Two-Phase Flow Pressure Drop in PEM Fuel Cell Flow Channels, Model Comparison and Improvement
Authors: Stolberg Preston R. , Suchocki Nicholas J. , Mortazavi Mehdi , Santamaria Anthony D. 
Published: February 2020

Proton exchange membrane (PEM) fuel cell liquid water management remains a topic of research as these technologies continue to penetrate commercial markets. Two-phase flow pressure drop may be considered an in-situ diagnostic tool that can reveal the amount of liquid water accumulating in a reactant flow channel. While the topic of two-phase flow has been studied extensively, having a reliable two-phase flow pressure drop model that can accurately predict the pressure drop in PEM fuel cell flow channels is still an issue. In this study, in-situ and ex-situ two-phase flow pressure drops in PEM fuel cell flow channels are measured and compared with existing models. The objectives of the current study are to compare experimentally measured two-phase flow pressure drops with existing models as well as to improve the two-phase flow pressure drop model for an accurate pressure drop prediction for the application of PEM fuel cell. In-situ and ex-situ experiments were conducted and analyzed for this purpose.
The models focused on in this work are all based on experimentally determined two-phase flow pressure drop for channel hydraulic diameters ranging from 0.15 mm to 12 mm. These models were developed for various applications and fluid/gas combinations. For this study’s ex-situ experiments, liquid-gas two-phase flow pressure drops were measured over 20 cm of a 2 mm x 1 mm flow channel machined from an aluminum plate. Water was injected through a Toray (TGP-060) gas diffusion layer (GDL) and emerged on its surface within the flow channel supplied with air flow. Fig. 1 compares 108 experimentally measured ex-situ two-phase flow pressure drops with nine two-phase flow pressure drop models. Figures a-g are based on the separated flow model and figures h-i are based on the homogeneous equilibrium model. The general trend observed in Fig. 1 suggests that although separated flow models outperform homogeneous equilibrium models, they mostly under-predict the two-phase flow pressure drop, especially at lower pressure drops.
The seven separated flow model shown in Fig. 1a-g are further compared with each other by defining the mean absolute error (MAE), shown by λ in Fig. 1,
(insert Equation 1 from JPG file)
In addition, ω, θ, and ε are defined as the percentage of data points predicted within ±10%, ±30%, and ±50%, respectively. It can be observed from Fig. 1 that the model proposed by Mishima and Hibiki [2], shown in Fig. 1c, reflects the best prediction capability with the lowest MAE value.
The MAE was further studied at different mass flow qualities and superficial air velocities as shown in Fig. 2. The numbers shown in parentheses indicate the number of experiment runs considered to calculate the MAE at each mass flow quality or superficial air velocity. Fig 2a shows the MAE at different mass flow qualities for each of the separated flow models. Other than mass flow qualities x = 0.87 and x = 0.97, the model proposed by Mishima and Hibiki [2] resulted in the lowest MAE compared to the other six models. However, the model proposed by Saisorn and Wongwises [1] showed a smaller MAE in these two mass flow qualities. Fig. 2b shows the MAE calculated at different superficial air velocities and air flow rates in the flow channel. For superficial air velocities of less than 2 m/s, the model proposed by Saisorn showed a superior performance. However, for superficial air velocities greater than 2 m/s, Mishima and Hibiki's model [2] outperformed.
In addition to ex-situ results, experimental in-situ liquid-gas two-phase flow pressure drops are also being measured in an operating PEM fuel cell as shown in Fig. 3. The PEM fuel cell used in this study has seven parallel flow channels, each with 1 mm x 1 mm cross section, machined through stainless steel bipolar plates backed with clear polycarbonate sheets to visualize water. Two high-precision pressure transducers measure pressure drop along 80 mm of two flow channels. In addition to pressure drop measurement, liquid water accumulation and transport with the flow channels is also recorded with a CCD camera mounted directly above the cathode. A combination of ex-situ and in-situ results will cover a large range of liquid/gas flow rates which will be useful for model validation.
References:

S. Saisorn, S. Wongwises, The effects of channel diameter on ow pattern, void fraction and pressure drop of two-phase air-water flow in circular micro-channels, Experimental Thermal and Fluid Science 34 (4) (2010) 454-462.

K. Mishima, T. Hibiki, Some characteristics of air-water two-phase ow in small diameter vertical tubes, International Journal of Multiphase Flow 22 (4) (1996) 703-712.

Figure 1