refers to the mole numbers (in kmol), of each produced species. However, by considering five dissociation reactions and eight species in gases products, the reaction could be rewritten as ݔ ܥଶ ܪହ ܱ ܪ ݔ ܱଶ ՜ ܰுమ ை ܪଶ ܱ ܰைమ ܱܥଶ ܰை ܱܥ ܰுమ ܪଶ ܰைమ ܱଶ ܰைு ܱ ܪ ܰை ܱ ܰு ܪ 422
Eq. 1 defines reagents enthalpy and Eq. 2 defines products enthalpy. ഥ ൯ ൌ ݔ ൫݄ι ഥ൯ തതതത ݄ത െ ݄ι തതതത ݄ത െ ݄ι ܰ ൫݄ι
ഥ൯ തതതത ݄ത െ ݄ι ܰ ൫݄ι ത ഥ൯ തതതത ൌ ܰு ை ൫݄ι ݄ െ ݄ι మ
మ ுఱ ைு
ைమ
ഥ൯ ഥ൯ തതതത ݄ത െ ݄ι തതതത ݄ത െ ݄ι ܰைమ ൫݄ι ܰை ൫݄ι ைమ ை ത ഥ ത ഥ തതതത തതതത ܰை ൫݄ι ݄ െ ݄ι൯ ܰைு ൫݄ι ݄ െ ݄ι൯
ுమ ை
ഥ൯ തതതത ݄ത െ ݄ι ܰுమ ൫݄ι మ ுమ ത ഥ ഥ൯ തതതത തതതത ܰை ൫݄ι ݄ െ ݄ι൯ ܰு ൫݄ι ݄ത െ ݄ι ை
(1)
ഥ൯ തതതത ݄ത െ ݄ι ݔ ൫݄ι
ு
ைమ
ைு
(2)
Where Nr is the mole number of reagents, Np is the mole number of products, all in kmol. The ഥ are in kJ/kmol. The enthalpy enthalpy ݄ത, enthalpy of formation തതതത ݄ι and standard state enthalpy ݄ι and the specific heat Cp, which is required to calculate the enthalpy, are found in literature [4], [5]. Absolute temperature is used. The carbon, hydrogen and oxygen balances are expressed by the following equations: ݊ ൌ ʹݔ ൌ ܰைమ ܰை
(3)
݊ை ൌ ݔ ʹݔ ൌ ܰுమ ை ʹܰைమ ܰை ʹܰைమ ܰைு ܰை
(5)
(4)
݊ு ൌ ݔ ൌ ʹܰுమ ை ʹܰுమ ܰைு ܰு
The dissociation reactions considered are listed below with their respective equilibrium constants: ଵȀଶ
ܰு ܰை ͳ ܪଶ ܱ ՞ ܪଶ ܱଶ ݇ ଵ ൌ మ మ ʹ ܰுమ ை ܰை ܰைమ ͳ ܱܥଶ ՞ ܱܥ ܱଶ ݇ ଶ ൌ ܰைమ ʹ
ଵȀଶ
ܰைு ܰுమ ͳ ܪଶ ܱ ՞ ܱ ܪ ܪଶ ݇ ଷ ൌ ܰுమ ை ʹ ܱଶ ՞ ʹܱ ݇ ସ ൌ
ቌ
ଶ
ቌ
ܰு ܪଶ ՞ ʹ݇ ܪହ ൌ ൬ ൰ൌ ݁ ܰுమ ܰ௧
൬ ൰ ܰ௧
ଵȀଶ
൬ ൰ ܰ௧
ଵȀଶ
ൌ ݁
ଵȀଶ
൬ ൰ ܰ௧
ൌ݁
ቌ
ቌ
ൌ݁
כሺ்ሻ൯ ି൫ כሺ்ሻ൯ כሺ்ሻ൯ ା൫ തതതതതതതത തതതതതതതത തതതതതതതത ቃ ିቂ൫ ಹమ ೀమ ಹమೀ
ோᇲ ்
כሺ்ሻ൯ ି൫ כሺ்ሻ൯ כሺ்ሻ൯ ା൫ തതതതതതതത തതതതതതതത തതതതതതതത ቃ ିቂ൫ ೀ ೀమ ೀమ
ቌ
ோᇲ ்
כሺ்ሻ൯ ି൫ כሺ்ሻ൯ ቃ തതതതതതതത തതതതതതതത ିቂ൫ ಹ ಹమ
ோᇲ ்
ቍ
(6)
ቍ
(7)
כሺ்ሻ൯ ି൫ כሺ்ሻ൯ כሺ்ሻ൯ തതതതതതതത തതതതതതതത തതതതതതതത ା൫ ቃ ିቂ൫ ೀಹ ಹమ ಹమೀ
ோᇲ ்
כሺ்ሻ൯ ቃ כሺ்ሻ൯ ି൫ തതതതതതതത തതതതതതതത ିቂ൫ ೀ ೀమ ቍ ோᇲ ்
ଶ
ܰை ൬ ൰ൌ ݁ ܰைమ ܰ௧
ଵȀଶ
ቍ
ቍ
(8)
(9)
(10)
Besides, the total moles produced Nt are described by Eq. 11: ܰ௧ ൌ ܰ ܱ ʹܪ ܰ ʹܱܥ ܰ ܱܥ ܰ ʹܪ ܱܰʹ ܱܰ ܪ ܱܰ ܰܪ
(11)
Where Nt is the total of moles numbers in the products of combustion, Y is the stoichiometric כሺܶሻ is the Gibbs function of some component and is defined തതതതതതതത coefficient of dissociation reaction, ݃ by [1]. In this case, the dissociated species are calculated by component balance equations. The complete model, involving all the above species, was solved by the freeware CEA 300 [6], designed to calculate complex chemical reactions. Because of the high number of species involved, a simplified approach may be used, where just the most abundant species are considered [7]: H2O, 423
CO2, CO, H2 and OH, by involving a water-gas equilibrium reaction. Eq. 12 defines the water-gas reaction and the equilibrium constant [7]: ܱܥଶ ܪଶ ՞ ܪଶ ܱ ݇ ܱܥൌ
ܰுଶை ܰை ݇ଶ ൌ ܰுଶ ܰைଶ ݇ଵ
(12)
To solve this problem, an initial temperature has to be set. The initial temperature considered is 3100K, an intermediate value between 200K and 6000K, which are the temperature limits for the coefficients proposed by reference [5]. Then, the next step requires the determination of the dissociation constants. To obtain the moles of species values, it is necessary to estimate the value of NCO2 until the pressure converges to the desired value. After that, the products enthalpy and reagents enthalpy are calculated. If the product enthalpy is different to the reagents enthalpy, another initial temperature needs to be set, and the whole procedure is repeated. Results between the simplified dissociation model and the complete model were then compared. Results The simulations considered mixture ratio O/F (oxidizer/fuel) between 1,894 and 1,191 (10% and 75% of fuel rich, respectively). The pressure of combustion chamber considered is 15atm (about 220psia), a reasonable pressure, according to the literature [8]. The initial propellants temperature is 298,15K. All thermodynamic properties like formation enthalpy, the enthalpy of standard state and molecular weight are in reference [5]. Fig. 1 compares the adiabatic flame temperature of the simplified model to the values obtained by using the CEA300. The most significant deviations between the two curves presented in Fig. 1 occur at low O/F mixture ratio, as expected, since in those concentrations more dissociation reactions are expected to happen, owing to the low amount of oxygen available. The adiabatic temperatures obtained by CEA 300 simulations are higher than those obtained by the simplified model, probably owing to the fact that the enthalpies of dissociation reactions are also considered. At mixture ratios between 1.6 and 1.7, however, both temperatures almost match, with a variation around 50K.
Fig. 1. The adiabatic flame temperature varying with the mixture ratio. Fig. 2 and Fig. 3 present the composition of combustion products, according to the mixture ratio. Results for the simplified model are shown in Fig. 2 and the results from CEA300 program are shown in Fig. 3.
424
Fig. 2. Products of combustion (simplified model) The comparison between Fig. 2 and Fig. 3 provides relevant information about the combustion processes.
Fig. 3. Products of combustion (CEA300). By comparing Fig. 2 and Fig. 3, it is possible to conclude, that, according to the simplified model, for O/F ratio higher than 1.7, the molar fraction of CO2 becomes higher than the CO molar fraction. However, the complete model just expects such situation to happen at mixture ratios higher than 1.9, probably because of the contribution of the dissociation reactions. The ratio of H2O to CO2 is, according to the simplified model, around 2, at the highest mixture ratio. Such result agrees with literature [9], for combustion of ethanol using air as oxidant. Finally, the behavior of the O2 curve helps to conclude that the O2 dissociation equations cannot be neglected, because the CEA 300 simulations provide lower results than those obtained by the simplified model, where the dissociated species molar fraction are calculated by a mere component balance rather than by specific dissociation reactions. Conclusions In order to model the combustion processes, fuel rich mixtures of ethanol and liquid oxygen were studied, by calculating the adiabatic flame temperature and combustion products by a simplified approach and by a complete dissociation model. The simplification method presented is a good approximation for adiabatic flame temperatures, especially for O/F mixture ratios between 1.6 and 1.7. In the simplified model, the ratio of H2O to CO2 is around 2 at the highest mixture ratio. There are no significant discrepancies for the prediction of molar fractions of major species, such as 425
carbon dioxide (CO2) and carbon monoxide (CO) by using the proposed models. Besides, in the simplified model the water/carbon dioxide ratio in the products agrees with literature data for similar experiments. On the other hand, the prediction of some dissociation products requires a more complete model, such as the CEA300 program, rather than component balances. References [1] M.A. Boles and Y.A. Çengel: Termodinâmica (McGraw-Hill, São Paulo, Brazil 2006). [2] O. Biblarz and G.P. Sutton: Rocket propulsion elements (John Wiley & Sons, Canada 2000). [3] J.P. Purdue: Combustion (Purdue University, USA, 2013). . Acessed on July 16th. 2014
Available
in:
[4] S. Gordon, B.J. McBride and M.A. Reno: Coefficients for calculating thermodynamic and transport properties of individual species (NASA Lewis Research Center, USA 1993). [5] S. Gordon, B.J. McBride and M. J, Zehe: Coefficients for calculating thermodynamic properties of individual species (NASA Glenn Research Center, USA, 2002). [6] S. Gordon and B.J. McBride: NASA Chemical Equilibrium Analysis Code (CEA) (NASA Glenn Research Center, USA 1971) Available in: < http://www.engr.colostate.edu/~marchese/combustion08/cec.html>. Acessed on July 16th. 2014. [7] M. Barrère, A. Jaumotte, B.F. de Veubeke and J.:Rocket propulsion (Elsevier, Amsterdam, Netherlands 1960). [8] S.W. Hart: Combustion performance and heat transfer characterization of LOX/Hydrocarbon type propellants (Aerojet Liquid Rocket Co., USA 1982). [9] P. Saxena and F.A. Williams: Proceedings of the Combustion Institute, Vol. 31 (2007) p.1149.
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