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A reduced mechanism for the prediction of methane-hydrogen flames in cooktop burners
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A reduced mechanism for the prediction of methane-hydrogen flames in cooktop burners Eduardo Gimeno-Escobedo a, Ana Cubero a, Jose Salvador Ochoa b, Norberto Fueyo a,* a
Fluid Dynamics Group, University of Zaragoza, Marı´a de Luna 3, 50018, Zaragoza, Spain Gas Competence Center, Product Division Cooking, BSH Home Appliances Group, Avd Eduardo Garcı´a del Rı´o 30, 39011, Santander, Spain
b
highlights A reduced chemical mechanism for methane-hydrogen cooktops with 26 species. Very good agreement for atmospheric 0D/1D flames, various methane-hydrogen contents. Good agreement for atmospheric 2D/3D flames (OpenFOAM). Transient analysis of light back events in a cooktop with several mechanisms. It replicates light back in 3D simulations of a cooktop burner, with a 4x speedup.
article info
abstract
Article history:
In order to reduce computing costs in the calculation of combustion in cooktops burning
Received 22 May 2019
methane-hydrogen mixtures, automatic reduction techniques have been used to develop a
Received in revised form
reduced mechanism for atmospheric, methane-hydrogen-air flames involving 26 species
14 August 2019
and 143 reactions starting from GRI-Mech 3.0. Validation for 0-D and 1-D calculations
Accepted 20 August 2019
shows good agreement with the original mechanism for gas mixtures ranging from pure
Available online 20 September 2019
methane up to a 1:1 methane-hydrogen ratio, showing that it can be used for a variety of methane-hydrogen mixtures. An improved, customized OpenFOAM solver has been
Keywords:
developed and employed to perform 2-D and 3-D calculations. Results from a computa-
Methane-hydrogen flames
tional experiment for an axisymmetric, partially premixed flame are in good agreement
Reduced mechanism
with the original mechanism and with published experimental results. Flame stability has
Cooktop burner
been studied in realistic 3-D methane-hydrogen cooktop calculations. Using the reduced
Light back
mechanism, light back phenomena are reproduced accurately while providing a fourfold
Cantera
speed-up over the original mechanism.
OpenFOAM
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. E-mail address: [email protected] (N. Fueyo). https://doi.org/10.1016/j.ijhydene.2019.08.165 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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Introduction
Table 1 e Overview of several available mechanisms for methane-hydrogen-air kinetics. Updated from [24].
The importance of methane-hydrogen kinetics
Mechanism
Year
Species
Reactions
Smooke [25] GRI-mech 3.0 [26] Konnov 0.5 [27] Leeds 1.5 [28] SKG03 [29] GDF-kin® [30] Dagaut [31] USC [32] Konnov 0.6 [33] Aramco [34] San Diego [35] Wang [36]
1991 2000 2000 2001 2004 2004 2005 2007 2009 2013 2016 2018
16 53 127 37 73 121 99 111 129 253 57 48
25 325 1207 351 520 883 735 784 1231 1542 268 308
Limited oil reserves and growing environmental concerns have encouraged research into alternatives that can replace oil derived fuels, at least to a certain extent. Hydrogen may be produced using renewable power, making it an attractive energy storage option that is being explored [1e3]. In addition, hydrogen may utilize some of the existing natural gas equipment and infrastructure, especially if blended with natural gas: blends can help tune some of the properties of the resulting fuel mixture in order to make it suitable for a particular application [4,5]. This makes methane-hydrogen mixtures an interesting option, and their use has been explored in different applications such as internal combustion engines [6,7], gas turbines [8], as well as both industrial and domestic appliances through the addition of hydrogen to the existing natural gas network [9e13]. Previous studies have confirmed the possibility of using natural gas-hydrogen blends as fuel for existing domestic appliances. The main issue regarding safe operation is light back, as reported in a study by de Vries et al. [14]. Several other studies support this, although the authors report different upper limits of hydrogen mole fraction to ensure safety. An upper limit of 20% by volume was found in a study in The Netherlands [15,16] while a study by Jones et al. in the UK reported an upper limit of 30% [17] and a recent study by Zhao et al. found an upper limit of 15% [13]. In addition, methanehydrogen mixtures are used in current certification tests for gas devices, for instance in the European Union [18,19]. This possibility has fostered interest in methane-hydrogen mechanisms that can be used in computational simulations, which are particularly interesting for gas appliances manufacturers since chemical kinetics models allow for efficient testing and design of equipment for these new fuel blends. Indeed, some efforts have been reported in previous studies regarding this application for other gases [20e22]. However, chemical kinetics involves tens to hundreds of species and hundreds to thousands of reactions for most widely-used fuels. The complexity of these detailed mechanisms has a huge impact on their applicability in the modeling of practical systems: in many Engineering applications, the size of the detailed mechanism would render a three-dimensional model impractical. This is true as well in the case of kinetic modeling in realistic cooktops, one of the main potential applications of methane-hydrogen mechanisms. Although several mechanisms available in the literature are suitable for methane-hydrogen kinetics, there exist few reduced mechanisms that aim to minimize the computing costs of including accurate chemical kinetics in CFD calculations. Table 1 presents a summary of currently available mechanisms for methane-hydrogen kinetics. Most of the mechanisms have at least 50 species, which drives computing costs impractical for many applications. All four most widely accepted mechanisms for methane-hydrogen kinetics have relatively large sizes as well: GRI-Mech 3.0, USC, Aramco and San Diego. Wang (48 species), and especially Smooke (16 species) and Leeds (37 species) are noteworthy exceptions.
Nonetheless, they are not as widely acknowledged and their size might not be optimal for the present modeling needs: the Smooke mechanism is not detailed enough to provide sufficient accuracy for this application, while the size of the Leeds mechanism will require too long computing times. A tailored solution that can provide a model with an optimized size for the study of methane-hydrogen domestic appliances is of great interest. Great efforts have been made by the combustion research community to find solutions that enable realistic chemistry calculations in demanding, real-life applications. A very promising approach consists in reduction techniques that produce mechanisms with a smaller number of species but that still retain high accuracy [23]. By constraining the reduction process with the most relevant chemico-physical phenomena, it is expected that a reduced version of a wellaccepted mechanism will retain enough accuracy to model chemistry in methane-hydrogen burners while lowering computing costs. The aim of this study is to explore the use of a reduced, customized kinetic model as a means to lower the cost of detailed chemical kinetics for domestic methane-hydrogen cooktops and enable more practical computational product development. Significant attention has been directed towards reproducing light back accurately in transient simulations of realistic methane-hydrogen cooktop burners. More generally, this study provides insights on the accuracy and effectiveness of specialised, significantly reduced mechanisms for their use in Engineering applications. To do so, a new mechanism has been reduced starting from GRI-Mech 3.0 and validated for several relevant methane-hydrogen mixtures using 0D and 1D calculations. Then, results for a 2D axisymmetric burner have been compared with experimental data. Finally, light back phenomena have been studied in realistic cooktop calculations using the original mechanism as a reference.
Selection of the original mechanism As shown in Table 1, there exist several mechanisms that can be used as a starting point in the reduction process. Chaumeix et al. [37], as part of their study, measured ignition delay times for different methane-hydrogen mixtures and compared their results to data obtained computationally with the GRI-Mech, Konnov, Marinov (a C4 mechanism) and Leeds mechanisms.
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Table 2 e Operating conditions employed for mechanism reduction. Equivalence ratios were sampled at intervals of 0.2. Unburnt gas temperature (K) 300 600
Pressure (atm)
Equivalence ratio range ()
1 1
0.8e1.6 0.8e2.2
They found Konnov to be the most accurate for ignition delay time, showing significantly better agreement for high vel et al. [38] evaluated the perforhydrogen contents. Me mance of GRI-Mech 3.0, Konnov and Dagaut mechanisms using a comprehensive experimental data set including laminar flame speed, ignition delay time, detonation cell size and species profiles from jet-stirred reactors. They concluded that all three of them give good results for laminar flame speed, while the most accurate mechanism was Dagaut for jet-stirred reactor data and ignition delay times and Konnov for detonation cell size. Nilsson et al. [39] obtained experimental laminar burning velocity data of methane and its blends with hydrogen, ethane and propane and compared their results with calculations using the Aramco v1.3, GRIMech 3.0, San Diego and USC mechanisms. They concluded that Aramco showed the best agreement overall while good agreement was found using GRI-Mech 3.0 for methanehydrogen mixtures containing neither ethane nor propane. Ji et al. [40] compared experimental laminar burning velocity data obtained from the literature with calculations using the GRI-Mech 3.0, Aramco v1.3, USC and San Diego mechanisms. It was found that Aramco v1.3 provided the best agreement overall, with all four mechanisms showing differences with experimental data for hydrogen contents between 60% and 80%. Donohoe et al. [41] measured ignition delay time and laminar flame speed experimentally for methane-hydrogen and natural gas-hydrogen mixtures and compared them to results obtained computationally using Aramco v1.3, GRIMech 3.0 and a modified version of GRI-Mech 3.0. Again, they concluded that Aramco v1.3 showed the best agreement overall. Khan et al. [42] provide new experimental data of methane-hydrogen laminar burning velocity and compare their results with calculations obtained with the San Diego, GRI-Mech 3.0 and USC mechanisms. Their findings indicate
Table 4 e Composition of all four test gases. Gas mixture G110 G222 G271 G20
H2 (% volume)
CH4 (% volume)
N2 (% volume)
50 23 0 0
26 77 74 100
24 0 26 0
that GRI-Mech 3.0 is the most accurate mechanism for laminar burning velocity. There exists significant variability in experimental data and conclusions obtained for these methane-hydrogen mixtures. Nonetheless, we believe most recent studies tend to view Aramco v1.3 as the mechanism available that shows better agreement with experimental data overall [39e41]. Nonetheless, GRI-Mech 3.0 was used as a starting point for several reasons: The use of GRI-Mech 3.0 for methane-hydrogen kinetics is well established: for cooktops, de Vries et al. [14] used GRIMech 3.0 to calculate flame speed values of natural gashydrogen mixtures to study their applicability in domestic appliances, showing excellent agreement with experimental data. More generally, it has been used extensively to model methane-hydrogen and natural gas-hydrogen flames [42e50]. The size of Aramco v1.3 makes realistic 3D cooktop calculations prohibitively costly, whereas the smaller size of GRI-Mech 3.0 allows for 3D calculations to validate results obtained with a reduced mechanism. GRI-Mech 3.0 provides comparable accuracy for our application: flame stability is paramount in the design of domestic methane-hydrogen gas cooktops, which operate at atmospheric pressure. GRI-Mech 3.0 provides high accuracy for flame speed under these conditions [14,42]; some differences with experimental data appear for ignition delay time data, high pressures or for mixtures containing
Table 3 e Summary of the reduction process. Column “Species” indicates the number of species of the resulting mechanism for that step. “Reduction technique” indicates the specific technique employed for each step. “Error [%]” indicates the maximum error for all targets under all operating conditions. Species Reactions Original mechanism Successful step 1 Successful step 2
Reduction technique
Error (%)
53
325
e
0
31
182
DRG
4.99
29
154
DRGEPSA
6.73
Fig. 1 e Flame speed values for the reduced mechanism gfn26 (lines) compared with the original mechanism GRIMech 3.0 (symbols) for all gas mixtures.
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GRI-Mech 3.0 has been shown to provide sub-optimal results for pure hydrogen flames and hydrogen-rich mixtures [51,52]. Nonetheless, we study mixtures with low to moderate hydrogen contents (up to 50% volume), which ensures good agreement with experimental data [40,42,53] while covering the maximum hydrogen contents recommended in previous studies for the existing gas infrastructure and appliances [13e17]. We suggest that our new reduced mechanism be used for methane-hydrogen ratios up to 1:1 by volume.
Methodology
Fig. 2 e Flame speed relative error for the reduced mechanism gfn26 compared with the original mechanism GRI-Mech 3.0 for all gas mixtures.
higher alkanes. Agreement for ignition delay time, although essential for internal combustion engines, was not deemed as important as flame speed and mechanism size for our application.
The starting mechanism for the reduction process is GRIMech 3.0. It comprises 53 species and 325 reactions. In order to reduce GRI-Mech 3.0, we used DRG, DRGEP and sensitivity analysis techniques. First, the faster (but less effective) directed relation graph (DRG [54]) and directed relation graph with error propagation (DRGEP [55]) are applied, alternating between them until they do not reduce the mechanism any further. Then, the more powerful but compute-intensive directed relation graph-aided sensitivity analysis (DRGASA [56,57]) and directed relation graph with error propagation and sensitivity analysis
Fig. 3 e Comparison of species profiles in freely propagating flames for all gas mixtures. Lines represent the reduced mechanism gfn26, symbols represent the original mechanism GRI-Mech 3.0.
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Fig. 4 e Comparison of ignition delay time as a function of equivalence ratio for all gas mixtures. Lines represent the reduced mechanism gfn26, symbols represent the original mechanism GRI-Mech 3.0.
Fig. 5 e Flame speed values for the reduced mechanism gfn26 (lines) compared with the original mechanism GRIMech 3.0 (symbols) using mixtures with several methanehydrogen contents. HXX represents XX% H2 contents by volume.
Fig. 6 e Flame speed relative error for the reduced mechanism gfn26 compared with the original mechanism GRI-Mech 3.0 using mixtures with different methanehydrogen contents. HXX represents XX% H2 contents by volume.
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Fig. 7 e Comparison of species profiles in freely propagating flames for several methane-hydrogen mixtures. HXX represents XX% H2 contents by volume. Lines represent the reduced mechanism gfn26, symbols represent the original mechanism GRI-Mech 3.0.
(DRGEPSA [58]) are employed, alternating between them until no further reduction is possible. Freely propagating flame calculations provide flame speed, an important property for flame stability. Therefore, the reduction process uses a set of one-dimensional, partially premixed, freely propagating flames. Since we intend to develop a mechanism suitable for gas mixtures with moderate hydrogen contents, these calculations were carried out using G110 as fuel. G110 is 50% H2 , 26% CH4 , 24% N2 , and is a
reference gas mixture used in European Union regulations for flame stability tests. This set of calculations is carried out using two temperatures for the unburnt mixture, 300 K and 600 K, and a range of equivalence ratios sampled at intervals of 0.2 for each temperature. Table 2 summarizes the range of operating conditions. Besides flame stability, carbon monoxide emissions and temperature play a key role in the design and operation of cooktop burners. Because of this, flame speed, maximum CO
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Fig. 8 e Comparison of ignition delay time as a function of equivalence ratio for several temperatures and methanehydrogen mixtures. HXX represents XX% H2 contents by volume. Lines represent the reduced mechanism gfn26, symbols represent the original mechanism GRI-Mech 3.0.
mole fraction and maximum temperature were used as target flame properties to drive the mechanism reduction methods. Temperature and CO profiles were not used in order to allow for a lighter final mechanism. In addition, comparisons with flame profiles are provided later in this study for validation. A relative tolerance of 10% is employed for all targets; that is, the reduced mechanism must be able to reproduce all three
targets under all operating conditions shown in Table 2 within a 10% error margin. The first DRG operation provides the greatest reduction, producing a mechanism with 31 species. After this step, only DRGEPSA succeeds in reducing the number of species, resulting in the final mechanism with 29 species and 154 reactions. Further reduction operations yield no positive results since removing additional species results in errors greater
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than 10%. Table 3 shows the results for each successful reduction step. The mechanism arising from this automatic reduction process still includes three species involved in the nitrogen chemistry: N, N2 H and NO. The influence of nitrogen chemistry in the main flame properties is very small, and, as shown in flame speed, ignition delay and species profiles data in the validation section, its removal does not change flame calculations noticeably when compared to results from the starting mechanism. The resulting mechanism comprises 26 species and 143 reactions, and is referred to in this study as gfn26.
Mechanism validation: 0D and 1D flames The open source software suite Cantera [59], version 2.3.0, is used to carry out calculations for simple flames to validate the new mechanism. A specific set of gas mixtures used in European Union regulations for testing flame stability in gas appliances has been used for mechanism validation. This set of benchmark gas mixtures includes a wide range of methane-hydrogen (and sometimes N2 ) contents and, thus, will ensure that the reduced mechanism can be used for a wide range of methanehydrogen ratios. These gas mixtures and their corresponding compositions are shown in Table 4. In all the validation calculations shown here, air is 78% N2 , 21% O2, and 1% Ar by volume.
Freely-propagating 1D flames The gfn26 reduced mechanism is first validated using partially premixed, freely-propagating flame calculations in Cantera. These calculations are carried out for all four gas mixtures, at a temperature of 300 K and pressure of 1 atm. Fig. 1 compares flame speed for the reduced mechanism (gfn26) and the original one (GRI-Mech 3.0); the agreement is very good. Fig. 2 shows the relative error in flame speed values obtained using gfn26 with respect to GRI-Mech 3.0. The relative error is less than 7% for all gas mixtures. Fig. 3 shows the molar fractions of several species along the freely propagating flames for each benchmark gas. These calculations were carried out at stoichiometric conditions. Good agreement is found, even for CO concentrations.
methane and natural gas ignition delay at lower temperatures [60,61].
Validation for several hydrogen contents The gfn26 mechanism has been developed to model chemical kinetics in methane-hydrogen-air flames with moderate amounts of H2 . In order to analyse its suitability for mixtures with varying methane-hydrogen contents in a more systematic way, its results are now compared to those of GRI-Mech 3.0 using mixtures with up to 50% H2 (by volume). Figs. 5 and 6 show flame speed data obtained using premixed fuel-air mixtures at a temperature of 300 K and pressure of 1 atm. Good agreement with GRI-Mech 3.0 is found for all H2 contents. The error is smaller than 5% in all cases. Fig. 7 shows good agreement for species profiles as well. Fig. 8 reveals that the reduced mechanism slightly underpredicts ignition delay times for mixtures with low H2 content at lower temperatures. Ignition delay calculations were carried out keeping pressure constant at 1 atm and using the temperatures shown in the graph as initial temperature.
Validation: yale flame This section presents the validation of the gfn26 reduced mechanism in a multidimensional flame that has been studied experimentally, the Yale flame [62]. The simulations are performed using the authors’ customized, OpenFOAM-based [63] solver for the prediction of laminar flames, that is introduced next.
Model and solver description For the simulation of multidimensional flames, including those in home appliances that will be presented below, the reduced mechanism has been embodied in a customized OpenFOAM solver that we call burnerFoam. The burnerFoam solver is based on rhoReactingFoam [64], with the addition of the following models: a P1 radiation
Ignition delay time in homogeneous 0D reactors The reduction procedure outlined in Section Methodology included neither ignition delay time as a target, nor calculations in Perfectly Stirred Reactors (PSR). Nonetheless, they have been included here for validation. Fig. 4 presents ignition delay time results obtained from closed, adiabatic, homogeneous, constant pressure calculations for all benchmark gas mixtures; pressure was held constant at 1 atm, and initial temperature for each set of data is shown on the graph. It shows generally an excellent agreement with the original mechanism; small differences are observed at 1000 K, especially for gas G222. Although GRIMech 3.0 was not originally validated for low temperatures, some studies subsequently published contain data for
Fig. 9 e Schematic of the experimental axisymmetric burner (adapted from reference [62]).
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Fig. 10 e Numerical configuration (left) and streamlines superimposed on temperature contours (right). model; a mass-diffusion library (see below); and conjugate heat transfer (including heat conduction in solid regions). The standard OpenFOAM solver for chemically reacting flows, rhoReactingFoam, inherits the assumption of unity Lewis number, a common approximation in turbulent combustion that is not generally applicable to laminar combusting flows. Instead, the burnerFoam solver makes use of a mass transport library developed by Novaresio et al. [65] for its use in OpenFOAM. It includes comprehensive models for mass !a diffusion in a multicomponent mixture ( j in the conservation equations shown in Appendix A), including the full multicomponent Stefan-Maxwell model. The binary (molecular) diffusion coefficients can be calculated using the Champan-Enskog or the Wilke-Lee models. We have migrated the original version of the mass transport library [65], compatible with OpenFOAM 1.5-dev, to the OpenFoam 5.0 and introduced some improvements. The original hard-coded species list has been avoided so that the chemical mechanism can be changed without having to recompile the code. Profiling (using the KCachegrind and Callgrind open-source toolkits [66]) revealed an inefficient implementation of loops over computational cells and species to calculate the binary diffusion coefficients. Our optimization has achieved a reduction in the whole solver execution time by two orders of magnitude when using the most accurate (but also the most computationally expensive) StefanMaxwell model. The design of domestic burners may also require the calculation of temperature variations within metal parts, such as the cooking vessel or the hob. The burnerFoam solver makes use of OpenFOAM toolkits for dealing with solid regions. Multiple regions can be defined in the problem domain by setting the mesh, models and conditions separately for each region. Flow and heat transfer in the complete domain are calculated by solving the conservation equations simultaneously in all the regions. Thermal coupling between
regions is taken into account through appropriate boundary conditions on both sides of the interface. Detailed chemistry in a multidimensional geometry means computationally expensive calculations. The burnerFoam solver allows for the use of capabilities available in OpenFOAM to mitigate the computational cost, such as Local Time Stepping (LTS) and Tabulation of Dynamically Adaptative Chemistry (TDAC). In the Local Time Step method, extended by Pang et al. [67] to reactive flows, the time step is calculated at each computational cell so that it is a large as possible (accounting for the local time scale of both the flow and enthalpy source); this reduces the computational effort needed to reach the steady-state. The TDAC method, developed by Contino et al. [68], provides efficient integration of complex laminar reaction chemistry by combining the
Fig. 11 e Comparison of axial velocity data obtained experimentally [62] and computationally with GRI-Mech 3.0 in this study.
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Since the original mechanism is smaller, less species conservation equations are built and solved The OpenFOAM solver developed by Cuoci et al. for laminar flames (called laminarSMOKE [69]) has been extensively and satisfactory tested on coflow diffusion flames using detailed chemical mechanisms and the Fickian diffusion model. Advantages of our new solver burnerFoam are the incorporation of the full multicomponent diffusion library, the LTS and TDAC method for accelerating chemistry calculations and the availability for the modeling of solid-gas thermal coupling. The results presented in this work are obtained using the Fick multicomponent diffusion model and the ChampanEnskog binary correlations. Fig. 12 e Prediction of temperature (K) evolution along the axis. advantages of automatic dynamic species and reaction reduction with In-Situ Adaptive Tabulation (ISAT). As part of TDAC, the DAC algorithm obtains a reduced mechanism based on local conditions. We believe this does not cancel the benefits of using a reduced original mechanism and that using a reduced mechanism such as gfn26 provides several advantages over using TDAC with a larger mechanism: Using a reduced original mechanism makes the reduction step in DAC less computationally expensive No reduction is carried out in the flame zone and, thus, a smaller original mechanism such as GFN26 lowers the computational cost
Validation For the validation of the gfn26 mechanism in multidimensional flames, we use the premixed methane-air flame studied experimentally and computationally by McEnally and Pfefferle [70] and Bennett et al. [62]. It is generated in the axisymmetric laboratory burner illustrated in Fig. 9. The premixed gas is methane and O2 -enriched air, with 25.5% oxygen concentration. It flows from a pipe with an inner radius rI ¼ 5:55 103 m. The secondary air flows from a coaxial pipe with an inner radius rO ¼ 4:76 102 m. The experimental study includes six fuel-rich mixtures, with equivalence ratios from F ¼ 2:464 to infinity (viz. a nonpremixed flame). We present here the comparison of experimental and computational results for the case with F ¼ 6:160.
Fig. 13 e Prediction of species molar fractions along the axis.
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Fig. 14 e Cooker burner configuration and picture during operation.
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The computational configuration is a 2D, axisymmetric domain spanning the whole burner in the radial direction, and L ¼ 0:136 m in the axial one, discretized with a structured, nonuniform mesh with 10; 719 cells (see Fig. 10, left). The boundary conditions are as follows. At the inner jet inlet, the velocity is set to 12:89 102 m=s and the CH4 , O2 and N2 mass fractions to 0.30226, 0.19627 and 0.50147 respectively. The inlet velocity of the secondary air is 12:89 102 m=s. Both jets enter at a temperature T ¼ 300 K. At the lateral wall, no-slip conditions are used for velocity, and the radial gradients of pressure, temperature and species are assumed to be zero. All these conditions are the same as those used by Bennett et al. [62] in their computational study using a vorticity-velocity formulation for the governing equations. At the domain outlet, the pressure is atmospheric and the velocity is extrapolated from the inner node. For temperature and species, an axial zero gradient is assumed if there is outflow; for inflows, the boundary values are fixed to the ambient conditions (air at T ¼ 300 K).
Fig. 15 e Schematic of the computational slice and detailed view of the port inlets.
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Fig. 10 displays temperature contours and streamlines obtained with the reduced gfn26 mechanism. The hightemperature region exhibits the typical wishbone shape, with the narrowing of streamlines indicating that the flow accelerates as the density decreases. Next to the outer lateral walls, two vortices are formed. In addition, Fig. 11 shows good agreement for axial velocity between our computational model using GRI-Mech 3.0 and experimental results obtained by Bennett et al. [62]. A quantitative comparison of experimental data and computational solutions is performed using three chemical mechanisms: the original GRI-Mech 3.0, the proposed reduced gfn26 mechanism with 26 species and the smaller Smooke mechanism [25] with 16 species. The latter is often used in industrial applications, although it is known to produce results that deviate with respect to GRI-Mech 3.0 in temperature, CO and H2 . Fig. 12 shows the evolution of temperature along the axis. The lines for the GRI-Mech 3.0 and gfn26 results overlap, and both predictions agree well with the experimental measurements. This is also true for both major species (e.g., CO2 ) and minor ones (such as OH), Fig. 13. There is some deviation with respect to the measurements, but the trend is reproduced and both GRI-Mech 3.0 and gfn26 yield the same results. The simpler Smooke mechanism, instead, fails in the prediction of temperature; and its solution for H2 and CO is significantly different from the GRI-Mech-3.0 one (Fig. 13). As for the computational cost, the converged solution is achieved four times as fast using gfn26 as compared with GRIMech 3.0. This speed-up is measured in cases where the chemical mechanism is directly integrated (i.e., not tabulated in-situ or dynamically reduced), and therefore, it suggests that the reduction decreases the system stiffness.
ports, with an additional propagation channel under the ports of the outer crown (see Fig. 14). Partially premixed fuel and air are supplied through the ports and the propagation channel. In order to reduce the computational cost, while retaining the geometrical complexity, we simulate a (periodicallyrepeating) sector involving one port in the inner ring and one and a half ports in the outer ring, as shown in Fig. 15. We do this by setting zero flux of all quantities (symmetry boundary conditions) for the lateral boundaries. Outer and upper boundaries are set as atmospheric pressure outlets with zero gradient of temperature and species if there is outflow, and ambient conditions (air at T ¼ 300 K) if there is inflow. For the burner and cooktop surfaces, no-slip conditions are used for velocity and radial gradients of pressure, temperature and species are set to zero. The resulting computational mesh has approximately 400; 000 cells. For certification, the burner is operated as heating an aluminum pan containing water. In this simulation this pan is accounted for as a solid region coupled to the gas region through conjugate heat transfer. The pan interior wall is assumed at constant temperature of T ¼ 350 K. The burner operates stably within a range of thermal powers. The lower end is limited by light back, and the higher one by flame lift off. Therefore, to study the onset of light back we have chosen to simulate the burner at a low thermal power. The detailed view in Fig. 15 (lower figure) shows this low-power, but stable, operation. For all three inlets (propagation channel, main port and interior ring), we used an
Prediction of light back propensity in a cooker burner This section shows the application of the gfn26 mechanism to investigate light back propensity in a real cooktop burner. First, the normal operation of the aerated burner, supplied with a rather fuel-rich mixture of methane and primary air, is simulated to obtain the reference solution for a stable flame. The fuel is then swapped with a hydrogen-enriched blend, with a CH4 -to-H2 ratio of 77/23 by volume. This is the composition of gas G222, which is the gas used in light back tests for burner certification. The stability limit is found by successively decreasing the equivalence ratio (increasing the primary air) until flame propagates upstream into the burner ports. This procedure for capturing light back requires solving accurately the flame transient evolution and involves chemistry integration for every time step; thus, it is very computeintensive. Both the GRI-Mech 3.0 and our reduced gfn26 mechanisms are used for comparison.
Stable flame The cooktop burner modeled is a commercially available, 6 kW burner. The burner has an inner and an outer crown of gas
Fig. 16 e Contours of temperature (top) and a detailed view of the flow represented by streamlines (bottom).
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Fig. 17 e Flame evolution after injecting the G222-air light back mixture (first stage). Filled contours: H2 mass fraction; line contours in red: flame position (represented by HCO mass fraction); black lines: Ux ¼ SL ¼ 1:09. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
equivalence ratio of 2.75 for the fuel-air mixture and temperature was set to 608 K, whereas velocity was set to 5:103 m=s for the interior ring and the main port and to 0:6 m= s for the propagation channel.
Fig. 16 shows three-dimensional images of the stable flames obtained using the gfn26 mechanism: temperature contours (top) and streamlines (bottom). The external and internal flames, anchored close to the respective ports,
Fig. 18 e Flame evolution after injecting the G222-air light back mixture (second stage). Filled contours: H2 mass fraction; line contours in red: flame position (represented by HCO mass fraction), showing light back in the propagation channel; black lines: Ux ¼ SL ¼ 1:09. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
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Fig. 19 e Comparison of mechanisms: laminar flame speeds for the premixed gas G222 at 608 K in the fuel-rich range.
become stretched and cooled as they approach the pan bottom. Stabilization vortices are formed around the flames.
Description of a light back event The flame speed for a mixture of air and G222 at an equivalence ratio of 4 ¼ 1:35 is SL ¼ 1:09 m=s at T ¼ 608 K. Therefore, once the methane-air mixture is replaced with this mixture, light back should be expected at the propagation channel, where the exit velocity of the fresh gases is 0:6 m=s (Fig. 15). The transient evolution of the flame is calculated at each time step using the burnerFOAM solver and the reduced gfn26 mechanism. The evolution, starting from the steady state solution for the stable mixture, is shown in Figs. 17 and 18, which present
snapshots at several times after the primary mixture is swapped at t ¼ 0. The figures show H2 mass fraction in solid contours, which indicates the presence of the fresh new fuel (since the previous one did not have any hydrogen contents); HCO mass fraction isolines, in red, which we use to mark the flame position; and the Ux ¼ SL locus, as a black solid line, which indicates the locations at which the axial velocity of the fluid equals the laminar flame speed. At t ¼ 0 s, the stable flame (Fig. 17(a)) is strongly anchored at the propagation channel (at the bottom of the burner main port), but it is somewhat lifted from the port eaves. At this initial time, the methane mixture is swapped with the G222 one; H2 can be seen entering the ports at t ¼ 0:001 s in Fig. 17(b). At t ¼ 0:005 s, Fig. 17(c), the new gas is flowing out of the main port and reaching the flame; at this point the initial flame is significantly changed, and the higher gas reactivity causes eventually its anchoring at main port eaves, as can be seen in Fig. 17(d). The gas in the propagation channel, flowing at a slower velocity, is only now starting to reach the port exit. The second stage of the flame evolution starts when the new gas mixture flows out the propagation channel, Fig. 18(a). The laminar flame speed here is greater than the gas velocity, and flame begins to move backwards towards the channel outlet (Fig. 18(b)), eventually entering the channel (Fig. 18(c)) and propagating upstream (Fig. 18(d)).
Effect of mechanisms on stability predictions Fig. 19 compares the flame speeds predicted by these three mechanisms for gas G222 at T ¼ 608 K in the fuel-rich range. The agreement between the full GRI-Mech 3.0 and the reduced gfn26 mechanisms is good. The Smooke mechanism, instead, predicts flame speeds significantly greater for mixtures closer to stoichiometry (4 < 1:6). The horizontal dashed line indicates
Fig. 20 e Comparison of the solutions obtained with the Smooke, gfn26 and GRI-Mech-3.0 mechanisms for the 6 kW burner with gas G222 at an equivalence ratio of 4 ¼ 1:53.
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 7 1 2 3 e2 7 1 4 0
the maximum flame speed to avoid light back in the propagation channel of the 6 kW burner (sL ¼ 0:67 m=s as obtained with gfn26). Therefore, the limiting equivalence ratio would be (approximately) 4 ¼ 1:53 for the GRI-Mech 3.0 and gfn26 mechanisms; the use of the Smooke mechanism would predict light back at this equivalence ratio. This performance of all three mechanisms is now confirmed in the practical burner. Starting with the solution for the stable flame, the new gas (G222 at 4 ¼ 1:53) is injected and the flame evolution solved. Fig. 20 shows that, as anticipated, the Smooke mechanism predicts flame propagation into the channel, whereas the solution obtained with the full GRI-Mech 3.0 mechanism and the reduced gfn26 are both close to the stability limit. We conclude that the gfn26 mechanism, which runs four times as fast as the full mechanism, provides a very good compromise between computational cost and accuracy in the prediction of light back.
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calculations show the gfn26 mechanism replicates flame stability and light back accurately. In addition, it provides a speedup factor of 4 compared to GRI-Mech 3.0, enabling the study of complex phenomena in methane-hydrogen cooktops with no significant loss of accuracy and at lower computing costs. This indicates similar reduction methods and strategies may provide lighter yet highly accurate models for other devices and fuels, making virtual testing more practical in some Engineering applications. Because of suboptimal performance of GRI-Mech 3.0 when used for high H2 content flames, we do not recommend using gfn26 for mixtures with methane-hydrogen ratios greater than 1:1. In addition, this mechanism was developed to be used in atmospheric pressure applications, and it may not be appropriate for higher pressures.
Acknowledgements Conclusions Methane-hydrogen mixtures pose an interesting alternative to traditional fuels. The most widely accepted mechanisms for modelling methane-hydrogen combustion kinetics involve many species and reactions, which makes them too computationally expensive for certain engineering applications. With the aim of exploring the potential of kinetic modelling for methane-hydrogen cooktops and developing a more computationally economical alternative, we have reduced and validated a new mechanism for methane-hydrogen flames with 26 species and 143 reactions using GRI-Mech 3.0 as the base mechanism. The resulting mechanism, gfn26, was validated through calculations for zero-dimensional perfectly-stirred reactors and one-dimensional freely propagating flames. These calculations were performed for a set of benchmark gas mixtures used in European Union legislation, as well as a set of gas mixtures within a range of methane-hydrogen ratios from pure methane up to a methane-hydrogen ratio of 1:1. Flame speed, species mole fraction and ignition delay time values obtained with the new gfn26 mechanism agree well with those obtained using GRI-Mech 3.0 for both sets of gases; errors for flame speed values remain below 7% for all gases and conditions tested, although some small differences were found for constant pressure ignition delay times at relatively low temperatures. This shows the versatility and robustness of this new mechanism, which make it suitable for a wide range of methane-hydrogen flames. Two-dimensional calculations replicating the experiment carried out by McEnally and Pfefferle [70] were performed using an improved, customized OpenFOAM solver. Good agreement was found between our reduced mechanism and the original one. Differences with experimental results were small; results obtained with our reduced mechanism were in better agreement with experimental data than those obtained using a smaller but specialised mechanism (16 species). Realistic, three-dimensional calculations of a cooktop burner were carried out in OpenFOAM and used to illustrate the flame behaviour during light back events. Further
Funding: This work was supported by the Agencia Estatal de n of Spain and the European Regional DevelopInvestigacio ment Fund [grant numbers RTC-2014-1847-6, ENE2016-80143R]. n Chorda produced a significant part of the software Ramo used in 0D/1D flames for managing calculations and analyzing results. The migration of the original version of the mass transport library [65] from OpenFOAM 1.5-dev to OpenFoam 5.0 was started by Dr Marı´a Garcı´a-Camprubı´. Some of the calculations were performed with computing time provided by the University of Cantabria on the Altamira supercomputer, a node in the Spanish National Supercomputing Network.
Appendix A. Conservation equations This appendix presents the conservation equations for species, mass, momentum and energy implemented in the OpenFOAM-based burnerFoam code to solve laminar flames. The conservation equation for the mass fraction ya of a species a is expressed as follows: !a vðrya Þ þ V $ ðr! v ya Þ þ V $ j ¼ u_ a (A.1) vt where r is the density, ! v is the velocity vector, a and u_ a are the !a generation of species a due to chemical reaction, and j is the diffusive mass flux of species which we calculated using previous work by Novaresio et al. [65]. The total mass balance results: vr þ V $ ðr! vÞ¼0 vt
(A.2)
The momentum conservation equation is: ! vðr! vÞ þ V $ ðr! v! vÞV $ ! t ¼ Vp þ r! g vt
(A.3)
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where p is the pressure, g is the gravitational acceleration and ! ! t is the viscous stress tensor. Newtonian fluid behaviour is assumed. Energy conservation is formulated as an equation for the sensible enthalpy, hs , as follows: X !a vðrhs Þ a þ V $ ðr! v hs Þ V $ ðkVTÞ þ V $ ¼ Q_ þ q_r hs j vt a
(A.4)
_ is the heat The first source term on the right-hand side, Q, release due to combustion and the second one, q_r , is due to thermal radiation.
Appendix B. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijhydene.2019.08.165.
references
[1] Gahleitner G. Hydrogen from renewable electricity: an international review of power-to-gas pilot plants for stationary applications. Int J Hydrogen Energy 2013;38(5):2039e61. https://doi.org/10.1016/ j.ijhydene.2012.12.010. [2] Schiebahn S, Grube T, Robinius M, Tietze V, Kumar B, Stolten D. Power to gas: technological overview, systems analysis and economic assessment for a case study in Germany. Int J Hydrogen Energy 2015;40(12):4285e94. https:// doi.org/10.1016/j.ijhydene.2015.01.123. [3] Qadrdan M, Abeysekera M, Chaudry M, Wu J, Jenkins N. Role of power-to-gas in an integrated gas and electricity system in Great Britain. Int J Hydrogen Energy 2015;40(17):5763e75. https://doi.org/10.1016/j.ijhydene.2015.03.004. [4] Schefer RW. Hydrogen enrichment for improved lean flame stability. Int J Hydrogen Energy 2003;28(10):1131e41. https:// doi.org/10.1016/S0360-3199(02)00199-4. [5] Karim GA, Wierzba I, Al-Alousi Y. Methane-hydrogen mixtures as fuels. Int J Hydrogen Energy 1996;21(7):625e31. https://doi.org/10.1016/0360-3199(95)00134-4. [6] Akansu SO, Dulger Z, Kahraman N, Veziroǧlu TN. Internal combustion engines fueled by natural gas-hydrogen mixtures. Int J Hydrogen Energy 2004;29(14):1527e39. https:// doi.org/10.1016/j.ijhydene.2004.01.018. [7] Bauer CG, Forest TW. Effect of hydrogen addition on the performance of methane-fueled vehicles. Part I: effect on S.I. engine performance. Int J Hydrogen Energy 2001;26(1):55e70. https://doi.org/10.1016/S0360-3199(00)00067-7. [8] Phillips JN, Roby RJ. Enhanced gas turbine combustor performance using H2-enriched natural gas. In: ASME 1999 international gas turbine and aeroengine congress and exhibition. American Society of Mechanical Engineers; 1999. https://doi.org/10.1115/99-GT-115. V002T02A020eV002T02A020. [9] Schouten JA, van Rosmalen RJ, Michels JPJ. Modeling hydrogen production for injection into the natural gas grid: balance between production, demand and storage. Int J Hydrogen Energy 2006;31(12):1698e706. https://doi.org/ 10.1016/j.ijhydene.2006.01.005. [10] Haeseldonckx D, D’haeseleer W. The use of the natural-gas pipeline infrastructure for hydrogen transport in a changing market structure. Int J Hydrogen Energy 2007;32(10):1381e6. https://doi.org/10.1016/j.ijhydene.2006.10.018. eHEC2005.
[11] Melaina MW, Antonia O, Penev M. Blending hydrogen into natural gas pipeline networks. In: A review of key issues, Tech. rep. National Renewable Energy Laboratory; 2013. [12] NaturalHy. Final publishable activity report, preparing for the hydrogen economy by using the existing natural gas system as a catalyst. Tech. Rep. 2010 N.V. Nederlandse Gasunie, Groningen, The Netherlands. [13] Zhao Y, McDonell V, Samuelsen S. Influence of hydrogen addition to pipeline natural gas on the combustion performance of a cooktop burner. Int J Hydrogen Energy 2019;44(23):12239e53. https://doi.org/10.1016/ j.ijhydene.2019.03.100. [14] de Vries H, Mokhov AV, Levinsky HB. The impact of natural gas/hydrogen mixtures on the performance of end-use equipment: interchangeability analysis for domestic appliances. Appl Energy 2017;208:1007e19. https://doi.org/ 10.1016/j.apenergy.2017.09.049. [15] Kippers M, De Laat J, Hermkens R, Overdiep J, van der Molen A, van Erp W, van der Meer A. Pilot project on hydrogen injection in natural gas on Island of Ameland in The Netherlands. International gas union research conference, vol. 19. Seoul: South Korea; 2011. [16] De Vries H, Florisson O, Tiekstra GC. Safe operation of natural gas appliances fueled with hydrogen/natural gas mixtures (progress obtained in the NATURALHY-project). In: International Conference on Hydrogen Safety, San Sebastian, Spain, September 11-13 2007; 2007. [17] Jones DR, Al-Masry WA, Dunnill C. Hydrogen-enriched natural gas as a domestic fuel: an analysis based on flashback and blow-off limits for domestic natural gas appliances within the UK. Sustainable Energy Fuels 2018;2:710e23. https://doi.org/10.1039/C7SE00598A. [18] Directive 2009/142/EC of the European Parliament and of the Council of 30 November 2009 relating to appliances burning gaseous fuels. 16.12 Orkesterjournalen L 2009;330. 10 (2009). [19] European standard EN 437:2003þa1:2009; test gases - test pressures - appliance categories. 2009. € _ Kantas‚ M. Investigation of partially-premixed [20] Ozdemir IB, combustion in a household cooker-top burner. Fuel Process Technol 2016;151:107e16. https://doi.org/10.1016/ j.fuproc.2016.04.039. € _ Use of computational combustion in the [21] Ozdemir IB. development and design of energy-efficient household cooker-top burners. J Energy Resour Technol 2016;139(2). https://doi.org/10.1115/1.4035256. 022206e022206e8. [22] Decker T, Baumgardner M, Prapas J, Bradley T. A mixed computational and experimental approach to improved biogas burner flame port design. Energy for Sustainable Development 2018;44:37e46. https://doi.org/10.1016/ j.esd.2018.02.008. [23] Lu T, Law CK. Toward accommodating realistic fuel chemistry in large-scale computations. Prog Energy Combust Sci 2009;35(2):192e215. https://doi.org/10.1016/ j.pecs.2008.10.002. [24] Hermanns RTE. Laminar burning velocities of methanehydrogen-air mixtures. PhD. thesis. Eindhoven: Technische Universiteit Eindhoven; 2007. https://doi.org/10.6100/IR630126. [25] Smooke M, Puri I, Seshadri K. A comparison between numerical calculations and experimental measurements of the structure of a counterflow diffusion flame burning diluted methane in diluted air. Symposium (International) on Combustion 1988;21(1):1783e92. https://doi.org/10.1016/ S0082-0784(88)80412-0. [26] Smith Gregory P, Golden David M, Frenklach Michael, Moriarty Nigel W, Eiteneer Boris, Goldenberg Mikhail, Thomas Bowman C, Hanson Ronald K, Song Soonho, William C, Gardiner Jr, Lissianski Vitali V, Qin Zhiwei. GRIMech 3.0. 1999. http://www.me.berkeley.edu/gri/_mech/.
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 7 1 2 3 e2 7 1 4 0
[27] Konnov AA. Detailed reaction mechanism for small hydrocarbons combustion. Release 0.5, available as Electronic Supplementary Material to: Coppens, F.H.V., de Ruyck, J. Konnov, A.A., The Effects of Composition on the Burning Velocity and Nitric Oxide Formation in Laminar Premixed Flames of CH4 þ H2 þ O2 þ N2. Combust Flame 2007;149:409e17. 2000. nyi T, Clague AR, Pilling MJ. Development [28] Hughes KJ, Tura and testing of a comprehensive chemical mechanism for the oxidation of methane. Int J Chem Kinet 2001;33(9):513e38. https://doi.org/10.1002/kin.1048. [29] Skreiberg Ø, Kilpinen P, Glarborg P. Ammonia chemistry below 1400 K under fuel-rich conditions in a flow reactor. Combust Flame 2004;136(4):501e18. https://doi.org/10.1016/ j.combustflame.2003.12.008. [30] El Bakali A, Dagaut P, Pillier L, Desgroux P, Pauwels J-F, Rida A, Meunier P. Experimental and modeling study of the oxidation of natural gas in a premixed flame, shock tube, and jet-stirred reactor. Combust Flame 2004;137(1):109e28. https://doi.org/10.1016/j.combustflame.2004.01.004. [31] Dagaut P, Nicolle A. Experimental and detailed kinetic modeling study of hydrogen-enriched natural gas blend oxidation over extended temperature and equivalence ratio ranges. Proc Combust Inst 2005;30(2):2631e8. https://doi.org/ 10.1016/j.proci.2004.07.030. [32] Wang H, You X, Joshi AV, Davis SG, Laskin A, Egolfopoulos F, Law CK. USC mech version II. High-temperature combustion reaction model of H2/CO/C1-C4 compounds. 2007. [33] Konnov AA. Implementation of the NCN pathway of promptNO formation in the detailed reaction mechanism. Combust Flame 2009;156(11):2093e105. https://doi.org/10.1016/ j.combustflame.2009.03.016. [34] Metcalfe WK, Burke SM, Ahmed SS, Curran HJ. A hierarchical and comparative kinetic modeling study of C1- h C2 ydrocarbon and oxygenated fuels. Int J Chem Kinet 2013;45(10):638e75. https://doi.org/10.1002/kin.20802. [35] Mechanical and Aerospace Engineering (Combustion Research). University of California at San Diego, chemicalkinetic mechanisms for combustion applications. San Diego Mechanism web page; 2016. URL, http://combustion.ucsd.edu. [36] Wang T, Zhang X, Zhang J, Hou X. Automatic generation of a kinetic skeletal mechanism for methane-hydrogen blends with nitrogen chemistry. Int J Hydrogen Energy 2018;43(6):3330e41. https://doi.org/10.1016/ j.ijhydene.2017.12.116. [37] Chaumeix N, Pichon S, Lafosse F, Paillard C-E. Role of chemical kinetics on the detonation properties of hydrogen/ natural gas/air mixtures. Int J Hydrogen Energy 2007;32(13):2216e26. https://doi.org/10.1016/ j.ijhydene.2007.04.008. ICHS-2005. vel R, Javoy S, Coudoro K, Dupre G, Paillard C-E. [38] Me Assessment of H2-CH4 air mixtures oxidation kinetic models used in combustion. Int J Hydrogen Energy 2012;37(1):698e714. https://doi.org/10.1016/ j.ijhydene.2011.09.099. 11th China Hydrogen Energy Conference. [39] Nilsson EJK, van Sprang A, Larfeldt J, Konnov AA. The comparative and combined effects of hydrogen addition on the laminar burning velocities of methane and its blends with ethane and propane. Fuel 2017;189:369e76. https:// doi.org/10.1016/j.fuel.2016.10.103. [40] Ji C, Wang D, Yang J, Wang S. A comprehensive study of light hydrocarbon mechanisms performance in predicting methane/hydrogen/air laminar burning velocities. Int J Hydrogen Energy 2017;42(27):17260e74. https://doi.org/ 10.1016/j.ijhydene.2017.05.203. [41] Donohoe N, Heufer A, Metcalfe WK, Curran HJ, Davis ML, Mathieu O, Plichta D, Morones A, Petersen EL, Gu¨the F.
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
27139
Ignition delay times, laminar flame speeds, and mechanism validation for natural gas/hydrogen blends at elevated pressures. Combust Flame 2014;161(6):1432e43. https:// doi.org/10.1016/j.combustflame.2013.12.005. Khan AR, Ravi MR, Ray A. Experimental and chemical kinetic studies of the effect of H2enrichment on the laminar burning velocity and flame stability of various multicomponent natural gas blends. Int J Hydrogen Energy 2019;44(2):1192e212. https://doi.org/10.1016/ j.ijhydene.2018.10.207. Ren J-Y, Qin W, Egolfopoulos FN, Tsotsis TT. Strain-rate effects on hydrogen-enhanced lean premixed combustion. Combust Flame 2001;124(4):717e20. https://doi.org/10.1016/ S0010-2180(00)00205-4. Ren J-Y, Qin W, Egolfopoulos FN, Mak H, Tsotsis TT. Methane reforming and its potential effect on the efficiency and pollutant emissions of lean methane-air combustion. Chem Eng Sci 2001;vol. 56(4):1541e9. https://doi.org/10.1016/S00092509(00)00381-X. 16th international conference on chemical reactor engineering. Briones AM, Aggarwal SK, Katta VR. Effects of H2enrichment on the propagation characteristics of -CH4 air triple flames. Combust Flame 2008;153(3):367e83. https://doi.org/10.1016/ j.combustflame.2008.02.005. Wang J, Huang Z, Tang C, Miao H, Wang X. Numerical study of the effect of hydrogen addition on methaneeair mixtures combustion. Int J Hydrogen Energy 2009;34(2):1084e96. https://doi.org/10.1016/j.ijhydene.2008.11.010. Bougrine S, Richard S, Nicolle A, Veynante D. Numerical study of laminar flame properties of diluted methanehydrogen-air flames at high pressure and temperature using detailed chemistry. Int J Hydrogen Energy 2011;36(18):12035e47. https://doi.org/10.1016/ j.ijhydene.2011.06.053. Okafor EC, Hayakawa A, Nagano Y, Kitagawa T. Effects of hydrogen concentration on premixed laminar flames of hydrogen-methane-air. Int J Hydrogen Energy 2014;39(5):2409e17. https://doi.org/10.1016/ j.ijhydene.2013.11.128. Liu J, Zhang X, Wang T, Hou X, Zhang J, Zheng S. Numerical study of the chemical, thermal and diffusion effects of H2 and CO addition on the laminar flame speeds of methane-air mixture. Int J Hydrogen Energy 2015;40(26):8475e83. https:// doi.org/10.1016/j.ijhydene.2015.04.133. Okafor EC, Nagano Y, Kitagawa T. Experimental and theoretical analysis of cellular instability in lean H2-CH4-air flames at elevated pressures. Int J Hydrogen Energy 2016;41(15):6581e92. https://doi.org/10.1016/ j.ijhydene.2016.02.151. Weydahl T, Poyyapakkam M, Seljeskog M, Haugen NEL. Assessment of existing H2/O2 chemical reaction mechanisms at reheat gas turbine conditions. Int J Hydrogen Energy 2011;36(18):12025e34. https://doi.org/10.1016/ j.ijhydene.2011.06.063. Conaire M, Curran HJ, Simmie JM, Pitz WJ, Westbrook CK. A O comprehensive modeling study of hydrogen oxidation. Int J Chem Kinet 2004;36(11):603e22. https://doi.org/10.1002/ kin.20036. Hu E, Huang Z, He J, Jin C, Zheng J. Experimental and numerical study on laminar burning characteristics of premixed methane-hydrogen-air flames. Int J Hydrogen Energy 2009;34(11):4876e88. https://doi.org/10.1016/ j.ijhydene.2009.03.058. 2nd International Workshop on Hydrogen. Lu T, Law CK. A directed relation graph method for mechanism reduction. Proc Combust Inst 2005;30(1):1333e41. https://doi.org/10.1016/ j.proci.2004.08.145.
27140
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 7 1 2 3 e2 7 1 4 0
[55] Pepiot-Desjardins P, Pitsch H. An efficient error-propagationbased reduction method for large chemical kinetic mechanisms. Combust Flame 2008;154(1):67e81. https:// doi.org/10.1016/j.combustflame.2007.10.020. [56] Sankaran R, Hawkes ER, Chen JH, Lu T, Law CK. Structure of a spatially developing turbulent lean methane-air Bunsen flame. Proc Combust Inst 2007;31(1):1291e8. https://doi.org/ 10.1016/j.proci.2006.08.025. [57] Zheng XL, Lu TF, Law CK. Experimental counterflow ignition temperatures and reaction mechanisms of 1,3-butadiene. Proc Combust Inst 2007;31(1):367e75. https://doi.org/10.1016/ j.proci.2006.07.182. [58] Niemeyer KE, Sung C-J, Raju MP. Skeletal mechanism generation for surrogate fuels using directed relation graph with error propagation and sensitivity analysis. Combust Flame 2010;157(9):1760e70. https://doi.org/10.1016/ j.combustflame.2009.12.022. [59] D. G. Goodwin, H. K. Moffat, R. L. Speth, Cantera: an objectoriented software toolkit for chemical kinetics, thermodynamics, and transport processes, http:// www.cantera.org, Version 2.3.0 (2017). doi:10.5281/ zenodo.170284. [60] Huang J, Hill PG, Bushe WK, Munshi SR. Shock-tube study of methane ignition under engine-relevant conditions: experiments and modeling. Combust Flame 2004;136(1):25e42. https://doi.org/10.1016/ j.combustflame.2003.09.002. [61] Herzler J, Naumann C. Shock-tube study of the ignition of methane/ethane/hydrogen mixtures with hydrogen contents from 0% to 100% at different pressures. Proc Combust Inst 2009;32(1):213e20. https://doi.org/10.1016/ j.proci.2008.07.034. [62] Bennett BAV, McEnally CS, Pfefferle LD, Smooke MD. Computational and experimental study of axisymmetric
[63] [64] [65]
[66] [67]
[68]
[69]
[70]
coflow partially premixed methane/air flames. Combust Flame 2000;123(4):522e46. https://doi.org/10.1016/S00102180(00)00158-9. OpenFOAM 5.0. The OpenFOAM Foundation; 2017. http:// www.openfoam.org/release/5-0. Source code for rhoReactingFoam, documentation, https:// cpp.openfoam.org/v5/rhoReactingFoam_8C.html. Novaresio V, Garcı´a-Camprubı´ M, Izquierdo S, Asinari P, Fueyo N. An open-source library for the numerical modeling of mass-transfer in solid oxide fuel cells. Comput Phys Commun 2012;183(1):125e46. https://doi.org/10.1016/ j.cpc.2011.08.003. Weidendorfer J. KCachegrind-call graph viewer. 2013. https:// kcachegrind.github.io/. Pang KM, Ivarsson A, Haider S, Schramm J. Development and validation of a local time stepping-based PaSR solver for combustion and radiation modeling. In: Proceedings of 8th international OpenFOAM workshop; 2013. Contino F, Jeanmart H, Lucchini T, D’Errico G. Coupling of in situ adaptive tabulation and dynamic adaptive chemistry: an effective method for solving combustion in engine simulations. Proc Combust Inst 2011;32(2):3057e64. https:// doi.org/10.1016/j.proci.2010.08.002. Cuoci A, Frassoldati A, Faravelli T, Ranzi E. A computational tool for the detailed kinetic modeling of laminar flames: application to C2H4/CH4 coflow flames. Combust Flame 2013;160(5):870e86. https://doi.org/10.1016/ j.combustflame.2013.01.011. McEnally CS, Pfefferle LD. Experimental study of nonfuel hydrocarbon concentrations in coflowing partially premixed methane/air flames. Combust Flame 1999;118(4):619e32. https://doi.org/10.1016/S0010-2180(99)00017-6.
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A reduced mechanism for the prediction of methane-hydrogen flames in cooktop burners Eduardo Gimeno-Escobedo a, Ana Cubero a, Jose Salvador Ochoa b, Norberto Fueyo a,* a
Fluid Dynamics Group, University of Zaragoza, Marı´a de Luna 3, 50018, Zaragoza, Spain Gas Competence Center, Product Division Cooking, BSH Home Appliances Group, Avd Eduardo Garcı´a del Rı´o 30, 39011, Santander, Spain
b
highlights A reduced chemical mechanism for methane-hydrogen cooktops with 26 species. Very good agreement for atmospheric 0D/1D flames, various methane-hydrogen contents. Good agreement for atmospheric 2D/3D flames (OpenFOAM). Transient analysis of light back events in a cooktop with several mechanisms. It replicates light back in 3D simulations of a cooktop burner, with a 4x speedup.
article info
abstract
Article history:
In order to reduce computing costs in the calculation of combustion in cooktops burning
Received 22 May 2019
methane-hydrogen mixtures, automatic reduction techniques have been used to develop a
Received in revised form
reduced mechanism for atmospheric, methane-hydrogen-air flames involving 26 species
14 August 2019
and 143 reactions starting from GRI-Mech 3.0. Validation for 0-D and 1-D calculations
Accepted 20 August 2019
shows good agreement with the original mechanism for gas mixtures ranging from pure
Available online 20 September 2019
methane up to a 1:1 methane-hydrogen ratio, showing that it can be used for a variety of methane-hydrogen mixtures. An improved, customized OpenFOAM solver has been
Keywords:
developed and employed to perform 2-D and 3-D calculations. Results from a computa-
Methane-hydrogen flames
tional experiment for an axisymmetric, partially premixed flame are in good agreement
Reduced mechanism
with the original mechanism and with published experimental results. Flame stability has
Cooktop burner
been studied in realistic 3-D methane-hydrogen cooktop calculations. Using the reduced
Light back
mechanism, light back phenomena are reproduced accurately while providing a fourfold
Cantera
speed-up over the original mechanism.
OpenFOAM
© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. E-mail address: [email protected] (N. Fueyo). https://doi.org/10.1016/j.ijhydene.2019.08.165 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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Introduction
Table 1 e Overview of several available mechanisms for methane-hydrogen-air kinetics. Updated from [24].
The importance of methane-hydrogen kinetics
Mechanism
Year
Species
Reactions
Smooke [25] GRI-mech 3.0 [26] Konnov 0.5 [27] Leeds 1.5 [28] SKG03 [29] GDF-kin® [30] Dagaut [31] USC [32] Konnov 0.6 [33] Aramco [34] San Diego [35] Wang [36]
1991 2000 2000 2001 2004 2004 2005 2007 2009 2013 2016 2018
16 53 127 37 73 121 99 111 129 253 57 48
25 325 1207 351 520 883 735 784 1231 1542 268 308
Limited oil reserves and growing environmental concerns have encouraged research into alternatives that can replace oil derived fuels, at least to a certain extent. Hydrogen may be produced using renewable power, making it an attractive energy storage option that is being explored [1e3]. In addition, hydrogen may utilize some of the existing natural gas equipment and infrastructure, especially if blended with natural gas: blends can help tune some of the properties of the resulting fuel mixture in order to make it suitable for a particular application [4,5]. This makes methane-hydrogen mixtures an interesting option, and their use has been explored in different applications such as internal combustion engines [6,7], gas turbines [8], as well as both industrial and domestic appliances through the addition of hydrogen to the existing natural gas network [9e13]. Previous studies have confirmed the possibility of using natural gas-hydrogen blends as fuel for existing domestic appliances. The main issue regarding safe operation is light back, as reported in a study by de Vries et al. [14]. Several other studies support this, although the authors report different upper limits of hydrogen mole fraction to ensure safety. An upper limit of 20% by volume was found in a study in The Netherlands [15,16] while a study by Jones et al. in the UK reported an upper limit of 30% [17] and a recent study by Zhao et al. found an upper limit of 15% [13]. In addition, methanehydrogen mixtures are used in current certification tests for gas devices, for instance in the European Union [18,19]. This possibility has fostered interest in methane-hydrogen mechanisms that can be used in computational simulations, which are particularly interesting for gas appliances manufacturers since chemical kinetics models allow for efficient testing and design of equipment for these new fuel blends. Indeed, some efforts have been reported in previous studies regarding this application for other gases [20e22]. However, chemical kinetics involves tens to hundreds of species and hundreds to thousands of reactions for most widely-used fuels. The complexity of these detailed mechanisms has a huge impact on their applicability in the modeling of practical systems: in many Engineering applications, the size of the detailed mechanism would render a three-dimensional model impractical. This is true as well in the case of kinetic modeling in realistic cooktops, one of the main potential applications of methane-hydrogen mechanisms. Although several mechanisms available in the literature are suitable for methane-hydrogen kinetics, there exist few reduced mechanisms that aim to minimize the computing costs of including accurate chemical kinetics in CFD calculations. Table 1 presents a summary of currently available mechanisms for methane-hydrogen kinetics. Most of the mechanisms have at least 50 species, which drives computing costs impractical for many applications. All four most widely accepted mechanisms for methane-hydrogen kinetics have relatively large sizes as well: GRI-Mech 3.0, USC, Aramco and San Diego. Wang (48 species), and especially Smooke (16 species) and Leeds (37 species) are noteworthy exceptions.
Nonetheless, they are not as widely acknowledged and their size might not be optimal for the present modeling needs: the Smooke mechanism is not detailed enough to provide sufficient accuracy for this application, while the size of the Leeds mechanism will require too long computing times. A tailored solution that can provide a model with an optimized size for the study of methane-hydrogen domestic appliances is of great interest. Great efforts have been made by the combustion research community to find solutions that enable realistic chemistry calculations in demanding, real-life applications. A very promising approach consists in reduction techniques that produce mechanisms with a smaller number of species but that still retain high accuracy [23]. By constraining the reduction process with the most relevant chemico-physical phenomena, it is expected that a reduced version of a wellaccepted mechanism will retain enough accuracy to model chemistry in methane-hydrogen burners while lowering computing costs. The aim of this study is to explore the use of a reduced, customized kinetic model as a means to lower the cost of detailed chemical kinetics for domestic methane-hydrogen cooktops and enable more practical computational product development. Significant attention has been directed towards reproducing light back accurately in transient simulations of realistic methane-hydrogen cooktop burners. More generally, this study provides insights on the accuracy and effectiveness of specialised, significantly reduced mechanisms for their use in Engineering applications. To do so, a new mechanism has been reduced starting from GRI-Mech 3.0 and validated for several relevant methane-hydrogen mixtures using 0D and 1D calculations. Then, results for a 2D axisymmetric burner have been compared with experimental data. Finally, light back phenomena have been studied in realistic cooktop calculations using the original mechanism as a reference.
Selection of the original mechanism As shown in Table 1, there exist several mechanisms that can be used as a starting point in the reduction process. Chaumeix et al. [37], as part of their study, measured ignition delay times for different methane-hydrogen mixtures and compared their results to data obtained computationally with the GRI-Mech, Konnov, Marinov (a C4 mechanism) and Leeds mechanisms.
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Table 2 e Operating conditions employed for mechanism reduction. Equivalence ratios were sampled at intervals of 0.2. Unburnt gas temperature (K) 300 600
Pressure (atm)
Equivalence ratio range ()
1 1
0.8e1.6 0.8e2.2
They found Konnov to be the most accurate for ignition delay time, showing significantly better agreement for high vel et al. [38] evaluated the perforhydrogen contents. Me mance of GRI-Mech 3.0, Konnov and Dagaut mechanisms using a comprehensive experimental data set including laminar flame speed, ignition delay time, detonation cell size and species profiles from jet-stirred reactors. They concluded that all three of them give good results for laminar flame speed, while the most accurate mechanism was Dagaut for jet-stirred reactor data and ignition delay times and Konnov for detonation cell size. Nilsson et al. [39] obtained experimental laminar burning velocity data of methane and its blends with hydrogen, ethane and propane and compared their results with calculations using the Aramco v1.3, GRIMech 3.0, San Diego and USC mechanisms. They concluded that Aramco showed the best agreement overall while good agreement was found using GRI-Mech 3.0 for methanehydrogen mixtures containing neither ethane nor propane. Ji et al. [40] compared experimental laminar burning velocity data obtained from the literature with calculations using the GRI-Mech 3.0, Aramco v1.3, USC and San Diego mechanisms. It was found that Aramco v1.3 provided the best agreement overall, with all four mechanisms showing differences with experimental data for hydrogen contents between 60% and 80%. Donohoe et al. [41] measured ignition delay time and laminar flame speed experimentally for methane-hydrogen and natural gas-hydrogen mixtures and compared them to results obtained computationally using Aramco v1.3, GRIMech 3.0 and a modified version of GRI-Mech 3.0. Again, they concluded that Aramco v1.3 showed the best agreement overall. Khan et al. [42] provide new experimental data of methane-hydrogen laminar burning velocity and compare their results with calculations obtained with the San Diego, GRI-Mech 3.0 and USC mechanisms. Their findings indicate
Table 4 e Composition of all four test gases. Gas mixture G110 G222 G271 G20
H2 (% volume)
CH4 (% volume)
N2 (% volume)
50 23 0 0
26 77 74 100
24 0 26 0
that GRI-Mech 3.0 is the most accurate mechanism for laminar burning velocity. There exists significant variability in experimental data and conclusions obtained for these methane-hydrogen mixtures. Nonetheless, we believe most recent studies tend to view Aramco v1.3 as the mechanism available that shows better agreement with experimental data overall [39e41]. Nonetheless, GRI-Mech 3.0 was used as a starting point for several reasons: The use of GRI-Mech 3.0 for methane-hydrogen kinetics is well established: for cooktops, de Vries et al. [14] used GRIMech 3.0 to calculate flame speed values of natural gashydrogen mixtures to study their applicability in domestic appliances, showing excellent agreement with experimental data. More generally, it has been used extensively to model methane-hydrogen and natural gas-hydrogen flames [42e50]. The size of Aramco v1.3 makes realistic 3D cooktop calculations prohibitively costly, whereas the smaller size of GRI-Mech 3.0 allows for 3D calculations to validate results obtained with a reduced mechanism. GRI-Mech 3.0 provides comparable accuracy for our application: flame stability is paramount in the design of domestic methane-hydrogen gas cooktops, which operate at atmospheric pressure. GRI-Mech 3.0 provides high accuracy for flame speed under these conditions [14,42]; some differences with experimental data appear for ignition delay time data, high pressures or for mixtures containing
Table 3 e Summary of the reduction process. Column “Species” indicates the number of species of the resulting mechanism for that step. “Reduction technique” indicates the specific technique employed for each step. “Error [%]” indicates the maximum error for all targets under all operating conditions. Species Reactions Original mechanism Successful step 1 Successful step 2
Reduction technique
Error (%)
53
325
e
0
31
182
DRG
4.99
29
154
DRGEPSA
6.73
Fig. 1 e Flame speed values for the reduced mechanism gfn26 (lines) compared with the original mechanism GRIMech 3.0 (symbols) for all gas mixtures.
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GRI-Mech 3.0 has been shown to provide sub-optimal results for pure hydrogen flames and hydrogen-rich mixtures [51,52]. Nonetheless, we study mixtures with low to moderate hydrogen contents (up to 50% volume), which ensures good agreement with experimental data [40,42,53] while covering the maximum hydrogen contents recommended in previous studies for the existing gas infrastructure and appliances [13e17]. We suggest that our new reduced mechanism be used for methane-hydrogen ratios up to 1:1 by volume.
Methodology
Fig. 2 e Flame speed relative error for the reduced mechanism gfn26 compared with the original mechanism GRI-Mech 3.0 for all gas mixtures.
higher alkanes. Agreement for ignition delay time, although essential for internal combustion engines, was not deemed as important as flame speed and mechanism size for our application.
The starting mechanism for the reduction process is GRIMech 3.0. It comprises 53 species and 325 reactions. In order to reduce GRI-Mech 3.0, we used DRG, DRGEP and sensitivity analysis techniques. First, the faster (but less effective) directed relation graph (DRG [54]) and directed relation graph with error propagation (DRGEP [55]) are applied, alternating between them until they do not reduce the mechanism any further. Then, the more powerful but compute-intensive directed relation graph-aided sensitivity analysis (DRGASA [56,57]) and directed relation graph with error propagation and sensitivity analysis
Fig. 3 e Comparison of species profiles in freely propagating flames for all gas mixtures. Lines represent the reduced mechanism gfn26, symbols represent the original mechanism GRI-Mech 3.0.
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Fig. 4 e Comparison of ignition delay time as a function of equivalence ratio for all gas mixtures. Lines represent the reduced mechanism gfn26, symbols represent the original mechanism GRI-Mech 3.0.
Fig. 5 e Flame speed values for the reduced mechanism gfn26 (lines) compared with the original mechanism GRIMech 3.0 (symbols) using mixtures with several methanehydrogen contents. HXX represents XX% H2 contents by volume.
Fig. 6 e Flame speed relative error for the reduced mechanism gfn26 compared with the original mechanism GRI-Mech 3.0 using mixtures with different methanehydrogen contents. HXX represents XX% H2 contents by volume.
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Fig. 7 e Comparison of species profiles in freely propagating flames for several methane-hydrogen mixtures. HXX represents XX% H2 contents by volume. Lines represent the reduced mechanism gfn26, symbols represent the original mechanism GRI-Mech 3.0.
(DRGEPSA [58]) are employed, alternating between them until no further reduction is possible. Freely propagating flame calculations provide flame speed, an important property for flame stability. Therefore, the reduction process uses a set of one-dimensional, partially premixed, freely propagating flames. Since we intend to develop a mechanism suitable for gas mixtures with moderate hydrogen contents, these calculations were carried out using G110 as fuel. G110 is 50% H2 , 26% CH4 , 24% N2 , and is a
reference gas mixture used in European Union regulations for flame stability tests. This set of calculations is carried out using two temperatures for the unburnt mixture, 300 K and 600 K, and a range of equivalence ratios sampled at intervals of 0.2 for each temperature. Table 2 summarizes the range of operating conditions. Besides flame stability, carbon monoxide emissions and temperature play a key role in the design and operation of cooktop burners. Because of this, flame speed, maximum CO
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Fig. 8 e Comparison of ignition delay time as a function of equivalence ratio for several temperatures and methanehydrogen mixtures. HXX represents XX% H2 contents by volume. Lines represent the reduced mechanism gfn26, symbols represent the original mechanism GRI-Mech 3.0.
mole fraction and maximum temperature were used as target flame properties to drive the mechanism reduction methods. Temperature and CO profiles were not used in order to allow for a lighter final mechanism. In addition, comparisons with flame profiles are provided later in this study for validation. A relative tolerance of 10% is employed for all targets; that is, the reduced mechanism must be able to reproduce all three
targets under all operating conditions shown in Table 2 within a 10% error margin. The first DRG operation provides the greatest reduction, producing a mechanism with 31 species. After this step, only DRGEPSA succeeds in reducing the number of species, resulting in the final mechanism with 29 species and 154 reactions. Further reduction operations yield no positive results since removing additional species results in errors greater
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than 10%. Table 3 shows the results for each successful reduction step. The mechanism arising from this automatic reduction process still includes three species involved in the nitrogen chemistry: N, N2 H and NO. The influence of nitrogen chemistry in the main flame properties is very small, and, as shown in flame speed, ignition delay and species profiles data in the validation section, its removal does not change flame calculations noticeably when compared to results from the starting mechanism. The resulting mechanism comprises 26 species and 143 reactions, and is referred to in this study as gfn26.
Mechanism validation: 0D and 1D flames The open source software suite Cantera [59], version 2.3.0, is used to carry out calculations for simple flames to validate the new mechanism. A specific set of gas mixtures used in European Union regulations for testing flame stability in gas appliances has been used for mechanism validation. This set of benchmark gas mixtures includes a wide range of methane-hydrogen (and sometimes N2 ) contents and, thus, will ensure that the reduced mechanism can be used for a wide range of methanehydrogen ratios. These gas mixtures and their corresponding compositions are shown in Table 4. In all the validation calculations shown here, air is 78% N2 , 21% O2, and 1% Ar by volume.
Freely-propagating 1D flames The gfn26 reduced mechanism is first validated using partially premixed, freely-propagating flame calculations in Cantera. These calculations are carried out for all four gas mixtures, at a temperature of 300 K and pressure of 1 atm. Fig. 1 compares flame speed for the reduced mechanism (gfn26) and the original one (GRI-Mech 3.0); the agreement is very good. Fig. 2 shows the relative error in flame speed values obtained using gfn26 with respect to GRI-Mech 3.0. The relative error is less than 7% for all gas mixtures. Fig. 3 shows the molar fractions of several species along the freely propagating flames for each benchmark gas. These calculations were carried out at stoichiometric conditions. Good agreement is found, even for CO concentrations.
methane and natural gas ignition delay at lower temperatures [60,61].
Validation for several hydrogen contents The gfn26 mechanism has been developed to model chemical kinetics in methane-hydrogen-air flames with moderate amounts of H2 . In order to analyse its suitability for mixtures with varying methane-hydrogen contents in a more systematic way, its results are now compared to those of GRI-Mech 3.0 using mixtures with up to 50% H2 (by volume). Figs. 5 and 6 show flame speed data obtained using premixed fuel-air mixtures at a temperature of 300 K and pressure of 1 atm. Good agreement with GRI-Mech 3.0 is found for all H2 contents. The error is smaller than 5% in all cases. Fig. 7 shows good agreement for species profiles as well. Fig. 8 reveals that the reduced mechanism slightly underpredicts ignition delay times for mixtures with low H2 content at lower temperatures. Ignition delay calculations were carried out keeping pressure constant at 1 atm and using the temperatures shown in the graph as initial temperature.
Validation: yale flame This section presents the validation of the gfn26 reduced mechanism in a multidimensional flame that has been studied experimentally, the Yale flame [62]. The simulations are performed using the authors’ customized, OpenFOAM-based [63] solver for the prediction of laminar flames, that is introduced next.
Model and solver description For the simulation of multidimensional flames, including those in home appliances that will be presented below, the reduced mechanism has been embodied in a customized OpenFOAM solver that we call burnerFoam. The burnerFoam solver is based on rhoReactingFoam [64], with the addition of the following models: a P1 radiation
Ignition delay time in homogeneous 0D reactors The reduction procedure outlined in Section Methodology included neither ignition delay time as a target, nor calculations in Perfectly Stirred Reactors (PSR). Nonetheless, they have been included here for validation. Fig. 4 presents ignition delay time results obtained from closed, adiabatic, homogeneous, constant pressure calculations for all benchmark gas mixtures; pressure was held constant at 1 atm, and initial temperature for each set of data is shown on the graph. It shows generally an excellent agreement with the original mechanism; small differences are observed at 1000 K, especially for gas G222. Although GRIMech 3.0 was not originally validated for low temperatures, some studies subsequently published contain data for
Fig. 9 e Schematic of the experimental axisymmetric burner (adapted from reference [62]).
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Fig. 10 e Numerical configuration (left) and streamlines superimposed on temperature contours (right). model; a mass-diffusion library (see below); and conjugate heat transfer (including heat conduction in solid regions). The standard OpenFOAM solver for chemically reacting flows, rhoReactingFoam, inherits the assumption of unity Lewis number, a common approximation in turbulent combustion that is not generally applicable to laminar combusting flows. Instead, the burnerFoam solver makes use of a mass transport library developed by Novaresio et al. [65] for its use in OpenFOAM. It includes comprehensive models for mass !a diffusion in a multicomponent mixture ( j in the conservation equations shown in Appendix A), including the full multicomponent Stefan-Maxwell model. The binary (molecular) diffusion coefficients can be calculated using the Champan-Enskog or the Wilke-Lee models. We have migrated the original version of the mass transport library [65], compatible with OpenFOAM 1.5-dev, to the OpenFoam 5.0 and introduced some improvements. The original hard-coded species list has been avoided so that the chemical mechanism can be changed without having to recompile the code. Profiling (using the KCachegrind and Callgrind open-source toolkits [66]) revealed an inefficient implementation of loops over computational cells and species to calculate the binary diffusion coefficients. Our optimization has achieved a reduction in the whole solver execution time by two orders of magnitude when using the most accurate (but also the most computationally expensive) StefanMaxwell model. The design of domestic burners may also require the calculation of temperature variations within metal parts, such as the cooking vessel or the hob. The burnerFoam solver makes use of OpenFOAM toolkits for dealing with solid regions. Multiple regions can be defined in the problem domain by setting the mesh, models and conditions separately for each region. Flow and heat transfer in the complete domain are calculated by solving the conservation equations simultaneously in all the regions. Thermal coupling between
regions is taken into account through appropriate boundary conditions on both sides of the interface. Detailed chemistry in a multidimensional geometry means computationally expensive calculations. The burnerFoam solver allows for the use of capabilities available in OpenFOAM to mitigate the computational cost, such as Local Time Stepping (LTS) and Tabulation of Dynamically Adaptative Chemistry (TDAC). In the Local Time Step method, extended by Pang et al. [67] to reactive flows, the time step is calculated at each computational cell so that it is a large as possible (accounting for the local time scale of both the flow and enthalpy source); this reduces the computational effort needed to reach the steady-state. The TDAC method, developed by Contino et al. [68], provides efficient integration of complex laminar reaction chemistry by combining the
Fig. 11 e Comparison of axial velocity data obtained experimentally [62] and computationally with GRI-Mech 3.0 in this study.
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Since the original mechanism is smaller, less species conservation equations are built and solved The OpenFOAM solver developed by Cuoci et al. for laminar flames (called laminarSMOKE [69]) has been extensively and satisfactory tested on coflow diffusion flames using detailed chemical mechanisms and the Fickian diffusion model. Advantages of our new solver burnerFoam are the incorporation of the full multicomponent diffusion library, the LTS and TDAC method for accelerating chemistry calculations and the availability for the modeling of solid-gas thermal coupling. The results presented in this work are obtained using the Fick multicomponent diffusion model and the ChampanEnskog binary correlations. Fig. 12 e Prediction of temperature (K) evolution along the axis. advantages of automatic dynamic species and reaction reduction with In-Situ Adaptive Tabulation (ISAT). As part of TDAC, the DAC algorithm obtains a reduced mechanism based on local conditions. We believe this does not cancel the benefits of using a reduced original mechanism and that using a reduced mechanism such as gfn26 provides several advantages over using TDAC with a larger mechanism: Using a reduced original mechanism makes the reduction step in DAC less computationally expensive No reduction is carried out in the flame zone and, thus, a smaller original mechanism such as GFN26 lowers the computational cost
Validation For the validation of the gfn26 mechanism in multidimensional flames, we use the premixed methane-air flame studied experimentally and computationally by McEnally and Pfefferle [70] and Bennett et al. [62]. It is generated in the axisymmetric laboratory burner illustrated in Fig. 9. The premixed gas is methane and O2 -enriched air, with 25.5% oxygen concentration. It flows from a pipe with an inner radius rI ¼ 5:55 103 m. The secondary air flows from a coaxial pipe with an inner radius rO ¼ 4:76 102 m. The experimental study includes six fuel-rich mixtures, with equivalence ratios from F ¼ 2:464 to infinity (viz. a nonpremixed flame). We present here the comparison of experimental and computational results for the case with F ¼ 6:160.
Fig. 13 e Prediction of species molar fractions along the axis.
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Fig. 14 e Cooker burner configuration and picture during operation.
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The computational configuration is a 2D, axisymmetric domain spanning the whole burner in the radial direction, and L ¼ 0:136 m in the axial one, discretized with a structured, nonuniform mesh with 10; 719 cells (see Fig. 10, left). The boundary conditions are as follows. At the inner jet inlet, the velocity is set to 12:89 102 m=s and the CH4 , O2 and N2 mass fractions to 0.30226, 0.19627 and 0.50147 respectively. The inlet velocity of the secondary air is 12:89 102 m=s. Both jets enter at a temperature T ¼ 300 K. At the lateral wall, no-slip conditions are used for velocity, and the radial gradients of pressure, temperature and species are assumed to be zero. All these conditions are the same as those used by Bennett et al. [62] in their computational study using a vorticity-velocity formulation for the governing equations. At the domain outlet, the pressure is atmospheric and the velocity is extrapolated from the inner node. For temperature and species, an axial zero gradient is assumed if there is outflow; for inflows, the boundary values are fixed to the ambient conditions (air at T ¼ 300 K).
Fig. 15 e Schematic of the computational slice and detailed view of the port inlets.
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Fig. 10 displays temperature contours and streamlines obtained with the reduced gfn26 mechanism. The hightemperature region exhibits the typical wishbone shape, with the narrowing of streamlines indicating that the flow accelerates as the density decreases. Next to the outer lateral walls, two vortices are formed. In addition, Fig. 11 shows good agreement for axial velocity between our computational model using GRI-Mech 3.0 and experimental results obtained by Bennett et al. [62]. A quantitative comparison of experimental data and computational solutions is performed using three chemical mechanisms: the original GRI-Mech 3.0, the proposed reduced gfn26 mechanism with 26 species and the smaller Smooke mechanism [25] with 16 species. The latter is often used in industrial applications, although it is known to produce results that deviate with respect to GRI-Mech 3.0 in temperature, CO and H2 . Fig. 12 shows the evolution of temperature along the axis. The lines for the GRI-Mech 3.0 and gfn26 results overlap, and both predictions agree well with the experimental measurements. This is also true for both major species (e.g., CO2 ) and minor ones (such as OH), Fig. 13. There is some deviation with respect to the measurements, but the trend is reproduced and both GRI-Mech 3.0 and gfn26 yield the same results. The simpler Smooke mechanism, instead, fails in the prediction of temperature; and its solution for H2 and CO is significantly different from the GRI-Mech-3.0 one (Fig. 13). As for the computational cost, the converged solution is achieved four times as fast using gfn26 as compared with GRIMech 3.0. This speed-up is measured in cases where the chemical mechanism is directly integrated (i.e., not tabulated in-situ or dynamically reduced), and therefore, it suggests that the reduction decreases the system stiffness.
ports, with an additional propagation channel under the ports of the outer crown (see Fig. 14). Partially premixed fuel and air are supplied through the ports and the propagation channel. In order to reduce the computational cost, while retaining the geometrical complexity, we simulate a (periodicallyrepeating) sector involving one port in the inner ring and one and a half ports in the outer ring, as shown in Fig. 15. We do this by setting zero flux of all quantities (symmetry boundary conditions) for the lateral boundaries. Outer and upper boundaries are set as atmospheric pressure outlets with zero gradient of temperature and species if there is outflow, and ambient conditions (air at T ¼ 300 K) if there is inflow. For the burner and cooktop surfaces, no-slip conditions are used for velocity and radial gradients of pressure, temperature and species are set to zero. The resulting computational mesh has approximately 400; 000 cells. For certification, the burner is operated as heating an aluminum pan containing water. In this simulation this pan is accounted for as a solid region coupled to the gas region through conjugate heat transfer. The pan interior wall is assumed at constant temperature of T ¼ 350 K. The burner operates stably within a range of thermal powers. The lower end is limited by light back, and the higher one by flame lift off. Therefore, to study the onset of light back we have chosen to simulate the burner at a low thermal power. The detailed view in Fig. 15 (lower figure) shows this low-power, but stable, operation. For all three inlets (propagation channel, main port and interior ring), we used an
Prediction of light back propensity in a cooker burner This section shows the application of the gfn26 mechanism to investigate light back propensity in a real cooktop burner. First, the normal operation of the aerated burner, supplied with a rather fuel-rich mixture of methane and primary air, is simulated to obtain the reference solution for a stable flame. The fuel is then swapped with a hydrogen-enriched blend, with a CH4 -to-H2 ratio of 77/23 by volume. This is the composition of gas G222, which is the gas used in light back tests for burner certification. The stability limit is found by successively decreasing the equivalence ratio (increasing the primary air) until flame propagates upstream into the burner ports. This procedure for capturing light back requires solving accurately the flame transient evolution and involves chemistry integration for every time step; thus, it is very computeintensive. Both the GRI-Mech 3.0 and our reduced gfn26 mechanisms are used for comparison.
Stable flame The cooktop burner modeled is a commercially available, 6 kW burner. The burner has an inner and an outer crown of gas
Fig. 16 e Contours of temperature (top) and a detailed view of the flow represented by streamlines (bottom).
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Fig. 17 e Flame evolution after injecting the G222-air light back mixture (first stage). Filled contours: H2 mass fraction; line contours in red: flame position (represented by HCO mass fraction); black lines: Ux ¼ SL ¼ 1:09. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
equivalence ratio of 2.75 for the fuel-air mixture and temperature was set to 608 K, whereas velocity was set to 5:103 m=s for the interior ring and the main port and to 0:6 m= s for the propagation channel.
Fig. 16 shows three-dimensional images of the stable flames obtained using the gfn26 mechanism: temperature contours (top) and streamlines (bottom). The external and internal flames, anchored close to the respective ports,
Fig. 18 e Flame evolution after injecting the G222-air light back mixture (second stage). Filled contours: H2 mass fraction; line contours in red: flame position (represented by HCO mass fraction), showing light back in the propagation channel; black lines: Ux ¼ SL ¼ 1:09. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)
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Fig. 19 e Comparison of mechanisms: laminar flame speeds for the premixed gas G222 at 608 K in the fuel-rich range.
become stretched and cooled as they approach the pan bottom. Stabilization vortices are formed around the flames.
Description of a light back event The flame speed for a mixture of air and G222 at an equivalence ratio of 4 ¼ 1:35 is SL ¼ 1:09 m=s at T ¼ 608 K. Therefore, once the methane-air mixture is replaced with this mixture, light back should be expected at the propagation channel, where the exit velocity of the fresh gases is 0:6 m=s (Fig. 15). The transient evolution of the flame is calculated at each time step using the burnerFOAM solver and the reduced gfn26 mechanism. The evolution, starting from the steady state solution for the stable mixture, is shown in Figs. 17 and 18, which present
snapshots at several times after the primary mixture is swapped at t ¼ 0. The figures show H2 mass fraction in solid contours, which indicates the presence of the fresh new fuel (since the previous one did not have any hydrogen contents); HCO mass fraction isolines, in red, which we use to mark the flame position; and the Ux ¼ SL locus, as a black solid line, which indicates the locations at which the axial velocity of the fluid equals the laminar flame speed. At t ¼ 0 s, the stable flame (Fig. 17(a)) is strongly anchored at the propagation channel (at the bottom of the burner main port), but it is somewhat lifted from the port eaves. At this initial time, the methane mixture is swapped with the G222 one; H2 can be seen entering the ports at t ¼ 0:001 s in Fig. 17(b). At t ¼ 0:005 s, Fig. 17(c), the new gas is flowing out of the main port and reaching the flame; at this point the initial flame is significantly changed, and the higher gas reactivity causes eventually its anchoring at main port eaves, as can be seen in Fig. 17(d). The gas in the propagation channel, flowing at a slower velocity, is only now starting to reach the port exit. The second stage of the flame evolution starts when the new gas mixture flows out the propagation channel, Fig. 18(a). The laminar flame speed here is greater than the gas velocity, and flame begins to move backwards towards the channel outlet (Fig. 18(b)), eventually entering the channel (Fig. 18(c)) and propagating upstream (Fig. 18(d)).
Effect of mechanisms on stability predictions Fig. 19 compares the flame speeds predicted by these three mechanisms for gas G222 at T ¼ 608 K in the fuel-rich range. The agreement between the full GRI-Mech 3.0 and the reduced gfn26 mechanisms is good. The Smooke mechanism, instead, predicts flame speeds significantly greater for mixtures closer to stoichiometry (4 < 1:6). The horizontal dashed line indicates
Fig. 20 e Comparison of the solutions obtained with the Smooke, gfn26 and GRI-Mech-3.0 mechanisms for the 6 kW burner with gas G222 at an equivalence ratio of 4 ¼ 1:53.
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 7 1 2 3 e2 7 1 4 0
the maximum flame speed to avoid light back in the propagation channel of the 6 kW burner (sL ¼ 0:67 m=s as obtained with gfn26). Therefore, the limiting equivalence ratio would be (approximately) 4 ¼ 1:53 for the GRI-Mech 3.0 and gfn26 mechanisms; the use of the Smooke mechanism would predict light back at this equivalence ratio. This performance of all three mechanisms is now confirmed in the practical burner. Starting with the solution for the stable flame, the new gas (G222 at 4 ¼ 1:53) is injected and the flame evolution solved. Fig. 20 shows that, as anticipated, the Smooke mechanism predicts flame propagation into the channel, whereas the solution obtained with the full GRI-Mech 3.0 mechanism and the reduced gfn26 are both close to the stability limit. We conclude that the gfn26 mechanism, which runs four times as fast as the full mechanism, provides a very good compromise between computational cost and accuracy in the prediction of light back.
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calculations show the gfn26 mechanism replicates flame stability and light back accurately. In addition, it provides a speedup factor of 4 compared to GRI-Mech 3.0, enabling the study of complex phenomena in methane-hydrogen cooktops with no significant loss of accuracy and at lower computing costs. This indicates similar reduction methods and strategies may provide lighter yet highly accurate models for other devices and fuels, making virtual testing more practical in some Engineering applications. Because of suboptimal performance of GRI-Mech 3.0 when used for high H2 content flames, we do not recommend using gfn26 for mixtures with methane-hydrogen ratios greater than 1:1. In addition, this mechanism was developed to be used in atmospheric pressure applications, and it may not be appropriate for higher pressures.
Acknowledgements Conclusions Methane-hydrogen mixtures pose an interesting alternative to traditional fuels. The most widely accepted mechanisms for modelling methane-hydrogen combustion kinetics involve many species and reactions, which makes them too computationally expensive for certain engineering applications. With the aim of exploring the potential of kinetic modelling for methane-hydrogen cooktops and developing a more computationally economical alternative, we have reduced and validated a new mechanism for methane-hydrogen flames with 26 species and 143 reactions using GRI-Mech 3.0 as the base mechanism. The resulting mechanism, gfn26, was validated through calculations for zero-dimensional perfectly-stirred reactors and one-dimensional freely propagating flames. These calculations were performed for a set of benchmark gas mixtures used in European Union legislation, as well as a set of gas mixtures within a range of methane-hydrogen ratios from pure methane up to a methane-hydrogen ratio of 1:1. Flame speed, species mole fraction and ignition delay time values obtained with the new gfn26 mechanism agree well with those obtained using GRI-Mech 3.0 for both sets of gases; errors for flame speed values remain below 7% for all gases and conditions tested, although some small differences were found for constant pressure ignition delay times at relatively low temperatures. This shows the versatility and robustness of this new mechanism, which make it suitable for a wide range of methane-hydrogen flames. Two-dimensional calculations replicating the experiment carried out by McEnally and Pfefferle [70] were performed using an improved, customized OpenFOAM solver. Good agreement was found between our reduced mechanism and the original one. Differences with experimental results were small; results obtained with our reduced mechanism were in better agreement with experimental data than those obtained using a smaller but specialised mechanism (16 species). Realistic, three-dimensional calculations of a cooktop burner were carried out in OpenFOAM and used to illustrate the flame behaviour during light back events. Further
Funding: This work was supported by the Agencia Estatal de n of Spain and the European Regional DevelopInvestigacio ment Fund [grant numbers RTC-2014-1847-6, ENE2016-80143R]. n Chorda produced a significant part of the software Ramo used in 0D/1D flames for managing calculations and analyzing results. The migration of the original version of the mass transport library [65] from OpenFOAM 1.5-dev to OpenFoam 5.0 was started by Dr Marı´a Garcı´a-Camprubı´. Some of the calculations were performed with computing time provided by the University of Cantabria on the Altamira supercomputer, a node in the Spanish National Supercomputing Network.
Appendix A. Conservation equations This appendix presents the conservation equations for species, mass, momentum and energy implemented in the OpenFOAM-based burnerFoam code to solve laminar flames. The conservation equation for the mass fraction ya of a species a is expressed as follows: !a vðrya Þ þ V $ ðr! v ya Þ þ V $ j ¼ u_ a (A.1) vt where r is the density, ! v is the velocity vector, a and u_ a are the !a generation of species a due to chemical reaction, and j is the diffusive mass flux of species which we calculated using previous work by Novaresio et al. [65]. The total mass balance results: vr þ V $ ðr! vÞ¼0 vt
(A.2)
The momentum conservation equation is: ! vðr! vÞ þ V $ ðr! v! vÞV $ ! t ¼ Vp þ r! g vt
(A.3)
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where p is the pressure, g is the gravitational acceleration and ! ! t is the viscous stress tensor. Newtonian fluid behaviour is assumed. Energy conservation is formulated as an equation for the sensible enthalpy, hs , as follows: X !a vðrhs Þ a þ V $ ðr! v hs Þ V $ ðkVTÞ þ V $ ¼ Q_ þ q_r hs j vt a
(A.4)
_ is the heat The first source term on the right-hand side, Q, release due to combustion and the second one, q_r , is due to thermal radiation.
Appendix B. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijhydene.2019.08.165.
references
[1] Gahleitner G. Hydrogen from renewable electricity: an international review of power-to-gas pilot plants for stationary applications. Int J Hydrogen Energy 2013;38(5):2039e61. https://doi.org/10.1016/ j.ijhydene.2012.12.010. [2] Schiebahn S, Grube T, Robinius M, Tietze V, Kumar B, Stolten D. Power to gas: technological overview, systems analysis and economic assessment for a case study in Germany. Int J Hydrogen Energy 2015;40(12):4285e94. https:// doi.org/10.1016/j.ijhydene.2015.01.123. [3] Qadrdan M, Abeysekera M, Chaudry M, Wu J, Jenkins N. Role of power-to-gas in an integrated gas and electricity system in Great Britain. Int J Hydrogen Energy 2015;40(17):5763e75. https://doi.org/10.1016/j.ijhydene.2015.03.004. [4] Schefer RW. Hydrogen enrichment for improved lean flame stability. Int J Hydrogen Energy 2003;28(10):1131e41. https:// doi.org/10.1016/S0360-3199(02)00199-4. [5] Karim GA, Wierzba I, Al-Alousi Y. Methane-hydrogen mixtures as fuels. Int J Hydrogen Energy 1996;21(7):625e31. https://doi.org/10.1016/0360-3199(95)00134-4. [6] Akansu SO, Dulger Z, Kahraman N, Veziroǧlu TN. Internal combustion engines fueled by natural gas-hydrogen mixtures. Int J Hydrogen Energy 2004;29(14):1527e39. https:// doi.org/10.1016/j.ijhydene.2004.01.018. [7] Bauer CG, Forest TW. Effect of hydrogen addition on the performance of methane-fueled vehicles. Part I: effect on S.I. engine performance. Int J Hydrogen Energy 2001;26(1):55e70. https://doi.org/10.1016/S0360-3199(00)00067-7. [8] Phillips JN, Roby RJ. Enhanced gas turbine combustor performance using H2-enriched natural gas. In: ASME 1999 international gas turbine and aeroengine congress and exhibition. American Society of Mechanical Engineers; 1999. https://doi.org/10.1115/99-GT-115. V002T02A020eV002T02A020. [9] Schouten JA, van Rosmalen RJ, Michels JPJ. Modeling hydrogen production for injection into the natural gas grid: balance between production, demand and storage. Int J Hydrogen Energy 2006;31(12):1698e706. https://doi.org/ 10.1016/j.ijhydene.2006.01.005. [10] Haeseldonckx D, D’haeseleer W. The use of the natural-gas pipeline infrastructure for hydrogen transport in a changing market structure. Int J Hydrogen Energy 2007;32(10):1381e6. https://doi.org/10.1016/j.ijhydene.2006.10.018. eHEC2005.
[11] Melaina MW, Antonia O, Penev M. Blending hydrogen into natural gas pipeline networks. In: A review of key issues, Tech. rep. National Renewable Energy Laboratory; 2013. [12] NaturalHy. Final publishable activity report, preparing for the hydrogen economy by using the existing natural gas system as a catalyst. Tech. Rep. 2010 N.V. Nederlandse Gasunie, Groningen, The Netherlands. [13] Zhao Y, McDonell V, Samuelsen S. Influence of hydrogen addition to pipeline natural gas on the combustion performance of a cooktop burner. Int J Hydrogen Energy 2019;44(23):12239e53. https://doi.org/10.1016/ j.ijhydene.2019.03.100. [14] de Vries H, Mokhov AV, Levinsky HB. The impact of natural gas/hydrogen mixtures on the performance of end-use equipment: interchangeability analysis for domestic appliances. Appl Energy 2017;208:1007e19. https://doi.org/ 10.1016/j.apenergy.2017.09.049. [15] Kippers M, De Laat J, Hermkens R, Overdiep J, van der Molen A, van Erp W, van der Meer A. Pilot project on hydrogen injection in natural gas on Island of Ameland in The Netherlands. International gas union research conference, vol. 19. Seoul: South Korea; 2011. [16] De Vries H, Florisson O, Tiekstra GC. Safe operation of natural gas appliances fueled with hydrogen/natural gas mixtures (progress obtained in the NATURALHY-project). In: International Conference on Hydrogen Safety, San Sebastian, Spain, September 11-13 2007; 2007. [17] Jones DR, Al-Masry WA, Dunnill C. Hydrogen-enriched natural gas as a domestic fuel: an analysis based on flashback and blow-off limits for domestic natural gas appliances within the UK. Sustainable Energy Fuels 2018;2:710e23. https://doi.org/10.1039/C7SE00598A. [18] Directive 2009/142/EC of the European Parliament and of the Council of 30 November 2009 relating to appliances burning gaseous fuels. 16.12 Orkesterjournalen L 2009;330. 10 (2009). [19] European standard EN 437:2003þa1:2009; test gases - test pressures - appliance categories. 2009. € _ Kantas‚ M. Investigation of partially-premixed [20] Ozdemir IB, combustion in a household cooker-top burner. Fuel Process Technol 2016;151:107e16. https://doi.org/10.1016/ j.fuproc.2016.04.039. € _ Use of computational combustion in the [21] Ozdemir IB. development and design of energy-efficient household cooker-top burners. J Energy Resour Technol 2016;139(2). https://doi.org/10.1115/1.4035256. 022206e022206e8. [22] Decker T, Baumgardner M, Prapas J, Bradley T. A mixed computational and experimental approach to improved biogas burner flame port design. Energy for Sustainable Development 2018;44:37e46. https://doi.org/10.1016/ j.esd.2018.02.008. [23] Lu T, Law CK. Toward accommodating realistic fuel chemistry in large-scale computations. Prog Energy Combust Sci 2009;35(2):192e215. https://doi.org/10.1016/ j.pecs.2008.10.002. [24] Hermanns RTE. Laminar burning velocities of methanehydrogen-air mixtures. PhD. thesis. Eindhoven: Technische Universiteit Eindhoven; 2007. https://doi.org/10.6100/IR630126. [25] Smooke M, Puri I, Seshadri K. A comparison between numerical calculations and experimental measurements of the structure of a counterflow diffusion flame burning diluted methane in diluted air. Symposium (International) on Combustion 1988;21(1):1783e92. https://doi.org/10.1016/ S0082-0784(88)80412-0. [26] Smith Gregory P, Golden David M, Frenklach Michael, Moriarty Nigel W, Eiteneer Boris, Goldenberg Mikhail, Thomas Bowman C, Hanson Ronald K, Song Soonho, William C, Gardiner Jr, Lissianski Vitali V, Qin Zhiwei. GRIMech 3.0. 1999. http://www.me.berkeley.edu/gri/_mech/.
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 7 1 2 3 e2 7 1 4 0
[27] Konnov AA. Detailed reaction mechanism for small hydrocarbons combustion. Release 0.5, available as Electronic Supplementary Material to: Coppens, F.H.V., de Ruyck, J. Konnov, A.A., The Effects of Composition on the Burning Velocity and Nitric Oxide Formation in Laminar Premixed Flames of CH4 þ H2 þ O2 þ N2. Combust Flame 2007;149:409e17. 2000. nyi T, Clague AR, Pilling MJ. Development [28] Hughes KJ, Tura and testing of a comprehensive chemical mechanism for the oxidation of methane. Int J Chem Kinet 2001;33(9):513e38. https://doi.org/10.1002/kin.1048. [29] Skreiberg Ø, Kilpinen P, Glarborg P. Ammonia chemistry below 1400 K under fuel-rich conditions in a flow reactor. Combust Flame 2004;136(4):501e18. https://doi.org/10.1016/ j.combustflame.2003.12.008. [30] El Bakali A, Dagaut P, Pillier L, Desgroux P, Pauwels J-F, Rida A, Meunier P. Experimental and modeling study of the oxidation of natural gas in a premixed flame, shock tube, and jet-stirred reactor. Combust Flame 2004;137(1):109e28. https://doi.org/10.1016/j.combustflame.2004.01.004. [31] Dagaut P, Nicolle A. Experimental and detailed kinetic modeling study of hydrogen-enriched natural gas blend oxidation over extended temperature and equivalence ratio ranges. Proc Combust Inst 2005;30(2):2631e8. https://doi.org/ 10.1016/j.proci.2004.07.030. [32] Wang H, You X, Joshi AV, Davis SG, Laskin A, Egolfopoulos F, Law CK. USC mech version II. High-temperature combustion reaction model of H2/CO/C1-C4 compounds. 2007. [33] Konnov AA. Implementation of the NCN pathway of promptNO formation in the detailed reaction mechanism. Combust Flame 2009;156(11):2093e105. https://doi.org/10.1016/ j.combustflame.2009.03.016. [34] Metcalfe WK, Burke SM, Ahmed SS, Curran HJ. A hierarchical and comparative kinetic modeling study of C1- h C2 ydrocarbon and oxygenated fuels. Int J Chem Kinet 2013;45(10):638e75. https://doi.org/10.1002/kin.20802. [35] Mechanical and Aerospace Engineering (Combustion Research). University of California at San Diego, chemicalkinetic mechanisms for combustion applications. San Diego Mechanism web page; 2016. URL, http://combustion.ucsd.edu. [36] Wang T, Zhang X, Zhang J, Hou X. Automatic generation of a kinetic skeletal mechanism for methane-hydrogen blends with nitrogen chemistry. Int J Hydrogen Energy 2018;43(6):3330e41. https://doi.org/10.1016/ j.ijhydene.2017.12.116. [37] Chaumeix N, Pichon S, Lafosse F, Paillard C-E. Role of chemical kinetics on the detonation properties of hydrogen/ natural gas/air mixtures. Int J Hydrogen Energy 2007;32(13):2216e26. https://doi.org/10.1016/ j.ijhydene.2007.04.008. ICHS-2005. vel R, Javoy S, Coudoro K, Dupre G, Paillard C-E. [38] Me Assessment of H2-CH4 air mixtures oxidation kinetic models used in combustion. Int J Hydrogen Energy 2012;37(1):698e714. https://doi.org/10.1016/ j.ijhydene.2011.09.099. 11th China Hydrogen Energy Conference. [39] Nilsson EJK, van Sprang A, Larfeldt J, Konnov AA. The comparative and combined effects of hydrogen addition on the laminar burning velocities of methane and its blends with ethane and propane. Fuel 2017;189:369e76. https:// doi.org/10.1016/j.fuel.2016.10.103. [40] Ji C, Wang D, Yang J, Wang S. A comprehensive study of light hydrocarbon mechanisms performance in predicting methane/hydrogen/air laminar burning velocities. Int J Hydrogen Energy 2017;42(27):17260e74. https://doi.org/ 10.1016/j.ijhydene.2017.05.203. [41] Donohoe N, Heufer A, Metcalfe WK, Curran HJ, Davis ML, Mathieu O, Plichta D, Morones A, Petersen EL, Gu¨the F.
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
27139
Ignition delay times, laminar flame speeds, and mechanism validation for natural gas/hydrogen blends at elevated pressures. Combust Flame 2014;161(6):1432e43. https:// doi.org/10.1016/j.combustflame.2013.12.005. Khan AR, Ravi MR, Ray A. Experimental and chemical kinetic studies of the effect of H2enrichment on the laminar burning velocity and flame stability of various multicomponent natural gas blends. Int J Hydrogen Energy 2019;44(2):1192e212. https://doi.org/10.1016/ j.ijhydene.2018.10.207. Ren J-Y, Qin W, Egolfopoulos FN, Tsotsis TT. Strain-rate effects on hydrogen-enhanced lean premixed combustion. Combust Flame 2001;124(4):717e20. https://doi.org/10.1016/ S0010-2180(00)00205-4. Ren J-Y, Qin W, Egolfopoulos FN, Mak H, Tsotsis TT. Methane reforming and its potential effect on the efficiency and pollutant emissions of lean methane-air combustion. Chem Eng Sci 2001;vol. 56(4):1541e9. https://doi.org/10.1016/S00092509(00)00381-X. 16th international conference on chemical reactor engineering. Briones AM, Aggarwal SK, Katta VR. Effects of H2enrichment on the propagation characteristics of -CH4 air triple flames. Combust Flame 2008;153(3):367e83. https://doi.org/10.1016/ j.combustflame.2008.02.005. Wang J, Huang Z, Tang C, Miao H, Wang X. Numerical study of the effect of hydrogen addition on methaneeair mixtures combustion. Int J Hydrogen Energy 2009;34(2):1084e96. https://doi.org/10.1016/j.ijhydene.2008.11.010. Bougrine S, Richard S, Nicolle A, Veynante D. Numerical study of laminar flame properties of diluted methanehydrogen-air flames at high pressure and temperature using detailed chemistry. Int J Hydrogen Energy 2011;36(18):12035e47. https://doi.org/10.1016/ j.ijhydene.2011.06.053. Okafor EC, Hayakawa A, Nagano Y, Kitagawa T. Effects of hydrogen concentration on premixed laminar flames of hydrogen-methane-air. Int J Hydrogen Energy 2014;39(5):2409e17. https://doi.org/10.1016/ j.ijhydene.2013.11.128. Liu J, Zhang X, Wang T, Hou X, Zhang J, Zheng S. Numerical study of the chemical, thermal and diffusion effects of H2 and CO addition on the laminar flame speeds of methane-air mixture. Int J Hydrogen Energy 2015;40(26):8475e83. https:// doi.org/10.1016/j.ijhydene.2015.04.133. Okafor EC, Nagano Y, Kitagawa T. Experimental and theoretical analysis of cellular instability in lean H2-CH4-air flames at elevated pressures. Int J Hydrogen Energy 2016;41(15):6581e92. https://doi.org/10.1016/ j.ijhydene.2016.02.151. Weydahl T, Poyyapakkam M, Seljeskog M, Haugen NEL. Assessment of existing H2/O2 chemical reaction mechanisms at reheat gas turbine conditions. Int J Hydrogen Energy 2011;36(18):12025e34. https://doi.org/10.1016/ j.ijhydene.2011.06.063. Conaire M, Curran HJ, Simmie JM, Pitz WJ, Westbrook CK. A O comprehensive modeling study of hydrogen oxidation. Int J Chem Kinet 2004;36(11):603e22. https://doi.org/10.1002/ kin.20036. Hu E, Huang Z, He J, Jin C, Zheng J. Experimental and numerical study on laminar burning characteristics of premixed methane-hydrogen-air flames. Int J Hydrogen Energy 2009;34(11):4876e88. https://doi.org/10.1016/ j.ijhydene.2009.03.058. 2nd International Workshop on Hydrogen. Lu T, Law CK. A directed relation graph method for mechanism reduction. Proc Combust Inst 2005;30(1):1333e41. https://doi.org/10.1016/ j.proci.2004.08.145.
27140
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 7 1 2 3 e2 7 1 4 0
[55] Pepiot-Desjardins P, Pitsch H. An efficient error-propagationbased reduction method for large chemical kinetic mechanisms. Combust Flame 2008;154(1):67e81. https:// doi.org/10.1016/j.combustflame.2007.10.020. [56] Sankaran R, Hawkes ER, Chen JH, Lu T, Law CK. Structure of a spatially developing turbulent lean methane-air Bunsen flame. Proc Combust Inst 2007;31(1):1291e8. https://doi.org/ 10.1016/j.proci.2006.08.025. [57] Zheng XL, Lu TF, Law CK. Experimental counterflow ignition temperatures and reaction mechanisms of 1,3-butadiene. Proc Combust Inst 2007;31(1):367e75. https://doi.org/10.1016/ j.proci.2006.07.182. [58] Niemeyer KE, Sung C-J, Raju MP. Skeletal mechanism generation for surrogate fuels using directed relation graph with error propagation and sensitivity analysis. Combust Flame 2010;157(9):1760e70. https://doi.org/10.1016/ j.combustflame.2009.12.022. [59] D. G. Goodwin, H. K. Moffat, R. L. Speth, Cantera: an objectoriented software toolkit for chemical kinetics, thermodynamics, and transport processes, http:// www.cantera.org, Version 2.3.0 (2017). doi:10.5281/ zenodo.170284. [60] Huang J, Hill PG, Bushe WK, Munshi SR. Shock-tube study of methane ignition under engine-relevant conditions: experiments and modeling. Combust Flame 2004;136(1):25e42. https://doi.org/10.1016/ j.combustflame.2003.09.002. [61] Herzler J, Naumann C. Shock-tube study of the ignition of methane/ethane/hydrogen mixtures with hydrogen contents from 0% to 100% at different pressures. Proc Combust Inst 2009;32(1):213e20. https://doi.org/10.1016/ j.proci.2008.07.034. [62] Bennett BAV, McEnally CS, Pfefferle LD, Smooke MD. Computational and experimental study of axisymmetric
[63] [64] [65]
[66] [67]
[68]
[69]
[70]
coflow partially premixed methane/air flames. Combust Flame 2000;123(4):522e46. https://doi.org/10.1016/S00102180(00)00158-9. OpenFOAM 5.0. The OpenFOAM Foundation; 2017. http:// www.openfoam.org/release/5-0. Source code for rhoReactingFoam, documentation, https:// cpp.openfoam.org/v5/rhoReactingFoam_8C.html. Novaresio V, Garcı´a-Camprubı´ M, Izquierdo S, Asinari P, Fueyo N. An open-source library for the numerical modeling of mass-transfer in solid oxide fuel cells. Comput Phys Commun 2012;183(1):125e46. https://doi.org/10.1016/ j.cpc.2011.08.003. Weidendorfer J. KCachegrind-call graph viewer. 2013. https:// kcachegrind.github.io/. Pang KM, Ivarsson A, Haider S, Schramm J. Development and validation of a local time stepping-based PaSR solver for combustion and radiation modeling. In: Proceedings of 8th international OpenFOAM workshop; 2013. Contino F, Jeanmart H, Lucchini T, D’Errico G. Coupling of in situ adaptive tabulation and dynamic adaptive chemistry: an effective method for solving combustion in engine simulations. Proc Combust Inst 2011;32(2):3057e64. https:// doi.org/10.1016/j.proci.2010.08.002. Cuoci A, Frassoldati A, Faravelli T, Ranzi E. A computational tool for the detailed kinetic modeling of laminar flames: application to C2H4/CH4 coflow flames. Combust Flame 2013;160(5):870e86. https://doi.org/10.1016/ j.combustflame.2013.01.011. McEnally CS, Pfefferle LD. Experimental study of nonfuel hydrocarbon concentrations in coflowing partially premixed methane/air flames. Combust Flame 1999;118(4):619e32. https://doi.org/10.1016/S0010-2180(99)00017-6.