### Summary

- Top of page
- Summary
- 1 Introduction
- 2 Porous Burner Geometry
- 3 Governing Equations
- 4 Initial and Boundary Conditions
- 5 Numerical Procedure
- 6 Validation of Results
- 7 Results and Discussion
- 8 Conclusions
- References

This paper presents results of numerical investigation on the effect of using variable porosity porous media burner on its performance and pollutant emission. A two-dimensional axisymmetric model for premixed methane/air combustion in porous media has been developed. This code solves the continuity, Navier Stokes, solid and gas energies, and chemical species transport equations using the finite volume method. The pressure and velocity have been coupled with the SIMPLE algorithm. In this paper, the results of applying two different profiles of porosity instead of constant porosity for two zones of burner have been presented. The results showed that by applying porosity variation along the burner, the peak temperature can be decreased about 4.5%, and subsequently, the amount of exhaust pollutants such as NO_{x} can also be decreased while increase in pressure losses along the burner is negligible. In addition, the effects of excess air ratio, volumetric heat transfer coefficient, inlet velocity, chemical kinetics, conductivity coefficient, and wall temperature on the porous media burners with variation of porosity are investigated. Copyright © 2014 John Wiley & Sons, Ltd.

### 1 Introduction

- Top of page
- Summary
- 1 Introduction
- 2 Porous Burner Geometry
- 3 Governing Equations
- 4 Initial and Boundary Conditions
- 5 Numerical Procedure
- 6 Validation of Results
- 7 Results and Discussion
- 8 Conclusions
- References

The aim of this paper is introducing variable porous medium combustion technology as a method for improving combustion efficiency and reducing pollutants emission. Because of the massive consumption of fossil fuel resources and the formation of noxious pollutants such as NO_{x}, SO_{x}, CO and CO_{2}, the requirement for improving the performance of existing combustion system and pollution reduction become increasingly significant daily.

Stick rules, which have been legislated up to now to reduce NO_{x}, have caused more researches to be carried out on reducing emissions and increasing the efficiency of combustion in the burners. Practical experience showed that conventional gas burners have a high production of pollutants; this is especially notable when the burners operates in the regime with low thermal power. The main reason for that is the classical way of burning by using an open flame combustion process. To avoid the mentioned difficulties and disadvantages of conventional burners, another means of combustion was discovered in the past, known as porous medium combustion. Today, new porous medium gas burners have been developed and applied in a wide range of application from household heating systems to industrial process.

The main advantages of combustion in porous media in comparison with the previous combustion systems are as follows:

- Approaching to complete combustion by passing the fuel/air mixture inside the pores of the porous medium.
- Reducing the peak temperature by bringing out a part of combustion energy and transferring it from the combustion products to the porous medium.
- Increasing the efficiency of combustion process through pre-heating the intake fuel/air mixture before reaching to the combustion zone

Furthermore, with premixed combustion in porous inert media, high power densities, high power dynamic range, low emission rates of pollutants such as NO_{x} and CO, and a free and suitable design could be achieved.

Development and optimization of porous media burners require experiment and numerical simulation; however, the experiments have some drawbacks such as necessity of more time and cost and a limited range of measurement accuracy and diversity.

The history of using porous media was started in 1982, when the Japanese researcher, Echigo [1], considered recycling energy from exhaust gases of high-temperature apparatus. He found out that in this way, it would be possible to transfer a major part of heat energy to the porous media via convection. Furthermore, the efficiency of porous layer in recycling is increased with increasing the temperature of the intake gas.

Wang and Tien [2] studied in this field by using the two-heat flux model for the equations of heat radiation and considering the distribution of radiation energy by the porous media. They found that the distribution of radiation energy by the porous layer resulted in reduction of the amount of absorbed energy by the porous media and reduction of the efficiency of the porous layer.

In 1987, Fiveland [3] presented a new solution by using a discrete ordinate method in solving problems; its accuracy was evaluated by Truelove at the same year.

Between 1988 and 1996, researchers such as Yoshizawa [4], Tong [5], and Kulkarni and Peck [6] conducted many studies in the field of combustion in porous media in which the spherical harmonic method for solving equations of radiation was used. Furthermore, Kulkarni and Peck performed heat analysis of the burners by using TRANFIT and CHEMKIN codes.

Pereira and Zhou [7] investigated the combustion of methane fuel by using four models of combustion such as full mechanism (49 species and 227 chemical reactions), skeletal mechanism (27 species and 77 chemical reactions), four-step-reduced mechanism (9 species and 4 chemical reactions) and one global mechanism (1GM, include 4species and 1 chemical reaction). They found that the four-step-reduced mechanism has the most agreement with full mechanism.

In 1999, Malico [8] performed a two-dimensional numerical study for combustion and emission of pollutants in porous media and investigated the effects of excess air ratio, thermal conductivity and convective heat transfer coefficient, and radiation properties.

In 2000, Brenner and co-worker [9] assumed a two-dimensional system and solved the governing equations for combustion, but they did not use any model for radiation.

Malico and Pereira [10] examined the effects of the radiative properties of the porous media on the performance of cylindrical shape burners in a two-dimensional state. They found that their results did not have a good agreement with experimental data because they neglected the radiative heat transfer.

In 2002, Chung [11] studied the effects of hydrogen addition on methane combustion inside a porous media burner in the one-dimensional system. He showed that by increasing hydrogen in the fuel, the speed of flame and the emission of CO would increase.

In 2003, Talukdar and his co-worker [12] studied a porous media burner in two conditions, in steady and transient states in the two-dimensional system.

Mishra [13] and Lari [14] performed a thermal analysis of the porous media burners. They found that the burners with higher optical thickness have a lower peak temperature. Finally, Hossainpour and Haddadi [15] surveyed the effects of several parameters on the combustion and the formation of pollutants in the one-dimensional state with multi step kinetics.

### 5 Numerical Procedure

- Top of page
- Summary
- 1 Introduction
- 2 Porous Burner Geometry
- 3 Governing Equations
- 4 Initial and Boundary Conditions
- 5 Numerical Procedure
- 6 Validation of Results
- 7 Results and Discussion
- 8 Conclusions
- References

In this paper, governing equations such as continuity, momentum, gas phase energy, solid phase energy and species conservation equations are discretized by a finite volume method. Pressure and velocity are coupled by the SIMPLE algorithm of Patankar.

The algebraic equations system are stiff by using a multistep kinetic model, and conventional iterative solution methods such as Tri-Diagonal Matrix Algorithm lead to divergence. Therefore, the source terms in gas phase energy and chemical species transfer equations, which are defined as follows, are solved by Variable-coefficient Ordinary Differential Equation solver (DVODE) subroutine [24].

- (18)

- (19)

DVODE subroutine solves the first-order ordinary differential equations by Hindermarsh–Gear algorithm in which the updated mass fraction and temperature [*Y*_{i}]^{new} and [*T*_{g}]^{new} are calculated by [17]

- (20)

- (21)

#### 5.1 Mesh independency

To check mesh independencies, various grid sizes were tested, and finally, 260 × 26 grid nodes were used. By choosing smaller grids, the changes of parameters such as gas and solid temperatures are negligible, but the computational time increases rapidly. Table 1 shows computational time for different grid sizes. Thus, the results are reported with 260 × 26 grid nodes.

Table 1. Computational time for different number of grid nodes.Grid nodes | 390 × 26 | 260 × 26 | 260 × 13 | 160 × 26 | 160 × 13 |

Computational time (min) | 920 | 802 | 672 | 433 | 375 |

### 7 Results and Discussion

- Top of page
- Summary
- 1 Introduction
- 2 Porous Burner Geometry
- 3 Governing Equations
- 4 Initial and Boundary Conditions
- 5 Numerical Procedure
- 6 Validation of Results
- 7 Results and Discussion
- 8 Conclusions
- References

The results are provided in several sections. In the first section, some of the species in the GRI 3.0 mechanism are shown. This section shows the accuracy of calculations.

Species that have been selected for this purpose include a product, a reactant and an intermediate one. In the second section, temperature, NO and pressure losses variation due to the porosity variation have been shown. In the third section, effects of excess air ratio, volumetric heat transfer, inlet velocity, conductivity coefficient, wall temperature and chemical kinetics are studied. Finally, the results are summarized in the last section.

Figure 4a–c shows mass fractions of the species. Because the total number of species is high in the GRI 3.0 mechanism, only a few of them have been reported.

Figure 4a displays sketch of methane mass fraction. The figure illustrates the consumption of this species.

Figure 4b is associated with mass fraction of H_{2}O for GRI 3.0 mechanism. The figure illustrates the production of this species.

In Figure 4c, a sketch of CH as an intermediate species has been shown for the GRI 3.0 mechanism. Intermediate species refers to species that are produced and consumed during the combustion process.

In Figure 5a, the profiles of gas temperature for the linear variable porosity, second-order variable porosity and constant porosity (0.7 for preheating zone and 0.85 for combustion zone) are presented.

As could be seen, the value of peak temperature will be reduced about 4.5% when the variable porosity is considered.

Figure 5b shows NO profiles. As expected with a lower peak temperature, the amount of NO emission will decrease.

Despite all the advantages, by choosing the variable porosity, pressure losses increase along the burner. Because the increase in pressure losses is very low (about 0.0001%), we can neglect it.

Figure 6a and b shows the effects of excess air ratio on the gas temperature and the mass fraction of NO. As could be seen, by increasing the excess air ratio, the flow rate increases, and consequently, the porous material in the upstream region is better cooled, and it caused the flame front to move downstream and the peak temperature to decrease. The formation of NO mainly depends on the peak temperature of the combustion region; therefore, by decreasing the peak temperature, the amount of NO emission at the outlet of burner decreases.

Figure 7a and b compares the effects of increasing volumetric heat transfer coefficient at the combustion zone while it is considered to be constant in the preheating zone.

As seen, by increasing the volumetric heat transfer coefficient, the flame front moves to the downstream and the flame thickness decreases. It means that the heat release occurs over a smaller distance, and as a consequence, the peak temperature and the amount of NO emission increase.

The effects of increasing volumetric heat transfer coefficient at the preheating zone, athough it is considered to be constant in the combustion zone, have been investigated on the gas temperature profile.

The result showed that increasing volumetric heat transfer coefficient has a little influence on the gas temperature profiles.

Figure 8 depicts the effects of inlet velocity on the gas temperature. By increasing inlet velocity, the flame front moves to the downstream, and the flame thickness increases and the peak temperature decreases.

Figure 9 demonstrates the effects of inlet velocity on the amount of mass fraction of NO. At higher speeds, there is not enough opportunities for reverse reactions; therefore, the amount of NO emission at the outlet of burner increases; in addition, differences between variable (cases a and b) and constant (case c) porosity are shown in this figure.

The effects of increasing conductivity coefficient in the preheating zone showed that by increasing conductivity coefficient, heat transfer from solid matrix to the gas in preheating zone increases, and therefore, the peak temperature and the amount of NO emission increases.

Figure 10 shows the effects of wall temperature on the following: (1) profiles of gas temperature and (b) mass fraction of NO. By decreasing the wall temperature, the heat losses increases; therefore, the peak temperature and the amount of NO emission decreases. It is due to the point that at the greater temperatures, the burner is closer to the adiabatic mode.

In this work, the gas temperature profiles for several chemical mechanisms have been compared. The results showed that when the profile of porosity variation is used, the differences in gas temperature among GRI.3.0, GRI.2.11 and GRI.1.2 mechanisms are not considerable, and the skeletal mechanism and the kinetic model with 17 species and 58 chemical are comparable results.