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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 2 4 0 4 3 e2 4 0 5 3
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Analysis of exergy losses in laminar premixed flames of methane/hydrogen blends Yusen Liu, Jiabo Zhang, Dehao Ju, Zhen Huang, Dong Han* Key Laboratory for Power Machinery and Engineering, Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China
highlights Exergy losses in laminar premixed flames of CH4/H2 blends were studied. Minimum exergy loss occurred at the equivalence ratio of 0.9 for different blends. Exergy losses from chemical reactions and heat conduction were dominant among all the sources. Total exergy loss declines as the H2 percentage or initial pressure rises.
article info
abstract
Article history:
Combustion is the primary source for exergy loss in power systems such as combustion
Received 23 May 2019
engines. To elucidate the exergy loss behaviors in combustion and explore the principle for
Received in revised form
efficiency improvement, the second-law thermodynamic analysis was conducted to
13 July 2019
analyze the energy conversion characteristics in laminar premixed flames of methane/
Accepted 16 July 2019
hydrogen binary fuels. The sources causing exergy losses in laminar premixed flames
Available online 7 August 2019
included five parts, namely heat conduction, mass diffusion, viscous dissipation, chemical reactions and incomplete combustion, respectively. The calculations were conducted at
Keywords:
both atmospheric and elevated pressures, with the equivalence ratio varying from 0.6 to 1.5
Exergy loss
and the hydrogen blending ratio increasing from 0% to 70%. The results indicated that the
Laminar premixed flame
total exergy loss firstly increased and then decreased with increased equivalence ratio, and
Methane
reached the minimum value at the equivalence ratio of 0.9. This was primarily due to the
Hydrogen
trade-off relation between the decreased exergy loss from entropy generation and the
Chemical kinetics
increased exergy loss from incomplete combustion, as equivalence ratio increased. As the hydrogen blending ratio increased from 0% to 70%, the total exergy loss decreased by 2%. Specifically, the exergy loss from heat conduction decreased, primarily due to the decreased flame thickness. Moreover, the reactions with H2, H and H2O as reactants were inhibited, leading to decreased the exergy loss from chemical reactions. As pressure increased from 1 atm to 5 atm, the total exergy loss decreased by 1%, because the exergy losses induced by heat conduction and chemical reactions decreased as the flame thickness was reduced. The exergy loss from incomplete combustion also decreased, because elevated pressure inhibited dissociations and decreased the mole fractions of incomplete combustion products. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. Mechanical Engineering, 800 Dongchuan Road, Shanghai Jiao Tong University, Shanghai 200240, China. E-mail address: [email protected] (D. Han). https://doi.org/10.1016/j.ijhydene.2019.07.123 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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Introduction Natural gas (NG) is considered as a potential alternative fuel for road and marine transportation, due to its abundant reserve and low particulate matter (PM) pollutants and carbon dioxide (CO2) emissions in combustion. The usage of NG in internal combustion (IC) engines as a replacement of the petroleum-based fuels has therefore been widely studied [1,2], especially in the compression ignition (CI) engines with dualfuel injection systems [3e5] or the spark ignition (SI) engines with high compression ratios [6e8]. Also, complex injection systems are not necessary for NG SI engines to prepare homogenous fuel and air charge. However, NG SI engines face several application challenges, especially at lean burn conditions, e.g. high combustion instability due to the lower flame propagation speeds and high misfire or partial burn probability due to the narrow flammability limits [9]. Partial supplement of NG with hydrogen (H2) was believed to be a solution to the aforementioned problems in NG SI combustion engines [10]. Fundamental studies have shown that H2 addition could generate more active radicals [11], increase combustion rate [12], enhance flame stability [13] and extend the lean ignition limit [14]. In engine experiments, it was also found that H2 addition to NG reduces flame initiation, burn duration and cycle variability [15], but elevates knock propensity due to the higher ignition tendency and higher cylinder temperature [16]. The elevated cylinder temperature also increases engine-out NOx emissions [17]. On the effects of H2 addition on the thermal efficiency of NG engines based on the first law of thermodynamics, there has not reached a consensus and it seemed to be dependent on the H2 substitution percentage. This is because two competing effects related to H2 addition, i.e. higher extent of constant-volume combustion and increased heat transfer, simultaneously affect engine efficiency [10]. Compared with the first law of thermodynamics, which is focus on energy quantity balance, the second law of thermodynamics pays more attention to the energy quality change. Based on the second law of thermodynamics, researchers found that engine exergy efficiency showed an increase with H2 addition to the NG. Ozcan [18] used a zero-dimensional two-zone model to study the effects of H2 addition on methane combustion irreversibility, and he indicated that the irreversibility was reduced with increased H2 addition and this reduction became more apparent at lean conditions. Rakopoulos and Kyritsis [19] and Rakopoulos et al. [20] attributed the reduction in combustion irreversibility to the interaction between CH4 and H2 molecules, but they also pointed out that the exergy carried by exhaust gases increased with increased H2 addition. Although there were already some studies aiming to figure out the exergy loss characteristics in premixed CH4/H2 flames, however, they were mainly parametric studies, whereas the exergy loss mechanism at different engine-like conditions has not been well understood [21,22]. Therefore, in this study, thermochemical and chemical kinetic analysis were employed to analyze the energy conversion processes in the premixed flames of methane and hydrogen blends at changed
conditions. Further, contributions from different sources, i.e. chemical reactions, heat conduction, mass diffusion, viscous dissipation and incomplete combustion to the total exergy losses in the context of changed H2 percentage were identified, and the interaction regime between CH4 and H2 molecules on these exergy losses sources were elucidated.
Methodology Model and algorithm The exergy losses in laminar premixed flames of CH4/H2 binary fuels are numerically analyzed in this study. The effects of equivalence ratios, H2 addition and pressure change on exergy loss are analyzed. Specifically, the equivalence ratio varies from 0.6 to 1.5, and the H2 volume fraction in fuel blends, which is termed as H2 blending ratio in the following, changes from 0% to 70%. The initial pressures are set as 1 atm and 5 atm, respectively. In all calculations, the initial temperature of the unburned mixture is set as 300 K and the ambient environment temperature is held as 298 K. Moreover, the flames are steady one-dimensional laminar ones and the heat transfer due to radiation is neglected. The calculation method used to characterize the energy conversion in the fundamental fuel combustion processes has been recently proposed by the authors, and has been used for the second-law thermodynamic analysis in the n-heptane auto-ignition [23] and hydrogen flame propagation with diluents [24]. Two categories of sources causing exergy losses are considered during the combustion processes. The first category represents the exergy loss induced by entropy generation, while the second category refers to the exergy loss induced by incomplete combustion. As the methodology details for the exergy loss calculation from each source could be found in the authors’ previous research [25], only some key equations are introduced as follows. The laminar premixed flame model in CHEMKIN Pro software [26] is a one-dimensional model, and the term of entropy generation can be expressed as Eq. (1), ‾
sgen ¼
Xi rui Yi lVT,VT t : Vu mi ,u_ ı þ R i¼1 ,VXi þ T2 T Xi T
(1)
Where R is universal gas constant, T is the local tem‾ perature, t is the local friction stress tensor，and l, r and u are the mean thermal conductivity, density and mixture velocity, respectively. Also, ui , Xi , Yi , mi and u_ ı represent the diffusion velocity, mole fraction, mass fraction, chemical potentials and the mass production rate of the ith species, respectively. The entropy generation rate (sgen ) caused by heat conduction, mass diffusion, viscous dissipation and chemical reactions can be further calculated by Eqs. (2)e(5). 2 1 dT sgen conduction ¼ l 2 T dx
(2)
2 4 m du sgen dissipation ¼ 3 T dx
(3)
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i X rRgi ui Yi dXi sgen diffusion ¼ Xi dx i¼1
(4)
i X mi u_ i sgen reaction ¼ T i¼1
(5)
where m is the viscosity coefficient, Rgi is the specific gas constant of the ith species,. As such, the exergy loss from the entropy generation can be calculated based on the Gouy-Stodla equation [27], Z Igen ¼ T0
Sgen dx
(6)
where Igen is the exergy loss by entropy generation and T0 is the environment temperature of 298 K. On the other hand, the exergy loss is also caused by incomplete combustion, which means that some combustion products other than water, carbon dioxide and nitrogen exist in the flame downstream. Although the chemical exergy contained in these products are not destroyed, however, it is hard to further utilize and is thus considered as another source causing exergy loss [28], which can be estimated by Eq. (7), Iin ¼
X X Gincom Gcom
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mechanisms for methane combustion, namely GRI 3.0 Mech [31], San Diego Mech [32], Konnov 0.5 Mech [33] and USC II Mech [34]. The application conditions of the four mechanisms are distinct. Specifically, GRI 3.0 Mech and San Diego Mech are concerned about high temperature combustion of methane, USC II Mech is a hybrid model for H2/CO/C1-C4 combustion and Konnov 0.5 Mech is developed for the combustion of small hydrocarbons. Further, the GRI 3.0 Mech has been validated against the combustion behaviors of methane/hydrogen mixtures [35]. Therefore, the GRI 3.0 Mech was tentatively used in this study, and its calculation results in flame speeds was compared with the those by San Diego Mech and experimental measurements. As shown in Fig. 1, the GRI 3.0 Mech agrees with the measured flame speeds of the CH4/H2 binary fuels more satisfactorily than the San Diego Mech. Additionally, to study the mechanism effects on the of exergy loss computation, the exergy loss rate caused by each individual source, calculated by the two mechanisms, were compared for 100%CH4 and 50%CH4-50%H2 at atmospheric pressure. As shown in Fig. 2, the loss contributions calculated by different mechanisms were highly consistent. Therefore, the GRI 3.0 Mech is selected for the following calculation and kinetics analysis.
(7)
where Iin is the exergy loss caused by incomplete combustion, and Gincom and Gcom mean the Gibbs free energy values of the complete and incomplete combustion products, respectively. Therefore, the total exergy loss can be expressed as Eq. (8), I% ¼
Igen þ Iin 100% Efuel
(8)
where I% is the total exergy loss percentage and Efuel is the initial chemical exergy carried by the unburned mixture, which can be calculated by Eq. 9 Efuel ¼ rfuel $SL $efuel
(9)
where rfuel is fuel density, SL is laminar premixed flame speed and efuel is the chemical exergy carried by per unit mass of the unburned mixture. Considering that the absolute chemical exergy in different mixtures varies with fuel composition, here the initial chemical exergy is normalized to unity in each flame. In this way, the relative contributions of different sources to the total exergy losses can be directly compared for different CH4/H2 flames. Moreover, according to the authors’ previous work [29], the exergy loss from viscous dissipation is so trivial that it is neglected in this study.
Chemical mechanism selection Thermodynamic parameters in flame propagation process, such as temperature, pressure, species mole fractions and reaction rates are needed for exergy calculation. It is therefore essential to select an optimized mechanism to generate these thermodynamic data. As pointed out by Konnov [30], there are four widely used chemical
Fig. 1 e Comparisons between calculated and experimental flame speeds: (a) P ¼ 1 atm: - Vagelopoulos et al. [36] and C Park et al. [37] for 100%CH4; :Halter et al. [38] for 90%CH410%H2; ; Hermanns et al. [39] and A Halter et al. [38] for 80% Donohoe et al. [40] for 50%CH4-50%H2. (b) CH4-20%H2; P ¼ 5 atm: C Rozenchan et al. [41] and - Kobayashi et al. [42] for 100%CH4; ; Halter et al. [38] for 80%CH4-20%H2.
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Fig. 2 e Exergy loss rate from each source in the laminar premixed flames of CH4 and a CH4/H2 blend.
Results and discussion Overview of exergy loss from different sources Based on the method above, the normalized entropy generation rates can be computed，and the CH4 flame at the atmospheric pressure and the stoichiometric condition is used as an example. The normalized entropy generation rates from heat conduction, mass diffusion and chemical reactions in the flame, as well as the temperature profile, are illustrated in Fig. 3. It is shown that the peak of normalized entropy generation rates from heat conduction occurs at the upstream of the flame, and the peaks of normalized entropy generation rates from mass diffusion and chemical reaction occur at the downstream. Moreover, the peak of normalized entropy generation rates from chemical reactions are much higher than the those from other sources, indicating that chemical reaction is the dominant source in entropy generation. According to Eq. (2), the entropy generation rate from heat conduction is determined by the temperature and temperature gradient. At the flame upstream, the higher temperature
gradient overcomes the effects of lower temperature, resulting in the peak of exergy loss rate from heat conduction. The exergy loss from mass diffusion, based on Eq. (4), is mainly influenced by the mole fraction gradient [43]. To explain the entropy generation rate from mass diffusion in detail, the exergy loss rates of the top eight species, which contribute most to the exergy loss, are listed in Table 1. The exergy loss rates are calculated by dividing the exergy losses from the mass diffusion of these species by the chemical exergy contained in the fuel. Moreover, their mole fraction distributions in the flame are plotted in Fig. 4, calculated by CHEMKIN Pro software. These species include reactants (CH4, H2 and O2), products (CO, CO2 and H2O) and active radicals (OH and H). It is observed that O2, CH4 and H2O contribute more than the other species to the exergy loss from mass diffusion, as they are the main reactants or products. On the contrary, the contribution rates of OH, H2, CO, CO2 and H to exergy loss from mass diffusion are secondary. At the flame downstream, the mole fractions of products, such as CO and CO2 increase suddenly, thus producing the peak of exergy loss rate from mass diffusion. In addition, the sudden increase of products also means that main reactions occur at the flame downstream, and according to Eq. (5), the entropy generation rates from chemical reactions are influenced by species production rates. As a result, the peak of the entropy generation rate from chemical reactions occurs at the downstream. Further, the total exergy losses of CH4/H2 binary fuels are studied under a wide range of equivalence ratios and H2 blending ratios at both atmospheric and elevated pressures as shown in Fig. 5, with the initial temperature set as 300 K and the ambient temperature held as 298 K. The equivalence ratio varies from 0.6 to 1.5 and the H2 equivalence ratio increases
Table 1 e Primary species for the exergy loss from mass diffusion in the laminar premixed flame of CH4: P ¼ 1 atm, F ¼ 1.0. Fig. 3 e Normalized entropy generation rates and temperature profile in the laminar premixed flame of CH4: P ¼ 1 atm, F ¼ 1.0.
Species Exergy Loss Rate Species Exergy Loss Rate
CH4 0.50% CO2 0.14%
O2 0.44% CO 0.11%
H2O 0.38% H2 0.10%
H 0.30% OH 0.09%
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Fig. 4 e Mole fraction distributions of H2, H, O2, OH, H2O, CH4, CO and CO2 in the laminar premixed flame of CH4: P ¼ 1 atm, F ¼ 1.0. from 0% to 70%. It is observed that the total exergy loss firstly decreases and then increases as the equivalence ratio increases. Meanwhile, the minimum total exergy loss generally is located at the equivalence ratio of 0.9 at both atmospheric and elevated pressures. As pressure increases from 1 atm (Fig. 5a) to 5 atm (Fig. 5b), the minimum exergy loss decreases by about 1%. On the other hand, the total exergy loss decreases with H2 addition. To explain the phenomenon, in the following study, the effects of equivalence ratios, H2 addition and pressure change on exergy losses in the flames of CH4 and CH4/H2 blends are analyzed.
Effects of equivalence ratios To study the effects of equivalence ratio, the exergy loss in laminar premixed flames of two fuels, namely 100%CH4 and 50%CH4-50%H2, are analyzed at both atmospheric and elevated pressures. The exergy loss rates from different sources are shown in Fig. 6. It is observed that in all the flames, as the equivalence ratio increases, the exergy losses from heat conduction and chemical reactions decrease, while the exergy loss from incomplete combustion increases. The change in the exergy loss from mass diffusion is slight.
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When the equivalence ratio varies increases from 0.6 to 0.9, the total exergy loss decreases, mainly because of the decreased exergy loss from heat conduction. Based on Eq. (6), the exergy loss is a function of the entropy generation rate and the flame thickness. In addition, the entropy generation rate from heat conduction is dominated by the temperature and temperature gradient, according to Eq. (2). Therefore, the profiles of temperature gradient and normalized entropy generation rate from heat conduction in CH4 laminar premixed flames at atmospheric pressure are plotted in Fig. 7, with the equivalence ratios set as 0.6 and 0.9, respectively. It is observed that the peak of the temperature gradient at F ¼ 0.9 is 3 times as high as that at F ¼ 0.6. In addition, the calculated adiabatic temperatures at equivalence ratios of 0.6 and 0.9 are 1670 K and 2140 K, respectively. As a result, the peak entropy generation rate from heat conduction is increased to about 2 times with increased equivalence ratio. On the other hand, the effects of equivalence ratios on the flame thickness are analyzed based on Eq. (10), d¼
Tad Tin ðdT=dxÞmax
(10)
where d, Tad and Tin represent the flame thickness, the adiabatic flame temperature and the initial temperature, respectively. As the initial temperatures of all flames are the same, according to Eq. (10), the flame thickness is mainly influenced by the adiabatic temperature and the maximum temperature gradient. As mentioned above, with increased equivalence ratio, the adiabatic temperature increases by 470 K, and the maximum temperature gradient is promoted to 3 times as high. Therefore, the flame thickness is reduced to one third, as shown in Fig. 7. The significant reduction in flame thickness overcomes the effect of increased entropy generation, as equivalence ratio increases. The exergy loss from heat conduction is as such reduced based on Eq. (6). Moreover, at fuellean conditions, the fuel and oxidants could react more completely, and thus the effects of chemical reactions and incomplete combustion are less dominant. As the equivalence ratio further increases from 0.9 to 1.5, the increase in the total exergy loss is dominated by the increased exergy loss from incomplete combustion. This is because with increased equivalence ratio, fuel-rich mixtures
Fig. 5 e Total exergy losses in the laminar premixed flames of CH4/H2 blends at different equivalence ratios: (a) P ¼ 1 atm, (b) P ¼ 5 atm.
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Fig. 6 e Exergy loss rate from each source in the laminar premixed flames of CH4 and a CH4/H2 blend with changed equivalence ratios. (a) P ¼ 1 atm, 100%CH4; (b) P ¼ 5 atm, 100%CH4; (c) P ¼ 1 atm, 50%CH4-50%H2; (d) P ¼ 5 atm, 50%CH4-50% H2.
Fig. 7 e Temperature gradient and normalized entropy generation rate from heat conduction in CH4 laminar premixed flames at atmospheric pressure, (a) F ¼ 0.6, (b) F ¼ 0.9.
inhibit fuel completed combustion, leading to the increased exergy loss from incomplete combustion. Therefore, the minimum total exergy loss occurs at the equivalence ratio of 0.9, and in the following study, this optimal equivalence ratio is selected to analyze the effects of H2 addition and pressure change.
Effects of H2 addition To study the effects of H2 addition, the exergy loss rates in different CH4/H2 blends are illustrated in Fig. 8. It is shown that with the fraction of H2 increasing from 0% to 70%, the total exergy loss continuously decreases. Specifically, with increased H2 mole fraction, the exergy loss rates from heat
conduction and chemical reaction decrease, while that from incomplete combustion increases. Compared with the other sources, the change of the exergy loss from mass diffusion can be neglected. Moreover, the effects of H2 addition on exergy loss from each source are similar at both atmospheric and elevated pressures. To explain this phenomenon, the exergy losses from heat conduction, chemical reactions and incomplete combustion in the laminar premixed flames of CH4 and the 50%CH4-50%H2 blend at the atmospheric pressure are compared. To study the exergy loss from heat conduction, the profiles of the temperature gradients and the normalized entropy generation rates in the two flames are plotted in Fig. 9. In addition, the adiabatic temperatures of the two flames are
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Fig. 8 e Exergy loss rate from each source in the laminar premixed flames of CH4 and different CH4/H2 blends: F ¼ 0.9, (a) P ¼ 1 atm, (b) P ¼ 5 atm.
Fig. 9 e Temperature gradient and normalized entropy generation rate from heat conduction in the laminar premixed flames of CH4 and a CH4/H2 blend: P ¼ 1 atm, F ¼ 0.9. approximate, which are 2139 K and 2173 K, respectively. Therefore, according to Eqs. 2 and 10, the temperature gradients of the two flames are the primary factors that influence the entropy generation rates and flame thicknesses. Specifically, the maximum temperature gradient in the 50%CH4-50% H2 flame is about 1.3 times as high as that in the 100%CH4 flames, leading to that the peak entropy generation rate
Table 2 e Primary reactions causing the exergy loss from chemical reactions in the laminar premixed flames of CH4 and a CH4/H2 blend. blends: F ¼ 0.9, P ¼ 1 atm. Reactions
Fuels 100%CH4 50%CH4e50%H2
R1: O þ CH3¼H þ H2þCO R2: O þ CH3¼H þ CH2O R3: H þ CH2O¼HCO þ H2 R4: OH þ CH4¼CH3þH2O R5: HCO þ O2¼HO2þCO R6: OH þ CH2O¼HCO þ H2O R7: H þ O2¼O þ OH R8: CH2þO2 ¼ 2H þ CO2 R9: H þ HO2 ¼ 2OH R10: CH2þO2¼OH þ H þ CO R11: H þ CH3(þM) ¼ CH4(þM) Exergy loss due to reactions above Exergy loss due to all reactions
2.38% 1.99% 0.78% 0.72% 0.68% 0.65% 0.63% 0.59% 0.52% 0.48% 0.42% 9.83% 16.03%
2.12% 1.85% 0.68% 0.68% 0.65% 0.46% 0.57% 0.39% 0.79% 0.31% 0.79% 9.28% 15.14%
increases to 1.2 times but the flame thickness is reduced to two thirds. Therefore, according to Eq. (6), the exergy loss from heat conduction is reduced with H2 addition. To study the effects of H2 addition on the exergy loss from chemical reaction, the top reactions causing exergy loss are listed in Table 2, which contribute most to the exergy loss in different flames. These reactions contribute about 60% to the exergy loss among all the reactions, and the analysis of these reactions may help understand the exergy loss from chemical reactions. According to the reaction path analysis, these reactions contain the H-abstraction reactions from CH4 to CH3 (R4 and R11), chain propagation reactions from CH3 to CH2O (R2), H-abstraction reactions from CH2O to HCO (R3 and R6), CO generation reactions (R1, R5, and R10) and CO2 generation reactions (R8). Additionally, some H2-O2 system reactions (R7 and R9) to generate active radicals are also important among the reactions causing exergy loss. Table 3 e Mole fractions of the primary incomplete combustion products in laminar premixed flames of CH4 and a CH4/H2 blend: P ¼ 1 atm, F ¼ 0.9. Fuels
100%CH4 50%CH4-50%H2
Species OH
CO
H2
O
H
2.8E-03 3.5E-03
2.3E-03 2.3E-03
9.3E-04 1.4E-03
2.6E-04 3.2E-04
1.2E-04 1.8E-04
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Fig. 10 e Exergy loss rates from each source in the laminar premixed flames of CH4 and a CH4/H2 blend: F ¼ 0.9, P ¼ 1 atm/ 5 atm.
Fig. 11 e Temperature gradient and normalized entropy generation rate from heat conduction in laminar premixed flames of the 50%CH4-50%H2 blend: F ¼ 0.9, (a) P ¼ 1 atm; (b) P ¼ 5 atm. With H2 addition, the mole fractions of H2 and H increase and the reactions involving these two species are dramatically influenced. The reactions such as R1, R2, R3, R8 and R10, in which H and H2 are products, are slowed sown, leading to their decreased contributions to exergy loss. On the contrary, the reactions in which H and H2 are reactants, such as R9 and R11, are accelerated and lead to the increased exergy loss. In addition, the mole fraction of H2O also increases with H2 addition. Therefore, the reactions R4 and R6, in which H2O is a product, are slowed down and contribute less to exergy loss. As a result, the exergy loss from chemical reaction is reduced with H2 addition. According to the combustion products analysis, the mole fractions of the dominant species in the incomplete combustion products at the equilibrium state at the atmospheric pressure are listed in Table 3. It is found that OH is the primary one, followed by CO, H2, O and H. With H2 addition, the mole fractions of H2 and active radicals, such as OH, O and H, increase at the equilibrium state. Therefore, the H2 addition leads to increased exergy loss from incomplete combustion.
Effects of pressure change The exergy loss rates in the laminar premixed flames of CH4 and the 50%CH4-50%H2 blend at both atmospheric and
elevated pressures are illustrated in Fig. 10. It is shown that with elevated pressure, the total exergy loss is reduced. Specifically, the exergy losses from heat conduction and mass diffusion increase, while those from chemical reaction and incomplete combustion decrease. The exergy losses in the
Table 4 e Primary reactions causing the exergy loss from chemical reactions in laminar premixed flames of the 50%CH4-50%H2 blend: F ¼ 0.9, P ¼ 1 atm/5 atm. Reactions R1: O þ CH3¼H þ H2þCO R2: O þ CH3¼H þ CH2O R3:H þ CH2O¼HCO þ H2 R4:OH þ CH4¼CH3þH2O R5:HCO þ O2¼HO2þCO R6:OH þ CH2O¼HCO þ H2O R7:H þ O2¼O þ OH R8:CH2þO2 ¼ 2H þ CO2 R9:H þ HO2 ¼ 2OH R10: CH2þO2¼OH þ H þ CO R11:H þ CH3(þM) ¼ CH4(þM) Exergy loss due to reactions above Exergy loss due to all reactions
Pressures 1 atm
5 atm
2.12% 1.85% 0.68% 0.68% 0.65% 0.46% 0.57% 0.39% 0.79% 0.31% 0.79% 9.28% 15.14%
1.39% 1.19% 0.55% 0.58% 0.43% 0.64% 0.68% 0.45% 0.59% 0.37% 0.47% 7.32% 12.99%
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Fig. 12 e Entropy generation rates due to R1, R2, R5, R9 and R11 in laminar premixed flames of the 50%CH4-50%H2 blend: F ¼ 0.9, (a) P ¼ 1 atm; (b) P ¼ 5 atm. laminar premixed flames of the 50%CH4-50%H2 blend at two pressures are further analyzed to identify the reasons for this observation. To explain the change of exergy loss caused by heat conduction, the profiles of temperature gradients and normalized entropy generation rates from heat conduction in the two flames are plotted in Fig. 11, and the adiabatic temperatures for the two flames are 2173 K and 2190 K, respectively. As is shown in Fig. 11, with pressure elevated from 1 atm to 5 atm, the temperature gradient is promoted to more than 3 times and according to Eqs. 2 and 10, the entropy generation rate is promoted to more than 3 times and the flame thickness is reduced to two fifths. Therefore, based on Eq. (6), the exergy loss from heat conduction increases with elevated pressure. The exergy loss from chemical reactions decreases with elevated pressure, and the top reactions causing exergy loss are listed in Table 4. These reactions lead to more than 60% of the exergy loss from chemical reactions. According to Table 4, the elevated pressure primarily influences the exergy losses from R1, R2, R5, R9 and R11. Therefore, the normalized entropy generation rates of these five reactions are plotted in Fig. 12. It is observed that the peak normalized entropy rates of R1, R2, R5, R9 and R11 at the elevated pressure are more than 2 times as high as those at the atmospheric pressure, while the flame thickness is reduced below one quarter. Therefore, the exergy losses due to these reactions decrease. Mole fractions of the dominant species in the incomplete combustion products at the equilibrium state at both atmospheric and elevated pressures are listed in Table 5. With elevated pressure, the exergy loss from incomplete combustion decrease, because the products dissociations are suppressed, and the mole fractions of incomplete combustion products are reduced [25].
Table 5 e Mole fractions of the primary incomplete combustion products in laminar premixed flames of the 50%CH4-50%H2 blend: F ¼ 0.9, P ¼ 1 atm/5 atm. Pressure
1 atm 5 atm
Species OH
CO
H2
O
H
3.5E-03 2.5E-03
2.3E-03 1.2E-03
1.4E-03 7.0E-04
3.2E-04 1.6E-04
1.8E-04 6.3E-05
Conclusions The analysis of exergy loss characteristics for the laminar premixed flames of CH4/H2 binary fuels was conducted. The sources causing exergy losses were separated into heat conduction, mass diffusion, viscous dissipation, chemical reactions and incomplete combustion. The calculations were conducted at both atmospheric and elevated pressures, with the equivalence ratio varying from 0.6 to 1.5 and the H2 blending ratio increasing from 0% to 70%. The results of this parametric study might provide theoretical guidance for exergy efficiency improvement in heat engines fueled with methane and hydrogen blends. Main conclusions are listed as follows: 1. As equivalence ratio increases from 0.6 to 1.5, the total exergy loss firstly decreases and then increases, and the minimum total exergy loss is obtained when the equivalence ratio is about 0.9 at both atmospheric and elevated pressures. Specifically, when the equivalence ratio increases from 0.6 to 0.9, the total exergy loss is reduced by about 4% mainly because of the reduced flame thickness. However, as the equivalence ratio increases from 0.9 to 1.5, the significant increase in exergy loss from incomplete combustion results in an increased total exergy loss by about 2 times. 2. The total exergy loss decreases by 2% as the H2 blending ratio increases from 0% to 70%. Specifically, the reduced flame thickness causes decreased exergy loss from heat conduction, and the exergy loss from chemical reactions is reduced because the net reaction rates of some dominant reactions with H, H2 and H2O as products slowed down. In contrast, increased incomplete combustion products, such as OH, H2 and H cause the exergy loss from incomplete combustion increases. 3. As pressure increases from 1 atm to 5 atm, the total exergy loss of a given fuel decreases by 1%. The elevated pressure significantly reduces the flame thickness, causing increased gradients of temperature and mole fractions, and the entropy generation rates are promoted. The exergy loss from heat conduction increases but that from chemical reaction decreases, as a result of the trade-off between
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flame thicknesses and entropy generation rates. The exergy loss from incomplete combustion decreases because the dissociation of completed combustion products is inhibited with elevated pressure.
[16] [17]
Acknowledgments [18]
This research work is supported by the National Natural Science Foundation of China (Grant No. 51776124). [19]
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Available online at www.sciencedirect.com
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Analysis of exergy losses in laminar premixed flames of methane/hydrogen blends Yusen Liu, Jiabo Zhang, Dehao Ju, Zhen Huang, Dong Han* Key Laboratory for Power Machinery and Engineering, Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China
highlights Exergy losses in laminar premixed flames of CH4/H2 blends were studied. Minimum exergy loss occurred at the equivalence ratio of 0.9 for different blends. Exergy losses from chemical reactions and heat conduction were dominant among all the sources. Total exergy loss declines as the H2 percentage or initial pressure rises.
article info
abstract
Article history:
Combustion is the primary source for exergy loss in power systems such as combustion
Received 23 May 2019
engines. To elucidate the exergy loss behaviors in combustion and explore the principle for
Received in revised form
efficiency improvement, the second-law thermodynamic analysis was conducted to
13 July 2019
analyze the energy conversion characteristics in laminar premixed flames of methane/
Accepted 16 July 2019
hydrogen binary fuels. The sources causing exergy losses in laminar premixed flames
Available online 7 August 2019
included five parts, namely heat conduction, mass diffusion, viscous dissipation, chemical reactions and incomplete combustion, respectively. The calculations were conducted at
Keywords:
both atmospheric and elevated pressures, with the equivalence ratio varying from 0.6 to 1.5
Exergy loss
and the hydrogen blending ratio increasing from 0% to 70%. The results indicated that the
Laminar premixed flame
total exergy loss firstly increased and then decreased with increased equivalence ratio, and
Methane
reached the minimum value at the equivalence ratio of 0.9. This was primarily due to the
Hydrogen
trade-off relation between the decreased exergy loss from entropy generation and the
Chemical kinetics
increased exergy loss from incomplete combustion, as equivalence ratio increased. As the hydrogen blending ratio increased from 0% to 70%, the total exergy loss decreased by 2%. Specifically, the exergy loss from heat conduction decreased, primarily due to the decreased flame thickness. Moreover, the reactions with H2, H and H2O as reactants were inhibited, leading to decreased the exergy loss from chemical reactions. As pressure increased from 1 atm to 5 atm, the total exergy loss decreased by 1%, because the exergy losses induced by heat conduction and chemical reactions decreased as the flame thickness was reduced. The exergy loss from incomplete combustion also decreased, because elevated pressure inhibited dissociations and decreased the mole fractions of incomplete combustion products. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. Mechanical Engineering, 800 Dongchuan Road, Shanghai Jiao Tong University, Shanghai 200240, China. E-mail address: [email protected] (D. Han). https://doi.org/10.1016/j.ijhydene.2019.07.123 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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Introduction Natural gas (NG) is considered as a potential alternative fuel for road and marine transportation, due to its abundant reserve and low particulate matter (PM) pollutants and carbon dioxide (CO2) emissions in combustion. The usage of NG in internal combustion (IC) engines as a replacement of the petroleum-based fuels has therefore been widely studied [1,2], especially in the compression ignition (CI) engines with dualfuel injection systems [3e5] or the spark ignition (SI) engines with high compression ratios [6e8]. Also, complex injection systems are not necessary for NG SI engines to prepare homogenous fuel and air charge. However, NG SI engines face several application challenges, especially at lean burn conditions, e.g. high combustion instability due to the lower flame propagation speeds and high misfire or partial burn probability due to the narrow flammability limits [9]. Partial supplement of NG with hydrogen (H2) was believed to be a solution to the aforementioned problems in NG SI combustion engines [10]. Fundamental studies have shown that H2 addition could generate more active radicals [11], increase combustion rate [12], enhance flame stability [13] and extend the lean ignition limit [14]. In engine experiments, it was also found that H2 addition to NG reduces flame initiation, burn duration and cycle variability [15], but elevates knock propensity due to the higher ignition tendency and higher cylinder temperature [16]. The elevated cylinder temperature also increases engine-out NOx emissions [17]. On the effects of H2 addition on the thermal efficiency of NG engines based on the first law of thermodynamics, there has not reached a consensus and it seemed to be dependent on the H2 substitution percentage. This is because two competing effects related to H2 addition, i.e. higher extent of constant-volume combustion and increased heat transfer, simultaneously affect engine efficiency [10]. Compared with the first law of thermodynamics, which is focus on energy quantity balance, the second law of thermodynamics pays more attention to the energy quality change. Based on the second law of thermodynamics, researchers found that engine exergy efficiency showed an increase with H2 addition to the NG. Ozcan [18] used a zero-dimensional two-zone model to study the effects of H2 addition on methane combustion irreversibility, and he indicated that the irreversibility was reduced with increased H2 addition and this reduction became more apparent at lean conditions. Rakopoulos and Kyritsis [19] and Rakopoulos et al. [20] attributed the reduction in combustion irreversibility to the interaction between CH4 and H2 molecules, but they also pointed out that the exergy carried by exhaust gases increased with increased H2 addition. Although there were already some studies aiming to figure out the exergy loss characteristics in premixed CH4/H2 flames, however, they were mainly parametric studies, whereas the exergy loss mechanism at different engine-like conditions has not been well understood [21,22]. Therefore, in this study, thermochemical and chemical kinetic analysis were employed to analyze the energy conversion processes in the premixed flames of methane and hydrogen blends at changed
conditions. Further, contributions from different sources, i.e. chemical reactions, heat conduction, mass diffusion, viscous dissipation and incomplete combustion to the total exergy losses in the context of changed H2 percentage were identified, and the interaction regime between CH4 and H2 molecules on these exergy losses sources were elucidated.
Methodology Model and algorithm The exergy losses in laminar premixed flames of CH4/H2 binary fuels are numerically analyzed in this study. The effects of equivalence ratios, H2 addition and pressure change on exergy loss are analyzed. Specifically, the equivalence ratio varies from 0.6 to 1.5, and the H2 volume fraction in fuel blends, which is termed as H2 blending ratio in the following, changes from 0% to 70%. The initial pressures are set as 1 atm and 5 atm, respectively. In all calculations, the initial temperature of the unburned mixture is set as 300 K and the ambient environment temperature is held as 298 K. Moreover, the flames are steady one-dimensional laminar ones and the heat transfer due to radiation is neglected. The calculation method used to characterize the energy conversion in the fundamental fuel combustion processes has been recently proposed by the authors, and has been used for the second-law thermodynamic analysis in the n-heptane auto-ignition [23] and hydrogen flame propagation with diluents [24]. Two categories of sources causing exergy losses are considered during the combustion processes. The first category represents the exergy loss induced by entropy generation, while the second category refers to the exergy loss induced by incomplete combustion. As the methodology details for the exergy loss calculation from each source could be found in the authors’ previous research [25], only some key equations are introduced as follows. The laminar premixed flame model in CHEMKIN Pro software [26] is a one-dimensional model, and the term of entropy generation can be expressed as Eq. (1), ‾
sgen ¼
Xi rui Yi lVT,VT t : Vu mi ,u_ ı þ R i¼1 ,VXi þ T2 T Xi T
(1)
Where R is universal gas constant, T is the local tem‾ perature, t is the local friction stress tensor，and l, r and u are the mean thermal conductivity, density and mixture velocity, respectively. Also, ui , Xi , Yi , mi and u_ ı represent the diffusion velocity, mole fraction, mass fraction, chemical potentials and the mass production rate of the ith species, respectively. The entropy generation rate (sgen ) caused by heat conduction, mass diffusion, viscous dissipation and chemical reactions can be further calculated by Eqs. (2)e(5). 2 1 dT sgen conduction ¼ l 2 T dx
(2)
2 4 m du sgen dissipation ¼ 3 T dx
(3)
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i X rRgi ui Yi dXi sgen diffusion ¼ Xi dx i¼1
(4)
i X mi u_ i sgen reaction ¼ T i¼1
(5)
where m is the viscosity coefficient, Rgi is the specific gas constant of the ith species,. As such, the exergy loss from the entropy generation can be calculated based on the Gouy-Stodla equation [27], Z Igen ¼ T0
Sgen dx
(6)
where Igen is the exergy loss by entropy generation and T0 is the environment temperature of 298 K. On the other hand, the exergy loss is also caused by incomplete combustion, which means that some combustion products other than water, carbon dioxide and nitrogen exist in the flame downstream. Although the chemical exergy contained in these products are not destroyed, however, it is hard to further utilize and is thus considered as another source causing exergy loss [28], which can be estimated by Eq. (7), Iin ¼
X X Gincom Gcom
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mechanisms for methane combustion, namely GRI 3.0 Mech [31], San Diego Mech [32], Konnov 0.5 Mech [33] and USC II Mech [34]. The application conditions of the four mechanisms are distinct. Specifically, GRI 3.0 Mech and San Diego Mech are concerned about high temperature combustion of methane, USC II Mech is a hybrid model for H2/CO/C1-C4 combustion and Konnov 0.5 Mech is developed for the combustion of small hydrocarbons. Further, the GRI 3.0 Mech has been validated against the combustion behaviors of methane/hydrogen mixtures [35]. Therefore, the GRI 3.0 Mech was tentatively used in this study, and its calculation results in flame speeds was compared with the those by San Diego Mech and experimental measurements. As shown in Fig. 1, the GRI 3.0 Mech agrees with the measured flame speeds of the CH4/H2 binary fuels more satisfactorily than the San Diego Mech. Additionally, to study the mechanism effects on the of exergy loss computation, the exergy loss rate caused by each individual source, calculated by the two mechanisms, were compared for 100%CH4 and 50%CH4-50%H2 at atmospheric pressure. As shown in Fig. 2, the loss contributions calculated by different mechanisms were highly consistent. Therefore, the GRI 3.0 Mech is selected for the following calculation and kinetics analysis.
(7)
where Iin is the exergy loss caused by incomplete combustion, and Gincom and Gcom mean the Gibbs free energy values of the complete and incomplete combustion products, respectively. Therefore, the total exergy loss can be expressed as Eq. (8), I% ¼
Igen þ Iin 100% Efuel
(8)
where I% is the total exergy loss percentage and Efuel is the initial chemical exergy carried by the unburned mixture, which can be calculated by Eq. 9 Efuel ¼ rfuel $SL $efuel
(9)
where rfuel is fuel density, SL is laminar premixed flame speed and efuel is the chemical exergy carried by per unit mass of the unburned mixture. Considering that the absolute chemical exergy in different mixtures varies with fuel composition, here the initial chemical exergy is normalized to unity in each flame. In this way, the relative contributions of different sources to the total exergy losses can be directly compared for different CH4/H2 flames. Moreover, according to the authors’ previous work [29], the exergy loss from viscous dissipation is so trivial that it is neglected in this study.
Chemical mechanism selection Thermodynamic parameters in flame propagation process, such as temperature, pressure, species mole fractions and reaction rates are needed for exergy calculation. It is therefore essential to select an optimized mechanism to generate these thermodynamic data. As pointed out by Konnov [30], there are four widely used chemical
Fig. 1 e Comparisons between calculated and experimental flame speeds: (a) P ¼ 1 atm: - Vagelopoulos et al. [36] and C Park et al. [37] for 100%CH4; :Halter et al. [38] for 90%CH410%H2; ; Hermanns et al. [39] and A Halter et al. [38] for 80% Donohoe et al. [40] for 50%CH4-50%H2. (b) CH4-20%H2; P ¼ 5 atm: C Rozenchan et al. [41] and - Kobayashi et al. [42] for 100%CH4; ; Halter et al. [38] for 80%CH4-20%H2.
◄
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Fig. 2 e Exergy loss rate from each source in the laminar premixed flames of CH4 and a CH4/H2 blend.
Results and discussion Overview of exergy loss from different sources Based on the method above, the normalized entropy generation rates can be computed，and the CH4 flame at the atmospheric pressure and the stoichiometric condition is used as an example. The normalized entropy generation rates from heat conduction, mass diffusion and chemical reactions in the flame, as well as the temperature profile, are illustrated in Fig. 3. It is shown that the peak of normalized entropy generation rates from heat conduction occurs at the upstream of the flame, and the peaks of normalized entropy generation rates from mass diffusion and chemical reaction occur at the downstream. Moreover, the peak of normalized entropy generation rates from chemical reactions are much higher than the those from other sources, indicating that chemical reaction is the dominant source in entropy generation. According to Eq. (2), the entropy generation rate from heat conduction is determined by the temperature and temperature gradient. At the flame upstream, the higher temperature
gradient overcomes the effects of lower temperature, resulting in the peak of exergy loss rate from heat conduction. The exergy loss from mass diffusion, based on Eq. (4), is mainly influenced by the mole fraction gradient [43]. To explain the entropy generation rate from mass diffusion in detail, the exergy loss rates of the top eight species, which contribute most to the exergy loss, are listed in Table 1. The exergy loss rates are calculated by dividing the exergy losses from the mass diffusion of these species by the chemical exergy contained in the fuel. Moreover, their mole fraction distributions in the flame are plotted in Fig. 4, calculated by CHEMKIN Pro software. These species include reactants (CH4, H2 and O2), products (CO, CO2 and H2O) and active radicals (OH and H). It is observed that O2, CH4 and H2O contribute more than the other species to the exergy loss from mass diffusion, as they are the main reactants or products. On the contrary, the contribution rates of OH, H2, CO, CO2 and H to exergy loss from mass diffusion are secondary. At the flame downstream, the mole fractions of products, such as CO and CO2 increase suddenly, thus producing the peak of exergy loss rate from mass diffusion. In addition, the sudden increase of products also means that main reactions occur at the flame downstream, and according to Eq. (5), the entropy generation rates from chemical reactions are influenced by species production rates. As a result, the peak of the entropy generation rate from chemical reactions occurs at the downstream. Further, the total exergy losses of CH4/H2 binary fuels are studied under a wide range of equivalence ratios and H2 blending ratios at both atmospheric and elevated pressures as shown in Fig. 5, with the initial temperature set as 300 K and the ambient temperature held as 298 K. The equivalence ratio varies from 0.6 to 1.5 and the H2 equivalence ratio increases
Table 1 e Primary species for the exergy loss from mass diffusion in the laminar premixed flame of CH4: P ¼ 1 atm, F ¼ 1.0. Fig. 3 e Normalized entropy generation rates and temperature profile in the laminar premixed flame of CH4: P ¼ 1 atm, F ¼ 1.0.
Species Exergy Loss Rate Species Exergy Loss Rate
CH4 0.50% CO2 0.14%
O2 0.44% CO 0.11%
H2O 0.38% H2 0.10%
H 0.30% OH 0.09%
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Fig. 4 e Mole fraction distributions of H2, H, O2, OH, H2O, CH4, CO and CO2 in the laminar premixed flame of CH4: P ¼ 1 atm, F ¼ 1.0. from 0% to 70%. It is observed that the total exergy loss firstly decreases and then increases as the equivalence ratio increases. Meanwhile, the minimum total exergy loss generally is located at the equivalence ratio of 0.9 at both atmospheric and elevated pressures. As pressure increases from 1 atm (Fig. 5a) to 5 atm (Fig. 5b), the minimum exergy loss decreases by about 1%. On the other hand, the total exergy loss decreases with H2 addition. To explain the phenomenon, in the following study, the effects of equivalence ratios, H2 addition and pressure change on exergy losses in the flames of CH4 and CH4/H2 blends are analyzed.
Effects of equivalence ratios To study the effects of equivalence ratio, the exergy loss in laminar premixed flames of two fuels, namely 100%CH4 and 50%CH4-50%H2, are analyzed at both atmospheric and elevated pressures. The exergy loss rates from different sources are shown in Fig. 6. It is observed that in all the flames, as the equivalence ratio increases, the exergy losses from heat conduction and chemical reactions decrease, while the exergy loss from incomplete combustion increases. The change in the exergy loss from mass diffusion is slight.
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When the equivalence ratio varies increases from 0.6 to 0.9, the total exergy loss decreases, mainly because of the decreased exergy loss from heat conduction. Based on Eq. (6), the exergy loss is a function of the entropy generation rate and the flame thickness. In addition, the entropy generation rate from heat conduction is dominated by the temperature and temperature gradient, according to Eq. (2). Therefore, the profiles of temperature gradient and normalized entropy generation rate from heat conduction in CH4 laminar premixed flames at atmospheric pressure are plotted in Fig. 7, with the equivalence ratios set as 0.6 and 0.9, respectively. It is observed that the peak of the temperature gradient at F ¼ 0.9 is 3 times as high as that at F ¼ 0.6. In addition, the calculated adiabatic temperatures at equivalence ratios of 0.6 and 0.9 are 1670 K and 2140 K, respectively. As a result, the peak entropy generation rate from heat conduction is increased to about 2 times with increased equivalence ratio. On the other hand, the effects of equivalence ratios on the flame thickness are analyzed based on Eq. (10), d¼
Tad Tin ðdT=dxÞmax
(10)
where d, Tad and Tin represent the flame thickness, the adiabatic flame temperature and the initial temperature, respectively. As the initial temperatures of all flames are the same, according to Eq. (10), the flame thickness is mainly influenced by the adiabatic temperature and the maximum temperature gradient. As mentioned above, with increased equivalence ratio, the adiabatic temperature increases by 470 K, and the maximum temperature gradient is promoted to 3 times as high. Therefore, the flame thickness is reduced to one third, as shown in Fig. 7. The significant reduction in flame thickness overcomes the effect of increased entropy generation, as equivalence ratio increases. The exergy loss from heat conduction is as such reduced based on Eq. (6). Moreover, at fuellean conditions, the fuel and oxidants could react more completely, and thus the effects of chemical reactions and incomplete combustion are less dominant. As the equivalence ratio further increases from 0.9 to 1.5, the increase in the total exergy loss is dominated by the increased exergy loss from incomplete combustion. This is because with increased equivalence ratio, fuel-rich mixtures
Fig. 5 e Total exergy losses in the laminar premixed flames of CH4/H2 blends at different equivalence ratios: (a) P ¼ 1 atm, (b) P ¼ 5 atm.
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Fig. 6 e Exergy loss rate from each source in the laminar premixed flames of CH4 and a CH4/H2 blend with changed equivalence ratios. (a) P ¼ 1 atm, 100%CH4; (b) P ¼ 5 atm, 100%CH4; (c) P ¼ 1 atm, 50%CH4-50%H2; (d) P ¼ 5 atm, 50%CH4-50% H2.
Fig. 7 e Temperature gradient and normalized entropy generation rate from heat conduction in CH4 laminar premixed flames at atmospheric pressure, (a) F ¼ 0.6, (b) F ¼ 0.9.
inhibit fuel completed combustion, leading to the increased exergy loss from incomplete combustion. Therefore, the minimum total exergy loss occurs at the equivalence ratio of 0.9, and in the following study, this optimal equivalence ratio is selected to analyze the effects of H2 addition and pressure change.
Effects of H2 addition To study the effects of H2 addition, the exergy loss rates in different CH4/H2 blends are illustrated in Fig. 8. It is shown that with the fraction of H2 increasing from 0% to 70%, the total exergy loss continuously decreases. Specifically, with increased H2 mole fraction, the exergy loss rates from heat
conduction and chemical reaction decrease, while that from incomplete combustion increases. Compared with the other sources, the change of the exergy loss from mass diffusion can be neglected. Moreover, the effects of H2 addition on exergy loss from each source are similar at both atmospheric and elevated pressures. To explain this phenomenon, the exergy losses from heat conduction, chemical reactions and incomplete combustion in the laminar premixed flames of CH4 and the 50%CH4-50%H2 blend at the atmospheric pressure are compared. To study the exergy loss from heat conduction, the profiles of the temperature gradients and the normalized entropy generation rates in the two flames are plotted in Fig. 9. In addition, the adiabatic temperatures of the two flames are
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Fig. 8 e Exergy loss rate from each source in the laminar premixed flames of CH4 and different CH4/H2 blends: F ¼ 0.9, (a) P ¼ 1 atm, (b) P ¼ 5 atm.
Fig. 9 e Temperature gradient and normalized entropy generation rate from heat conduction in the laminar premixed flames of CH4 and a CH4/H2 blend: P ¼ 1 atm, F ¼ 0.9. approximate, which are 2139 K and 2173 K, respectively. Therefore, according to Eqs. 2 and 10, the temperature gradients of the two flames are the primary factors that influence the entropy generation rates and flame thicknesses. Specifically, the maximum temperature gradient in the 50%CH4-50% H2 flame is about 1.3 times as high as that in the 100%CH4 flames, leading to that the peak entropy generation rate
Table 2 e Primary reactions causing the exergy loss from chemical reactions in the laminar premixed flames of CH4 and a CH4/H2 blend. blends: F ¼ 0.9, P ¼ 1 atm. Reactions
Fuels 100%CH4 50%CH4e50%H2
R1: O þ CH3¼H þ H2þCO R2: O þ CH3¼H þ CH2O R3: H þ CH2O¼HCO þ H2 R4: OH þ CH4¼CH3þH2O R5: HCO þ O2¼HO2þCO R6: OH þ CH2O¼HCO þ H2O R7: H þ O2¼O þ OH R8: CH2þO2 ¼ 2H þ CO2 R9: H þ HO2 ¼ 2OH R10: CH2þO2¼OH þ H þ CO R11: H þ CH3(þM) ¼ CH4(þM) Exergy loss due to reactions above Exergy loss due to all reactions
2.38% 1.99% 0.78% 0.72% 0.68% 0.65% 0.63% 0.59% 0.52% 0.48% 0.42% 9.83% 16.03%
2.12% 1.85% 0.68% 0.68% 0.65% 0.46% 0.57% 0.39% 0.79% 0.31% 0.79% 9.28% 15.14%
increases to 1.2 times but the flame thickness is reduced to two thirds. Therefore, according to Eq. (6), the exergy loss from heat conduction is reduced with H2 addition. To study the effects of H2 addition on the exergy loss from chemical reaction, the top reactions causing exergy loss are listed in Table 2, which contribute most to the exergy loss in different flames. These reactions contribute about 60% to the exergy loss among all the reactions, and the analysis of these reactions may help understand the exergy loss from chemical reactions. According to the reaction path analysis, these reactions contain the H-abstraction reactions from CH4 to CH3 (R4 and R11), chain propagation reactions from CH3 to CH2O (R2), H-abstraction reactions from CH2O to HCO (R3 and R6), CO generation reactions (R1, R5, and R10) and CO2 generation reactions (R8). Additionally, some H2-O2 system reactions (R7 and R9) to generate active radicals are also important among the reactions causing exergy loss. Table 3 e Mole fractions of the primary incomplete combustion products in laminar premixed flames of CH4 and a CH4/H2 blend: P ¼ 1 atm, F ¼ 0.9. Fuels
100%CH4 50%CH4-50%H2
Species OH
CO
H2
O
H
2.8E-03 3.5E-03
2.3E-03 2.3E-03
9.3E-04 1.4E-03
2.6E-04 3.2E-04
1.2E-04 1.8E-04
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Fig. 10 e Exergy loss rates from each source in the laminar premixed flames of CH4 and a CH4/H2 blend: F ¼ 0.9, P ¼ 1 atm/ 5 atm.
Fig. 11 e Temperature gradient and normalized entropy generation rate from heat conduction in laminar premixed flames of the 50%CH4-50%H2 blend: F ¼ 0.9, (a) P ¼ 1 atm; (b) P ¼ 5 atm. With H2 addition, the mole fractions of H2 and H increase and the reactions involving these two species are dramatically influenced. The reactions such as R1, R2, R3, R8 and R10, in which H and H2 are products, are slowed sown, leading to their decreased contributions to exergy loss. On the contrary, the reactions in which H and H2 are reactants, such as R9 and R11, are accelerated and lead to the increased exergy loss. In addition, the mole fraction of H2O also increases with H2 addition. Therefore, the reactions R4 and R6, in which H2O is a product, are slowed down and contribute less to exergy loss. As a result, the exergy loss from chemical reaction is reduced with H2 addition. According to the combustion products analysis, the mole fractions of the dominant species in the incomplete combustion products at the equilibrium state at the atmospheric pressure are listed in Table 3. It is found that OH is the primary one, followed by CO, H2, O and H. With H2 addition, the mole fractions of H2 and active radicals, such as OH, O and H, increase at the equilibrium state. Therefore, the H2 addition leads to increased exergy loss from incomplete combustion.
Effects of pressure change The exergy loss rates in the laminar premixed flames of CH4 and the 50%CH4-50%H2 blend at both atmospheric and
elevated pressures are illustrated in Fig. 10. It is shown that with elevated pressure, the total exergy loss is reduced. Specifically, the exergy losses from heat conduction and mass diffusion increase, while those from chemical reaction and incomplete combustion decrease. The exergy losses in the
Table 4 e Primary reactions causing the exergy loss from chemical reactions in laminar premixed flames of the 50%CH4-50%H2 blend: F ¼ 0.9, P ¼ 1 atm/5 atm. Reactions R1: O þ CH3¼H þ H2þCO R2: O þ CH3¼H þ CH2O R3:H þ CH2O¼HCO þ H2 R4:OH þ CH4¼CH3þH2O R5:HCO þ O2¼HO2þCO R6:OH þ CH2O¼HCO þ H2O R7:H þ O2¼O þ OH R8:CH2þO2 ¼ 2H þ CO2 R9:H þ HO2 ¼ 2OH R10: CH2þO2¼OH þ H þ CO R11:H þ CH3(þM) ¼ CH4(þM) Exergy loss due to reactions above Exergy loss due to all reactions
Pressures 1 atm
5 atm
2.12% 1.85% 0.68% 0.68% 0.65% 0.46% 0.57% 0.39% 0.79% 0.31% 0.79% 9.28% 15.14%
1.39% 1.19% 0.55% 0.58% 0.43% 0.64% 0.68% 0.45% 0.59% 0.37% 0.47% 7.32% 12.99%
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Fig. 12 e Entropy generation rates due to R1, R2, R5, R9 and R11 in laminar premixed flames of the 50%CH4-50%H2 blend: F ¼ 0.9, (a) P ¼ 1 atm; (b) P ¼ 5 atm. laminar premixed flames of the 50%CH4-50%H2 blend at two pressures are further analyzed to identify the reasons for this observation. To explain the change of exergy loss caused by heat conduction, the profiles of temperature gradients and normalized entropy generation rates from heat conduction in the two flames are plotted in Fig. 11, and the adiabatic temperatures for the two flames are 2173 K and 2190 K, respectively. As is shown in Fig. 11, with pressure elevated from 1 atm to 5 atm, the temperature gradient is promoted to more than 3 times and according to Eqs. 2 and 10, the entropy generation rate is promoted to more than 3 times and the flame thickness is reduced to two fifths. Therefore, based on Eq. (6), the exergy loss from heat conduction increases with elevated pressure. The exergy loss from chemical reactions decreases with elevated pressure, and the top reactions causing exergy loss are listed in Table 4. These reactions lead to more than 60% of the exergy loss from chemical reactions. According to Table 4, the elevated pressure primarily influences the exergy losses from R1, R2, R5, R9 and R11. Therefore, the normalized entropy generation rates of these five reactions are plotted in Fig. 12. It is observed that the peak normalized entropy rates of R1, R2, R5, R9 and R11 at the elevated pressure are more than 2 times as high as those at the atmospheric pressure, while the flame thickness is reduced below one quarter. Therefore, the exergy losses due to these reactions decrease. Mole fractions of the dominant species in the incomplete combustion products at the equilibrium state at both atmospheric and elevated pressures are listed in Table 5. With elevated pressure, the exergy loss from incomplete combustion decrease, because the products dissociations are suppressed, and the mole fractions of incomplete combustion products are reduced [25].
Table 5 e Mole fractions of the primary incomplete combustion products in laminar premixed flames of the 50%CH4-50%H2 blend: F ¼ 0.9, P ¼ 1 atm/5 atm. Pressure
1 atm 5 atm
Species OH
CO
H2
O
H
3.5E-03 2.5E-03
2.3E-03 1.2E-03
1.4E-03 7.0E-04
3.2E-04 1.6E-04
1.8E-04 6.3E-05
Conclusions The analysis of exergy loss characteristics for the laminar premixed flames of CH4/H2 binary fuels was conducted. The sources causing exergy losses were separated into heat conduction, mass diffusion, viscous dissipation, chemical reactions and incomplete combustion. The calculations were conducted at both atmospheric and elevated pressures, with the equivalence ratio varying from 0.6 to 1.5 and the H2 blending ratio increasing from 0% to 70%. The results of this parametric study might provide theoretical guidance for exergy efficiency improvement in heat engines fueled with methane and hydrogen blends. Main conclusions are listed as follows: 1. As equivalence ratio increases from 0.6 to 1.5, the total exergy loss firstly decreases and then increases, and the minimum total exergy loss is obtained when the equivalence ratio is about 0.9 at both atmospheric and elevated pressures. Specifically, when the equivalence ratio increases from 0.6 to 0.9, the total exergy loss is reduced by about 4% mainly because of the reduced flame thickness. However, as the equivalence ratio increases from 0.9 to 1.5, the significant increase in exergy loss from incomplete combustion results in an increased total exergy loss by about 2 times. 2. The total exergy loss decreases by 2% as the H2 blending ratio increases from 0% to 70%. Specifically, the reduced flame thickness causes decreased exergy loss from heat conduction, and the exergy loss from chemical reactions is reduced because the net reaction rates of some dominant reactions with H, H2 and H2O as products slowed down. In contrast, increased incomplete combustion products, such as OH, H2 and H cause the exergy loss from incomplete combustion increases. 3. As pressure increases from 1 atm to 5 atm, the total exergy loss of a given fuel decreases by 1%. The elevated pressure significantly reduces the flame thickness, causing increased gradients of temperature and mole fractions, and the entropy generation rates are promoted. The exergy loss from heat conduction increases but that from chemical reaction decreases, as a result of the trade-off between
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flame thicknesses and entropy generation rates. The exergy loss from incomplete combustion decreases because the dissociation of completed combustion products is inhibited with elevated pressure.
[16] [17]
Acknowledgments [18]
This research work is supported by the National Natural Science Foundation of China (Grant No. 51776124). [19]
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