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Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method
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Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method Rouxian Chen, Yanzhou Qin*, Suhui Ma, Qing Du** State Key Laboratory of Engines, Tianjin University, Tianjin, China
highlights Water removal modes from the gas diffusion layer surface depend on water velocity. Water directly impinges the channel surface and is removed for high water velocity. Small droplets are frequently detached from water hole for high airflow velocity. Surface wettability determines water flow patterns after impacting channel surface. U-turn of channel promotes water removal from the gas diffusion layer surface.
article info
abstract
Article history:
Three-dimensional numerical simulation of liquid water emerging from the gas diffusion
Received 4 December 2018
layer (GDL) surface to the gas flow channel in the proton exchange membrane (PEM) fuel
Received in revised form
cell (PEMFC) is carried out using the volume of fluid (VOF) method. The effects of the water
18 July 2019
velocity in the GDL hole, the airflow velocity and the wettability of the channel surfaces on
Accepted 22 July 2019
the water emerging process and transport in the flow channel are investigated. It is found
Available online xxx
that at low water velocity, the water detaches from the water hole, forming discrete water droplets on the GDL surface, and is transported downstream on the GDL surface until
Keywords:
removed from the GDL surface by the U-turn part of the flow channel; whereas at high
PEMFC
water velocity, the continuous water column impinges the hydrophilic channel surface
Water flow
counter to the GDL surface, being directly removed from the GDL surface. The airflow
Water detachment
velocity affects water detachment and impact process in the channel corner, and water
Flow velocity
droplet breakup is observed under high airflow velocity. The channel surface wettability
Surface wettability
influences water droplet shape and its transport in the channel. Rather than forming corner water films at the U-turn for hydrophilic channel surface, water maintains the droplet shape and smoothly passes through the U-turn for hydrophobic channel surface. The importance of the U-turn to the water removal is also discussed. The U-turn promotes water removal from the GDL surface at low water velocity and water breakup at high airflow velocity. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Qin), [email protected] (Q. Du). https://doi.org/10.1016/j.ijhydene.2019.07.169 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Introduction Proton exchange membrane (PEM) fuel cell (PEMFC) is a clean energy conversion device which converts chemical energy directly into electrical energy through electrochemical reactions. It has drawn worldwide attention for its advantages of high efficiency, low emissions and fast start-up response. The process of practical application and commercialization of PEMFC is fraught with challenges, among which water management is critical due to its tremendous impacts on the performance and durability of the cell. Understanding the water transport and removal mechanism in the gas flow channel is the key to optimizing water management and preventing flooding [1,2]. Water in PEMFC is usually composed of two sources, one is vapor in humidified reaction gas, which significantly enhances the effective hydration of the membrane in order to strengthen proton conductivity. And the other one is water generated by electrochemical reaction in the cathode. In some working conditions such as high current density, a large amount of water is generated in the cathode catalyst layer (CL). Although there is back diffusion effect of water transmembrane transport, the GDL and channel are the main access for water removal from the reaction site. In case that liquid water accumulates in the GDL and channel, the flow and diffusion resistance into the CL would increase, hindering the reactants transport. For water management in PEMFC, a rational control strategy relies on a variety of parameters, such as the wettability of the GDL and channel, the shape of the structure, the gas velocity and the location of water emergence [3]. The comprehensive effect of these factors needs to be fully understood for the optimization of flow and diffusion of reactant gas, pressure drop, and finally ideal performance and durability of the cell. The gas-liquid two phase flow in PEMFC has been investigated experimentally, utilizing visualization techniques, including in-situ and ex-situ testing methods [4]. Direct photography, neutron radiography, X-ray graph and nuclear magnetic resonance imaging (MRI) have been used for observing the liquid water in the channel. Flow patterns are observed in the form of water droplet, film and slug flow by direct photography [5,6]. Grimm et al. [7] summarized flow regime criterion and described it as a function of air and water velocity. A parameter, wetted area ratio, was introduced to quantitatively describe water accumulation in the channel under different working conditions by manual channel images [8]. Neutron radiography was applied to study the effect of liquid water blockage on the performance of the cell, which suggested that water accumulation in the GDL tended to be availably removed by the cross-leakage flow through the GDL to the adjacent flow channels [9]. Details of fast water transport processes such as the “eruptive” water expulsion from the GDL pores into the channel were demonstrated by in-situ synchrotron X-ray radiography [10]. Dunbar et al. examined water distribution quantitatively utilizing the MRI for the first time and found that the flow pattern in the channel tended to be wavy-stratified rather than slug flow [11]. Two-phase flow pressure drop was measured to investigate the effects of load and temperature condition, and the transient response was
characterized [12]. Water accumulation and channel pressure drop of serpentine and parallel flow fields were investigated and a new type of serpentine flow field was designed to effectively modify the length of the channel, achieving higher fuel cell performance [13]. Ex-situ experiments were also introduced by measuring the pressure drop and flow rate so that the gas flow distribution and its effect on the water flow could be obtained [14]. Yoon et al. conducted ex-situ experiment to observe the water droplet growth and removal in the cathode, suggesting the micro structures of GDL and microporous layer (MPL) have significant influence on water removal in the channel [15]. The pressure loss of two-phase flow existing from microchannel to manifold was also investigated [16]. The flow regimes were visualized and analytically recognized as jet, bubble, churn, stratified and annular flow [17]. Experiments are indispensable to investigate the effects of material and structural properties, and operating conditions on water transport in the channel. However, there are still limitations on precise and impeccable characterization of the two-phase flow pattern in a working PEM fuel cell. Direct photography is convenient for instantaneously direct observation at a reasonable cost, nonetheless, optical window employed changes the inherent attribute of the cell by changing the material properties including wettability, roughness, and thermal and electrical conductivity [18]. Neutron radiography, X-ray graph and MRI suffer the disadvantages that special materials or structures are needed to satisfy the test conditions, and the spatial and temporal resolution are lower comparing to direct photography. The disadvantages in conducting experiments to reveal water transport mechanism motivate researchers to carry out computational fluid dynamics simulations. The volume of fluid (VOF) method is widely used to simulate water transport in the PEM fuel cell channel. The liquid water, in the form of droplet or liquid film, was usually introduced directly onto the surface of GDL which is considered flat and impermeable in most previous studies [19]. Due to its importance, a large number of researches have investigated the water behaviors in the channel, focusing on the single water droplet, discussing the effect of the gas velocity, the channel surface wettability and roughness, the channel geometry and the droplet size, and a few involve multiple water droplets interactions [20,21]. Quan et al. [22] directly introduced initial water droplets and film into the channel corresponding to different working conditions of fuel cell and investigated two phase flow in the bend area of serpentine channels. Jiao et al. [23] studied the air-water flow in PEM fuel cell stacks and observed “collecting-and-separating” effect in serpentine channels with different initial water distributions. Although these studies obtained much useful information of the water transport mechanism in the flow channel, the initial water state on the GDL surface in the channel is deficiently simulated considering the water emerges or erupts from the inside of the GDL [10]. The more realistic method in simulation is to apply a water hole in the GDL which is connected to the channel and emerges water continuously to the channel. Using this method, Zhu et al. [24,25] numerically investigated the influence of multiple parameters, including the surface wettability, the air velocity, the water velocity and the channel
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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geometry, on the water emergence from the water hole and the afterward water behaviors in the flow channel. Ding et al. [26] further investigated the effect of GDL surface microstructure on the water emergence and transport in the flow channel, by changing the pore size and pore number. It was identified that the wettability dominated the flow pattern rather than the pore diameter when the pore size was small enough. Vertical and horizontal fuel cells were simulated to study the effect of flow field orientation. Gravity was found assisting in water removal in the vertical direction, but hindering water purging from the horizontal elbow position. Ashrafi et al. [27] proposed a model using a random function to generate heterogeneous GDL surfaces so that the roughness of the surface could be reasonably considered. The roughness of the GDL was found to have significant effect on droplet transport, and rolling small droplets and translational large droplets were correspondingly observed. Hydrophilic plates [28] and needles [29] were introduced into the channel to facilitate water removal from the GDL surface, and multiple design parameters were discussed for water transport and removal. Water droplet deformation and detachment were theoretically analyzed, simulated and experimentally validated. The expression corresponding to water droplet shape change was obtained and the correlation to calculate the water detachment velocity with Weber number and Reynolds number was derived [30,31]. The previous studies usually made the water emerging velocity at a low range, based on uniform and continuous water emerging assumptions. However, water usually emerges only at a few preferred water holes which are randomly distributed on the GDL surface, and the water emerging rate is not continuous but intermissive, probably making the water flow rate very high, orders of the real-time water generation rate in PEMFC. This is supported by the Xray imaging showing that multiple water clusters intersected at particular pores and established specific breakthrough paths [6], and “eruptive-like” water transport mechanism was observed [32,33]. A PEMFC performance model coupled with the VOF method was built to predict the fuel cell performance and water transport in the cathode channel simultaneously, and the liquid water inlet velocity could reach 1.2 m s1 in their study [34]. The water transport characteristics in the flow channel at high velocity can be quite different from the previous predictions and require further investigation. In this study, a large range of water velocity, air velocity and channel surface wettability are applied in the simulation of water transport in a U-shaped channel to investigate the water removal process. Especially, the phenomenon of water impingement to the channel surface under high water velocity is revealed and discussed. The importance of the U-turn effect is also discussed on the water removal from the GDL surface.
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Fig. 1 e Computational domain in the present study.
straight single channels connected by a U-turn and a water inlet hole. The channel cross-section is 0.5 mm 0.5 mm, and the channel length in the x direction is 7 mm. Water is introduced into the channel from the water inlet hole, which corresponds to the water transport path in the GDL. The water hole connected with the channel bottom surface has the cross-section of 0.05 mm 0.05 mm and the length of 0.2 mm, and the center of the hole locates at the quarter of the channel from the inlet to eliminate the entrance region effect. The flow is assumed laminar, isothermal and incompressible due to the small Reynolds number. The gravitational force is considered in the negative y direction. The phase change between water and gas is neglected due to the fast water transport process. The channel walls and the GDL surface are considered impermeable.
Governing equations The interface of two-phase flow can be captured by utilizing the VOF method. Governing equations of mass and momentum for the two-phase flow in the channel can be written as: vr þ V,ðrVÞ ¼ 0 vt
(1)
vðrVÞ þ V,ðrV , VÞ ¼ VP þ mV,ðVV þ VVT Þ þ rg þ FS vt
(2)
The gas phase is set as primary phase expressed by subscript 1, and the liquid phase is set as secondary phase expressed by subscript 2. The relation of two-phase volume fraction is: f1 þ f2 ¼ 1
(3)
The density and viscosity can be calculated as: r ¼ f2 r2 þ ð1 f2 Þr1
(4)
m ¼ f2 m2 þ ð1 f2 Þm1
(5)
Model formulation
The source term in Equation (2) representing the effect of surface tension and wall adhesion is expressed as:
Computation domain and assumptions
FS ¼ slg
As shown in Fig. 1, the computational domain is a U-shaped section of a serpentine flow channel, comprised of two
where slg is the surface tension coefficient between the two phases, k is the surface curvature of the two-phase interface,
rkVf1 0:5ðr1 þ r2 Þ
(6)
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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and f1 is the liquid phase volume fraction which is calculated by a continuity-like equation as shown below: vf1 þ V,ðf1 VÞ ¼ 0 vt
(7)
In the vicinity of the channel wall the surface curvature is determined by the contact angle reflecting the channel surface wettability as: b w cosðqÞ þ bt w sinðqÞ k ¼ V,½ n
Boundary conditions A parabolic velocity of air in the x direction is adopted at the channel inlet and water is injected from the water hole. Constant pressure is set at the channel outlet of Pout¼ 1 atm. For the boundary of the wall surfaces, the no slip wall boundary condition is used for all the surfaces. The wettability is studied by varying the surface contact angle. These boundary conditions can be expressed mathematically as: Gas inlet: (9)
Water inlet: vy ¼ vy,0, vx ¼ vz ¼ 0
(10)
Channel outlet: P ¼ Pout
(11)
Channel and GDL surfaces: vx ¼ vy ¼ vz ¼ 0
The effects of water velocity, airflow velocity and channel surface wettability are investigated. In all the cases investigated, the contact angles for the GDL surface are set as 140 . The channel surface contact angle qchannel, the airflow velocity at the channel inlet center vx,0 and the water velocity vy,0 for all the cases are listed in Table 1.
(8)
b w and bt w are the where q is the contact angle of the wall, and n unit vectors normal and tangent to the wall, respectively. In the VOF method, the continuity of volume fraction is firstly solved, and then the reconstruction of the air-liquid interface is performed by piecewise linear approximation so that the dynamic of the two-phase interface can be captured.
vx ¼ vx,0, vy ¼ vz ¼ 0
Results and discussion
(12)
For initialization of the calculation, the inlet velocity and outlet gauge pressure are set as zero and the channel is occupied with air. Thereafter, aforementioned boundary conditions are adopted.
Effect of water velocity The water velocity significantly influences its emerging and transport process in the flow channel. The water velocity investigated includes 1, 2 and 5 m s1, corresponding to the base case, Case 1 and Case 2, respectively. Fig. 2 shows the water transport and dynamics in the channel for the water velocity of 1 m s1. Water is produced continuously in the cathode CL and a pressure difference is built up between the two sides of the GDL. The water emerges from the water hole, forming a water droplet. The water droplet grows continuously until it detaches from the water hole at a critical point when the airflow shear force overcomes the water internal surface tension as the water frontal area exposed to the airflow is large enough, which is typical droplet detachment type. A succeeding water droplet grows again at the water hole after the previous water droplet detaches from the water hole. The detached water droplet is transported downstream along the GDL surface in the channel until it hits the channel surface at the U-turn. Since the channel surface is hydrophilic, the water spreads out on the channel surface and is removed from the GDL surface due to the capillary force of the channel surface caused by the difference of wettability. The detached water droplets periodically hit the channel surface, spread out and merge on the channel surface, forming water films on the channel surface which is transported along the channel corners. The simulation results agree with the experiments that liquid water tends to accumulate in the hydrophilic channel corners [35]. The U-turn changes the water transport characteristics significantly. The water is removed from the GDL surface after it reaches the channel surface at the U-turn, which clears the reactant gas passage to the GDL; otherwise, the water would transport along the GDL surface, blocking the GDL surface all the time, as in a straight channel. The U-turn promotes the water removal from the GDL surface for the channel having
Numerical procedures The governing equations and boundary conditions are implemented in the Fluent platform. The pressure-implicit with splitting of operator scheme (PISO) is used for the pressure-velocity coupling. The pressure staggering option scheme (PRESTO) is selected for the pressure discretization. The second order upwind scheme is applied for solving the momentum equation and the volume fraction equation. The grid independence is studied and proper grid number is used in the simulation.
Table 1 e Computational cases and parameter values. Cases Base case Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7
vx,0 (m s1)
Vy,0 (m s1)
qchannel ( )
20 20 20 10 30 20 20 20
1 2 5 1 1 1 1 1
50 50 50 50 50 80 110 140
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 2 e Water transport and dynamics in the channel for the water velocity of 1 m s¡1, corresponding to the base case given in Table 1.
hydrophilic channel surface, which is beneficial for the PEMFC performance. Water transport and dynamics in the channel for the water velocity of 2 m s1 is shown in Fig. 3. It is apparent that the water emerges from the water hole in the form of a water column for the higher water velocity, comparing to the water droplet moving on the GDL surface for a lower water velocity. Due to the strong airflow shear force, the water column is inclined in the air stream and separates out water droplets at the top of the water column. The separated water droplet is transported upward to reach the hydrophilic channel top surface under the inertia effect. Then, the water spreads out on the hydrophilic channel surface and moves to the two channel corners. Since the water is immediately removed from the GDL surface after it emerges out, no water droplet is observed on the GDL surface and it will not block the GDL at all. The process of water impact and breakup occurs on the channel top wall, and the water spreads to the channel side walls. Due to the strong capillary force, the spreading droplet is divided into two parts, accumulating in the channel corners. Different from water droplet flow patterns for lower water velocity, when the water velocity is high enough to produce a water column and impact the channel wall directly, liquid films are formed and transported along the straight channel before the U-turn. Consolidation of the liquid films is observed at the front of the flow after t ¼ 10 ms, because the volume of
films increases and the surface tension is enough to preserve the film shape. The water film flow is much slower, it barely approaches to the inner side of the U-turn until t ¼ 15 ms, whereas the water droplet on the hydrophobic GDL surface reaches outer side of the U-turn before t ¼ 6 ms, as shown in Fig. 2. Due to the strong capillary force and small frontal area (or small gas shear force), the water films will not reach the outer side of the U-turn, but move along the inner corner of the channel after the U-turn. Fig. 4 shows the water transport and dynamics in the channel for the water velocity of 5 m s1. The water is also directly removed from the GDL surface after it emerges out from the water hole, similar to the result shown in Fig. 3 for the water velocity of 2 m s1. The water column directly impinges the hydrophilic channel top surface without separating out water droplets. The water column is not inclined noticeably as for Case 2. Similarly, thin water film is formed at the two channel corners after the water reaches the hydrophilic channel surface. However, water velocity of 5 m s1 makes it possible to accumulate a large amount of water in the U-turn and both the inner and outer corners are filled with water. It reveals that the water emerging from the water hole in GDL can be directly removed from the GDL surface for the water velocity higher than a critical water velocity. The water is transported along the GDL surface and is removed from the GDL surface by the U-turn effect for the water velocity lower than the critical velocity, whereas the water is directly
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 3 e Water transport and dynamics in the channel for the water velocity of 2 m s¡1, corresponding to Case 1 given in Table 1.
Fig. 4 e Water transport and dynamics in the channel for the water velocity of 5 m s¡1, corresponding to Case 2 given in Table 1.
removed from the GDL surface and reaches the channel top surface for the water velocity higher than the critical velocity. The critical velocity is found slightly smaller than 2 m s1 in the present study.
The evolution of pressure drop corresponds to the twophase flow patterns [36]. Fig. 5 displays the effect of water velocity on the temporary pressure drop, which indicates pressure difference between inlet and outlet of the channel. It
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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900 Base case Case 1 Case 2
Pressure Drop (Pa)
850 800 750 700 650 600 550
0
4
8
12
16
20
Time (ms) Fig. 5 e The effect of water velocity on the temporary pressure drop in the flow channel. The corresponding cases are given in Table 1. is obvious that the pressure drop increases by time with the water injection for all cases, due to the blockage effect of water in the channel. Because of the periodic process of water droplet formation and detachment due to airflow shear force, the pressure drop curve exhibits jagged fluctuations for the base case. The pressure drop increases with the formation and decreases with the detachment of the droplet. After the detachment of the third water droplet and the flow tends to be stable, each crest corresponds to the detachment time of the droplet, when the droplet grows to the critical size for the base case. The peak pressure drops appear around t ¼ 16 ms for Case 1 and Case 2, when the frontiers of water get close to the U-turn. Pressure drop decreases after the water film moves forward in the U-turn. More water injection results that the average pressure drops for Case 1 and Case 2 are significantly higher than the base case. It reveals that quantitative analysis of pressure drop can be effective to investigate water transport in the channel.
Effect of airflow velocity The airflow velocity can normally range from lower than 0.5 m s1 to 30 m s1 under different PEMFC structure designs and operating conditions. Water is deformed and detached by airflow shear force after it is injected into the channel. In addition, the airflow serves as the driving force to motive the droplet to move forward. The effect of airflow velocity on water detachment and transport is studied at the water velocity of 1 m s1, corresponding to the base case, Case 3 and Case 4 given in Table 1. The airflow velocity investigated includes 10, 20 and 30 m s1, with the corresponding maximum Reynolds number ranging from 330 to 1000. As mentioned before, water droplets, which are in the “pendant shape”, are transported downstream on the GDL surface [37]. The shape of the droplet is dominated by the inertia force and the surface tension. As shown in Fig. 6, a stronger airflow for Case 4 results that the droplets tend to be more flatten, although the surface tension tends to minimize the size of the droplet and maintain the spherical shape, the
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inertia force drives it to be elongated and move forward. Detachment volume, defined as the volume of the droplet just separated from the water inlet, is a valid quantitative index of the characteristics of the GDL surface to remove droplets [38]. The detachment processes under measurable observation are listed in Table 2. As expected, shorter detachment time, higher detachment frequency and smaller detachment volume are observed with higher airflow velocity. Higher airflow velocity is preferred in the prospective of water removal, since smaller detached water reduces the blockage area on the GDL surface. Fig. 7 and Fig. 8 show the water transport and dynamics in the channel for the airflow velocity of 10 m s1 for Case 3 and 30 m s1 for Case 4, respectively. A longer detachment time and a larger water volume than the base case can be observed for Case 3. Notable water gathers in the first corner of the Uturn and has difficulty being expelled from the U-turn. On the contrary, water occupies both corners of the U-turn and is transported out in the form of liquid films for a larger gas velocity. The water leading edge for Case 4 shown in Fig. 8 is further than that for the base case, which indicates that the water movement velocity is higher with higher airflow velocity. Although larger droplets signify that the windward surface enlarges in the detachment process, the decrease of airflow shear force takes the primary role in droplet movement. The airflow velocity affects water transport along the channel in two aspects. One is the forward velocity of droplets and films, which directly contributes to the transport and removal of water, and the other is the impact velocity. Water impinges the channel wall in the U-turn with different velocities and exhibits various motion characteristics. Droplets spread after impingement for Case 3, resulting in water accumulation in the corner. The breakup of droplets is obtained for the base case, and partial of them gain an extra lateral velocity because of momentum conservation. The extra velocity, smaller breakup droplet size and higher airflow velocity make it possible that water moves to the next corner and sequentially transports out of the U-turn. A handful of water on the inner U-turn wall is identified with the highest airflow velocity for Case 4, which indicates that besides spreading and breakup, rebound or splash phenomenon occurs. Increasing the airflow velocity results in higher shear force, larger droplet forward and impact velocity, hence stronger water removal effect. However, it also leads to higher pressure drops as shown in Fig. 9. The aforementioned periodic detachment, which is displayed by the wave crests of the curve, causes the fluctuation of the pressure drop. Uniform and distinct crests appear for the base case, corresponding to the detachment time. A slighter variation is observed for Case 3, where low frequency of detachment and overall pressure drop limit the instability of the fluctuation. The impingement effect and the interaction of quick-released droplets complicate the flow in the channel, and eventually induce the violent fluctuation of the pressure drop for Case 4.
Effect of channel wall wettability The channel wall wettability, characterized by the contact angle, has significant influences on water transport. The effect
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 6 e The effect of airflow velocity on the detachment processes.
Table 2 e The details of the water detachment process. Cases Detachment time (ms) Water volume (mL) Detachment frequency (Hz)
Case 3
Base case
Case 4
6.1 1.53 104 164
2.4 6.0 105 417
1.6 4.0 105 625
of channel wall wettability is investigated, and the contact angle is set as 50 , 80 ,110 and 140 , corresponding to the base case and Cases 5e7 given in Table 1, respectively. Fig. 10 displays the water transport and dynamics in the channel for the channel wall contact angle of 80 for Case 5.
Water is accumulated at the channel top corners after impingement, similar to that for the base case. Water shape is close to globularity rather than film for the base case. Fig. 11 displays the water transport and dynamics in the channel for the channel wall contact angle of 110 for Case 6. Water is mainly transported in the form of droplets instead of films after impingement on the channel wall, which differs from the situation of hydrophilic wall. Water droplets may roll on hydrophobic surfaces owing to the fact that large contact angle leads to large surface tension and the droplets tend to maintain the spherical shape, and the water-channel contact area is small. Due to the weak channel wall function on the water, the water is less spread and does not break up. Finally,
Fig. 7 e Water transport and dynamics in the channel for the air velocity of 10 m s¡1, corresponding to Case 3 given in Table 1. Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 8 e Water transport and dynamics in the channel for the air velocity of 30 m s¡1, corresponding to Case 4 given in Table 1.
there is only the accumulation of droplets in the U-turn without breakage and rebound, which limits the backward movements of water to the first U-turn corner. The flow pattern changes from the spreading film form on hydrophilic surfaces to droplet form on hydrophobic surfaces. The water droplets movements before the U-turn are similar under fixed conditions of airflow velocity and wettability of the GDL surface. For hydrophilic channel walls, water is dragged to and accumulates at the top corner in the U-turn shown in the base case and Case 5. The enormous difference in the wettability between the GDL and channel wall surface causes the difference in surface tension. Thus, the droplets spontaneously move toward the hydrophilic channel wall 1600 Base case Case 3 Case 4
Pressure Drop (Pa)
1400 1200 1000 800 600 400 200
0
4
8
12
16
Time (ms) Fig. 9 e The effect of airflow velocity on the temporary pressure drop in the flow channel. The corresponding cases are given in Table 1.
20
surfaces, and eventually the droplets depart from the bottom corner to the top corner in the U-turn due to the strong capillary force there. When the difference between wettability decreases, the capillary force from the channel wall surface is not sufficient to drive the droplet to detach from the channel bottom corner, and a critical state is obtained for Case 6 where water appears at both top and bottom corners in the U-turn. As the channel wall surface becomes more hydrophobic with the contact angle of 140 for Case 7, the channel wall surface is equally hydrophobic with the GDL surface, it can no longer holds any water at the channel corners, and the water, mainly in spherical shape, passes through the U-turn smoothly, without any water accumulation, as shown in Fig. 12. In general, the wettability affects the water transport and removal in the channel by changing the surface tension, which influences on two aspects. One is the impact behavior in the U-turn, which leads to spreading, breakup, splash, adhesion or rebound on the channel surfaces. The breakup droplets obtain backward speed and ultimately cause water accumulation in the first U-turn corner for hydrophilic channel surfaces. The other aspect is the flow patterns which are recognized as thin film flow at the top corner, thick film flow at both top and bottom corners, consolidated droplet flow at the bottom corner, and independent droplet flow or droplet oscillation in the channel. Hydrophilic channel surface with small contact angle (50 , the base case) can directly remove water from the GDL surface by the U-turn effect and forms thin film flow at the channel top corner. This channel surface design is desirable because water is effectively removed from the GDL surface which is beneficial to the reactant transport and fuel cell performance. The hydrophilic channel surface design is best suited when the amount of water produced is small and the produced water can be drained out of the
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 10 e Water transport and dynamics in the channel for the contact angle of 80 , corresponding to Case 5 given in Table 1.
Fig. 11 e Water transport and dynamics in the channel for the contact angle of 110 , corresponding to Case 6 given in Table 1. Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
international journal of hydrogen energy xxx (xxxx) xxx
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Fig. 12 e Water transport and dynamics in the channel for the contact angle of 140 , corresponding to Case 7 given in Table 1.
channel timely, while large amount of water may occupy all the channel surfaces and forms annular or slug flow in the channel, causing severe blockage issues. Hydrophobic channel and GDL surface design (140 , Case 7) is also a good choice for the water removal, since water can be transported to the downstream quickly after emerging out of the GDL surface without water accumulation in the channel corners. Although water may be in contact with the GDL surface throughout its transport, the blocking time is much decreased for hydrophobic surfaces. This is better suited when the amount of produced water is large, ensuring the efficient water removal from the flow channel.
800 Base case Case 5 Case 6 Case 7
Pressure Drop (Pa)
750
700
650
600
550
0
4
8
12
16
Time (ms) Fig. 13 e The effect of channel wall wettability on the temporary pressure drop in the flow channel. The corresponding cases are given in Table 1.
Fig. 13 shows the effect of channel wall wettability on the temporary pressure drop. The pressure drops in the first 5 ms for all the cases investigated are almost the same, since the flow conditions, the water detachment processes and water movements before the U-turn are identical. Then, periodic pressure drops are found for all the cases, with the frequency approximately corresponding to the detachment process. Theamplitude of the curves distinguishes different flow regimes. The pressure drop for hydrophilic channel walls is relatively small, because the water tends to spread on the channel wall surfaces and the liquid films decrease the windward area so as to reduce the airflow resistance. The lower airflow resistance is at the expense of longer water removal time on the channel wall surfaces. On the contrary, the pressure drop for hydrophobic channel walls is relatively large, since water in the droplet shape increases the water frontal area, decreases the channel cross section area and thus causes greater airflow resistance. The simulation results are in agreement with the experiments that the pressure drop increases as the contact angle increases [39]. The peak value of amplitude isobserved for Case 6 with thecontact angleof110 . As mentioned earlier, droplets consolidation occurs in the U-turn which blocks the channel severely, as shown in Fig. 11. As the hydrophobicity continues to increase to 140 for Case 7, the emerged droplets are removed from the channel independently, without consolidation, and the wall adhesion force is also smaller for the larger contact angle, both contribute to the smaller flow resistance and hence lower pressure drop.
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Conclusions Water transport and dynamics in a U-shaped flow channel of proton exchange membrane (PEM) fuel cell (PEMFC) with a
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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water hole is investigated numerically using the volume of fluid (VOF) method. The water emerging process from the water hole and transport in the flow channel is simulated with various water velocities, airflow velocities and channel surface wettability. The following conclusions can be drawn from this study: 1. The water velocity influences the mode of water removal from the GDL surface. Detached water droplets from the water hole are transported along the GDL surface and are removed from the GDL surface by the Uturn effect at low water velocity. Water column is directly removed from the GDL surface and reaches the channel surface at high gas velocity. The critical water velocity distinguishing the two removal modes is found slightly smaller than 2 m s1. The water removal mode at high velocity is more desirable due to the immediate water removal from the GDL surface. It also reveals that the water flooding of the GDL surface is mitigated for high water velocity above the critical velocity. 2. The airflow velocity significantly affects water detachment and impact process. Smaller water droplets are detached with higher frequency from the water hole for higher airflow velocity. Water breakup, rebound and splash phenomena occur during the impact process for higher airflow velocity. 3. The channel surface wettability determines water flow patterns after impacting the channel surface. Hydrophilic channel surface with small contact angle can directly remove water from the hydrophobic GDL surface by the U-turn effect and forms thin film flow at the channel top corner, benefiting water removal from the GDL surface; whereas hydrophobic channel surface makes water to pass through the U-turn quickly without water accumulation in the channel corners. Both designs are desirable due to their good water removal ability. A medium contact angle range of the channel surface may result in a transitional flow pattern where water film or droplet flow is formed at both top and bottom corners of the channel. 4. The U-turn promotes water removal from the GDL surface by the impact effect on the hydrophilic channel surface. Nevertheless, partial water can be stuck in the first corner of the U-turn. The pressure drop reflects the flow resistance in the flow channel, and it predicts the water detachment frequency well.
Acknowledgements This work is financially supported by the National Natural Science Foundation of China (Grant No. 51706153).
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijhydene.2019.07.169.
references
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[19] Lu Z, Rath C, Zhang G. Water management studies in PEM fuel cells, part IV: effects of channel surface wettability, geometry and orientation on the two-phase flow in parallel gas channels. Int J Hydrogen Energy 2011;36(16):9864e75. [20] Koz M, Kandlikar SG. Numerical investigation of interfacial transport resistance due to water droplets in proton exchange membrane fuel cell air channels. J Power Sources 2013;243(6):946e57. [21] Dincer I, Acar C. Review and evaluation of hydrogen production methods for better sustainability. Int J Hydrogen Energy 2015;40:11094e111. [22] Quan P, Zhou B, Sobiesiak A. Water behavior in serpentine micro-channel for proton exchange membrane fuel cell cathode. J Power Sources 2005;152(1):131e45. [23] Jiao K, Zhou B, Peng Q. Liquid water transport in parallel serpentine channels with manifolds on cathode side of a PEM fuel cell stack. J Power Sources 2006;154(1):124e37. [24] Zhu X, Sui PC, Djilali N. Three-dimensional numerical simulations of water droplet dynamics in a PEMFC gas channel. J Power Sources 2008;181(1):101e15. [25] Wu R, Zhu X, Liao Q. A pore network study on the role of micro-porous layer in control of liquid water distribution in gas diffusion layer. Int J Hydrogen Energy 2010;35(14):7588e93. [26] Ding Y, Bi HT, Wilkinson DP. Three-dimensional numerical simulation of water droplet emerging from a gas diffusion layer surface in micro-channels. J Power Sources 2010;195(21):7278e88. [27] Ashrafi M, Shams M. Effects of heterogeneous surface of gas diffusion layers on droplet transport in microchannels of PEM fuel cells. Int J Hydrogen Energy 2016;41(3):1974e89. [28] Qin Y, Li X, Jiao K. Effective removal and transport of water in a PEM fuel cell flow channel having a hydrophilic plate. Appl Energy 2014;113(1):116e26. [29] Qin Y, Li X, Yin Y. Modeling of liquid water transport in a proton exchange membrane fuel cell gas flow channel with dynamic wettability. Int J Energy Res 2018;42:3315e27.
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[30] Cho S, Wang Y, Chen K. Droplet dynamics in a polymer electrolyte fuel cell gas flow channel: forces, deformation, and detachment. I: theoretical and numerical analyses. J Power Sources 2012;206:119e28. [31] Cho S, Wang Y, Chen K. Droplet dynamics in a polymer electrolyte fuel cell gas flow channel: forces, Deformation and detachment. II: comparisons of analytical solution with numerical and experimental results. J Power Sources 2012;210:191e7. [32] Lee J, Yip R, Antonacci P. Synchrotron investigation of microporous layer thickness on liquid water distribution in a PEM fuel cell. J Electrochem Soc 2015;162(7):F669e76. [33] Alrwashdeh SS, Markotter H, Haubmann J. Investigation of water transport dynamics in polymer electrolyte membrane fuel cells based on high porous micro porous layers. Energy 2016;102:161e5. ~ o D, Oliveira V, Pinto A. 1D þ 3D two-phase [34] Ferreira R, Falca flow numerical model of a proton exchange membrane fuel cell. Appl Energy 2017;203:474e95. [35] Cho S, Wang Y. Two-phase flow dynamics in a micro channel with heterogeneous surfaces. Int J Heat Mass Transf 2014;71:349e60. [36] Cho S, Wang Y. Two-phase flow dynamics in a micro hydrophilic channel: a theoretical and experimental study. Int J Heat Mass Transf 2014;70:340e52. [37] Le AD, Zhou B, Shiu HR. Numerical simulation and experimental validation of liquid water behaviors in a proton exchange membrane fuel cell cathode with serpentine channels. J Power Sources 2010;195(21):7302e15. [38] Chen L, He YL, Tao WQ. Effects of surface microstructures of gas diffusion layer on water droplet dynamic behaviors in a micro gas channel of proton exchange membrane fuel cells. Int J Heat Mass Transf 2013;60(5):252e62. [39] Lewis J, Wang Y. Two-phase frictional pressure drop in a thin mixed-wettability microchannel. Int J Heat Mass Transf 2019;128:649e67.
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Available online at www.sciencedirect.com
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Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method Rouxian Chen, Yanzhou Qin*, Suhui Ma, Qing Du** State Key Laboratory of Engines, Tianjin University, Tianjin, China
highlights Water removal modes from the gas diffusion layer surface depend on water velocity. Water directly impinges the channel surface and is removed for high water velocity. Small droplets are frequently detached from water hole for high airflow velocity. Surface wettability determines water flow patterns after impacting channel surface. U-turn of channel promotes water removal from the gas diffusion layer surface.
article info
abstract
Article history:
Three-dimensional numerical simulation of liquid water emerging from the gas diffusion
Received 4 December 2018
layer (GDL) surface to the gas flow channel in the proton exchange membrane (PEM) fuel
Received in revised form
cell (PEMFC) is carried out using the volume of fluid (VOF) method. The effects of the water
18 July 2019
velocity in the GDL hole, the airflow velocity and the wettability of the channel surfaces on
Accepted 22 July 2019
the water emerging process and transport in the flow channel are investigated. It is found
Available online xxx
that at low water velocity, the water detaches from the water hole, forming discrete water droplets on the GDL surface, and is transported downstream on the GDL surface until
Keywords:
removed from the GDL surface by the U-turn part of the flow channel; whereas at high
PEMFC
water velocity, the continuous water column impinges the hydrophilic channel surface
Water flow
counter to the GDL surface, being directly removed from the GDL surface. The airflow
Water detachment
velocity affects water detachment and impact process in the channel corner, and water
Flow velocity
droplet breakup is observed under high airflow velocity. The channel surface wettability
Surface wettability
influences water droplet shape and its transport in the channel. Rather than forming corner water films at the U-turn for hydrophilic channel surface, water maintains the droplet shape and smoothly passes through the U-turn for hydrophobic channel surface. The importance of the U-turn to the water removal is also discussed. The U-turn promotes water removal from the GDL surface at low water velocity and water breakup at high airflow velocity. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Y. Qin), [email protected] (Q. Du). https://doi.org/10.1016/j.ijhydene.2019.07.169 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Introduction Proton exchange membrane (PEM) fuel cell (PEMFC) is a clean energy conversion device which converts chemical energy directly into electrical energy through electrochemical reactions. It has drawn worldwide attention for its advantages of high efficiency, low emissions and fast start-up response. The process of practical application and commercialization of PEMFC is fraught with challenges, among which water management is critical due to its tremendous impacts on the performance and durability of the cell. Understanding the water transport and removal mechanism in the gas flow channel is the key to optimizing water management and preventing flooding [1,2]. Water in PEMFC is usually composed of two sources, one is vapor in humidified reaction gas, which significantly enhances the effective hydration of the membrane in order to strengthen proton conductivity. And the other one is water generated by electrochemical reaction in the cathode. In some working conditions such as high current density, a large amount of water is generated in the cathode catalyst layer (CL). Although there is back diffusion effect of water transmembrane transport, the GDL and channel are the main access for water removal from the reaction site. In case that liquid water accumulates in the GDL and channel, the flow and diffusion resistance into the CL would increase, hindering the reactants transport. For water management in PEMFC, a rational control strategy relies on a variety of parameters, such as the wettability of the GDL and channel, the shape of the structure, the gas velocity and the location of water emergence [3]. The comprehensive effect of these factors needs to be fully understood for the optimization of flow and diffusion of reactant gas, pressure drop, and finally ideal performance and durability of the cell. The gas-liquid two phase flow in PEMFC has been investigated experimentally, utilizing visualization techniques, including in-situ and ex-situ testing methods [4]. Direct photography, neutron radiography, X-ray graph and nuclear magnetic resonance imaging (MRI) have been used for observing the liquid water in the channel. Flow patterns are observed in the form of water droplet, film and slug flow by direct photography [5,6]. Grimm et al. [7] summarized flow regime criterion and described it as a function of air and water velocity. A parameter, wetted area ratio, was introduced to quantitatively describe water accumulation in the channel under different working conditions by manual channel images [8]. Neutron radiography was applied to study the effect of liquid water blockage on the performance of the cell, which suggested that water accumulation in the GDL tended to be availably removed by the cross-leakage flow through the GDL to the adjacent flow channels [9]. Details of fast water transport processes such as the “eruptive” water expulsion from the GDL pores into the channel were demonstrated by in-situ synchrotron X-ray radiography [10]. Dunbar et al. examined water distribution quantitatively utilizing the MRI for the first time and found that the flow pattern in the channel tended to be wavy-stratified rather than slug flow [11]. Two-phase flow pressure drop was measured to investigate the effects of load and temperature condition, and the transient response was
characterized [12]. Water accumulation and channel pressure drop of serpentine and parallel flow fields were investigated and a new type of serpentine flow field was designed to effectively modify the length of the channel, achieving higher fuel cell performance [13]. Ex-situ experiments were also introduced by measuring the pressure drop and flow rate so that the gas flow distribution and its effect on the water flow could be obtained [14]. Yoon et al. conducted ex-situ experiment to observe the water droplet growth and removal in the cathode, suggesting the micro structures of GDL and microporous layer (MPL) have significant influence on water removal in the channel [15]. The pressure loss of two-phase flow existing from microchannel to manifold was also investigated [16]. The flow regimes were visualized and analytically recognized as jet, bubble, churn, stratified and annular flow [17]. Experiments are indispensable to investigate the effects of material and structural properties, and operating conditions on water transport in the channel. However, there are still limitations on precise and impeccable characterization of the two-phase flow pattern in a working PEM fuel cell. Direct photography is convenient for instantaneously direct observation at a reasonable cost, nonetheless, optical window employed changes the inherent attribute of the cell by changing the material properties including wettability, roughness, and thermal and electrical conductivity [18]. Neutron radiography, X-ray graph and MRI suffer the disadvantages that special materials or structures are needed to satisfy the test conditions, and the spatial and temporal resolution are lower comparing to direct photography. The disadvantages in conducting experiments to reveal water transport mechanism motivate researchers to carry out computational fluid dynamics simulations. The volume of fluid (VOF) method is widely used to simulate water transport in the PEM fuel cell channel. The liquid water, in the form of droplet or liquid film, was usually introduced directly onto the surface of GDL which is considered flat and impermeable in most previous studies [19]. Due to its importance, a large number of researches have investigated the water behaviors in the channel, focusing on the single water droplet, discussing the effect of the gas velocity, the channel surface wettability and roughness, the channel geometry and the droplet size, and a few involve multiple water droplets interactions [20,21]. Quan et al. [22] directly introduced initial water droplets and film into the channel corresponding to different working conditions of fuel cell and investigated two phase flow in the bend area of serpentine channels. Jiao et al. [23] studied the air-water flow in PEM fuel cell stacks and observed “collecting-and-separating” effect in serpentine channels with different initial water distributions. Although these studies obtained much useful information of the water transport mechanism in the flow channel, the initial water state on the GDL surface in the channel is deficiently simulated considering the water emerges or erupts from the inside of the GDL [10]. The more realistic method in simulation is to apply a water hole in the GDL which is connected to the channel and emerges water continuously to the channel. Using this method, Zhu et al. [24,25] numerically investigated the influence of multiple parameters, including the surface wettability, the air velocity, the water velocity and the channel
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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geometry, on the water emergence from the water hole and the afterward water behaviors in the flow channel. Ding et al. [26] further investigated the effect of GDL surface microstructure on the water emergence and transport in the flow channel, by changing the pore size and pore number. It was identified that the wettability dominated the flow pattern rather than the pore diameter when the pore size was small enough. Vertical and horizontal fuel cells were simulated to study the effect of flow field orientation. Gravity was found assisting in water removal in the vertical direction, but hindering water purging from the horizontal elbow position. Ashrafi et al. [27] proposed a model using a random function to generate heterogeneous GDL surfaces so that the roughness of the surface could be reasonably considered. The roughness of the GDL was found to have significant effect on droplet transport, and rolling small droplets and translational large droplets were correspondingly observed. Hydrophilic plates [28] and needles [29] were introduced into the channel to facilitate water removal from the GDL surface, and multiple design parameters were discussed for water transport and removal. Water droplet deformation and detachment were theoretically analyzed, simulated and experimentally validated. The expression corresponding to water droplet shape change was obtained and the correlation to calculate the water detachment velocity with Weber number and Reynolds number was derived [30,31]. The previous studies usually made the water emerging velocity at a low range, based on uniform and continuous water emerging assumptions. However, water usually emerges only at a few preferred water holes which are randomly distributed on the GDL surface, and the water emerging rate is not continuous but intermissive, probably making the water flow rate very high, orders of the real-time water generation rate in PEMFC. This is supported by the Xray imaging showing that multiple water clusters intersected at particular pores and established specific breakthrough paths [6], and “eruptive-like” water transport mechanism was observed [32,33]. A PEMFC performance model coupled with the VOF method was built to predict the fuel cell performance and water transport in the cathode channel simultaneously, and the liquid water inlet velocity could reach 1.2 m s1 in their study [34]. The water transport characteristics in the flow channel at high velocity can be quite different from the previous predictions and require further investigation. In this study, a large range of water velocity, air velocity and channel surface wettability are applied in the simulation of water transport in a U-shaped channel to investigate the water removal process. Especially, the phenomenon of water impingement to the channel surface under high water velocity is revealed and discussed. The importance of the U-turn effect is also discussed on the water removal from the GDL surface.
3
Fig. 1 e Computational domain in the present study.
straight single channels connected by a U-turn and a water inlet hole. The channel cross-section is 0.5 mm 0.5 mm, and the channel length in the x direction is 7 mm. Water is introduced into the channel from the water inlet hole, which corresponds to the water transport path in the GDL. The water hole connected with the channel bottom surface has the cross-section of 0.05 mm 0.05 mm and the length of 0.2 mm, and the center of the hole locates at the quarter of the channel from the inlet to eliminate the entrance region effect. The flow is assumed laminar, isothermal and incompressible due to the small Reynolds number. The gravitational force is considered in the negative y direction. The phase change between water and gas is neglected due to the fast water transport process. The channel walls and the GDL surface are considered impermeable.
Governing equations The interface of two-phase flow can be captured by utilizing the VOF method. Governing equations of mass and momentum for the two-phase flow in the channel can be written as: vr þ V,ðrVÞ ¼ 0 vt
(1)
vðrVÞ þ V,ðrV , VÞ ¼ VP þ mV,ðVV þ VVT Þ þ rg þ FS vt
(2)
The gas phase is set as primary phase expressed by subscript 1, and the liquid phase is set as secondary phase expressed by subscript 2. The relation of two-phase volume fraction is: f1 þ f2 ¼ 1
(3)
The density and viscosity can be calculated as: r ¼ f2 r2 þ ð1 f2 Þr1
(4)
m ¼ f2 m2 þ ð1 f2 Þm1
(5)
Model formulation
The source term in Equation (2) representing the effect of surface tension and wall adhesion is expressed as:
Computation domain and assumptions
FS ¼ slg
As shown in Fig. 1, the computational domain is a U-shaped section of a serpentine flow channel, comprised of two
where slg is the surface tension coefficient between the two phases, k is the surface curvature of the two-phase interface,
rkVf1 0:5ðr1 þ r2 Þ
(6)
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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and f1 is the liquid phase volume fraction which is calculated by a continuity-like equation as shown below: vf1 þ V,ðf1 VÞ ¼ 0 vt
(7)
In the vicinity of the channel wall the surface curvature is determined by the contact angle reflecting the channel surface wettability as: b w cosðqÞ þ bt w sinðqÞ k ¼ V,½ n
Boundary conditions A parabolic velocity of air in the x direction is adopted at the channel inlet and water is injected from the water hole. Constant pressure is set at the channel outlet of Pout¼ 1 atm. For the boundary of the wall surfaces, the no slip wall boundary condition is used for all the surfaces. The wettability is studied by varying the surface contact angle. These boundary conditions can be expressed mathematically as: Gas inlet: (9)
Water inlet: vy ¼ vy,0, vx ¼ vz ¼ 0
(10)
Channel outlet: P ¼ Pout
(11)
Channel and GDL surfaces: vx ¼ vy ¼ vz ¼ 0
The effects of water velocity, airflow velocity and channel surface wettability are investigated. In all the cases investigated, the contact angles for the GDL surface are set as 140 . The channel surface contact angle qchannel, the airflow velocity at the channel inlet center vx,0 and the water velocity vy,0 for all the cases are listed in Table 1.
(8)
b w and bt w are the where q is the contact angle of the wall, and n unit vectors normal and tangent to the wall, respectively. In the VOF method, the continuity of volume fraction is firstly solved, and then the reconstruction of the air-liquid interface is performed by piecewise linear approximation so that the dynamic of the two-phase interface can be captured.
vx ¼ vx,0, vy ¼ vz ¼ 0
Results and discussion
(12)
For initialization of the calculation, the inlet velocity and outlet gauge pressure are set as zero and the channel is occupied with air. Thereafter, aforementioned boundary conditions are adopted.
Effect of water velocity The water velocity significantly influences its emerging and transport process in the flow channel. The water velocity investigated includes 1, 2 and 5 m s1, corresponding to the base case, Case 1 and Case 2, respectively. Fig. 2 shows the water transport and dynamics in the channel for the water velocity of 1 m s1. Water is produced continuously in the cathode CL and a pressure difference is built up between the two sides of the GDL. The water emerges from the water hole, forming a water droplet. The water droplet grows continuously until it detaches from the water hole at a critical point when the airflow shear force overcomes the water internal surface tension as the water frontal area exposed to the airflow is large enough, which is typical droplet detachment type. A succeeding water droplet grows again at the water hole after the previous water droplet detaches from the water hole. The detached water droplet is transported downstream along the GDL surface in the channel until it hits the channel surface at the U-turn. Since the channel surface is hydrophilic, the water spreads out on the channel surface and is removed from the GDL surface due to the capillary force of the channel surface caused by the difference of wettability. The detached water droplets periodically hit the channel surface, spread out and merge on the channel surface, forming water films on the channel surface which is transported along the channel corners. The simulation results agree with the experiments that liquid water tends to accumulate in the hydrophilic channel corners [35]. The U-turn changes the water transport characteristics significantly. The water is removed from the GDL surface after it reaches the channel surface at the U-turn, which clears the reactant gas passage to the GDL; otherwise, the water would transport along the GDL surface, blocking the GDL surface all the time, as in a straight channel. The U-turn promotes the water removal from the GDL surface for the channel having
Numerical procedures The governing equations and boundary conditions are implemented in the Fluent platform. The pressure-implicit with splitting of operator scheme (PISO) is used for the pressure-velocity coupling. The pressure staggering option scheme (PRESTO) is selected for the pressure discretization. The second order upwind scheme is applied for solving the momentum equation and the volume fraction equation. The grid independence is studied and proper grid number is used in the simulation.
Table 1 e Computational cases and parameter values. Cases Base case Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7
vx,0 (m s1)
Vy,0 (m s1)
qchannel ( )
20 20 20 10 30 20 20 20
1 2 5 1 1 1 1 1
50 50 50 50 50 80 110 140
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 2 e Water transport and dynamics in the channel for the water velocity of 1 m s¡1, corresponding to the base case given in Table 1.
hydrophilic channel surface, which is beneficial for the PEMFC performance. Water transport and dynamics in the channel for the water velocity of 2 m s1 is shown in Fig. 3. It is apparent that the water emerges from the water hole in the form of a water column for the higher water velocity, comparing to the water droplet moving on the GDL surface for a lower water velocity. Due to the strong airflow shear force, the water column is inclined in the air stream and separates out water droplets at the top of the water column. The separated water droplet is transported upward to reach the hydrophilic channel top surface under the inertia effect. Then, the water spreads out on the hydrophilic channel surface and moves to the two channel corners. Since the water is immediately removed from the GDL surface after it emerges out, no water droplet is observed on the GDL surface and it will not block the GDL at all. The process of water impact and breakup occurs on the channel top wall, and the water spreads to the channel side walls. Due to the strong capillary force, the spreading droplet is divided into two parts, accumulating in the channel corners. Different from water droplet flow patterns for lower water velocity, when the water velocity is high enough to produce a water column and impact the channel wall directly, liquid films are formed and transported along the straight channel before the U-turn. Consolidation of the liquid films is observed at the front of the flow after t ¼ 10 ms, because the volume of
films increases and the surface tension is enough to preserve the film shape. The water film flow is much slower, it barely approaches to the inner side of the U-turn until t ¼ 15 ms, whereas the water droplet on the hydrophobic GDL surface reaches outer side of the U-turn before t ¼ 6 ms, as shown in Fig. 2. Due to the strong capillary force and small frontal area (or small gas shear force), the water films will not reach the outer side of the U-turn, but move along the inner corner of the channel after the U-turn. Fig. 4 shows the water transport and dynamics in the channel for the water velocity of 5 m s1. The water is also directly removed from the GDL surface after it emerges out from the water hole, similar to the result shown in Fig. 3 for the water velocity of 2 m s1. The water column directly impinges the hydrophilic channel top surface without separating out water droplets. The water column is not inclined noticeably as for Case 2. Similarly, thin water film is formed at the two channel corners after the water reaches the hydrophilic channel surface. However, water velocity of 5 m s1 makes it possible to accumulate a large amount of water in the U-turn and both the inner and outer corners are filled with water. It reveals that the water emerging from the water hole in GDL can be directly removed from the GDL surface for the water velocity higher than a critical water velocity. The water is transported along the GDL surface and is removed from the GDL surface by the U-turn effect for the water velocity lower than the critical velocity, whereas the water is directly
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 3 e Water transport and dynamics in the channel for the water velocity of 2 m s¡1, corresponding to Case 1 given in Table 1.
Fig. 4 e Water transport and dynamics in the channel for the water velocity of 5 m s¡1, corresponding to Case 2 given in Table 1.
removed from the GDL surface and reaches the channel top surface for the water velocity higher than the critical velocity. The critical velocity is found slightly smaller than 2 m s1 in the present study.
The evolution of pressure drop corresponds to the twophase flow patterns [36]. Fig. 5 displays the effect of water velocity on the temporary pressure drop, which indicates pressure difference between inlet and outlet of the channel. It
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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900 Base case Case 1 Case 2
Pressure Drop (Pa)
850 800 750 700 650 600 550
0
4
8
12
16
20
Time (ms) Fig. 5 e The effect of water velocity on the temporary pressure drop in the flow channel. The corresponding cases are given in Table 1. is obvious that the pressure drop increases by time with the water injection for all cases, due to the blockage effect of water in the channel. Because of the periodic process of water droplet formation and detachment due to airflow shear force, the pressure drop curve exhibits jagged fluctuations for the base case. The pressure drop increases with the formation and decreases with the detachment of the droplet. After the detachment of the third water droplet and the flow tends to be stable, each crest corresponds to the detachment time of the droplet, when the droplet grows to the critical size for the base case. The peak pressure drops appear around t ¼ 16 ms for Case 1 and Case 2, when the frontiers of water get close to the U-turn. Pressure drop decreases after the water film moves forward in the U-turn. More water injection results that the average pressure drops for Case 1 and Case 2 are significantly higher than the base case. It reveals that quantitative analysis of pressure drop can be effective to investigate water transport in the channel.
Effect of airflow velocity The airflow velocity can normally range from lower than 0.5 m s1 to 30 m s1 under different PEMFC structure designs and operating conditions. Water is deformed and detached by airflow shear force after it is injected into the channel. In addition, the airflow serves as the driving force to motive the droplet to move forward. The effect of airflow velocity on water detachment and transport is studied at the water velocity of 1 m s1, corresponding to the base case, Case 3 and Case 4 given in Table 1. The airflow velocity investigated includes 10, 20 and 30 m s1, with the corresponding maximum Reynolds number ranging from 330 to 1000. As mentioned before, water droplets, which are in the “pendant shape”, are transported downstream on the GDL surface [37]. The shape of the droplet is dominated by the inertia force and the surface tension. As shown in Fig. 6, a stronger airflow for Case 4 results that the droplets tend to be more flatten, although the surface tension tends to minimize the size of the droplet and maintain the spherical shape, the
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inertia force drives it to be elongated and move forward. Detachment volume, defined as the volume of the droplet just separated from the water inlet, is a valid quantitative index of the characteristics of the GDL surface to remove droplets [38]. The detachment processes under measurable observation are listed in Table 2. As expected, shorter detachment time, higher detachment frequency and smaller detachment volume are observed with higher airflow velocity. Higher airflow velocity is preferred in the prospective of water removal, since smaller detached water reduces the blockage area on the GDL surface. Fig. 7 and Fig. 8 show the water transport and dynamics in the channel for the airflow velocity of 10 m s1 for Case 3 and 30 m s1 for Case 4, respectively. A longer detachment time and a larger water volume than the base case can be observed for Case 3. Notable water gathers in the first corner of the Uturn and has difficulty being expelled from the U-turn. On the contrary, water occupies both corners of the U-turn and is transported out in the form of liquid films for a larger gas velocity. The water leading edge for Case 4 shown in Fig. 8 is further than that for the base case, which indicates that the water movement velocity is higher with higher airflow velocity. Although larger droplets signify that the windward surface enlarges in the detachment process, the decrease of airflow shear force takes the primary role in droplet movement. The airflow velocity affects water transport along the channel in two aspects. One is the forward velocity of droplets and films, which directly contributes to the transport and removal of water, and the other is the impact velocity. Water impinges the channel wall in the U-turn with different velocities and exhibits various motion characteristics. Droplets spread after impingement for Case 3, resulting in water accumulation in the corner. The breakup of droplets is obtained for the base case, and partial of them gain an extra lateral velocity because of momentum conservation. The extra velocity, smaller breakup droplet size and higher airflow velocity make it possible that water moves to the next corner and sequentially transports out of the U-turn. A handful of water on the inner U-turn wall is identified with the highest airflow velocity for Case 4, which indicates that besides spreading and breakup, rebound or splash phenomenon occurs. Increasing the airflow velocity results in higher shear force, larger droplet forward and impact velocity, hence stronger water removal effect. However, it also leads to higher pressure drops as shown in Fig. 9. The aforementioned periodic detachment, which is displayed by the wave crests of the curve, causes the fluctuation of the pressure drop. Uniform and distinct crests appear for the base case, corresponding to the detachment time. A slighter variation is observed for Case 3, where low frequency of detachment and overall pressure drop limit the instability of the fluctuation. The impingement effect and the interaction of quick-released droplets complicate the flow in the channel, and eventually induce the violent fluctuation of the pressure drop for Case 4.
Effect of channel wall wettability The channel wall wettability, characterized by the contact angle, has significant influences on water transport. The effect
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 6 e The effect of airflow velocity on the detachment processes.
Table 2 e The details of the water detachment process. Cases Detachment time (ms) Water volume (mL) Detachment frequency (Hz)
Case 3
Base case
Case 4
6.1 1.53 104 164
2.4 6.0 105 417
1.6 4.0 105 625
of channel wall wettability is investigated, and the contact angle is set as 50 , 80 ,110 and 140 , corresponding to the base case and Cases 5e7 given in Table 1, respectively. Fig. 10 displays the water transport and dynamics in the channel for the channel wall contact angle of 80 for Case 5.
Water is accumulated at the channel top corners after impingement, similar to that for the base case. Water shape is close to globularity rather than film for the base case. Fig. 11 displays the water transport and dynamics in the channel for the channel wall contact angle of 110 for Case 6. Water is mainly transported in the form of droplets instead of films after impingement on the channel wall, which differs from the situation of hydrophilic wall. Water droplets may roll on hydrophobic surfaces owing to the fact that large contact angle leads to large surface tension and the droplets tend to maintain the spherical shape, and the water-channel contact area is small. Due to the weak channel wall function on the water, the water is less spread and does not break up. Finally,
Fig. 7 e Water transport and dynamics in the channel for the air velocity of 10 m s¡1, corresponding to Case 3 given in Table 1. Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
international journal of hydrogen energy xxx (xxxx) xxx
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Fig. 8 e Water transport and dynamics in the channel for the air velocity of 30 m s¡1, corresponding to Case 4 given in Table 1.
there is only the accumulation of droplets in the U-turn without breakage and rebound, which limits the backward movements of water to the first U-turn corner. The flow pattern changes from the spreading film form on hydrophilic surfaces to droplet form on hydrophobic surfaces. The water droplets movements before the U-turn are similar under fixed conditions of airflow velocity and wettability of the GDL surface. For hydrophilic channel walls, water is dragged to and accumulates at the top corner in the U-turn shown in the base case and Case 5. The enormous difference in the wettability between the GDL and channel wall surface causes the difference in surface tension. Thus, the droplets spontaneously move toward the hydrophilic channel wall 1600 Base case Case 3 Case 4
Pressure Drop (Pa)
1400 1200 1000 800 600 400 200
0
4
8
12
16
Time (ms) Fig. 9 e The effect of airflow velocity on the temporary pressure drop in the flow channel. The corresponding cases are given in Table 1.
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surfaces, and eventually the droplets depart from the bottom corner to the top corner in the U-turn due to the strong capillary force there. When the difference between wettability decreases, the capillary force from the channel wall surface is not sufficient to drive the droplet to detach from the channel bottom corner, and a critical state is obtained for Case 6 where water appears at both top and bottom corners in the U-turn. As the channel wall surface becomes more hydrophobic with the contact angle of 140 for Case 7, the channel wall surface is equally hydrophobic with the GDL surface, it can no longer holds any water at the channel corners, and the water, mainly in spherical shape, passes through the U-turn smoothly, without any water accumulation, as shown in Fig. 12. In general, the wettability affects the water transport and removal in the channel by changing the surface tension, which influences on two aspects. One is the impact behavior in the U-turn, which leads to spreading, breakup, splash, adhesion or rebound on the channel surfaces. The breakup droplets obtain backward speed and ultimately cause water accumulation in the first U-turn corner for hydrophilic channel surfaces. The other aspect is the flow patterns which are recognized as thin film flow at the top corner, thick film flow at both top and bottom corners, consolidated droplet flow at the bottom corner, and independent droplet flow or droplet oscillation in the channel. Hydrophilic channel surface with small contact angle (50 , the base case) can directly remove water from the GDL surface by the U-turn effect and forms thin film flow at the channel top corner. This channel surface design is desirable because water is effectively removed from the GDL surface which is beneficial to the reactant transport and fuel cell performance. The hydrophilic channel surface design is best suited when the amount of water produced is small and the produced water can be drained out of the
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 10 e Water transport and dynamics in the channel for the contact angle of 80 , corresponding to Case 5 given in Table 1.
Fig. 11 e Water transport and dynamics in the channel for the contact angle of 110 , corresponding to Case 6 given in Table 1. Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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Fig. 12 e Water transport and dynamics in the channel for the contact angle of 140 , corresponding to Case 7 given in Table 1.
channel timely, while large amount of water may occupy all the channel surfaces and forms annular or slug flow in the channel, causing severe blockage issues. Hydrophobic channel and GDL surface design (140 , Case 7) is also a good choice for the water removal, since water can be transported to the downstream quickly after emerging out of the GDL surface without water accumulation in the channel corners. Although water may be in contact with the GDL surface throughout its transport, the blocking time is much decreased for hydrophobic surfaces. This is better suited when the amount of produced water is large, ensuring the efficient water removal from the flow channel.
800 Base case Case 5 Case 6 Case 7
Pressure Drop (Pa)
750
700
650
600
550
0
4
8
12
16
Time (ms) Fig. 13 e The effect of channel wall wettability on the temporary pressure drop in the flow channel. The corresponding cases are given in Table 1.
Fig. 13 shows the effect of channel wall wettability on the temporary pressure drop. The pressure drops in the first 5 ms for all the cases investigated are almost the same, since the flow conditions, the water detachment processes and water movements before the U-turn are identical. Then, periodic pressure drops are found for all the cases, with the frequency approximately corresponding to the detachment process. Theamplitude of the curves distinguishes different flow regimes. The pressure drop for hydrophilic channel walls is relatively small, because the water tends to spread on the channel wall surfaces and the liquid films decrease the windward area so as to reduce the airflow resistance. The lower airflow resistance is at the expense of longer water removal time on the channel wall surfaces. On the contrary, the pressure drop for hydrophobic channel walls is relatively large, since water in the droplet shape increases the water frontal area, decreases the channel cross section area and thus causes greater airflow resistance. The simulation results are in agreement with the experiments that the pressure drop increases as the contact angle increases [39]. The peak value of amplitude isobserved for Case 6 with thecontact angleof110 . As mentioned earlier, droplets consolidation occurs in the U-turn which blocks the channel severely, as shown in Fig. 11. As the hydrophobicity continues to increase to 140 for Case 7, the emerged droplets are removed from the channel independently, without consolidation, and the wall adhesion force is also smaller for the larger contact angle, both contribute to the smaller flow resistance and hence lower pressure drop.
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Conclusions Water transport and dynamics in a U-shaped flow channel of proton exchange membrane (PEM) fuel cell (PEMFC) with a
Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169
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water hole is investigated numerically using the volume of fluid (VOF) method. The water emerging process from the water hole and transport in the flow channel is simulated with various water velocities, airflow velocities and channel surface wettability. The following conclusions can be drawn from this study: 1. The water velocity influences the mode of water removal from the GDL surface. Detached water droplets from the water hole are transported along the GDL surface and are removed from the GDL surface by the Uturn effect at low water velocity. Water column is directly removed from the GDL surface and reaches the channel surface at high gas velocity. The critical water velocity distinguishing the two removal modes is found slightly smaller than 2 m s1. The water removal mode at high velocity is more desirable due to the immediate water removal from the GDL surface. It also reveals that the water flooding of the GDL surface is mitigated for high water velocity above the critical velocity. 2. The airflow velocity significantly affects water detachment and impact process. Smaller water droplets are detached with higher frequency from the water hole for higher airflow velocity. Water breakup, rebound and splash phenomena occur during the impact process for higher airflow velocity. 3. The channel surface wettability determines water flow patterns after impacting the channel surface. Hydrophilic channel surface with small contact angle can directly remove water from the hydrophobic GDL surface by the U-turn effect and forms thin film flow at the channel top corner, benefiting water removal from the GDL surface; whereas hydrophobic channel surface makes water to pass through the U-turn quickly without water accumulation in the channel corners. Both designs are desirable due to their good water removal ability. A medium contact angle range of the channel surface may result in a transitional flow pattern where water film or droplet flow is formed at both top and bottom corners of the channel. 4. The U-turn promotes water removal from the GDL surface by the impact effect on the hydrophilic channel surface. Nevertheless, partial water can be stuck in the first corner of the U-turn. The pressure drop reflects the flow resistance in the flow channel, and it predicts the water detachment frequency well.
Acknowledgements This work is financially supported by the National Natural Science Foundation of China (Grant No. 51706153).
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijhydene.2019.07.169.
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Please cite this article as: Chen R et al., Numerical simulation of liquid water emerging and transport in the flow channel of PEMFC using the volume of fluid method, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2019.07.169