Net drag coefficient

The net drag coefficient Ud is a parameter used to express the net drag of water from the anode to the cathode and accounts for the total effect of the modes in Eq. (6.29) ... 

The net drag coefficient represents the total transport of water to the cathode. In an ideal situation for water management, ad would be uniformly —0.5 along the electrode. In this case, the exact amount of water generated by reaction is exactly balanced and moved... 

As a result of Schroeder s paradox, there is a very high electro-osmotic drag coefficient of 2-5 H2O/H+ in applications where the anode is in contact with liquid-phase water such as the DMFC. This and the lack of back diffusion result in a very positive net drag coefficient and more severe cathode flooding without special engineering of the DM to provide a strong capillary pressure gradient toward the anode. 

Example 6.5 Calculating Internal Water Balance Given a net drag coefficient of 0.1, determine the molar rate of water accumulation at the catalyst layer that must be removed to prevent flooding. 

COMMENTS For thin membranes in fully humidified conditions, we can typically assume a net drag value close to zero. If there is an imbalance in the inlet RH values between the anode and cathode, the diffnsion flnx will change the net drag coefficient. If the anode flow is relatively underhumidified compared to the cathode flow, the net drag... 

The factor of 1 in Eq. (6.49) is a result of the consumption of oxygen in the cathode by the electrochemical oxygen reduction reaction. A plot of this minimum boundary as a function of pressure over the relevant temperature range is shown in Figure 6.54. This boundary serves as a baseline for discussion purposes. Depending on the use other methods to control the net drag coefficient of water, this boundary can shift considerably. 

For a 100-cm fuel cell at 1 A/cm operation, with a net drag coefficient of 0.1, and the other conditions shown in the accompanying table, solve for the cathode flow rate that must be used to achieve a water balance with no liquid water ejection from the fuel cell... 

For a net drag coefficient of 4.0, no hydraulic permeation effects, and an electro-osmotic drag coefficient of 3.0, calculate the water crossover and equivalent f)ower lost per day for a 10 M methanol solution at idle in the anode of a 10-cell, 10-cm /cell DMFC stack. 

Expand your program in problem 6.27 to include a net drag coefficient and the effects of anode flow. For the same cathode conditions as problem 6.27, (a) and (b), determine the anode/cathode (assume they are the same) exit temperature needed to balance the water generated. The flow of humidified hydrogen into the anode is at RH = 100%, 80°C, 3.2 atm pressure, and stoichiometry 1.5 at 1 A/cm for a 100-cm ceU. The anode flow leaves at 3.1 atm and 100% RH at the chosen exit temperature. Plot the required exit temperature as a function of net drag coefficient. 

The net dynamic pressure on a structure is the product of the dynamic pressure and a drag coefficient, Cd. The drag coefficient depends on the shape and orientation of the obstructing surface. For a rectangular building, the drag coefficient may be taken as +3.0 for the front wall, and -0.4 for the side and rear walls, and roof. 

To shed some light on these issues and to be able to have a better understanding of the water transport when using MPLs, Atiyeh et al. [152] presented an experimental method designed to investigate the net water drag coefficient in order to have a better indication of the amount of water flowing from fhe cathode to the anode. They observed that the performance of fhe fuel cell improved when the anode, the cathode, or both had microporous layers. 

However, after implementing the water balance measurements, they were not able to observe a significant difference on the net water drag coefficient for a fuel cell with a cathode MPL and an anode without an MPL compared to a cell without any MPLs. It is important to note that they were able to observe that the MPL does in fact improve the fuel cell performance and stability when operating at constant conditions (i.e., the voltage fluctuations are significantly reduced when the cathode DL has an MPL). These results do not correlate with the observations presented earlier thus, more experimental work is necessary to investigate the process behind how the MPL helps the performance of the fuel cell. 

As briefly mentioned in Section 4.3.S.2, Atiyeh et al. [152] performed water balance measurements and calculations to determine the effect of using DLs with MPLs (on either or both cathode and anode sides). In their fuel cell test station, water collection systems were added in order to be able to collect and measure accurately the water leaving both anode and cathode sides of the fuel cell. Based on the operating conditions (e.g., pressures, temperatures, relative humidities, etc.) and the total amount of water accumulated at the outlets of the test station, water balance calculations were performed fo defermine the net water drag coefficient. Janssen and Overvelde [171] used this method to observe how different operating conditions and fuel cell maferials affected... 

Unfortunately for production facility design, it can be shown that Stokes Law does net govern, and the following more complete formula for drag coefficient must be used ... 

Figure 6.24 Measured local and net effective drag coefficients along gas flow channel of PEFC operating at 0.7 V, with a dry anode inlet and cathode inlet at 50% RH at 9 C. The net drag is negative, indicating a net drag of water toward the dry anode. Toward the exit, however, the local effective drag becomes positive. (Adapted from Ref. [24].)...

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