**9.2. Initial and boundary conditions**

The test section was a vertical quartz glass-tube with 1.3 m in length and 0.076 m in diameter, that was isolated from the environment. The test section was filled with a packed bed of 0.0056 m solid alumina spheres. For simulation a cylinder with 0.076 m in diameter and 0.60 m in length that filled with PM, was considered (Fig. 5). The boundary condition applied to the momentum and energy equation with the assumption of zero gradients for temperature of both phase of PM and for species transport through the downstream boundary. At the upstream boundary, the gas temperature is 300K, composition is premixed methane-air with equivalence ratio 0.15, and velocity is 0.43 m/s of the premixed reactants and zero gradient for solid phase, were specified. For initial temperature for both phase of PM experimental measured data was used. Fuel is methane, porosity of PM is 0.4. The laminar flow considered for simulation. For validation of numerical simulation, modified KIVA code was used for simulation of unsteady combustion is a cylindrical tube with the experiments of Zhdanok et al. Fig. 6 plots a comparison of computation results to the experimental results of Zhdanok at the time of 147 s, which shows that the computed speed of combustion wave agrees well with the same condition of the experimental results. It is seen that methane is completely consumed in flame front that has maximum temperature.

Numerical Simulation of Combustion in Porous Media 547

**Figure 7.** Mass fraction of methane in cross section x = 0 after a) t = 10 s b) t = 50 s c) t = 100 s

**Figure 8.** Mass fraction of Carbon-dioxide in cross section x = 0 after a) t = 10 s b) t = 50 s c) t = 100 s

**Figure 9.** Gas phase temperature in cross section x = 0 after a) t = 10 s b) t = 50 s c) t = 100 s

**Figure 6.** Comparison of combustion wave propagation between CFD and experiment in time 147 s

## **9.3. Discussion**

In Figs. 7-10, contours of methane, carbon dioxide, temperature in gas and solid phases of PM, in cross section of tube for several times (10, 50, and 100 second) are shown. In Fig. 7 mass fraction of methane is shown. With entering of methane-air to porous tube that has high initial temperature, approximately 1800 K, in a narrow zone near inlet location, the temperature of gas increases until it reaches to self-ignition temperature. Methane consumes in a narrow region that is thicker relative to conventional flame front. In Figs. 8a, b, c, it is seen that after 10, 50 and 100 second combustion is started in respectively at x = 0.8, 2, 6 cm from entrance of mixture. The value of mass fraction of methane in PM tube is between 0.002 and this Fig indicates that the flame front has arc-shape.

Fig. 8 shows mass fraction of carbon dioxide in different time after start of simulation. Mixture flows through the porous tube that has initially heated and combustion in narrow zone of high temperature takes place. It is seen that reactions occur around the flame front in PM and its thickness is about 0.4 cm, which is very thick in compare with flame front in normal combustion. Carbon-dioxide disperses in pre heat region of entering mixture by diffusion of CO2 and disperses in post flame by flow motion. In Fig. 9 temperature distribution in gas phase of PM in different time is shown. Flame front is recognizable from its high temperature region. Maximum fluid temperature is about 1600 K. Also, because effect of solid phase of PM, part of heat release of combustion is absorbed by it and prevents from high temperature gradient in fluid. Energy is re-circulated to the unburned gas mixture through the heat combustion and radiation of the solid. Fig. 10 shows temperature distribution in solid phase. At initial condition, mixture temperature is 300 K. The inlet temperature of solid phase is higher than gas temperature and heat is transferred from solid to gas, so allow it to reach the ignition temperature. Maximum temperature in solid phase is about 1600 K. Then the gas delivers its energy to the solid. Also, due to high heat capacity of solid phase of PM, low-temperature gradient occurs in it.

**Figure 7.** Mass fraction of methane in cross section x = 0 after a) t = 10 s b) t = 50 s c) t = 100 s

**9.3. Discussion** 

**Figure 6.** Comparison of combustion wave propagation between CFD and experiment in time 147 s

In Figs. 7-10, contours of methane, carbon dioxide, temperature in gas and solid phases of PM, in cross section of tube for several times (10, 50, and 100 second) are shown. In Fig. 7 mass fraction of methane is shown. With entering of methane-air to porous tube that has high initial temperature, approximately 1800 K, in a narrow zone near inlet location, the temperature of gas increases until it reaches to self-ignition temperature. Methane consumes in a narrow region that is thicker relative to conventional flame front. In Figs. 8a, b, c, it is seen that after 10, 50 and 100 second combustion is started in respectively at x = 0.8, 2, 6 cm from entrance of mixture. The value of mass fraction of methane in PM tube is between

Fig. 8 shows mass fraction of carbon dioxide in different time after start of simulation. Mixture flows through the porous tube that has initially heated and combustion in narrow zone of high temperature takes place. It is seen that reactions occur around the flame front in PM and its thickness is about 0.4 cm, which is very thick in compare with flame front in normal combustion. Carbon-dioxide disperses in pre heat region of entering mixture by diffusion of CO2 and disperses in post flame by flow motion. In Fig. 9 temperature distribution in gas phase of PM in different time is shown. Flame front is recognizable from its high temperature region. Maximum fluid temperature is about 1600 K. Also, because effect of solid phase of PM, part of heat release of combustion is absorbed by it and prevents from high temperature gradient in fluid. Energy is re-circulated to the unburned gas mixture through the heat combustion and radiation of the solid. Fig. 10 shows temperature distribution in solid phase. At initial condition, mixture temperature is 300 K. The inlet temperature of solid phase is higher than gas temperature and heat is transferred from solid to gas, so allow it to reach the ignition temperature. Maximum temperature in solid phase is about 1600 K. Then the gas delivers its energy to the solid. Also, due to high heat capacity of

0.002 and this Fig indicates that the flame front has arc-shape.

solid phase of PM, low-temperature gradient occurs in it.

**Figure 8.** Mass fraction of Carbon-dioxide in cross section x = 0 after a) t = 10 s b) t = 50 s c) t = 100 s

**Figure 9.** Gas phase temperature in cross section x = 0 after a) t = 10 s b) t = 50 s c) t = 100 s

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**10. Two applications of PM technology** 

The major target for further development of the current IC engines is to reduce their harmful emissions to environment. The most important difficulty with existing IC engines that currently exists is non-homogeneity of mixture formation within the combustion chamber which is the cause heterogeneous heat release and high temperature gradient in combustion chamber which is the main source of excess emissions such as NOx, unburned hydrocarbons (HC), carbon monoxide (CO), soot and suspended particles. At present, the IC engine exhaust gas emission could be reduced by catalyst, but these are costly, sensitive to fuel and with low efficiency. Another strategy has been initiated to avoid the temperature gradient in IC engines that is using homogeneous charge compression ignition (HCCI)

**Figure 11.** Mean temperature distribution in gas phase of PM versus axial direction

**Figure 12.** Mean mass fraction of methane versus axial direction

**10.1. Internal combustion engines** 

**Figure 10.** Temperature of solid phase in cross section x = 0 after a) t = 10 s b) t = 50s c) t= 100 s

Figs. 11, 12 show results for distribution of temperature in center line of PM tube in both phase of PM (solid and fluid) for different times versus axial direction. Heat transport is related to thermal properties of the solid material and fluid property. Flame core transports heat to incoming methane-air mixture with conduction and radiation, that its temperature is 300 K. At time t = 10 s maximum temperature in gas phase is about 1700 K. After 10 s flame moves to right with constant speed and maximum temperature of about 1600 K. After this time equilibrium between conduction, convection and radiation, causes to no change in maximum value of combustion. At the end of the tube temperature in all cases is about 325 K. In solid phase due to preheating of inlet mixture, at t = 10 s in inlet solid phase temperature is about 1450 K, in t = 50 s and t = 100 s, upstream temperature is about 850 K and 580 K, respectively and this temperature finally reach to 300 K approximately. Fig. 13 shows distribution of methane mass fraction from 10 to 100 s. Inlet mass fraction of methane is 0.016. Decrease in mass fraction of methane shows location of flame front. Flame location after 10 s is in location 3.8 cm and its thickness is thickness of 4 cm, after 50 s, is about 1.6 cm with the thickness 4.3 cm, and after 100 s is about 3.3 cm with the thickness 2.4 cm. From this Fig. inferred in 50 s and 100 s after simulation variation in flame thickness is very low value and the CH4 is almost completely consumed in this zone. Fig. 14 shows mass fraction of CO2 value in axial direction. Carbon dioxide is produced during combustion and its mass fraction reaches to highest value in x = 2.4, 5.5, 7.1 cm respectively to 0.036, 0.035, 0.024 mass fraction after 10, 50 and 100 s from simulation. Fig. 15 shows mass fraction of CO value in axial direction. Carbon monoxide is produced during combustion with entering of mixture and as an intermediate species produced and consumes gradually in axial direction. CO concentration reaches its highest value near the flame front at x = 1.8, 4.1, 6 cm respectively after 10, 50 and 100 s and gradually decreases at x = 4.8, 7.2 and 9.1 cm to approximately zero. With completeness of combustion and it oxidizes slowly and converted to CO2, because of enough accessible oxygen for converting CO to CO2. Fig. 16 shows mass fraction of CH3 value in axial direction. Methyl concentration reaches its highest value in x = 1.4, 3.6, 9.2 cm respectively 10, 50 and 100 s after simulation. But after 100s due to fluid flow, it disperses in porous tube and oscillation occurs in value of it.
