Numerical Method

The solution to the governing equations is obtained by employing a finite volume method with the model domain divided into a number of cells and used as control volumes.

The governing equations are numerically integrated over each of these computational cells or control volumes. The method exploits a collocated cell-centered variable arrangement with the local or cell-averaged values of the physical quantities evaluated and stored at each cell center.

A generalized form of the transport equation for mass, momentum, energy can be expressed in a conservative form as follows:

( v) ( ) S_φ

∇ ⋅ ρφ = ∇ ⋅ Γ∇φ +r (3-1)

where φ is a general dependent variable, vr is velocity vector, S_φ is the source per unit volume and ρ is the density. With the discretization of the governing equations, the coupled finite-difference equations become

P P E E W W N N S S

a φ = φ +a a φ + φ + φ + (3-2) a a S_φ

where φ is the value of φ at the current point P, _P φ …_E φ stand for the values of the grid _S points adjacent to the point P, and a …_P a are known as the link coefficients. The _S discretised form for the scalar control volume shows in Fig. 3-2. All equations were numerically solved using the commercial CFD program, FLUENT^® 6.1. The SIMPLE algorithm was employed to solve the convection-diffusion equations. The convergence criteria for the normalized residuals for each variable were restricted to be less than 10⁻⁶.

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Fig. 3-1 Numerical flow diagram of the solution procedure

W

N

S P E

I-1 I I+1

J+1

J-1 J

Scalar control volume

n

s

w e

i+1 i-1

j-1 j+1

Fig. 3-2 The scalar control volume used for the discretization of the governing equation

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CHAPTER 4 RESULTS AND DISCUSSION

4.1 Two-Dimensional Channel Model of a Plate Methanol Steam Micro-Reformer

In this section, the effects of the geometric and thermo-fluid parameters on the plate methanol steam micro-reformer performance and the heat and mass transfer are numerically investigated in detail. In this work, a two-dimensional numerical model was developed to study the methanol conversion and local heat and mass transfer in the channel of a micro-reformer. The information reported here would be useful in improving plate methanol steam reformer performance. When working in micro-reformers, it is very important to check the validity of the continuum model and evaluate possible rarefied gas flow effects. To this end, the Knudsen number (Kn) has been evaluated. This number compares the molecular mean free path with the characteristic geometric dimension of the system. The molecular mean free path has been evaluated according to Arzamendi et al.[63] for both the methanol steam reforming and combustion gases in the 250-350℃ range resulting values between 93 and 115 nm. In my base case, the characteristic dimension is the channel height (H =0.2 mm), the Knudsen numbers are between 1.86x10^-4 and 5.75x10^-4. These values are lower than 10^-3 which assures the validity of the continuum model and the Navier-Stokes equations for the systems considered in this work. The parameters used in the work are listed in Table 4-1.

Then, the effects of the number of gridlines on the numerical results are shown in Table 4-2 for three different grids. The predicted methanol mole fraction distributions show that the deviations of the methanol mole fraction among these three grids are 1%. Therefore, the 91x26 grid is used in this work. The accuracy of the numerical results was validated by

comparing the predicted methanol conversion with experimental results of Park et al. [16].

Figure 4-1 compares numerical and experimental results under various wall temperature and inlet velocities. The results show that the numerical results agree reasonably well with the experimental data.

4.1.1 Effects of the Geometric Parameters on the Heat and Mass Transfer and Methanol Conversion in a Micro-Reformer Channel

The influences of the geometric parameters and thermo-fluid parameters on the performance of micro-reformer are considered of great importance. To this end, the effects of the channel length (L=22 mm, 33 mm, and 44 mm), channel height (H=0.1 mm, 0.2 mm, and 1.0 mm), catalyst thickness (δ2=10 µm, 30 µm and 50 µm) and catalyst porosity (ε=0.28, 0.38, and 0.48) on the methanol conversion and CO concentration in the micro-reformer were investigated.

For fixed Reynolds number (Re=2.2), the effects of geometric parameters on methanol conversion of micro-reformer channel are presented in Fig. 4-2(a). The results show that the methanol conversion increases with an increase in the wall temperature Tw for all geometric conditions, implying that a better micro-reformer performance can be archived at higher wall temperature. By comparing the results of Tw = 200 ℃ and Tw = 260 with ℃ L=33 mm, H=0.2 mm, δ2=30 µm and ε=0.38, it shows that the methanol conversion for Tw = 260 ℃ could be improved by 49% relative to that of Tw = 200 ℃. Comparison of the corresponding curves of the channel lengths of L=22 mm, 33 mm, and 44 mm indicates that better methanol

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methanol conversion. Additionally, it is seen in Fig. 4-2(a) that the methanol conversion in the micro-reformer is enhanced by the increased catalyst thickness. The channel with thicker catalyst layer has a larger chemical reaction area, which in turn causes a better methanol conversion. The results show that methanol conversion improves from 80% to 99% at Tw = 260 with the catalyst thickness ranging from 10μm to 50μm. The effects of the porosity of ℃ catalyst layer (ε=0.28, 0.38, and 0.48) on methanol conversion of micro-reformer channel are also shown in Fig. 4-2(a). It is found that the methanol conversion increases with an increase in the porosity of catalyst layer. This means that reaction surface is enlarged via an increase in the catalyst porosity. In addition, the best methanol conversion is noted for the case with L=33 mm, H=0.2 mm, δ2=50 µm and ε=0.38 at Tw = 260 . This implies that the appropriate ℃ channel geometry and catalyst thickness are very critical for improving methanol conversion.

The CO concentration must be reduced for further use in a PEM fuel cell. Therefore, the CO concentration distributions for various geometric parameters are presented in Fig. 4-2(b).

It is clearly observed that the CO concentration increases with increasing wall temperature.

This is because the endothermic reverse water-gas-shift reaction increases as the wall temperature increases. It is clear in Fig. 4-2(b) that lower CO concentration is found for a micro-reformer with a shorter channel length. A detailed comparison of the corresponding curves shows that lower CO concentration is noted for a micro-reformer with a thinner catalyst thickness or a lower porosity. It is clearly seen that the CO concentration is about 16000ppm for the case with L=33 mm, H=0.2 mm, δ2=30 μm, ε=0.38 and a wall temperature of 260 . ℃

The effects of inlet fuel ratio on the CO concentration (ppm) at the outlet were also investigated. The effect of the molar ratio of H2O/CH3OH on the CO concentration for various geometric parameters and wall temperatures are shown in Fig 4-3. A careful inspection of Fig. 4-3 discloses that the CO concentration decreases with an increase in the

inlet molar ratio of H2O/CH3OH. This is due to the fact that the higher H2O concentration enhances the water-gas-shift reaction which, in turn, reduces the CO concentration. The results also show that the CO concentration would be reduced from 1.72% to 0.95% at Tw = 260 ℃with the H2O/CH3OH molar ratio values ranging from 1.0 to 1.6. However, the higher molar ratio of H2O/CH3OH also reduces the H2 concentration at the channel outlet. It is also found that the effects of the H2O/CH3OH molar ratio on the CO concentration are more significant for a case with a higher wall temperature.

The impact of channel height on temperature distribution along the centerline of the channel, at a fixed Reynolds number, was examined for the heights 0.1 mm, 0.2 mm and 1cm.

The hydraulic diameters of channel vary depending on channel heights. A higher channel height has a greater hydraulic diameter. Fig. 4-4 illustrates that the centerline temperature increases along the channel as a consequence of the heated wall. For a smaller channel height, the temperature distribution is much more uniform due to the shorter thermal entrance length.

This kind of uniform temperature distribution improves the chemical reaction rate. Therefore, as shown in Fig. 4-2 (a), the methanol conversion of the micro-reformer is slightly enhanced with the smaller channel height at higher wall temperature. A comparison of the temperature distributions for wall temperatures of 200 and ℃ 260 indicates that the centerline ℃ temperature increases with an increase in the wall temperature.

Figure 4-5 shows the effects of wall temperature on the cross-sectioned temperature at different axial locations for H=1.0mm at the wall temperatures of 200 and ℃ 260 . It is ℃ clearly found that near the entrance (X=0.076), the cross-sectioned temperature shows a significant variation. As the flow move downstream, the cross-sectioned temperature becomes

52

expected, there is a large difference on the velocity scale between the catalyst layer and flow channel. The velocity distributions in the catalyst layer are down to two orders of magnitude smaller than that in the flow channel, indicating that gas diffusion is the dominant transport mechanism in the porous media. The results also indicate the wall temperature of 260 ℃ generates higher gas velocity distributions than that of 200 .℃

Figure 4-7 shows the local distributions of the different species at wall temperatures of 200 ℃and 260 along the centerline of the channel for the same operating conditions. Fig.℃ 4-7 discloses that both the mole fractions of the CH3OH and H2O decrease as the fluid moves downstream, while the H2, CO2 and CO mole fractions increase with axial location. Fig. 4-7 clearly demonstrates that the mole fractions of the products increase with an increase in the wall temperature. In addition, Fig. 4-7 (b) shows that the methanol conversion is greater than 99% at a wall temperature of 260 , with ℃ a product gas composition of 74.7% H2, 23.6%

CO2 and 1.7% CO at the outlet of the channel. The results agree reasonably with experimental data [16]. For the PEM fuel cell, the CO concentration should be less than 10 ppm, so cleanup step is required after reforming. The utilization of the PrOx or water-gas-shift reaction equipment can reduce the CO concentration in the gas from the micro-reformer.

Studies of the reactant gas transport in micro-reformer channels have shown that a detailed understanding of the local distribution of the CH3OH mole fraction along the channel is important for designing the micro-reformer. Therefore, the effects of geometric parameters on the local distributions of the CH3OH mole fraction along the channel center line are presented in Fig. 4-8. The results reveal that geometric parameters have a considerable impact on the local CH3OH distributions. It is found that the CH3OH mole fractions decrease as the fluid moves downstream due to the chemical reaction. For various channel heights, there appears to be little variation in the CH3OH mole fraction distributions. The higher methanol concentration is noted for a system with a longer channel length or with a lower catalyst layer

thickness and porosity. This implies that the chemical reaction rate is weaker for a system with a shorter channel length or with a lower catalyst layer thickness and porosity. The effect of wall temperature on the local CH3OH mole fraction can be found by comparing the corresponding curves in Figs. 4-8 (a) and (b). It is clear that smaller methanol concentration is noted for a case with a higher wall temperature. This can be explained by the fact that a stronger chemical reaction is experienced for a micro-reformer channel with a higher wall temperature.

The distributions of the H2 mole fraction along the channel are shown in Fig. 4-9 for various geometric parameters and wall temperatures. A higher H2 mole fraction along the channel represents a higher methanol conversion. Thus, the variation of the H2 fraction is opposite to that of the CH3OH mole fraction in Fig. 4-8. In Fig. 4-9, a higher H2 mole fraction is found for a micro-reformer channel with a longer channel length or with a higher catalyst thickness, porosity and wall temperature. Figure 4-10 presents the effects of the geometric parameters on the local CO mole fraction distribution along the center line at wall temperatures of 200 and 260℃ . ℃ The trends of the variations in Fig. 4-10 can be interpreted in a similar way as for the results in Fig. 4-8 since a higher methanol conversion results in a higher CO production.

4.1.2 Effects of Thermo-Fluid Parameters on the Heat and Mass transfer and Methanol Conversion in a Micro-Reformer Channel

Additionally, the Reynolds number (Re=2.2, 4.4 and 8.8), fuel ratio (S/C=1.0, 1.3 and

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4-11 shows the effects of the Reynolds number on the local distributions of the CH3OH mole fraction along the channel at the same catalyst layer thickness and porosity. Three cases with Reynolds number of 2.2, 4.4 and 8.8 are presented in Fig. 4-11. It is clearly observed a lower methanol concentration (better methanol conversion) is found for a micro-reformer channel with a lower Reynolds number. This is due to the fact micro-reformer channel with a lower Reynolds number would experience a longer reactant gas resident time and reaction time, which in turn causes a better methanol conversion. In this work, we considered the H2O/CH3OH molar ratio values 1.0, 1.3 and 1.6. The predicted results in Fig. 4-11 show that the CH3OH concentration decreases with an increase in the H2O/CH3OH molar ratio. Also, the impact of different inlet fuel temperatures was examined for the values of 100 , 120 ℃ ℃ and 140 . ℃ It is found that a lower CH3OH concentration (a better methanol conversion) is found for a system with a higher inlet fuel temperature which increases the reaction rate.

Comparison of the local CH3OH mole fractions in Figs. 4-11 (a) and (b) for the wall temperatures of 200 and 260℃ ℃ for the various operating parameters shows that the local CH3OH mole fraction decreases with increasing wall temperature due to a strong chemical reaction for a high wall temperature.

The dependence of the local H2 mole fraction distribution on the Reynolds number, fuel ratio and inlet temperature are presented in Fig. 4-12. The results show that a higher H2 mole fraction is noted for a micro-reformer channel with a lower Reynolds number. This is due to the longer gas resident time which results in a better methanol conversion and a higher H2

production. The influences of the H2O/CH3OH molar ratio on the H2 mole fraction are presented in Fig. 4-12. The results show that a higher molar ratio of H2O/CH3OH causes the H2 mole fraction to fall. Additionally, the H2 mole fraction increases with increasing inlet fuel temperature. Comparison of Figs. 4-12 (a) and (b) indicates that a higher local H2 mole fraction is experienced for a micro-reformer channel with a higher wall temperature owing to

a stronger chemical reaction.

Figure 4-13 presents the variations of the CO mole fractions along the channel for the various thermo-fluid parameters. By comparing Figs. 4-12 and 4-13, it is found that the CO distributions in Fig. 4-13 have the same trends as the H2 distributions in Fig. 4-12. This confirms the common concept that a micro-reformer with a H2 production indicates a higher CO concentration.

4.2 Three-Dimensional Channel Model of a Plate Methanol Steam Micro-Reformer

In this section, the numerical results are obtained for a channel of a plate methanol steam micro-reformer. A three-dimensional channel model was developed to investigate the geometric sizes (aspect ratios and channel size) and thermo-fluid parameters (Reynolds number and wall temperature) on methanol conversion and local transport phenomena in the channel of a plate steam methanol micro-reformer.

In past studies of heat and mass transfer in a micro-reformer, simplified models without wall conduction effects have been developed. In this work, a detailed analysis of the 3-dimensional modeling with wall conduction effects has been proposed to examine the transport phenomena of heat and mass transfer in a micro-reformer channel. Figure 4-14 presents the effects of wall conduction on the local temperature distributions and CH3OH mole fraction distributions along the centerline of the channel. In this plot, X denotes the dimensionless distance from the channel inlet to outlet. It is clearly seen that the temperature

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addition, it is found in Fig. 4-14 that the effects of wall conduction on the methanol distribution are negligible, whereas their effect on the temperatures distribution is remarkable and cannot be neglected in the modeling. Therefore, wall conduction effects are taken into account in this work. This is the different between two-dimensional channel model and three-dimensional channel model.

The validation of the numerical results is performed by comparing the present predictions with previous experimental results. Figure 4-15 shows the comparison of the present predictions and experimental results. The solid symbols denote the experimental results of Park et al. [16] and the curve is the present prediction. The results show that the numerical results agree reasonably well with the experimental data.

4.2.1 Effects of Channel with Various Height and Width Ratios on Micro-Reformer Performance and Local Transport Phenomena

Using previously stated the numerical model, the effects of aspect ratios of channel on methanol conversion and transport phenomena were emphasized. The various cases for different aspect ratios are shown in Table 4-3. The aspect ratios, γ, are defined as follows:

1 2

WR

δ + δ

γ = (4-1)

Where (δ1+δ2) and WR are the channel height and width, respectively. The corresponding hydraulic diameters in Table 4-3 are fixed to be 0.286 mm.

In the present study, the mass fractions of the inlet reactant gas including methanol vapor and water vapor of 0.38 and 0.62, respectively, were tested. Thus, the molar ratio of H2O/CH3OH was kept constant at 1.1. The inlet flow velocity of 0.266 m/s used and therefore, the corresponding Reynolds number Re was 3.14 for each test. The geometric dimensions and

physical properties of the channel are listed in Table 4-4.

The grid independence was examined in preliminary test runs. Three grid configurations were evaluated for the channel of the plate methanol steam micro-reformer at a wall temperature of 200 . The numbers of grid lines in the x, y and z directions were: 41x1℃ 6x18, 51x21x23, and 71x31x33. The influence of grid lines on the local methanol mole fraction is shown in Table 4-5. The deviations of methanol mole friction are 0.4% for grids 41x16x18 and 51x21x23, and 0.4% for grids 51x21x23 and 71x31x33. Grid 51x21x23 was, therefore, chosen for the simulation in the present study as a tradeoff between accuracy and CPU computation time.

For aspect ratio of γ=0.5, Fig. 4-16 presents the local distributions of the different species at wall temperatures of 200 and 260℃ along the center of the channel. Overall inspection ℃ of Fig. 4-16 disclosed that the CH3OH and H2O mole fractions decrease along the channel, while the H2, CO2 and CO mole fractions increase along the center of the channel. The results demonstrate that as the mole fractions of the products increase as the wall temperature increases. The results also show that the methanol conversion is about 49% for a wall temperature of 200 , wit℃ h a gas composition of 24％ CH3OH, 28% H2O, 36% H2, and 12%

CO2 at the channel outlet. However, the CO concentration is only 244 ppm. For a wall temperature of 260 , the results℃ indicates that the methanol conversion is greater than 96%, with a product gas composition of 74.05% H2, 24.28% CO2, and 1.67% CO at the channel outlet. For the PEMFC, the CO concentration must be less than 10 ppm which can be achieved using a CO oxidation reactor. The utilization of the preferential oxidizer (PrOx) reactor or water-gas-shift reaction can reduce the CO concentration in the gas from the

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and CO concentration (ppm). In this work, the catalyst thicknesses are fixed to be 30μm. A careful examination of Fig. 4-17 reveals that the methanol conversion increases with an increase in wall temperature. Thus, the methanol conversion can be improved by increasing wall temperature, which in turn, increases the chemical reaction rate. It is also found form Fig.

4-17 that the methanol conversion increases with a decrease in aspect ratio due to the large chemical reaction area for a low aspect-ratio channel. This implies that better performance is

4-17 that the methanol conversion increases with a decrease in aspect ratio due to the large chemical reaction area for a low aspect-ratio channel. This implies that better performance is