Exergy losses in premixed flames of dimethyl ether and hydrogen blends

Abstract

A second-law thermodynamic analysis was conducted for stoichiometric premixed dimethyl ether (DME)/hydrogen (H₂)/air flames at atmospheric pressure. The exergy losses from the irreversibility sources, i.e., chemical reaction, heat conduction and species diffusion, and those from partial combustion products were analyzed in the flames with changed fuel blends. It is observed that, regardless of the fuel blends, chemical reaction contributes most to the exergy losses, followed by incomplete combustion, and heat conduction, while mass diffusion has the least contribution to exergy loss. The results also indicate that increased H₂ substitution decreases the exergy losses from reactions, conduction, and diffusion, primarily because of the flame thickness reduction at elevated H₂ substitution. The decreases in exergy losses by chemical reactions and heat conduction are higher, but the exergy loss reduction by diffusion is slight. However, the exergy losses from incomplete combustion increase with H₂ substitution, because the fractions of the unburned fuels and combustion intermediates, e.g., H₂ and OH radical, increase. The overall exergy losses in the DME/H₂ flames decrease by about 5% with increased H₂ substitution from 0% to 100%.

Keywords

second law analysis / flame / dimethyl ether (DME) / hydrogen / binary fuels

Introduction

The petroleum shortage requires us to seek potential alternative fuels, such as biodiesel [¹–³], alcohols [⁴–⁷], dimethyl ether (DME) [⁸,⁹] and hydrogen (H₂) [¹⁰,¹¹] for power and propulsion systems. Among the above alternative fuels, DME and H₂ have complementary ignition and combustion behaviors. Besides, as pointed out in Refs. [¹²,¹³], the addition of hydrogen can increase the burning velocity and improve the engine combustion and emissions. Therefore, some researchers tried to use hydrogen and DME binary fuels in internal combustion (IC) engines. The effects of H₂ substitution on the combustion and emissions of a DME dual fuel engine were numerically studied in Ref. [¹⁴]. The simulation results indicated that there existed advanced ignition timing and an elevated peak pressure with H₂ addition. Further, NO_x emissions increased with H₂ addition but could be mitigated with injection strategy optimization. The performance of a H₂-DME premixed charge compression ignition (PCCI) engine with H₂ port injection and DME direct injection was experimentally studied in Ref. [¹⁵]. The maximum hydrogen percentage was 64% to avoid misfire and the maximum indicated mean effective pressure was achieved with a 50% hydrogen addition.

The potential of the application of hydrogen and DME binary fuels in combustion engines attracted researchers’ attention to understand their fundamental combustion behaviors. For example, the ignition delays of lean DME-H₂ charge at engine-like conditions were measured in Refs. [¹⁶,¹⁷] in which it was pointed that the heat release processes of the mixtures were three-staged at lean conditions, and the overall ignition delay increased nonlinearly with hydrogen percentage. Wang et al. [¹⁸] numerically compared the auto-ignition tendency of DME/H₂ and DME/methane blends, and indicated that methane was more effective than H₂ in retarding the DME auto-ignition event. The primary reason for this was that the molecular structure of methane was more stable. Pan et al. [¹⁹] and Hu et al. [²⁰] numerically identified the nonlinear influences of H₂ addition on DME auto-ignition and explained this phenomenon by kinetic analysis. The laminar flame propagation of premixed DME/CH₄/H₂-air flames at atmospheric pressure was studied by Wang et al. [²¹], who found that the increase in the propagation speed with H₂ addition was more significant for CH₄ than for DME. Liu [²²] analyzed the chemical effects of H₂ blending on premixed DME flames, and pointed H₂ addition suppressed C₂H₂ and C₂H₄ but promoted CH₂O production. The blending effects of H₂-DME on a diffusion flame were investigated by Kang et al. [²³], who quantitatively characterized the DME- and H₂-dominated combustion regimes.

Conventionally, the first-law thermodynamics was utilized to analyze the energy conversion processes in power systems, which is based on energy quantity balance but does not concerns the changes in energy quality. Therefore, analysis using the second-law thermodynamics was performed by some researchers to explore the pathway to improve energy conversion efficiency in power systems [²⁴,²⁵]. Recently, the second-law thermodynamics has been used to analyze the energy conversion characteristics in fundamental combustion processes, such as fuel auto-ignition [²⁶–²⁸] and premixed flame propagation [²⁹–³³]. The observations in these fundamental studies can contribute to a deeper understanding in the energy conversion characteristics in combustion and may provide theoretical guidance for combustion efficiency improvement in practical power systems. This paper aims to clarify the characteristics of exergy losses in laminar premixed flames of DME and H₂ binary fuels. Thermochemical and chemical kinetic analysis have been combined to analyze the energy conversion processes in DME/H₂-fueled premixed flames, and the exergy losses in the flames with varied DME/H₂ blending ratios have been identified. Specifically, first, the methodology combining the thermochemical and chemical kinetic analysis to identify the exergy loss features in premixed flames are introduced. Besides, the distribution characteristics of exergy loss from irreversibility sources and incomplete combustion are delineated and analyzed for different fuel blends. In addition, some primary conclusions are drawn at the end.

Methodology

The DME/H₂-fueled laminar premixed flame propagation was first calculated using three widely used detailed chemical models, which were denoted as the NUIG mechanism by the National University of Ireland, Galway [³⁴], the LLNL mechanism by Lawrence Livermore National Laboratories [³⁵], and the USTC mechanism by the University of Science and Technology of China [³⁶], respectively. Further, the calculated flame speeds of different blending ratio DME/H₂/air mixtures were validated against the experimental flame speed measurements of pure DME [³⁷], pure H₂ and, DME/H₂ blends with changed molar percentages [³⁸–⁴⁰]. The experimental and calculation results are plotted in Fig. 1. It is shown that the prediction of the USTC mechanism has more satisfactory agreement with the experimental results than the other mechanisms, especially for high-H₂-ratio flames, and as such the USTC mechanism was selected in the following calculation and analysis. The flame speed calculation of the stoichiometric mixture was conducted at an inlet temperature of 298 K and the atmospheric pressure. Six blending percentages, namely 100% DME, 80% DME-20% H₂, 60% DME-40%H₂, 40% DME-60% H₂, 20% DME-80% H₂, and 100% H₂ on a molar basis, were calculated.

The calculation of the exergy losses in premixed flames could be described by Eqs. (1)–(17), and the definition of the terms used in these equations could be referred to in the Notations in this paper. The calculation is mainly based on three governing conservation equations, i.e., mass conservation, energy conservation, and species conservation equations, which are listed as follows.

Mass conservation equation

(1)\dot{M}=\rho uA.

Energy conservation equation

(2)\dot{M}{\displaystyle \frac{\mathrm{d}T}{\mathrm{d}x}}-{\displaystyle \frac{\mathrm{1}}{c_{\mathrm{p}}}}{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}\left(\lambda A{\displaystyle \frac{\mathrm{d}T}{\mathrm{d}x}}\right)+{\displaystyle \frac{A}{c_{\mathrm{p}}}}{\displaystyle {\sum }_{k=\mathrm{1}}^k}\rho Y_k{V}_k{c}_{\mathrm{p}k}{\displaystyle \frac{\mathrm{d}T}{\mathrm{d}x}}+{\displaystyle \frac{A}{c_{\mathrm{p}}}}{\displaystyle {\sum }_{k=\mathrm{1}}^k}\stackrel{\cdot }{{\omega }_k}{h}_k{W}_k+{\displaystyle \frac{A}{c_{\mathrm{p}}}}\stackrel{\cdot }{Q_{\mathrm{rad}}}=\mathrm{0.}

Species conservation equation

(3)\dot{M}{\displaystyle \frac{\mathrm{d}{Y}_k}{\mathrm{d}x}}+{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}(\rho A{Y}_k{V}_k)-A\stackrel{\cdot }{{\omega }_k}{W}_k=\mathrm{0.}

The CHEMKIN PRO [⁴¹] software was utilized to solve the above-mentioned equations by the finite differential method, with the gradient and curvature values for adaptive grid control set as 0.1 and 0.01, respectively. By solving these equations, the variables such as temperature, pressure, mole fraction, and reaction rates can be obtained. Next, the exergy loss induced by entropy generation could be calculated using an in-house code based on Eq. (4) [⁴²].

(4)S_{\mathrm{gen}}={\displaystyle \frac{\tau :\nabla u}{T}}-{\displaystyle \frac{q_c\cdot \nabla T}{T^{\mathrm{2}}}}-{\displaystyle \frac{\mathrm{1}}{T}}{\displaystyle {\sum }_k^{}}[j_k\cdot (s_k\nabla T+\nabla {\mu }_k)]+{\displaystyle {\sum }_k^{}}{\displaystyle \frac{f_k\cdot j_k}{T}}-{\displaystyle \frac{{\mu }_k\cdot \stackrel{\cdot }{{\omega }_k}}{T}}.

Equation (4) can be further simplified to the one-dimensional flames according to the Fourier law.

(5)q_c=-\lambda \nabla T.

Meanwhile, only gravity is considered as the body force in the calculation. According to the Fick laws

(6)j_k=-\rho D_{k-\mathrm{mi}\mathrm{x}}\nabla Y_k,

(7){\displaystyle {\sum }_k^{}}{f}_k\cdot j_k={\displaystyle {\sum }_k^{}}g\cdot j_k=g\cdot {\displaystyle {\sum }_k^{}}{j}_k=\mathrm{0.}

Therefore, Eq. (4) can be simplified to Eq. (8) [⁴³,⁴⁴]

(8)S_{\mathrm{gen}}={\displaystyle \frac{\tau :\nabla u}{T}}\mathrm{+}{\displaystyle \frac{\lambda \nabla T\cdot \nabla T}{T^{\mathrm{2}}}}+\mathrm{R}{\displaystyle {\sum }_k^{}}{\displaystyle \frac{\rho D_{k-\mathrm{mi}\mathrm{x}}}{X_k}}\nabla Y_k\cdot \nabla X_k-{\displaystyle \frac{{\mu }_k\cdot \stackrel{\cdot }{{\omega }_k}}{T}}.

Specifically, the entropy generation rate (S_{\mathrm{gen}}) caused by dissipation, conduction, diffusion, and reaction can be expressed as the terms on the right side of Eq. (8) which can be further calculated by Eqs. (9) to (12) [³³].

(9)S_{\mathrm{gen}}|\mathrm{dissipation}={\displaystyle \frac{\mathrm{4}}{\mathrm{3}}}{\displaystyle \frac{\mu }{T}}{\left({\displaystyle \frac{\mathrm{d}u}{\mathrm{d}x}}\right)}^{\mathrm{2}},

(10)S_{\mathrm{gen}}|\mathrm{conduction}=\lambda {\displaystyle \frac{\mathrm{1}}{T^{\mathrm{2}}}}{\left({\displaystyle \frac{\mathrm{d}T}{\mathrm{d}x}}\right)}^{\mathrm{2}},

(11)S_{\mathrm{gen}}|\mathrm{diffusion}={\displaystyle {\sum }_{k=\mathrm{1}}^k}{\displaystyle \frac{\rho R_{gk}{D}_{k-\mathrm{mi}\mathrm{x}}}{X_k}}{\displaystyle \frac{\mathrm{d}{Y}_k}{\mathrm{d}x}}{\displaystyle \frac{\mathrm{d}{X}_k}{\mathrm{d}x}},

(12)S_{\mathrm{gen}}|\mathrm{reaction}=-{\displaystyle {\sum }_k}{\displaystyle \frac{{\mu }_{k,j}{\omega }_{k,j}}{T}}.

The chemical potential in Eq. (12) is defined as

(13){\mu }_{k,j}=h_{k,j}(T)-T{s}_{k,j}(T)+RT\ln \left({\displaystyle \frac{X_{k}P}{P_{\mathrm{0}}}}\right).

Then, the exergy loss from the entropy generation is calculated using the Gouy-Stodla equation [⁴⁵],

(14)B_{\mathrm{destruction}}=T_{\mathrm{0}}\int S_{\mathrm{gen}}\mathrm{d}x.

Furthermore, some incomplete combustion products exist in the flame downstream region. Although the chemical exergy contained in these products is not destroyed, it is hard to further utilize and is thus considered as sources causing exergy loss here [⁴⁶,⁴⁷]. The exergy loss from incomplete combustion products is calculated according to Eq. (15),

(15)B_{\mathrm{incomplete}}={\displaystyle \sum G_{\mathrm{complete,}\mathrm{}\mathrm{pro}}}-{\displaystyle \sum G_{\mathrm{incomplete,}\mathrm{}\mathrm{pro}}}.

As mentioned above, the total exergy loss is the sum of those by both incomplete combustion and entropy generation. Therefore, the total exergy loss percentage can be expressed as Eq. (16).

(16)B\%={\displaystyle \frac{B_{\mathrm{destruction}}+B_{\mathrm{incomplete}}}{B_{\mathrm{fuel}}}}\times \mathrm{100}\%,

B_{\mathrm{fuel}} is the fuel chemical exergy, which is calculated by Eq. (17) [⁴⁸].

(17)B_{\mathrm{fuel}}=b_{\mathrm{fuel}}\cdot {\rho }_u\cdot S_L.

Considering that the chemical exergies vary with different DME/H₂ blending ratios, the fuel chemical exergy is normalized to unity in each flame and as such the contributions to exergy losses from different sources can be better compared in different DME/H₂ flames.

Results and discussion

The fuel blending effects on the distributions to the exergy losses from different sources are illustrated in Fig. 2. Chemical reaction is always the primary contributor to the exergy loss in all the flames, while the exergy losses from viscous dissipation are always negligible. Due to the negligible contribution from the viscous dissipation, the analysis of the exergy loss from viscous dissipation is not included in the following discussion. The changed H₂ percentage has some different influences on the exergy loss from different sources. With increased H₂ substitution, the exergy losses from chemical reactions, mass diffusion, and heat conduction monotonically decrease. However, the exergy loss from incomplete combustion rises with increased H₂ substitution. The overall exergy losses are declined by about 5% with increased H₂ substitution.

Considering the fact that the total entropy generation in the premixed flames is primarily induced by the irreversibility from chemical reactions, mass diffusion and heat conduction, the normalized entropy generation rate from these three irreversibility sources are plotted in Fig. 3. To describe flame structures, the temperature profiles are illustrated simultaneously. For all the flames, it is found that the entropy generation rate by chemical reactions is far higher than those by heat conduction and mass diffusion. The peak entropy generation from heat conduction is adjacent to the location with the maximum temperature gradient, as heat conduction is significantly enhanced by the elevated temperature gradient. The occurrences of the peak entropy generation by mass diffusion and chemical reaction are behind that by conduction, because of the higher temperatures and intermediate mole/mass fraction gradients at the flame downstream. The increased H₂ substitution does not significantly change the peak magnitudes of the total entropy generation, as well as the entropy generation from each individual source. However, with increased H₂ substitution, the reaction zone is slightly narrowed due to the higher flame speed of H₂ than DME. Therefore, the reduced flame thickness may be the primary reason for the reduced exergy loss contribution by each source with increased H₂ substitution, as shown in Fig. 2. As the exergy loss characteristics of premixed H₂ flames has been thoroughly studied by Nishida et al. [³¹], only five H₂ blending percentages, namely 100% DME, 80% DME-20% H₂, 60% DME-40%H₂, 40% DME-60% H₂,and 20% DME-80% H₂ on a molar basis were evaluated in the following discussion.

As the initial and adiabatic temperatures indifferent flames show negligible variances, the changes of the flame thickness are mainly caused by the maximum temperature gradient [⁴⁹]. The temperature gradients in the DME/H₂-fueled laminar premixed flames are then demonstrated in Fig. 4. With increased H₂ substitution, the maximum temperature gradient slightly increases. The elevation in the maximum temperature gradient could further lead to the decrease in flame thickness. Besides, since the exergy loss from entropy generation is the integral of the entropy generation rate in the total reaction zone, the reduced flame thickness results in an overall decrease in the exergy loss with H₂ addition.

As discussed above, chemical reactions are the primary contributor to the exergy losses in premixed flames and increased H₂ substitution decreases the exergy losses from chemical reactions. To elucidate the chemical regime of H₂ addition on exergy loss reduction, the top contribution reactions are listed in Table 1, which contribute to over half of the exergy losses from chemical reactions. It seems that these contribution reactions are mainly related with the C1-C2 species and increased H₂ substitution generally decreases their contribution. The reason for this is that the carbon-containing fraction decreases as H₂ substitution increases, thus reducing the reaction rates of those C1-C2 reactions. However, among the listed C1-C2 reactions, two exceptions, R6 (HCO+ O₂ = CO+ HO₂) and R9 (CH₃OCH₃ + OH= CH₃OCH₂ + H₂O), are observed, which have more contributions to exergy losses with increased H₂ substitution in fuel blends. Further, reactions R3 (HCO+ M= H+ CO+ M), R6 (HCO+ O₂ = CO+ HO₂), and R10 (HO₂ + H= OH+ OH) are the most sensitive reactions to the changes in H₂ percentage in fuel blends, as the exergy losses induced by them change most significantly with increased H₂ substitution.

The normalized entropy generation rates from conduction in the DME/H₂-fueled flames are depicted in Fig. 5. From Eq. (10), it is observed that the determining factors of entropy generation caused by heat conduction are thermal conductivity coefficient, temperature, and temperature gradients. The coupled impacts of the above factors cause increased peak entropy generation rate with H₂ substitution. However, it is also observed that H₂ addition has more apparent effects on the flame thickness reduction, which may overcome the increased magnitude of the peak entropy generation rate from conduction. Therefore, the exergy loss from conduction is declined with H₂ substitution.

Primary species for the exergy losses from diffusion are exhibited in Fig. 6. These contribution species involve reactants (DME, H₂, and O₂) and products (CO, H₂O, and CO₂), as well as some key intermediate species, e.g., formaldehyde, H, O, and OH radicals. Increased H₂ substitution in fuel blends reduces the exergy losses by the diffusion of carbon-containing species as DME, formaldehyde, CO, and CO₂, which is reasonable due to the reduced carbon-containing DME percentage in fuel blends. Correspondingly, some hydrogen-containing species, such as H₂O and H₂ have more contribution with increased H₂ percentage in fuel blends. However, H and OH radicals show reduced contribution with increased H₂ substitution, although they are also hydrogen-containing species. This could be analyzed by Fig. 7, in which the entropy generation rate by H diffusion slightly increases, but the distribution region of the entropy generation has a more apparent reduction, thus causing an overall reduction of the exergy loss by the H radical diffusion. For the OH radical, the magnitude of the entropy generation rate by its diffusion decreases with increasing H₂ substitution, further causing reduced exergy loss by its diffusion based on its reduced distribution region. Generally, most species show reduced exergy losses with increased H₂ fraction, and thus the overall exergy loss from diffusion is slightly inhibited as H₂ substitution increases.

Table 2 lists the mole fractions of the species which are dominant in incomplete combustion products at the equilibrium state of the premixed flames of different DME/H₂ blends. It seems that all the major incomplete combustion products are carbon-free species. The H₂ and OH radical are two primary incomplete combustion products, followed by the H and O radicals. Increased H₂ substitution in fuel blends increases the mole fractions of the unburned fuels and combustion intermediates, e.g., H₂, H, and OH, but does not have obvious effects on the O radical. The increased fractions of these incomplete combustion products with increased H₂ substitution, therefore, enhance the exergy losses from incomplete combustion.

Conclusions

A second-law thermodynamic analysis for the DME/H₂/air premixed flames with changed fuel blending percentages was conducted. The exergy losses from the irreversibility sources and those from incomplete combustion products were analyzed and compared in the flames with changed fuel blends. Major conclusions are drawn as follows:

Chemical reaction and incomplete combustion are the key reasons for the exergy losses in all the flames studied, while heat conduction and mass diffusion are secondary contributors. The overall exergy losses in DME/H₂ premixed flames decrease by about 5% as the H₂ substitution increases from 0% to 100% on the molar basis.

Elevated H₂ substitution decreases the exergy losses from irreversibility sources, i.e., reactions, conduction, and diffusion, primarily because of the reduced flame thickness. The decreases in the exergy losses by chemical reactions and heat conduction are obvious, but the exergy loss reduction by diffusion is slight. For the exergy losses from reactions, the dominant contribution reactions are related with the C1-C2 species, which are reduced with increased H₂ substitution.

Primary incomplete combustion products are all carbon-free species, with H₂ and OH being the most dominant ones. Increased H₂ substitution increases the mole fractions of the unburned fuels and combustion intermediates, thus enhancing the exergy losses from incomplete combustion.

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