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Signature analysis of two-phase flow pressure drop in proton exchange membrane fuel cell flow channels
Journal Pre-proof Signature analysis of two-phase flow pressure drop in proton exchange membrane fuel cell flow channels Seyed A. Niknam, Mehdi Mortazavi, Anthony D. Santamaria PII:
S2590-1230(19)30071-4
DOI:
https://doi.org/10.1016/j.rineng.2019.100071
Reference:
RINENG 100071
To appear in:
Results in Engineering
Received Date: 1 September 2019 Revised Date:
19 November 2019
Accepted Date: 20 November 2019
Please cite this article as: S.A. Niknam, M. Mortazavi, A.D. Santamaria, Signature analysis of two-phase flow pressure drop in proton exchange membrane fuel cell flow channels, Results in Engineering, https:// doi.org/10.1016/j.rineng.2019.100071. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Signature analysis of two-phase flow pressure drop in proton exchange membrane fuel cell flow channels Seyed A. Niknam*, 1, Mehdi Mortazavi2, Anthony D. Santamaria2 * 1 2
Corresponding author, [email protected]
Department of Industrial Engineering, Western New England University, Springfield, MA
Department of Mechanical Engineering, Western New England University, Springfield, MA
Abstract Proton exchange membrane (PEM) fuel cells are promising alternatives to conventional power sources mainly because of potential environmental impacts. Although PEM fuel cells have been considered for various applications, there are still certain technical challenges toward large-scale commercialization of this type of energy system. This study concentrates on analyzing and modeling the experimentally measured two-phase flow pressure drop signatures in fuel cell flow channels. PEM fuel cells produce water during operation which results in liquidgas two-phase flow inside their flow channels. Due to small length scale of the flow channels, the two-phase flow in a PEM fuel cell is mainly dominated by capillary forces. These forces tend to hold droplets which eventually increase the pressure drop along the flow channels. This study concentrates on pressure drop analysis which is critical in realizing time-dependent changes in the current density and quantifying water accumulation. In this way, a prediction model for pressure drop signatures is presented based on Auto Associative Kernel Regression. This model has a great potential for real-time monitoring and diagnostic in PEM fuel cells. The experimental data was collected through an ex-situ test section by injecting water and supplying air at different flow rates into two parallel flow channels. Keywords: Proton exchange membrane (PEM) fuel cell, peak analysis, empirical model decomposition, Auto Associative Kernel Regression 1. Introduction Proton-exchange membrane (PEM) fuel cells are considered a viable alternative to internal combustion engines due to their high volumetric power density and zero emission of greenhouse gases [1–6]. PEM fuel cells are being utilized for various applications because of 1
their quick response time and low operating temperature range. However, there are still certain technical challenges toward large-scale commercialization of PEM fuel cells. There are strong research underway to enhance durability, performance, and operation cost of fuel cells [6–9]. In this regard, it should be mentioned that the performance of PEM fuel cells is affected by many factors including operating temperature, current density, heat transfer, reactants stoichiometric ratios, and humidity. In practice, water and heat are two byproducts of PEM fuel cells. The produced water emerges at some preferential locations from the surface of the gas diffusion layer (GDL) and enters the flow channel [10]. Water transport through the porous structure of the GDL has been extensively studied by different research groups [11]. Nam and Kaviany [12], in an early study, investigated the formation and distribution of condensed water in the diffusion medium of PEM fuel cells. They described water transport in the porous structure of PEM fuel cells with a branching-type geometry caused by capillary motion of water in a large main stream extended from the catalyst layer to the gas channel. The model was later confirmed by Pasaogullari and Wang [13] when they took a one-dimensional analytical solution of water transport through the GDL. Water transport through the GDL was also visualized by Litster et al. [14] by utilizing fluorescence microscopy. It was suggested that water transport through the GDL occurs in a fingering and channel configuration through which water recedes when a dead-end channel forms within the GDL and transports through adjacent channel. A comprehensive review of modeling transport phenomena in PEM fuel cells is conducted by Weber el al. [1]. In addition to GDLs with uniform porosity structure, transport phenomena in graded GDLs with varying porosity has been also investigated in literature [15–17]. As water emerges from the surface of the GDL, liquid-gas two-phase flow forms within the flow channel which has been investigated by different groups [18–22]. The porous structure of the GDL has an important influence on water emergence rate in flow channels [23–25]. This creates the need for an efficient GDL design to improve water balance in PEM fuel cells [26, 27]. In this vein, researchers have conducted studies on water management within PEM fuel cells to prevent water flooding [28, 29]. The excess liquid water may occupy open pores of the GDL which can lead to blocking the flow of reactants to the catalyst layer, i.e. GDL flooding [13, 30]. Moreover, at some preferential locations, liquid water may enter flow channels as droplets [10, 23, 31]. Water transport
2
mechanisms are observed and classified in [32]. Removing the accumulated water in the flow channel remains a concern for the efficient performance of PEM fuel cells [33, 34]. There are direct and indirect methods to investigate liquid-gas two-phase flow in flow channels of fuel cells. The former includes transparent cell [35], X-ray tomography [36, 37], Neutron imaging [38, 39], and gas chromatography [40]. The indirect method is centered on measuring the two-phase flow pressure drop as an immediate result of water accumulation in the flow channel. The readers are referred to [41] for a compressive review on two-phase flow pressure drop in PEM fuel cell flow channels. This study is concerned with post-processing analysis of the experimentally measured liquid-gas two-phase flow pressure signatures in PEM fuel cell flow channels. The pressure drop analysis is critical in realizing time-dependent changes in current density and water accumulation. This area of research has been conspicuously overlooked in published literature. The current study investigates the transient and steady-state flow pressure drops. In this context, transient pressure drop refers to the pressure drop at the beginning of the experiment once water enters into dry flow channels. The steady-state pressure drop refers to a condition at which the pressure drop signature has been stabilized. In addition, a prediction model for pressure drop signatures is presented based on Auto Associative Kernel Regression (AAKR). This model has a great potential for real-time monitoring and diagnostic in PEM fuel cells. The experimental data was collected through an ex-situ test section which is explained in Section 3. 2. Background: predictive models for two-phase flow pressure drop The liquid-gas two-phase flow in flow channels of a PEM fuel cell is a unique type of flow mainly due to: (i) small length scales of flow channels which make them a capillary-scale system; (ii) the exceptional liquid water emergence mechanism within the flow channels, and (iii) the different surface energies of the channel walls. A capillary-scale system is defined as a system which has a Bond number less than one in normal gravity. In capillary-scale systems, capillary forces define the shape of a static gas-liquid interface. The Bond number is a dimensionless ratio of gravitational to capillary forces on a static liquid surface and is defined as
= (/ ) , where L and L are the characteristic system length and capillary length,
respectively. According to Kandlikar and Grande [42], PEM fuel cell flow channels are classified as minichannels because of their width and height sizes which are typically less than 1 3
mm. Triplett et al. [43] classified the two-phase flow in minichannels into slug flow, slugannular flow, bubbly flow, annular flow, and churn flow. However, the formation of churn flow and bubbly flow is not possible in PEM fuel cell flow channels due to the lower superficial velocities. Allen [44] reported that slug flow and annular flow are the main categories of twophase flow in capillary-scale systems. Slug flow, also known as plug flow, occurs when the gas is blocked in a flow channel by the plugs of liquid. In annual flow, however, there is an unimpeded path for gas to follow, which happens at high superficial gas velocities. The superficial velocity of a fluid is defined as the bulk velocity of the fluid as it flows within the channel cross sectional area. Despite the well-understood single-phase flow pressure drop, the liquid-gas two-phase flow pressure drop is not thoroughly identified at different ranges of flow conditions. Although two-phase flow in PEM fuel cell flow channels has been the subject of many studies [45–48], an accurate prediction of two-phase flow pressure drop is still a challenge for researchers. In theory, the two-phase flow pressure drop (∆ ) is a function of frictional (F), gravitational (G) and
acceleration (A) pressure drop:
∆ = ∆ + ∆ + ∆
(1)
The acceleration pressure loss is negligible because of the low gas superficial velocities in PEM fuel cell flow channels. In addition, gravitational pressure loss is insignificant in minichannels due to the dominant influence of surface tension. Accordingly, the frictional two-phase flow pressure drop is adequate to approximately explain the total pressure loss in PEM fuel cell minichannels. The frictional two-phase flow pressure drop can be predicted through homogeneous equilibrium or separated flow models. The former model works well at high mass qualities [47, 48], and therefore, the model is not a useful aid for the application of PEM fuel cell. The separated flow model, first introduced by Lockhart and Martinelli [49], is based upon the summation of pressure gradients in gas phase, liquid phase, and the interaction of gas-liquid, as shown in the equation below −
= −
+ −
+ −
−
/
(2)
where p, z, and C are the pressure, streamwise coordinate, and parameter in Lockhart-Martinelli correlation, respectively. The subscripts TP, f, and g represent two-phase, saturated liquid, and 4
saturated vapor, respectively.
Practically, the accuracy of prediction depends on Chisholm
parameter, C [50]. This parameter is a function of multiple factors such as flow regime and capillaries geometry [51, 52]. Recently, Mortazavi et al. [53] compared the prediction capability of nine widely accepted models proposed based on separated flow model as well as the homogeneous equilibrium model. 3. Experimental setup and data description In this study, an ex-situ approach was taken to measure liquid-gas two phase flow pressure drop. The test section consists of two parallel flow channels (each 26 cm (length) x 2 mm (width) x 0.95 mm (depth)) supplied with air and liquid water. Figure 1 shows the schematic of the experimental setup used in this research. The flow channels were machined on a 0.5-inchthick polycarbonate plate. The two polycarbonate plates were separated by Toray carbon paper (TGP-060). The procedure in [54] was followed for GDL sample preparation using Polytetrafluoroethylene (PTFE). All 117 experiments started with dry channel (i.e. single-phase air pressure drop) and performed at atmospheric pressure and room temperature. The liquid-gas two-phase flow pressure drop was measured with a pressure transducer with 0-500 Pa range (Omega, PX653-02D5V). The pressure measurement was done over 20 cm length of the channel. Two stainless-steel capillaries (Upchurch-U111) were utilized to inject deionized water into the parallel flow channels. Table 1 provides the experimental conditions in this study. It is to be noted that the Reynolds number was calculated based upon the superficial velocities of air or water and hydraulic diameter of the flow channels.
5
(a)
(b)
Figure 1. (a) Experimental setup (b) the side view of the test section Table 1. Experimental conditions Property Mass flux (kg/m2s) Superficial velocity (m/s) Reynolds number Mass Flow Quality (-)
Air 1.36 - 5.44 1.13 – 4.52 96.0 – 385.3 -
Water 0.04 – 0.45 4.4 × 10-5 – 4.53 × 10-4 0.063 – 0.654 -
Mixture 1.56 – 5.78 0.869 – 0.986
Figure 2 illustrates typical pressure drop data. The data visualization suggests less spikes as water flow rate (WFR) increases. The general trend in all pressure drop signatures indicates a sharp increase in the pressure drop at the beginning of the experiment, i.e. transient signal. This can be explained by the acceleration of the liquid plugs up to the velocity of the gas phase within the flow channel. Furthermore, the data displays greater slope in the transient part for higher WFR, i.e. faster rate of pressure drop as WFR increases. In other words, the steady state part of data starts faster for higher values of water flow rates. Figure 3 shows the mean values of pressure drops for all the experiments as a function of air flow. For the range of air and water flow rates tested in this study, it is evident that pressure drop increases linearly as air flow increases. For constant air flow rate of 300 ml/min, it was observed that an increase in water flow rate from 300 to 2000 µl/h results in only 5% increase in pressure drop.
6
Figure 2. Typical pressure drop data for various water flow rates. The air flow rate was 300 ml/min equivalent to 2.6 m/s superficial velocity.
Figure 3. Mean values of pressure drop for all experiments as a function of air flow 7
4. Pressure drop signature analysis Peak analysis is a simple statistical analysis, which seems suitable for pressure drop analysis. The pressure drop signatures contain numerous spikes due to the slug formation. The data also exhibits harsh fluctuation in pressure drop due to film flow. Figure 4 shows the number of peaks for all the pressure drop peaks with an amplitude greater than 350 Pa. The amplitude of 350 Pa was chosen because the majority of pressure drop signatures had an average below this number, and therefore, it was possible to capture the spikes in the data. Furthermore, to have a better sense of peak frequencies, the time interval between successive peaks are considered and the average of peak interval was calculated for all the experiments. Figure 4 shows the mean of peak intervals. It is clear that the number of peaks would rise by increasing the airflow in the channels. However, the interval between peaks seems to become smaller as the airflow rate increases. This suggests an increase in the number and frequency of gas blockage as the airflow rate increases. It remains to add that for the range of air and water flow rates tested in this study there is no notable relationship between peaks and water flow rate. Next, an appropriate analysis requires noise removal from the pressure drop signatures. For this, empirical mode decomposition (EMD) was applied as a popular algorithm to decompose a nonlinear and nonstationary signal into finite sets of components, known as intrinsic mode functions (IMF) [55, 56]. Using EMD, the pressure drop signatures was decomposed to four components as shown in Figure 5. It is obvious that signal components 2, 3, and 4 (with an average close to zero) has no considerable impact on the main portion of pressure drop signal, i.e. component 1. Thus, only component 1 was used for further analysis and modeling.
8
Figure 4. Number of peaks greater than 350 Pa (top plot) and mean of peak intervals (bottom plot)
Figure 5. EMD for a typical pressure drop signal. The top plot shows four components of the pressure drop signal. Component 1 is clearly separated from other components. As previously depicted in Figure 2, we observe high-amplitude repetitive spikes for low water flow rates. By increasing the water flow rate, the pressure drop signals show highfrequency low-amplitude continuous signal rather than large spikes with low frequencies. This is 9
illustrated in Figure 6, which shows the typical frequency domain analysis (i.e. Fast Fourier Transform) of pressure drops for different water flow rates. It is evident that lower flow rates come with high-amplitude frequency components. The figure shows a spectral line for low flow rates (600 & 900 µl/h) that are clearly larger than any other frequency component. However, there is no major frequency components for high flow rates. The difference in the amplitude of spectral line indicates the change in two-phase flow pattern as WFR increases. In other words,
Amplitude [-]
for low WFR, the magnitude of gas blockage in a flow channel is higher but it is less repetitive.
Figure 6. Frequency domain analysis for several experiments with different water flow rates described in the legend Next, we apply Autoassociative Kernel Regression (AAKR) to develop a prediction model for pressure drop signatures. In essence, using pressure drop across the flow channel as a diagnostic tool has been investigated by many researchers [44–48, 57, 58]. AAKR is a non-linear and non-parametric empirical modeling technique which interpolates historical error-free observations for fault detection and error correction [59, 60]. The AAKR model learns the variables relationship form the non-faulty data stored in a memory matrix (X). Using m historical observation vectors for n variables, the matrix is expressed as $
( )
" = # ⋮ $)(
)
⋯ $ (&) ⋱ ⋮ * ⋯ $)(&)
(3)
Each observation vector represents a non-faulty operating state measured at time i for n variables $+ = ,$
(+)
$ (+) … $)(+) . 10
(4)
Then, the distance between an observation vector and each of the memory vectors is computed. In this way, various distance functions can be used. Euclidean distance is the most commonly used function. The distance calculation (D) results in a vector of distances / = ,0 , 0 , … 0& .
(5)
The distances are used to determine the weights (W) of the m vectors of X by evaluating the Gaussian kernel 2 = ,3
3 …
3& . =
√ 567
8 9: /6 7
7
(6)
In this respect, it is important to find the optimal bandwidth (h) to minimize the prediction error. Afterwards, the prediction is obtained by combining the weights and the memory matrix $ =
∑> :?@ <: =: ∑> :?@ <:
(7)
Therefore, by introducing new inputs, the model interpolated the new data and the memory matrix using kernel regression. If the new inputs have any deviation from the normal behaviors, the model will highlight the significant residuals, i.e. noteworthy variation between the measured and predicted values. The reader are referred to [59, 61] for the mathematical details of AAKR. This modeling technique has a great potential for real-time monitoring and diagnostic in PEM fuel cells because of relatively high correlation between the variables such as water flow rate, air flow, and pressure drop. Figure 7 shows the prediction capability of AAKR for pressure drop signatures. All the 117 experimental data were applied. However, to improve the predictability of AAKR, only the continuous part, i.e. steady state, of the pressure data was used. The inputs include pressure drops, air flow, and water flow data. It should be noted that high values of airflow and WFR were intentionally included in the second half of the test set. In essence, these high values of airflow and WFR could denote the deviation from the normal behavior, causing a significant difference between the measured and predicted value, i.e. higher residuals. It is important to note that the AAKR model precisely reacts to the extreme values for both air flow and pressure drop and resulted in upward surge of residuals as shown in Figure 8. This implies the capability of this model for real-time monitoring of PEM fuel cell to detect abrupt changes in pressure drop signatures. Furthermore, it is interesting to note the small deviation between measured and
11
predicted value for the last data point in the test set. This resulted in sharp decrease in the
P [Pa]
residual depicted in Figure 8.
Air Flow [ml/min]
Air flow Residuals [ml/min]
P [Pa]
P Residuals [Pa]
Figure 7. Prediction capability of AAKR for pressure drop signatures;
Figure 8. (left) Residuals with respect to increase in pressure drop; (right) residuals with respect to increase in air flow 5. Summary and conclusions This study intends to investigate the experimentally measured liquid-gas two-phase flow pressure signatures in PEM fuel cell flow channels. A thorough analysis of pressure drop signatures is essential in realizing time-dependent changes in current density and water accumulation. In this study, an ex-situ approach was taken to measure liquid-gas two phase flow pressure drop. It should be emphasized that the ranges of air and water flow rates used in this research provide similar conditions as fuel cell operating conditions. The pressure signatures show periodic cycles which vary based on water flow rates i.e. high-frequency low-amplitude 12
spikes for lower flow rates. In effect, further analysis is required to identify the uncertainty in liquid flow rate and its impact on pressure drop signatures. Moreover, it was observed that air flow is correlated with the mean of peaks and peak intervals. The analysis and modeling in this research was based on the first component of pressure drop signal which was obtained using empirical mode decomposition. It is believed that other components have no significant influence on the signal. Based on the frequency domain analysis of the signal’s first component, it is possible to see the change in two-phase flow pattern as WFR varies. In addition, a prediction model for pressure drop signatures is presented based on Auto Associative Kernel Regression (AAKR). The model precisely reacts to the extreme values of air flow and water flow and displays notable variations in the residual plot. This implies a great potential of AAKR in detecting abrupt changes in pressure drop signatures which is useful for real-time monitoring and diagnostic. While the GDL used in this study had uniform porosity distribution, the same technique can still be implemented on fuel cells with graded GDLs which incorporate a gradient in porosity. In addition, the same analysis method can still be applied on patterned interfaces between the GDL and flow channels [62]. Future works regarding PEM fuel cell performance and durability will move toward more sophisticated models related to prognostics and life estimation. For this, further significant development is required in understanding PEM fuel cell degradation due to operation conditions and the crucial failure mechanisms.
Acknowledgements Western New England University is gratefully acknowledged for supporting this project. The authors also would like to thank Peter Bennett for fabricating the test section used in this study.
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Highlights: • Two-phase flow pressure drop in a flow channel of a proton exchange membrane fuel cell is studied. • A prediction model for pressure drop signatures is presented based on Auto Associative Kernel Regression. • The proposed model can be utilized for real-time monitoring and diagnostic in proton exchange membrane fuel cells.
Signature analysis of two-phase flow pressure drop in proton exchange membrane fuel cell flow channels Seyed A. Niknam*, 1, Mehdi Mortazavi2, Anthony D. Santamaria2 * 1 2
Corresponding author, [email protected]
Department of Industrial Engineering, Western New England University, Springfield, MA
Department of Mechanical Engineering, Western New England University, Springfield, MA
Conflicts of Interest: The authors declare no conflict of interest.
S2590-1230(19)30071-4
DOI:
https://doi.org/10.1016/j.rineng.2019.100071
Reference:
RINENG 100071
To appear in:
Results in Engineering
Received Date: 1 September 2019 Revised Date:
19 November 2019
Accepted Date: 20 November 2019
Please cite this article as: S.A. Niknam, M. Mortazavi, A.D. Santamaria, Signature analysis of two-phase flow pressure drop in proton exchange membrane fuel cell flow channels, Results in Engineering, https:// doi.org/10.1016/j.rineng.2019.100071. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Signature analysis of two-phase flow pressure drop in proton exchange membrane fuel cell flow channels Seyed A. Niknam*, 1, Mehdi Mortazavi2, Anthony D. Santamaria2 * 1 2
Corresponding author, [email protected]
Department of Industrial Engineering, Western New England University, Springfield, MA
Department of Mechanical Engineering, Western New England University, Springfield, MA
Abstract Proton exchange membrane (PEM) fuel cells are promising alternatives to conventional power sources mainly because of potential environmental impacts. Although PEM fuel cells have been considered for various applications, there are still certain technical challenges toward large-scale commercialization of this type of energy system. This study concentrates on analyzing and modeling the experimentally measured two-phase flow pressure drop signatures in fuel cell flow channels. PEM fuel cells produce water during operation which results in liquidgas two-phase flow inside their flow channels. Due to small length scale of the flow channels, the two-phase flow in a PEM fuel cell is mainly dominated by capillary forces. These forces tend to hold droplets which eventually increase the pressure drop along the flow channels. This study concentrates on pressure drop analysis which is critical in realizing time-dependent changes in the current density and quantifying water accumulation. In this way, a prediction model for pressure drop signatures is presented based on Auto Associative Kernel Regression. This model has a great potential for real-time monitoring and diagnostic in PEM fuel cells. The experimental data was collected through an ex-situ test section by injecting water and supplying air at different flow rates into two parallel flow channels. Keywords: Proton exchange membrane (PEM) fuel cell, peak analysis, empirical model decomposition, Auto Associative Kernel Regression 1. Introduction Proton-exchange membrane (PEM) fuel cells are considered a viable alternative to internal combustion engines due to their high volumetric power density and zero emission of greenhouse gases [1–6]. PEM fuel cells are being utilized for various applications because of 1
their quick response time and low operating temperature range. However, there are still certain technical challenges toward large-scale commercialization of PEM fuel cells. There are strong research underway to enhance durability, performance, and operation cost of fuel cells [6–9]. In this regard, it should be mentioned that the performance of PEM fuel cells is affected by many factors including operating temperature, current density, heat transfer, reactants stoichiometric ratios, and humidity. In practice, water and heat are two byproducts of PEM fuel cells. The produced water emerges at some preferential locations from the surface of the gas diffusion layer (GDL) and enters the flow channel [10]. Water transport through the porous structure of the GDL has been extensively studied by different research groups [11]. Nam and Kaviany [12], in an early study, investigated the formation and distribution of condensed water in the diffusion medium of PEM fuel cells. They described water transport in the porous structure of PEM fuel cells with a branching-type geometry caused by capillary motion of water in a large main stream extended from the catalyst layer to the gas channel. The model was later confirmed by Pasaogullari and Wang [13] when they took a one-dimensional analytical solution of water transport through the GDL. Water transport through the GDL was also visualized by Litster et al. [14] by utilizing fluorescence microscopy. It was suggested that water transport through the GDL occurs in a fingering and channel configuration through which water recedes when a dead-end channel forms within the GDL and transports through adjacent channel. A comprehensive review of modeling transport phenomena in PEM fuel cells is conducted by Weber el al. [1]. In addition to GDLs with uniform porosity structure, transport phenomena in graded GDLs with varying porosity has been also investigated in literature [15–17]. As water emerges from the surface of the GDL, liquid-gas two-phase flow forms within the flow channel which has been investigated by different groups [18–22]. The porous structure of the GDL has an important influence on water emergence rate in flow channels [23–25]. This creates the need for an efficient GDL design to improve water balance in PEM fuel cells [26, 27]. In this vein, researchers have conducted studies on water management within PEM fuel cells to prevent water flooding [28, 29]. The excess liquid water may occupy open pores of the GDL which can lead to blocking the flow of reactants to the catalyst layer, i.e. GDL flooding [13, 30]. Moreover, at some preferential locations, liquid water may enter flow channels as droplets [10, 23, 31]. Water transport
2
mechanisms are observed and classified in [32]. Removing the accumulated water in the flow channel remains a concern for the efficient performance of PEM fuel cells [33, 34]. There are direct and indirect methods to investigate liquid-gas two-phase flow in flow channels of fuel cells. The former includes transparent cell [35], X-ray tomography [36, 37], Neutron imaging [38, 39], and gas chromatography [40]. The indirect method is centered on measuring the two-phase flow pressure drop as an immediate result of water accumulation in the flow channel. The readers are referred to [41] for a compressive review on two-phase flow pressure drop in PEM fuel cell flow channels. This study is concerned with post-processing analysis of the experimentally measured liquid-gas two-phase flow pressure signatures in PEM fuel cell flow channels. The pressure drop analysis is critical in realizing time-dependent changes in current density and water accumulation. This area of research has been conspicuously overlooked in published literature. The current study investigates the transient and steady-state flow pressure drops. In this context, transient pressure drop refers to the pressure drop at the beginning of the experiment once water enters into dry flow channels. The steady-state pressure drop refers to a condition at which the pressure drop signature has been stabilized. In addition, a prediction model for pressure drop signatures is presented based on Auto Associative Kernel Regression (AAKR). This model has a great potential for real-time monitoring and diagnostic in PEM fuel cells. The experimental data was collected through an ex-situ test section which is explained in Section 3. 2. Background: predictive models for two-phase flow pressure drop The liquid-gas two-phase flow in flow channels of a PEM fuel cell is a unique type of flow mainly due to: (i) small length scales of flow channels which make them a capillary-scale system; (ii) the exceptional liquid water emergence mechanism within the flow channels, and (iii) the different surface energies of the channel walls. A capillary-scale system is defined as a system which has a Bond number less than one in normal gravity. In capillary-scale systems, capillary forces define the shape of a static gas-liquid interface. The Bond number is a dimensionless ratio of gravitational to capillary forces on a static liquid surface and is defined as
= (/ ) , where L and L are the characteristic system length and capillary length,
respectively. According to Kandlikar and Grande [42], PEM fuel cell flow channels are classified as minichannels because of their width and height sizes which are typically less than 1 3
mm. Triplett et al. [43] classified the two-phase flow in minichannels into slug flow, slugannular flow, bubbly flow, annular flow, and churn flow. However, the formation of churn flow and bubbly flow is not possible in PEM fuel cell flow channels due to the lower superficial velocities. Allen [44] reported that slug flow and annular flow are the main categories of twophase flow in capillary-scale systems. Slug flow, also known as plug flow, occurs when the gas is blocked in a flow channel by the plugs of liquid. In annual flow, however, there is an unimpeded path for gas to follow, which happens at high superficial gas velocities. The superficial velocity of a fluid is defined as the bulk velocity of the fluid as it flows within the channel cross sectional area. Despite the well-understood single-phase flow pressure drop, the liquid-gas two-phase flow pressure drop is not thoroughly identified at different ranges of flow conditions. Although two-phase flow in PEM fuel cell flow channels has been the subject of many studies [45–48], an accurate prediction of two-phase flow pressure drop is still a challenge for researchers. In theory, the two-phase flow pressure drop (∆ ) is a function of frictional (F), gravitational (G) and
acceleration (A) pressure drop:
∆ = ∆ + ∆ + ∆
(1)
The acceleration pressure loss is negligible because of the low gas superficial velocities in PEM fuel cell flow channels. In addition, gravitational pressure loss is insignificant in minichannels due to the dominant influence of surface tension. Accordingly, the frictional two-phase flow pressure drop is adequate to approximately explain the total pressure loss in PEM fuel cell minichannels. The frictional two-phase flow pressure drop can be predicted through homogeneous equilibrium or separated flow models. The former model works well at high mass qualities [47, 48], and therefore, the model is not a useful aid for the application of PEM fuel cell. The separated flow model, first introduced by Lockhart and Martinelli [49], is based upon the summation of pressure gradients in gas phase, liquid phase, and the interaction of gas-liquid, as shown in the equation below −
= −
+ −
+ −
−
/
(2)
where p, z, and C are the pressure, streamwise coordinate, and parameter in Lockhart-Martinelli correlation, respectively. The subscripts TP, f, and g represent two-phase, saturated liquid, and 4
saturated vapor, respectively.
Practically, the accuracy of prediction depends on Chisholm
parameter, C [50]. This parameter is a function of multiple factors such as flow regime and capillaries geometry [51, 52]. Recently, Mortazavi et al. [53] compared the prediction capability of nine widely accepted models proposed based on separated flow model as well as the homogeneous equilibrium model. 3. Experimental setup and data description In this study, an ex-situ approach was taken to measure liquid-gas two phase flow pressure drop. The test section consists of two parallel flow channels (each 26 cm (length) x 2 mm (width) x 0.95 mm (depth)) supplied with air and liquid water. Figure 1 shows the schematic of the experimental setup used in this research. The flow channels were machined on a 0.5-inchthick polycarbonate plate. The two polycarbonate plates were separated by Toray carbon paper (TGP-060). The procedure in [54] was followed for GDL sample preparation using Polytetrafluoroethylene (PTFE). All 117 experiments started with dry channel (i.e. single-phase air pressure drop) and performed at atmospheric pressure and room temperature. The liquid-gas two-phase flow pressure drop was measured with a pressure transducer with 0-500 Pa range (Omega, PX653-02D5V). The pressure measurement was done over 20 cm length of the channel. Two stainless-steel capillaries (Upchurch-U111) were utilized to inject deionized water into the parallel flow channels. Table 1 provides the experimental conditions in this study. It is to be noted that the Reynolds number was calculated based upon the superficial velocities of air or water and hydraulic diameter of the flow channels.
5
(a)
(b)
Figure 1. (a) Experimental setup (b) the side view of the test section Table 1. Experimental conditions Property Mass flux (kg/m2s) Superficial velocity (m/s) Reynolds number Mass Flow Quality (-)
Air 1.36 - 5.44 1.13 – 4.52 96.0 – 385.3 -
Water 0.04 – 0.45 4.4 × 10-5 – 4.53 × 10-4 0.063 – 0.654 -
Mixture 1.56 – 5.78 0.869 – 0.986
Figure 2 illustrates typical pressure drop data. The data visualization suggests less spikes as water flow rate (WFR) increases. The general trend in all pressure drop signatures indicates a sharp increase in the pressure drop at the beginning of the experiment, i.e. transient signal. This can be explained by the acceleration of the liquid plugs up to the velocity of the gas phase within the flow channel. Furthermore, the data displays greater slope in the transient part for higher WFR, i.e. faster rate of pressure drop as WFR increases. In other words, the steady state part of data starts faster for higher values of water flow rates. Figure 3 shows the mean values of pressure drops for all the experiments as a function of air flow. For the range of air and water flow rates tested in this study, it is evident that pressure drop increases linearly as air flow increases. For constant air flow rate of 300 ml/min, it was observed that an increase in water flow rate from 300 to 2000 µl/h results in only 5% increase in pressure drop.
6
Figure 2. Typical pressure drop data for various water flow rates. The air flow rate was 300 ml/min equivalent to 2.6 m/s superficial velocity.
Figure 3. Mean values of pressure drop for all experiments as a function of air flow 7
4. Pressure drop signature analysis Peak analysis is a simple statistical analysis, which seems suitable for pressure drop analysis. The pressure drop signatures contain numerous spikes due to the slug formation. The data also exhibits harsh fluctuation in pressure drop due to film flow. Figure 4 shows the number of peaks for all the pressure drop peaks with an amplitude greater than 350 Pa. The amplitude of 350 Pa was chosen because the majority of pressure drop signatures had an average below this number, and therefore, it was possible to capture the spikes in the data. Furthermore, to have a better sense of peak frequencies, the time interval between successive peaks are considered and the average of peak interval was calculated for all the experiments. Figure 4 shows the mean of peak intervals. It is clear that the number of peaks would rise by increasing the airflow in the channels. However, the interval between peaks seems to become smaller as the airflow rate increases. This suggests an increase in the number and frequency of gas blockage as the airflow rate increases. It remains to add that for the range of air and water flow rates tested in this study there is no notable relationship between peaks and water flow rate. Next, an appropriate analysis requires noise removal from the pressure drop signatures. For this, empirical mode decomposition (EMD) was applied as a popular algorithm to decompose a nonlinear and nonstationary signal into finite sets of components, known as intrinsic mode functions (IMF) [55, 56]. Using EMD, the pressure drop signatures was decomposed to four components as shown in Figure 5. It is obvious that signal components 2, 3, and 4 (with an average close to zero) has no considerable impact on the main portion of pressure drop signal, i.e. component 1. Thus, only component 1 was used for further analysis and modeling.
8
Figure 4. Number of peaks greater than 350 Pa (top plot) and mean of peak intervals (bottom plot)
Figure 5. EMD for a typical pressure drop signal. The top plot shows four components of the pressure drop signal. Component 1 is clearly separated from other components. As previously depicted in Figure 2, we observe high-amplitude repetitive spikes for low water flow rates. By increasing the water flow rate, the pressure drop signals show highfrequency low-amplitude continuous signal rather than large spikes with low frequencies. This is 9
illustrated in Figure 6, which shows the typical frequency domain analysis (i.e. Fast Fourier Transform) of pressure drops for different water flow rates. It is evident that lower flow rates come with high-amplitude frequency components. The figure shows a spectral line for low flow rates (600 & 900 µl/h) that are clearly larger than any other frequency component. However, there is no major frequency components for high flow rates. The difference in the amplitude of spectral line indicates the change in two-phase flow pattern as WFR increases. In other words,
Amplitude [-]
for low WFR, the magnitude of gas blockage in a flow channel is higher but it is less repetitive.
Figure 6. Frequency domain analysis for several experiments with different water flow rates described in the legend Next, we apply Autoassociative Kernel Regression (AAKR) to develop a prediction model for pressure drop signatures. In essence, using pressure drop across the flow channel as a diagnostic tool has been investigated by many researchers [44–48, 57, 58]. AAKR is a non-linear and non-parametric empirical modeling technique which interpolates historical error-free observations for fault detection and error correction [59, 60]. The AAKR model learns the variables relationship form the non-faulty data stored in a memory matrix (X). Using m historical observation vectors for n variables, the matrix is expressed as $
( )
" = # ⋮ $)(
)
⋯ $ (&) ⋱ ⋮ * ⋯ $)(&)
(3)
Each observation vector represents a non-faulty operating state measured at time i for n variables $+ = ,$
(+)
$ (+) … $)(+) . 10
(4)
Then, the distance between an observation vector and each of the memory vectors is computed. In this way, various distance functions can be used. Euclidean distance is the most commonly used function. The distance calculation (D) results in a vector of distances / = ,0 , 0 , … 0& .
(5)
The distances are used to determine the weights (W) of the m vectors of X by evaluating the Gaussian kernel 2 = ,3
3 …
3& . =
√ 567
8 9: /6 7
7
(6)
In this respect, it is important to find the optimal bandwidth (h) to minimize the prediction error. Afterwards, the prediction is obtained by combining the weights and the memory matrix $ =
∑> :?@ <: =: ∑> :?@ <:
(7)
Therefore, by introducing new inputs, the model interpolated the new data and the memory matrix using kernel regression. If the new inputs have any deviation from the normal behaviors, the model will highlight the significant residuals, i.e. noteworthy variation between the measured and predicted values. The reader are referred to [59, 61] for the mathematical details of AAKR. This modeling technique has a great potential for real-time monitoring and diagnostic in PEM fuel cells because of relatively high correlation between the variables such as water flow rate, air flow, and pressure drop. Figure 7 shows the prediction capability of AAKR for pressure drop signatures. All the 117 experimental data were applied. However, to improve the predictability of AAKR, only the continuous part, i.e. steady state, of the pressure data was used. The inputs include pressure drops, air flow, and water flow data. It should be noted that high values of airflow and WFR were intentionally included in the second half of the test set. In essence, these high values of airflow and WFR could denote the deviation from the normal behavior, causing a significant difference between the measured and predicted value, i.e. higher residuals. It is important to note that the AAKR model precisely reacts to the extreme values for both air flow and pressure drop and resulted in upward surge of residuals as shown in Figure 8. This implies the capability of this model for real-time monitoring of PEM fuel cell to detect abrupt changes in pressure drop signatures. Furthermore, it is interesting to note the small deviation between measured and
11
predicted value for the last data point in the test set. This resulted in sharp decrease in the
P [Pa]
residual depicted in Figure 8.
Air Flow [ml/min]
Air flow Residuals [ml/min]
P [Pa]
P Residuals [Pa]
Figure 7. Prediction capability of AAKR for pressure drop signatures;
Figure 8. (left) Residuals with respect to increase in pressure drop; (right) residuals with respect to increase in air flow 5. Summary and conclusions This study intends to investigate the experimentally measured liquid-gas two-phase flow pressure signatures in PEM fuel cell flow channels. A thorough analysis of pressure drop signatures is essential in realizing time-dependent changes in current density and water accumulation. In this study, an ex-situ approach was taken to measure liquid-gas two phase flow pressure drop. It should be emphasized that the ranges of air and water flow rates used in this research provide similar conditions as fuel cell operating conditions. The pressure signatures show periodic cycles which vary based on water flow rates i.e. high-frequency low-amplitude 12
spikes for lower flow rates. In effect, further analysis is required to identify the uncertainty in liquid flow rate and its impact on pressure drop signatures. Moreover, it was observed that air flow is correlated with the mean of peaks and peak intervals. The analysis and modeling in this research was based on the first component of pressure drop signal which was obtained using empirical mode decomposition. It is believed that other components have no significant influence on the signal. Based on the frequency domain analysis of the signal’s first component, it is possible to see the change in two-phase flow pattern as WFR varies. In addition, a prediction model for pressure drop signatures is presented based on Auto Associative Kernel Regression (AAKR). The model precisely reacts to the extreme values of air flow and water flow and displays notable variations in the residual plot. This implies a great potential of AAKR in detecting abrupt changes in pressure drop signatures which is useful for real-time monitoring and diagnostic. While the GDL used in this study had uniform porosity distribution, the same technique can still be implemented on fuel cells with graded GDLs which incorporate a gradient in porosity. In addition, the same analysis method can still be applied on patterned interfaces between the GDL and flow channels [62]. Future works regarding PEM fuel cell performance and durability will move toward more sophisticated models related to prognostics and life estimation. For this, further significant development is required in understanding PEM fuel cell degradation due to operation conditions and the crucial failure mechanisms.
Acknowledgements Western New England University is gratefully acknowledged for supporting this project. The authors also would like to thank Peter Bennett for fabricating the test section used in this study.
13
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Highlights: • Two-phase flow pressure drop in a flow channel of a proton exchange membrane fuel cell is studied. • A prediction model for pressure drop signatures is presented based on Auto Associative Kernel Regression. • The proposed model can be utilized for real-time monitoring and diagnostic in proton exchange membrane fuel cells.
Signature analysis of two-phase flow pressure drop in proton exchange membrane fuel cell flow channels Seyed A. Niknam*, 1, Mehdi Mortazavi2, Anthony D. Santamaria2 * 1 2
Corresponding author, [email protected]
Department of Industrial Engineering, Western New England University, Springfield, MA
Department of Mechanical Engineering, Western New England University, Springfield, MA
Conflicts of Interest: The authors declare no conflict of interest.