Numerical and Experimental Investigations on Combustion Characteristics of Premixed Lean Methane–Air in a Staggered Arrangement Burner with Discrete Cylinders

: Premixed combustion of lean methane–air in an artiﬁcial porous media burner with staggered alumina cylinders was experimentally and numerically performed. Numerical simulations were conducted at gas mixture velocities of 0.43–0.86 m / s and equivalence ratios of 0.162 and 0.243, respectively. Through comparison with experimental results, temperature distribution, peak temperature and ﬂame propagation velocity are analyzed and discussed in detail. The numerical calculated temperature proﬁle over the axis of the combustor coincided well with test data in the post-ﬂame zone, however a certain deviation was found in the preheated zone. A two-dimensional ﬂame shape was observed and the ﬂame thickness was the size of cylinder diameter. The peak temperature increased with the gas mixture inlet velocity at the certain equivalence ratio, and its peak value was about 1.8–2.16 times higher than the adiabatic combustion temperature under the desired equivalence ratio, which indicates that super-adiabatic combustion was the case for all the numerical simulations. The ﬂame propagating velocity had a positive correlation with the gas mixture inlet velocity.

Many types of porous media structures have been encountered in the applications mentioned above, including pellets, lamellas, and foam materials. Among them, randomly packed pebble bed is

Experimental Setup
The experimental system is presented in Figure 1; such a system consists of three parts, i.e., a gas supply system, combustor, and experimental data acquisition system. The gas supply system contained air and fuel supply units. The air was furnished by an air compressor, and then entered into the premixed chamber through the gas tank and the oil-gas separator, while the fuel was provided by the methane tank. The flow rates of the methane and the air were regulated and gauged by mass flow controllers (Beijing Sevenstar Electronics Co., Ltd., Beijing, China) with the range of 0-200 L/min for the air and 0-2 L/min for the methane, respectively. By altering the flow rates of the methane and the air, the equivalence ratio under the experimental conditions can be obtained. The equivalence ratio is generally stated as quantitative relationship of fuel/oxidant mixture, which is defined as ϕ = (A/F) stoic /(A/F).
Energies 2020, 13, x 3 of 13 numerical studies on the combustion characteristics of a staggered cylinders burner were conducted, and more attention was focused on the flame propagation velocity, peak temperature, and interstitial flame thickness.

Experimental Setup
The experimental system is presented in Figure 1; such a system consists of three parts, i.e., a gas supply system, combustor, and experimental data acquisition system. The gas supply system contained air and fuel supply units. The air was furnished by an air compressor, and then entered into the premixed chamber through the gas tank and the oil-gas separator, while the fuel was provided by the methane tank. The flow rates of the methane and the air were regulated and gauged by mass flow controllers (Beijing Sevenstar Electronics Co., Ltd., Beijing, China) with the range of 0-200 L/min for the air and 0-2 L/min for the methane, respectively. By altering the flow rates of the methane and the air, the equivalence ratio under the experimental conditions can be obtained. The equivalence ratio is generally stated as quantitative relationship of fuel/oxidant mixture, which is defined as φ = (A/F)stoic/(A/F).  The body of the burner had a rectangular shaped stainless-steel shell with a length of 500 mm and a width of 63.5 mm, as depicted by Figure 2, in which 330 alumina cylinders were arranged in a staggered formation. For the alumina cylinder (as shown in Figure 3), its diameter was 6.5 mm and the length was 19.5 mm, and it was made of 99.99% experimental-grade alumina and supplied by Shenyang Sunio Chemical Co., Ltd., Shenyang, China. The corresponding porosity of the porous media region was about 0.43 eventually. To measure the temperatures in the burner, eleven K-type thermocouples labeled as T1-T11 were inserted to the bottom part of the burner with an interval of 27.71 mm, whose signals were transferred to a computer via an NI-PXIe-1073 (Shanghai Juxing Instrument Co., Ltd, shanghai, China) data acquisition system. A pair of ignition electrodes were used to ignite the methane-air mixture. The burnt products were collected by a probe placed at the axis 40 mm upstream from the burner exit and measured by way of a gas analyzer (Gasmet DX4000, Finland).  The body of the burner had a rectangular shaped stainless-steel shell with a length of 500 mm and a width of 63.5 mm, as depicted by Figure 2, in which 330 alumina cylinders were arranged in a staggered formation. For the alumina cylinder (as shown in Figure 3), its diameter was 6.5 mm and the length was 19.5 mm, and it was made of 99.99% experimental-grade alumina and supplied by Shenyang Sunio Chemical Co., Ltd., Shenyang, China. The corresponding porosity of the porous media region was about 0.43 eventually. To measure the temperatures in the burner, eleven K-type thermocouples labeled as T1-T11 were inserted to the bottom part of the burner with an interval of 27.71 mm, whose signals were transferred to a computer via an NI-PXIe-1073 (Shanghai Juxing Instrument Co., Ltd., shanghai, China) data acquisition system. A pair of ignition electrodes were used to ignite the methane-air mixture. The burnt products were collected by a probe placed at the axis 40 mm upstream from the burner exit and measured by way of a gas analyzer (Gasmet DX4000, Helsinki, Finland).

Experimental Steps
To achieve sufficient preheating for the porous region, lower flow rates were provided for the methane and the air, 1.34 L/min and 19 L/min, respectively. When T1 reached the objective temperature of 1473 K, the flow rates of the methane and the air were adjusted to the test conditions and stop the trials once the peak temperature of T11 was observed. In this procedure, the temperatures were recorded at 5 s intervals. The uncertainty analyses of the temperature, inlet gas mixture velocity and equivalence ratio were conducted through the root-sum-squares approach by Moffat [34]. The uncertainties of the temperature, inlet gas velocity and equivalence ratio were 7.5 °C, 1.6%, and 6.5%, respectively.

Mathematical Model
To make a comparison with the experiment, a numerical study was conducted with a two-dimensional packed bed. The length of the burner was 349.99 mm. The porous region was 304.49 mm in length and 63.5 mm in width. To eliminate the effect from the inlet and outlet boundaries, it extended 19.5 mm upstream and 26 mm downstream from the porous region. In order to save computation cost, only half of the burner was selected as the computational domain, as shown in Figure 4.

Experimental Steps
To achieve sufficient preheating for the porous region, lower flow rates were provided for the methane and the air, 1.34 L/min and 19 L/min, respectively. When T1 reached the objective temperature of 1473 K, the flow rates of the methane and the air were adjusted to the test conditions and stop the trials once the peak temperature of T11 was observed. In this procedure, the temperatures were recorded at 5 s intervals. The uncertainty analyses of the temperature, inlet gas mixture velocity and equivalence ratio were conducted through the root-sum-squares approach by Moffat [34]. The uncertainties of the temperature, inlet gas velocity and equivalence ratio were 7.5 °C, 1.6%, and 6.5%, respectively.

Mathematical Model
To make a comparison with the experiment, a numerical study was conducted with a two-dimensional packed bed. The length of the burner was 349.99 mm. The porous region was 304.49 mm in length and 63.5 mm in width. To eliminate the effect from the inlet and outlet boundaries, it extended 19.5 mm upstream and 26 mm downstream from the porous region. In order to save computation cost, only half of the burner was selected as the computational domain, as shown in Figure 4.

Experimental Steps
To achieve sufficient preheating for the porous region, lower flow rates were provided for the methane and the air, 1.34 L/min and 19 L/min, respectively. When T1 reached the objective temperature of 1473 K, the flow rates of the methane and the air were adjusted to the test conditions and stop the trials once the peak temperature of T11 was observed. In this procedure, the temperatures were recorded at 5 s intervals. The uncertainty analyses of the temperature, inlet gas mixture velocity and equivalence ratio were conducted through the root-sum-squares approach by Moffat [34]. The uncertainties of the temperature, inlet gas velocity and equivalence ratio were 7.5 • C, 1.6%, and 6.5%, respectively.

Mathematical Model
To make a comparison with the experiment, a numerical study was conducted with a two-dimensional packed bed. The length of the burner was 349.99 mm. The porous region was 304.49 mm in length and 63.5 mm in width. To eliminate the effect from the inlet and outlet boundaries, it extended 19.5 mm upstream and 26 mm downstream from the porous region. In order to save computation cost, only half of the burner was selected as the computational domain, as shown in Figure 4.

Experimental Steps
To achieve sufficient preheating for the porous region, lower flow rates were provided for the methane and the air, 1.34 L/min and 19 L/min, respectively. When T1 reached the objective temperature of 1473 K, the flow rates of the methane and the air were adjusted to the test conditions and stop the trials once the peak temperature of T11 was observed. In this procedure, the temperatures were recorded at 5 s intervals. The uncertainty analyses of the temperature, inlet gas mixture velocity and equivalence ratio were conducted through the root-sum-squares approach by Moffat [34]. The uncertainties of the temperature, inlet gas velocity and equivalence ratio were 7.5 °C, 1.6%, and 6.5%, respectively.

Mathematical Model
To make a comparison with the experiment, a numerical study was conducted with a two-dimensional packed bed. The length of the burner was 349.99 mm. The porous region was 304.49 mm in length and 63.5 mm in width. To eliminate the effect from the inlet and outlet boundaries, it extended 19.5 mm upstream and 26 mm downstream from the porous region. In order to save computation cost, only half of the burner was selected as the computational domain, as shown in Figure 4.

Governing Equations
In order to streamline the numerical calculations, some assumptions were made as follows: (1) The matrix was considered as opaque and inert homogenous porous media.
(2) Given the lower gas flow velocities, it was assumed to be laminar for all the cases to be discussed.
(3) The heat loss by the burner outer walls to the surroundings was neglected. (4) Pressure drop in the burner was ignored.
Under these assumptions, all the equations involved are shown as follows: (1) Continuity equations: where ρ g is gas density; t is time, and v is the gas velocity vector.
(2) Momentum equations: where u i is the ith component of velocity vector; µ is dynamic viscosity.
(3) Species conservation equation: are the mass fraction, diffusion coefficient, reaction rate, and the molecular weight of species i, respectively. The reaction of methane is represented by one-step reaction mechanism provided by ANSYS Fluent (version 15.0, ANSYS Inc., Park City, UT, USA). The reaction rate of methane is calculated as where A is pre-exponential factor and the value is used to 2.119 × 10 11 m 1.5 /(kmol 0.5 ·s); E is activation energy and its value is 2.027 × 10 8 J/(kmol); R is the universal gas constant.
(4) Gas phase energy equation where T g , c g , λ g are the gas mixture temperature, special heat, and thermal conductivity, respectively. Q is the heat content of the premixed mixture.
(5) Solid phase energy equation where ρ s , T s , c s , λ s are the solid density, temperature, special heat, and thermal conductivity, respectively.
(6) Ideal gas state equation where p is the pressure.

Boundary Conditions
The boundary conditions were adopted in the numerical simulations. Gas temperature, velocities, and species mass fraction were set at the inlet zone of the burner: The outflow boundary condition was selected at the outlet: At the interface of the burner walls and gas-solid interfaces, we used the no slip boundary condition for velocity. The outer wall of the burner was set up to the adiabatic condition. The solid radiative heat transfer between alumina cylinders was considered as the discrete ordinate model.

Computation Scheme
The numerical simulation was conducted with the CFD software package ANSYS 15.0. Two computational domains with the solid phase and the fluid phase were created by Gambit software. The solid phase domain was made of alumina cylinders and the fluid phase domain was composed of the gas mixture. At the inlet and outlet zones, the structure meshes were used. A structured grid was used in the outer wall region of combustion. Within the porous media domain, unstructured meshes were exploited and the local refinements at the interface between the gas mixture and alumina cylinder were made by the boundary layers to advance the calculation accuracy.
To perform a grid-independence check, three meshes with different resolutions in the interstitials were presented, i.e., Mesh 1, Mesh 2, and Mesh 3. The minimum cell volume and cell total numbers are listed in Table 1. A pure flow (no reaction) with inlet gas mixture velocity of 0.86 m/s was considered, and the comparison of velocity profiles at some specific points for different mesh is depicted in Figure 5. From the simulated results, one can see that the discrepancy between Mesh 2 and Mesh 3 was very fine, and the maximum relative error was about 0.36; this indicates that the mesh independency was achieved. Finally, a non-uniform grid generation system with 27,780 cells was employed in the following numerical computation. The mesh quality was evaluated by the EquiSize Skew. In our simulations, this value was in the range of 0.1 to 0.5. In particular, the cells with EquiSize Skew values less than 0.2 accounted for 85%, and the remainder were still required to be less than 0.5, which were concentrated in the narrow gaps between cylinders and the outer wall of the burner. where p is the pressure.

Boundary Conditions
The boundary conditions were adopted in the numerical simulations. Gas temperature, velocities, and species mass fraction were set at the inlet zone of the burner: The outflow boundary condition was selected at the outlet: At the interface of the burner walls and gas-solid interfaces, we used the no slip boundary condition for velocity. The outer wall of the burner was set up to the adiabatic condition. The solid radiative heat transfer between alumina cylinders was considered as the discrete ordinate model.

Computation Scheme
The numerical simulation was conducted with the CFD software package ANSYS 15.0. Two computational domains with the solid phase and the fluid phase were created by Gambit software. The solid phase domain was made of alumina cylinders and the fluid phase domain was composed of the gas mixture. At the inlet and outlet zones, the structure meshes were used. A structured grid was used in the outer wall region of combustion. Within the porous media domain, unstructured meshes were exploited and the local refinements at the interface between the gas mixture and alumina cylinder were made by the boundary layers to advance the calculation accuracy.
To perform a grid-independence check, three meshes with different resolutions in the interstitials were presented, i.e., Mesh 1, Mesh 2, and Mesh 3. The minimum cell volume and cell total numbers are listed in Table 1. A pure flow (no reaction) with inlet gas mixture velocity of 0.86 m/s was considered, and the comparison of velocity profiles at some specific points for different mesh is depicted in Figure 5. From the simulated results, one can see that the discrepancy between Mesh 2 and Mesh 3 was very fine, and the maximum relative error was about 0.36; this indicates that the mesh independency was achieved. Finally, a non-uniform grid generation system with 27,780 cells was employed in the following numerical computation. The mesh quality was evaluated by the EquiSize Skew. In our simulations, this value was in the range of 0.1 to 0.5. In particular, the cells with EquiSize Skew values less than 0.2 accounted for 85%, and the remainder were still required to be less than 0.5, which were concentrated in the narrow gaps between cylinders and the outer wall of the burner.   The pressure and velocity coupling in this work employed the SIMPLE numerical algorithm. The residual of the energy equations was set to 10 −6 , while the other numerical equations were taken as 10 −3 . To model the ignition process exactly, the initial solid temperature profiles were set to be the same as those in the experimental work. The numerical cases are presented in Table 2.

Flame Temperature Distributions
The validation of the two-dimension pore lever combustion model needed to be confirmed, therefore the predicted temperatures along the axis in the bottom of the burner were compared with the experimental data. The temperature profiles by numerical simulation and experimental data are presented in Figure 6 for the equivalence ratio of ϕ = 0.162 and gas mixture inlet velocity of u 0 = 0.86 m/s. The predicted temperatures were selected by the gas and solid phases along the centerline of the porous burner. The profile of the predicted temperature was continuous but not smooth, due to the two-dimensional numerical simulation and the thermal non-equilibrium in the interface between the premixed gas and the alumina cylinders. The peak temperature in the numerical simulation held at 1520 K, about 103 K larger than that in the experiment. The temperature difference between the simulation and the experiment became smaller until the position of the temperature was located at around 128.9 mm. The predicted temperature was larger than that of the experiment at the downstream zone. Overall, the predicted temperature trend had a good agreement with that of the experimental data.
The pressure and velocity coupling in this work employed the SIMPLE numerical algorithm. The residual of the energy equations was set to 10 −6 , while the other numerical equations were taken as 10 −3 . To model the ignition process exactly, the initial solid temperature profiles were set to be the same as those in the experimental work. The numerical cases are presented in Table 2.

Flame Temperature Distributions
The validation of the two-dimension pore lever combustion model needed to be confirmed, therefore the predicted temperatures along the axis in the bottom of the burner were compared with the experimental data. The temperature profiles by numerical simulation and experimental data are presented in Figure 6 for the equivalence ratio of φ = 0.162 and gas mixture inlet velocity of u 0 = 0.86 m/s. The predicted temperatures were selected by the gas and solid phases along the centerline of the porous burner. The profile of the predicted temperature was continuous but not smooth, due to the two-dimensional numerical simulation and the thermal non-equilibrium in the interface between the premixed gas and the alumina cylinders. The peak temperature in the numerical simulation held at 1520 K, about 103 K larger than that in the experiment. The temperature difference between the simulation and the experiment became smaller until the position of the temperature was located at around 128.9 mm. The predicted temperature was larger than that of the experiment at the downstream zone. Overall, the predicted temperature trend had a good agreement with that of the experimental data.
The main reason of discrepancy between the predicted and experimental temperature is that the global methane oxidation kinetics mechanism was used in this study. Hus and Matthews [35] suggested that the multistep kinetics mechanism has an important influence on the temperature. However, in this work it was still not feasible to perform the multistep kinetics mechanism because of restrictions by the computational conditions. The heat loss from the outer wall of the combustor in the experiment was not considered in the simulation, which may also have attributed to the discrepancy between the predicted results and experimental data.  The main reason of discrepancy between the predicted and experimental temperature is that the global methane oxidation kinetics mechanism was used in this study. Hus and Matthews [35] suggested that the multistep kinetics mechanism has an important influence on the temperature. However, in this work it was still not feasible to perform the multistep kinetics mechanism because of restrictions by the computational conditions. The heat loss from the outer wall of the combustor in the experiment was not considered in the simulation, which may also have attributed to the discrepancy between the predicted results and experimental data.  Figure 7 shows the mass fractions of methane, Y CH4 and carbon dioxide, Y CO2 , along with chemical reaction rate of methane, ω CH4 , in the porous combustor for the equivalence ratio ϕ = 0.162 and gas mixture inlet velocity u 0 = 0.43 m/s at 656 s. Figure 7 shows the mass fractions of methane, YCH4 and carbon dioxide, YCO2, along with chemical reaction rate of methane, ωCH4, in the porous combustor for the equivalence ratio φ = 0.162 and gas mixture inlet velocity u0 = 0.43 m/s at 656 s.

Species Fractions and Reaction Rate
It is noted that the distributions of YCH4, YCO2, and ωCH4 represent the similar sharp peak at the chemical reaction zone, which was located in the range of 130-136 mm. Their structures show highly two-dimensional characteristics. Major changes of YCH4, YCO2, and ωCH4 between the cylinders at the chemical reaction zone are observed. The chemical reaction zone is not uniform over cylinders and the flame thickness is about one-cylinder in diameter.  Figure 8 presents the peak temperature during the flame propagation under various equivalence ratios and inlet velocities. The peak flame temperature is the parameter that reflects the combustion characteristics of PMC. The magnitude of the peak was in the range of 1500-1800 K. The peak flame temperature had a positive correlation with the equivalence ratio. With the same equivalence ratio, the peak temperature increased with gas mixture inlet velocity. As the gas mixture inlet velocity increased from 0.43 m/s to 0.645 m/s at the situation of ϕ = 0.162, the increment of the peak flame temperature was 59 K. The results indicate that at a smaller equivalence ratio, a bigger gas mixture inlet velocity leads to the lower increment of the maximum flame temperature. At the certain equivalence ratio, the increment of the maximum temperature is 157 K, 168 K and 177 K at inlet velocities of 0.43 m/s, 0.645 m/s and 0.86 m/s, respectively. With the increases in equivalence ratio and gas mixture inlet velocity, more fuel can be supplied, which It is noted that the distributions of Y CH4 , Y CO2 , and ω CH4 represent the similar sharp peak at the chemical reaction zone, which was located in the range of 130-136 mm. Their structures show highly two-dimensional characteristics. Major changes of Y CH4 , Y CO2 , and ω CH4 between the cylinders at the chemical reaction zone are observed. The chemical reaction zone is not uniform over cylinders and the flame thickness is about one-cylinder in diameter. Figure 8 presents the peak temperature during the flame propagation under various equivalence ratios and inlet velocities. The peak flame temperature is the parameter that reflects the combustion characteristics of PMC. The magnitude of the peak was in the range of 1500-1800 K. The peak flame temperature had a positive correlation with the equivalence ratio. With the same equivalence ratio, the peak temperature increased with gas mixture inlet velocity. As the gas mixture inlet velocity increased from 0.43 m/s to 0.645 m/s at the situation of φ = 0.162, the increment of the peak flame temperature was 59 K. The results indicate that at a smaller equivalence ratio, a bigger gas mixture inlet velocity leads to the lower increment of the maximum flame temperature. At the certain equivalence ratio, the increment of the maximum temperature is 157 K, 168 K and 177 K at inlet velocities of 0.43 m/s, 0.645 m/s and 0.86 m/s, respectively. With the increases in equivalence ratio and gas mixture inlet Energies 2020, 13, 6397 9 of 13 velocity, more fuel can be supplied, which induces more intensive burning of the gas mixture in the porous combustor. The greater energy released by combustion increases the peak flame temperature.

Effect of u 0 on the Peak Flame Temperature
induces more intensive burning of the gas mixture in the porous combustor. The greater energy released by combustion increases the peak flame temperature.
The calculated adiabatic combustion temperatures of the CH4-air mixture at the equivalence ratio of 0.162 and 0.243 were 737 K and 934 K, respectively. However, the peak temperature was 2.16 times larger than the adiabatic combustion temperature under the condition of φ = 0.162 and u0 = 0.86 m/s, due to the existence of a porous matrix. All the numerical results were higher than the flame adiabatic temperature at the same equivalence. This indicates that the combustions were super-adiabatic under all the test conditions.  Figure 9 presents the influence of gas mixture inlet velocity on the flame propagation velocity for experimental data, and the numerical results. The flame propagation velocity is computed by dividing of the length of the porous media zone by the propagating time through the porous media zone. It was found that the magnitudes of the flame propagation velocity by experiment and simulation are the order of 0.1 mm/s, which belongs to the range of low-velocity filtration combustion by Babkin et al. [36]. They reported that the classification of filtration combustion is based on the combustion mechanism, which is the heat exchange between the gas mixture and the solid matrix. With the increases in gas mixture inlet velocity, the flame propagation velocity increases at the same equivalence ratio. At a certain equivalence ratio, more combustion heat released by the gas mixture in unit time can be generated with increasing the gas mixture inlet velocity, resulting in a higher flame propagation velocity.

Effect of u 0 on the Flame Propagation Velocity
The flame propagation velocities in simulation agreed well with the experimental results. The flame propagation velocity in the simulation was 0.145 mm/s at φ = 0.162 and u0= 0.43 m/s, under the same condition which was 0.173 mm/s for the experiment. The relative error of the flame propagation velocity was less than 16% for φ = 0.162 and different inlet velocities. The peak relative error of the flame propagation velocity under the equivalence ratio of 0.243 was 14%. As expected, the flame propagation velocities by the simulation showed high quality representations of those in the experiment. The calculated adiabatic combustion temperatures of the CH 4 -air mixture at the equivalence ratio of 0.162 and 0.243 were 737 K and 934 K, respectively. However, the peak temperature was 2.16 times larger than the adiabatic combustion temperature under the condition of ϕ = 0.162 and u 0 = 0.86 m/s, due to the existence of a porous matrix. All the numerical results were higher than the flame adiabatic temperature at the same equivalence. This indicates that the combustions were super-adiabatic under all the test conditions. Figure 9 presents the influence of gas mixture inlet velocity on the flame propagation velocity for experimental data, and the numerical results. The flame propagation velocity is computed by dividing of the length of the porous media zone by the propagating time through the porous media zone. It was found that the magnitudes of the flame propagation velocity by experiment and simulation are the order of 0.1 mm/s, which belongs to the range of low-velocity filtration combustion by Babkin et al. [36]. They reported that the classification of filtration combustion is based on the combustion mechanism, which is the heat exchange between the gas mixture and the solid matrix. With the increases in gas mixture inlet velocity, the flame propagation velocity increases at the same equivalence ratio. At a certain equivalence ratio, more combustion heat released by the gas mixture in unit time can be generated with increasing the gas mixture inlet velocity, resulting in a higher flame propagation velocity.

Effect of u 0 on the Flame Propagation Velocity
Energies 2020, 13, x 10 of 13 Figure 9. Effect of gas mixture inlet velocity on the flame propagation velocity.

Conclusions
Numerical and experimental flame propagations of a methane-air mixture in a staggered arrangement porous burner were performed with inlet velocities of u0 = 0.43-0.86 m/s and equivalence ratios of φ = 0.162, 0.243. The temperature distributions for the numerical result were compared with those by experimental data. The maximum temperature and flame propagation velocity by simulation under various situations were investigated and analyzed. The results below  The flame propagation velocities in simulation agreed well with the experimental results. The flame propagation velocity in the simulation was 0.145 mm/s at ϕ = 0.162 and u 0 = 0.43 m/s, under the same condition which was 0.173 mm/s for the experiment. The relative error of the flame propagation velocity was less than 16% for ϕ = 0.162 and different inlet velocities. The peak relative error of the flame propagation velocity under the equivalence ratio of 0.243 was 14%. As expected, the flame propagation velocities by the simulation showed high quality representations of those in the experiment.

Conclusions
Numerical and experimental flame propagations of a methane-air mixture in a staggered arrangement porous burner were performed with inlet velocities of u 0 = 0.43-0.86 m/s and equivalence ratios of ϕ = 0.162, 0.243. The temperature distributions for the numerical result were compared with those by experimental data. The maximum temperature and flame propagation velocity by simulation under various situations were investigated and analyzed. The results below were found: (1) At ϕ = 0.162 and u 0 = 0.86 m/s, the trends of the temperature distributions towards the centerline of the burner between the simulation and experiment were similar. The peak temperature by numerical calculation was maintained at 1520 K, about 103 K greater than that by the experiment.
The main reason of discrepancy between the predicted and experimental temperatures was that the global methane oxidation kinetics mechanism was used in the two-dimensional pore level simulation model.