Magnetic fields were measured by inserting the magnetic sensor into the cooling holes of the stack. Figure 2 shows a schematic diagram of the magnetic field measurement device and the picture of the magnetic sensor probe. The magnetic sensor was a tri-axis electronic compass (Aichi Micro Intelligent: AMI306). This sensor has dimensions of 2.0 × 2.0 × 1.0 mm and was embedded with MI sensors. Each sensor outputs the magnetic flux density of the corresponding axis. Output values were recorded on a PC through the I2C interface.

The electric current generated by the PEMFC produces a magnetic field by the Biot-Savart law. Reference axes were set for the current distribution measurements. The x-axis was the cell width, the y-axis was the cell height, and the z-axis was perpendicular to the cell surface. The x, y component of magnetic flux density was corresponded the stack current by the law. Additionally, the z component was explained the current parallel to the surface of the cell by the fault such as flooding.

The measurement device outputs the x, y, and z components of the magnetic flux density: B_x, B_y, and B_z, respectively. The following x and y components of the current were used:

where i_xn and i_yn [A] denote the x and y components, respectively, of the current density at n A; α_x and α_y denote the magnetic field response values for the current; B_xn and B_yn [G] denote the x and y components, respectively, of the magnetic flux density at n A; and B_x0 and B_y0 [G] denote the x and y components, respectively, of the magnetic flux density at 0 A, which are used for removing the effects of geomagnetism and the earth’s magnetic field of environment. The current density i_jn [A/cm²] is expressed as follows:

where S [cm²] denotes the target area of measurement. However, the sum of i_jn for the entire cell may not be equals to the stack current I. Therefore, we revised the expression such that the sum of the current density for the whole cell is equals to the stack current I as follows:

where [A/cm²] denotes the revised current density at n A; and [A] denote the x and y components, respectively, of the revised current density at n A; and k denotes the number of divisions of the target area for measurement.

The cell area was segmented into 15 parts for calculation, and the measuring points of each cell were set at 15 grid points. Therefore, k = 15 in Equation (5). The measured points were (x, y) = (9, 9), (9, 27), (9, 45), (27, 9), (27, 27), (27, 45), (45, 9), (45, 27), (45, 45), (63, 9), (63, 27), (63, 45), (81, 9), (81, 27) and (81, 45). Here, (x, y) denotes position, with units of mm, on the cell surface. The cathode inlet and outlet is located at (x, y) = (9, 45) and (81, 9), respectively.

In order to measure the magnetic fields of cells all at once, the stack was installed in the downward inlet of fuels. The measured cells were cell No. 2, 6, 11, 15, and 20.

In order to evaluate the fault such as flooding, measured the z component of the magnetic field and variations in voltage have been used [14] .

The z component of magnetic flux density was evaluated to study the three-dimensional current. The z-axis was perpendicular to the surface of the cell. We used the z component of magnetic flux density as an index to explain the current parallel to the surface of the cell. The parallel current is likely arisen the fault such as flooding. The ratio between the value of the z component and the value of the xyz compound vector was calculated at each measurement point. This ratio is defined as follows:

and the parallel current was relatively large when was large.

The variation in the voltage was useful to identify the cell to arise the flooding. When the cell was flooding, the voltages undergo a change widely because the generated water disturbed the reaction of hydrogen and oxygen. In particular, this trend arises if the flow channel was plug up by the generated water.

Figure 3 shows the average stack voltage at each air flow rate. The stack voltage decreased as the air flow rate decreased. These air flow rates sufficed the reaction with hydrogen. During these operations, the generated water was steady because the stack current was constant. Furthermore, the experiment started from the 20 L/min. Therefore, the reduction of voltage was attributed to reaction inhibition by the generated water on reactant surface. The cell voltage at 9 and 10 L/min was different however the stack voltage does not appear at Figure 3. The reason was that the stack voltages were average values and the cell voltages undergo a change widely.

Figure 4 shows vectors of magnetic flux density at 9 L/min. The direction of the vectors was anticlockwise when viewed from the cathode side. This indicates that the direction of the macroscopic current was from the anode side to the cathode side in the stack because of Ampere’s law. This direction accorded with the polarity of the stack. In this manner, the macroscopic current in the stack was detected. At cells No. 6, 11, and 15, the values of the z components were smaller than those of the x and y components. In cells No. 2 and 20, the direction of the vectors is different from that in the other cells because they were affected by the end terminals of the stack. Furthermore, in cell No. 2, the values of the z components were larger than those of the x and y components at (x, y) = (81, 9). At the point (x, y) = (81, 9), the current was likely to avoid and flow parallel to the cell surface be-

cause of the high electric resistance.

Figure 5 shows the current distribution directed toward the z-axis at 20 L/min. The each part of a current was calculated by the Equation (3). The maximum value of current density is 357.5 mA/cm² at (x, y) = (81, 27) in cell No. 20. The current distribution tended to be concentrated in the cells at each end of the stack because these cells were affected by the end terminals of the stack. However, current distributions of the cells were not uniform, because each cell exhibited different performance and condition. In the next section, the relationships among the current distributions, the magnetic flux densities, and the cell faults are evaluated.

Figure 6 shows the distribution of on the each cell at 20 L/min. The parallel current increased with increasing. The cell No. 2 showed the largest than the other cells. The maximum value of was 0.75, and this occurred at (x, y) = (45, 27) on the center of cell No. 2. At this point, the current was likely to avoid and flow parallel to the cell surface because of the high electric resistance. Therefore, the current distributions in the center of cells were smaller than those at the other points. The second-highest value of was 0.31, occurred at (x, y) = (81, 9). At this point, current flow parallel to the cell surface was detected; this was also the case at (x, y) = (45, 27). However, the current distributions were not smaller at these points than at the other points. Therefore, it is considered that the results of the two points are derived from the different phenomena.

Figure 7 shows the distribution of in cell No. 2 each air flow rate. Figure 8 shows at the cathode inlet and outlet in cell No. 2 each air flow rate. At the cell center, (x, y) = (45, 27), decreased with decreasing in the air flow rate. If the flooding occurs in the stack, increases because of the high electric resistance by the produced water. Therefore, this point did not undergo flooding, and multiple problems of the stack were evaluated. The pressure of membrane might be unequal because the current density was small at this place.

At the cathode inlet, (x, y) = (9, 45), was almost no variation with the air flow rates. In contrast, at the cathode outlet, (x, y) = (81, 9) increased with the air flow rate of 9 L/min. The cell voltages varied considerably in cell No. 2, as shown in Figure 9. This cell was expected to undergo flooding because the stack was installed in the downward inlet of fuels. Therefore, the point (x, y) = (81, 9) had high electric resistance owing to flooding by the generated water.