«by Te-Chun Wu B.Sc., Chung Yuan Christian University, 1993 M.Sc., National Cheng Kung University, 1995 Ph.D., National Cheng Kung University, 2000 A ...»
Two-Phase Flow in Microchannels with Application to PEM Fuel Cells
B.Sc., Chung Yuan Christian University, 1993
M.Sc., National Cheng Kung University, 1995
Ph.D., National Cheng Kung University, 2000
A Dissertation Submitted in Partial Fulfillment of the
Requirements for the Degree of
DOCTOR OF PHILOSOPHY
in the Department of Mechanical Engineering
Te-Chun Wu, 2015
University of Victoria
All rights reserved. This thesis may not be reproduced in whole or in part, by photocopy or other means, without the permission of the author.
ii Two-Phase Flow in Microchannels with Application to PEM Fuel Cells by Te-Chun Wu B.Sc., Chung Yuan Christian University, 1993 M.Sc., National Cheng Kung University, 1995 Ph.D., National Cheng Kung University, 2000 Supervisory Committee Dr. Ned Djilali, Supervisor (Department of Mechanical Engineering, University of Victoria) Dr. Rustom Bhiladvala, Departmental Member (Department of Mechanical Engineering, University of Victoria) Dr. Alexandra Branzan Albu, Outside Member (Department of Electrical and Computer Engineering, University of Victoria) iii Supervisory Committee Dr. Ned Djilali, Supervisor (Department of Mechanical Engineering, University of Victoria) Dr. Rustom Bhiladvala, Departmental Member (Department of Mechanical Engineering, University of Victoria) Dr. Alexandra Branzan Albu, Outside Member (Department of Electrical and Computer Engineering, University of Victoria)
ABSTRACTThe performance of PEM fuel cells (PEMFC) relies on the proper control and management of the liquid water that forms as a result of the electrochemical process, especially at high current densities. The liquid water transport and removal process in the gas flow channel is highly dynamic and many of its fundamental features are not well understood. This thesis presents an experimental and theoretical investigation of the emergence of water droplets from a single pore into a microchannel. The experiments are performed in a 250 µm × 250 µm air channel geometry with a single 50 µm pore that replicates a PEMFC cathode gas channel. A droplet manipulation platform is constructed using a microfluidics soft lithographic process to allow observation of the dynamic nature of the water droplets. Flow conditions that correspond to typical operating conditions in a PEMFC are selected. A test matrix of experiments comprised of different water injection velocities and air velocities in the gas microchannel is studied. Emergence, detachment and subsequent dynamic evolution of water droplets are analyzed, both qualitatively and quantitatively. Quantitative image analysis tools are implemented and applied to the timeresolved images to document the time evolution of the shape and location of the droplets, iv characteristic frequencies, dynamic contact angles, flow regime and stability maps.
Three different flow regimes are identified, slug, droplet, and film flow. The effects of the air flow rate and droplet size on the critical detachment conditions are also investigated.
Numerical simulations using Volume-of-Fluid method are presented to investigate the water dynamics in the droplet flow. The focus of the modeling is on methods that account for the dynamic nature of the contact line evolution. Results of different approaches of dynamic contact angle formulations derived empirically and by using the theoretically based Hoffmann function are compared with the static contact angle models used to date.
The importance of the dynamic formulation as well as the necessity for high numerical resolution is highlighted. The Hoffmann function implementation is found to better capture the salient droplet motion dynamics in terms of advancing and receding contact angle and periodicity of the emergence process.
To explore the possibility of using the pressure drop signal as a diagnostic tool in operational fuel cells that are not optically accessible, a flow diagnostic tool was developed based on pressure drop measurements in a custom designed two-phase flow fixture with commercial flow channel designs. Water accumulation at the channel outlet was found to be the primary cause of a low-frequency periodic oscillation of pressure drop signal. It is shown that the flow regimes can be characterized using the power spectrum density of the normalized pressure drop signal. This is used to construct a flow map correlating pressure drop signals to the flow regimes, and opens the possibility for practical flow diagnostics in operating fuel cells.
Table of Contents
Table of Contents
List of Tables
List of Figures
1.1. Background and Motivation
1.2. Scope and Organization of the Thesis
2 Literature Review
2.1. Dynamic Behavior of Liquid Water
2.2. Flow Regime
2.3. Pressure Drop
2.4. Effect of Channel Geometry and Surface Properties
2.5. Status of Prediction Method
2.5.1. Force balance method on droplet detachment
2.5.2. Volume-of-Fluid (VOF) method
2.5.3. Level set method (LSM)
2.5.4. Lattice Boltzmann method (LBM)
2.5.5. Modeling of the dynamic contact angle
3 Experimental Investigation of Water Droplet Emergence
3.1. Method and Apparatus
3.1.1. Microchannel design
3.1.2. Measurement apparatus
3.1.3. Flow conditions
3.2. Results and Discussions
3.2.1. Flow regimes
3.2.2. Droplet emergence frequency
3.2.3. Further image analysis of droplet emergence
3.2.4. Dynamic contact angle
3.2.5. Droplet dynamic at the onset of detachment
4 Numerical Simulation Using VOF Method
4.1. Volume of Fluid Method
4.2. Implementation of Dynamic Contact Angle
4.2.2. ANSYS FLUENT
4.3. Simulation Domain and Mesh, Boundary and Initial Conditions
4.3.2. ANSYS FLUENT
4.4. Results and Discussions
4.4.2. ANSYS FLUENT
5 Pressure Signature and Diagnostic Tool
5.2. Method and Apparatus
5.3. Results and Discussions
5.3.1. Characterization of mean pressure drop
5.3.2. Dynamic characteristics
6 Conclusion and future works
6.2. Future works
Appendix A – Microfluidic chip fabrication
8 vii Appendix B – MATLAB source code
9 Appendix C – FLUENT UDF source code for DCA
10 Appendix D – FLUENT UDF source code for droplet impact
11 Appendix E – Pressure drop measurement data
12 viii List of Tables Table 2.1. Slip models examined by Shikhmurzaev 
Flow inlet conditions.
Properties of liquid and flow conditions.
Test conditions matrix
Pressure drop measurement of Plastic-0A using single water injection.......... 93 Table 12.1. Pressure drop measurement of Plastic-0A using dual water injection......... 121 Table 12.2. Pressure drop measurement of Plastic-02 using single water injection....... 122 Table 12.3 Pressure drop measurement of CFP-010A using single water injection...... 122 Table 12.4 Pressure drop measurement of CFP-0D using single water injection.
......... 122 ix List of Figures Figure 1.1.
An emerged water droplet from the GDL entering the cathode gas flow channel (reproduced from  with permission of Journal of Power Sources)................. 2 Figure 2.1.
Typical flow patterns in gas channel of PEMFC (reproduced from  with permission of Journal of Power Sources).
Correlation between fluctuations in cathode P signal and cell voltage (reproduced from  with permission of Heat Transfer Engineering).
Two-phase friction multiplier versus the superficial air velocity under different superficial water velocities (reproduced from  with permission of Chemical Engineering Progress).
Cross sectional view of typical flow channel. r, rib width; c, channel width; d, channel depth; α, wall angle (reproduced from  with permission of International Journal of Hydrogen Energy)
Schematic of channel design (left) and integration into PEMFC (right) (reproduced from  with permission of Sensors and Actuators A).
Schematic of (a) droplet height and contact angle, (b) droplet subjected to a shear flow with resulting deformation and dynamic contact angles (c) spherical droplet geometry (d) control volume (reproduced from  with permission of ASME Conference Proceedings).
(a) PDMS chip for droplet manipulation. (b) Cross sectional view of chip. (c) Field of view in microscope.
Schematic diagram of experimental apparatus.
Typical flow regime in microchannel
Flow map of water emergence phenomena in a model PEMFC cathode gas microchannel.
(a) Time domain signal and (b) frequency distribution of droplet emergence process
x Figure 3.6.
Emergence frequency in droplet flow regime under different flow conditions.
Time resolved images of water emerging from a 50 µm square pore in a 250 µm square gas microchannel with the flow condition of Case 2. a) t = 1 ms, b) t = 3 ms,
c) t = 5 ms, d) t = 10 ms, e) t = 15 ms, f) t = 20 ms, g) t = 25 ms, h) t = 45 ms, i) t = 65 ms, j) t = 75 ms
Dynamic contact angle evolution through an emergence cycle (13.2 Hz under Case 2 flow conditions). Period I: surface tension force dominant. Period II: transition.
Period III: drag force dominant
Effect of air flow velocity on characteristic droplet size (chord C and height
H) at detachment.
Effect of air flow on contact angle hysteresis.
Contact angle interpretations and effect of airflow on droplet aspect ratio at the onset of detachment.
Image of water droplet subjected to the air flow stream. Points A and B are the receding and advancing points in a 2-D plane of view, whereas r and a designate the receding and advancing contact angle, respectively.
Position of advancing point (XB), velocity function and DCA distribution for droplet emergence cycle Case 2.
Velocity dependent contact angle function from droplet emergence experiment
Schematic diagram of capillary rise experiment.
Velocity dependent contact angle function.
Three-dimensional domain and mesh for the numerical simulations of droplet emergence using CFD-ACE+.
Illustration of numerical grids used for the droplet impact computations. The region of an adaptive refinement is presented.
Computation domain and mesh illustration for the droplet emergence study, presenting the region of an adaptive refinement.
(a) Top view. (b) Side view of the instant at droplet detachment using SCA. 67 xi Figure 4.10.
Comparison of contact angle evolution of VOF simulation (SCA, mesh
12.5um) and experiments.
(a) Side view of the instant at droplet detachment using DCA Eq. (4.17). (b) Comparison of contact angle evolution of VOF simulation (DCA, method 1, mesh 12.5 m) and experiment.
(a) Side view of the instant at droplet detachment using DCA Eq. (4.19) and . (b) Comparison of contact angle evolution of VOF simulation (DCA, method 2, mesh 12.5 m) and experiment.
(a) Side view of the instant at droplet detachment using DCA Eq. (4.19) and . (b) Comparison of contact angle evolution of VOF simulation (DCA, method 2, mesh 6.25 m) and experiment.
Comparison of time sequence of water droplet impact onto wax surface (We = 90), experiment (left) and numerical (right) (reproduced from  with permission of Experimental Thermal and Fluid Science).
Time series images during the spreading phase for SCA modeling of droplet impact on wax surface.
Time series images during the recoiling phase for SCA modeling of droplet impact on wax surface.
Time series images during the spreading phase for DCA modeling of droplet impact on wax surface.
Time series images during the recoiling phase for DCA modeling of droplet impact on wax surface.
Schematics of spreading diameter and apex height of drop impacts............ 78 Figure 4.20.
Numerical simulation of the temporal evolution of the spread diameter in comparison with the results of Sikalo et. al .