Modeling of PEM fuel cell system with newly formulated water transport properties in membranes of stack and humidifier for a fuel cell electric vehicle = 수소전기차용 스택 및 가습기 막의 새롭게 정립된 수분 수송 특성을 반영한 고분자전해질 연료전지 시스템 모델링

국문 초록 (Abstract)

무공해 및 고효율 운송 수단에 대한 수요가 증가함에 따라, 수소전기차 (fuel cell electric vehicle, FCEV)는 특히 장시간 운행과 높은 출력이 요구되는 상용 분야에서 유망한 대안으로 부각되고 있다. 기존 세대의 FCEV는 주로 Nafion 기반 막을 사용해왔으나, 차세대 FCEV 시스템에서는 연료전지 스택 내에서 expanded polytetrafluoroethylene (ePTFE) 기반의 강화 복합막과 가습기에서는 폴리설폰 중공사막과 같은 소재가 점차 채택되고 있다. 이와 같은 신소재는 기존 Nafion 막과는 본질적으로 상이한 흡착 및 수분 수송 거동을 나타내므로, 이들의 수송 물성 특성을 정확히 규명하고 고분자 전해질막 연료전지 (polymer electrolyte membrane fuel cell, PEMFC) 시스템 모델에 통합하는 것이 실제 운전 조건 하에서의 성능을 신뢰성 있게 예측하기 위해 필수적이다.
이를 위해 다음의 요소를 포함하는 포괄적인 모델링 프레임워크를 개발하였다: (i) 보강 복합막의 수분 수송 특성에 대한 in-situ 분석, (ii) 단일 셀 및 스택 수준에서 검증된 PEMFC 모델링, (iii) 폴리설폰 막 가습기에 대한 실험 및 이론적 분석, (iv) 단품 및 시스템 수준의 BOP (Balance of plant) 모델링.
첫째, ePTFE 강화 복합막의 수분 수송 특성을 규명하였으며, 이는 기존 Nafion 막에 초점을 맞춘 기존 연구에 비해 현저한 진전이다. 동적 수분 흡착 (DVS) 등온선을 통해 막의 수분 함량을 측정하고, NDMS (new dual-mode sorption) 모델을 통해 흡착의 온도 의존성을 분석하였다. 이 모델은 조정된 결정계수 (Radj²)가 0.96 이상인 우수한 적합도를 보였다. 수소 펌핑 모드 및 PEMFC 운전 모드를 활용하여 수분 확산 계수, 전기삼투 계수 (EOD), 이온 전도도에 대해 수분 함량과 온도의 함수로 경험적 상관식을 도출하였으며, 이들의 최대 상대 오차는 3.14 % 미만이었다.
둘째, 수소전기차 내 단일 셀 및 스택 수준에서 검증된 포괄적인 PEMFC 모델을 개발하였다. 이는 온도, 상대습도, 압력 등 실제 운전 조건의 변동에 크게 영향을 받는 PEMFC의 과도 응답 특성을 정확히 반영하는 데 필수적이다. 다양한 작동 조건에서의 단일 셀 실험을 기반으로, 강화 복합막의 수분 수송 특성을 통합한 상세한 PEMFC 모델을 구성하였다. 해당 모델은 Radj²가 0.988, 최대 상대 오차 2.01 % 미만의 높은 정확도를 나타냈다. 특히 강화 복합막 (RCM) 모델은 기존 Nafion 기반 상관식에 기초한 모델 (CM) 대비 예측 정확도가 크게 향상되었으며, 최대 RMSE는 41.0 mV (CM)에서 6.3 mV (RCM)로 감소하였고, Radj²는 0.957에서 0.996으로 증가하였다. 또한, 전류 밀도에 따른 온도 및 수분(증기 및 액체) 농도의 관통방향 분포를 정확히 예측하였으며, 스택 수준에서는 차대동력계 시험을 통해 동적 부하 조건에서 검증을 수행하였다. 유로 형상 보정계수를 통해 Radj²는 0.994, 최대 상대 오차 3.15 % 미만의 예측 정확도를 달성하였다.
셋째, 95 kW급 수소전기차에 적용된 쉘-앤-튜브 타입 가스-가스 막가습기 모듈에 대한 포괄적인 실험적 및 이론적 분석이 수행되었다. 이 가습기는 친수성과 비불소계 특성을 갖는 polysulfone 중공사막을 특징으로 하며, 열 및 물질전달율과 approach 이슬점 온도 (ADT)에 미치는 유입 온도, 상대습도, 온도 차의 영향을 평가하였다. 온도 차가 15 ℃ 일 때 유량이 1,000에서 3,400 L/min으로 증가함에 따라 ADT는 12.42에서 15.89 ℃로 증가하였으며, 유량이 낮을수록 성능이 가장 높게 나타났다. 온도 효과를 고려하기 위해 용해-확산 메커니즘을 포함한 NDMS 모델을 적용하였으며, 상대오차 5 % 이하의 정확도를 달성하였다. 또한, 유량 변화에 대한 과도 응답도 정확히 예측되어, 부하 변동 조건에서 가습기의 적응성과 응답성을 반영하였다.
마지막으로 공기압축기, 인터쿨러, 냉각수 펌프, 라디에이터, 팬 펌프 등을 포함하는 BOP 시스템을 단품 및 차량 단위 실험 데이터를 바탕으로 모델링하였다. 공기압축기는 단품 실험을 통해 특성을 분석하고, 이를 바탕으로 lumped map-based 모델로 구현하였으며, 인터쿨러 및 라디에이터는 교차류 (cross-flow) 열교환기 구조를 기반으로 한 유용도-NTU 기법을 적용하여 준동적 (quasi-dynamic) 모델로 구현하였다. 이들 모델은 실제 주행 조건 하의 실험 데이터로 검증되었으며, 이를 통합하여 다양한 운전 조건에서 시스템 거동을 정확히 예측할 수 있는 PEMFC 시스템 모델을 완성하였다. 본 연구에서 개발된 시스템 모델은 차세대 상용 수소전기차의 에너지 효율성과 신뢰성 향상을 위한 기반을 제공한다.

다국어 초록 (Multilingual Abstract)

The growing demand for zero-emission and high-efficiency transportation has highlighted fuel cell electric vehicles (FCEVs) as a promising alternative, particularly for commercial applications requiring long operating hours and high load capacity. While earlier generations of FCEVs primarily utilized Nafion-based membranes, next-generation FCEV systems increasingly adopt advanced materials such as the expanded polytetrafluoroethylene (ePTFE)-reinforced composite membrane in the polymer electrolyte membrane fuel cell (PEMFC) stack and polysulfone hollow fiber membrane in the membrane humidifier. These new materials exhibit fundamentally different sorption and water transport behaviors compared to conventional Nafion membranes. Accordingly, it is essential to accurately characterize their water transport properties and integrate them into the PEMFC system model to enable reliable performance prediction under realistic operating conditions.
To this end, a comprehensive modeling framework was developed, encompassing: (i) in-situ analysis of water transport properties in the reinforced composite membrane, (ii) PEMFC modeling validated at both the single-cell and stack levels, (iii) experimental and theoretical investigation of a polysulfone membrane humidifier, and (iv) component- and system-level modeling of the balance of plant (BOP).
First, the water transport properties of an ePTFE-reinforced composite membrane were characterized, representing a notable advancement over previous studies that primarily focused on Nafion membranes. The membrane water content was measured using dynamic vapor sorption (DVS) isotherms, and the temperature dependence of sorption was investigated using a new dual-mode sorption (NDMS) model, which showed an excellent fit with an adjusted coefficient of determination (Radj2) greater than 0.96. By employing the hydrogen pumping mode and PEMFC mode, empirical correlations were established for the coefficients of water diffusion, electro-osmotic drag (EOD), and ionic conductivity as functions of water content and cell temperature. These correlations demonstrated a maximum relative error of less than 3.14 %.
Second, a comprehensive PEMFC model was developed and validated at both the single-cell and stack levels in the FCEV. This is crucial for capturing the transient behavior of PEMFCs, which are heavily influenced by fluctuations in real-world operating conditions (i.e., temperature, relative humidity, and pressure). An extensive single-cell experiment was conducted to examine these effects, leading to the development of a detailed PEMFC model incorporating newly established water transport properties of the reinforced composite membrane. The model achieved remarkable accuracy, with an adjusted coefficient of determination (Radj2) of 0.988 and a maximum relative error below 2.01 %. Notably, the reinforced composite membrane (RCM) model explicitly accounted for the distinct water transport behavior of the reinforced membrane, resulting in significantly improved predictive accuracy compared to the conventional model (CM) based on Nafion correlations. This enhancement was demonstrated by a reduction in the maximum RMSE from 41.0 mV (CM) to 6.3 mV (RCM), and an increase in Radj² from 0.957 to 0.996, indicating much closer agreement with polarization curve data across various operating conditions. Furthermore, the model accurately captured through-plane distributions of temperature and water concentration (vapor and liquid), highlighting the variation in transport behavior under different current densities. In addition, stack-level validation was performed through chassis dynamometer tests under dynamic load conditions, where correction factors were applied to account for flow channel geometry. With these refinements, the stack model achieved an Radj2 of 0.994 and a maximum relative error below 3.15 %.
Third, an experimental and theoretical analysis was performed on a shell-and-tube type gas-to-gas humidifier module applied in a 95 kW-class FCEV. The humidifier, featuring a polysulfone hollow fiber membrane with hydrophilic and non-fluorinated properties, was evaluated under varying inlet temperature, relative humidity, and temperature differences to assess its effect on heat and mass transfer rates and the approach dew point temperature (ADT). The ADT was observed to increase from 12.42 to 15.89 ℃ as the flow rate rose from 1,000 to 3,400 L/min under a 15 ℃ temperature difference, with peak performance at lower flow rates. A new dual-mode sorption model incorporating the solution-diffusion mechanism was developed to account for temperature effects, achieving a relative error of less than 5 %. Additionally, the dynamic response to step changes in flow rate was accurately predicted, reflecting the humidifier’s adaptability under load variation conditions.
Finally, the BOP system, which includes the air compressor, intercooler, coolant pump, radiator, and fan pump, was modeled using both component-level and vehicle-level experimental data. The air compressor was characterized through single-component testing and implemented as a lumped, map-based model. The intercooler and radiator were modeled using a quasi-dynamic approach based on the effectiveness-NTU method, with a cross-flow heat exchanger configuration. These models were validated against experimental data obtained from vehicle tests under realistic driving conditions. The resulting BOP models were integrated into a unified PEMFC system model, enabling accurate prediction of system-level behavior across various operating conditions. The developed PEMFC system model offers a pathway to enhance the energy efficiency and reliability of commercial FCEVs.

목차 (Table of Contents)

• Chapter 1. Introduction 1
• 1.1. Background and motivation 1
• 1.2. Literature review 8
• 1.2.1. Water transport in membranes 8
• 1.2.2. Membrane humidifier in PEMFC system 13
• 1.3. Research objectives 17
• 1.4. Structure of dissertation 19
• Chapter 2. Experiment 22
• 2.1. Experimental setup and materials 22
• 2.1.1. Measurement of the water transport properties 22
• 2.1.2. PEMFC single-cell 30
• 2.1.3. Balance of plant (BOP) system 32
• 2.1.3.1. Air compressor 32
• 2.1.3.2. Intercooler 34
• 2.1.3.3. Membrane humidifier 37
• 2.2. Experimental procedures and conditions 41
• 2.2.1. Measurement of the water transport properties 41
• 2.2.2. PEMFC single-cell 45
• 2.2.3. Balance of plant (BOP) system 47
• 2.2.3.1. Air compressor and intercooler 47
• 2.2.3.2. Membrane humidifier 50
• 2.3. Measurement of water vapor sorption and isotherm data analysis 54
• 2.3.1. Reinforced composite membrane for PEMFC 54
• 2.3.1.1. Measurement of water vapor sorption 54
• 2.3.1.2. Isotherm model description 55
• 2.3.1.3. Characteristics of water vapor isotherm in reinforced composite membrane 59
• 2.3.2. Polysulfone membrane for membrane humidifier 65
• 2.3.2.1. Measurement of the water vapor sorption 65
• 2.3.2.2. Isotherm model description 66
• 2.3.2.3. Characteristics of water vapor isotherm in polysulfone membrane 67
• Chapter 3. Theoretical model 71
• 3.1. PEMFC single-cell model 71
• 3.1.1. Transport equation in bulk streams 71
• 3.1.2. Electrochemical model in PEMFC single-cell 75
• 3.1.3. Water transport model 78
• 3.1.3.1. Water vapor diffusion coefficient in gas diffusion layers and catalyst layers 79
• 3.1.3.2. Water diffusion coefficient in membrane 81
• 3.1.3.3. Electro-osmotic drag coefficient in membrane 83
• 3.1.3.4. Ionic conductivity in membrane 84
• 3.1.3.5. Capillary pressure in porous media 85
• 3.1.4. PEMFC stack model in fuel cell electric vehicle: scale-up 87
• 3.1.4.1. Heat transfer rate through the gas and coolant channels 87
• 3.1.4.2. Mass transfer rate through the gas channel 89
• 3.1.5. Estimation of the model parameters 90
• 3.2. Balance of plant (BOP) system model 91
• 3.2.1. Air compressor 91
• 3.2.2. Intercooler 93
• 3.2.3. Membrane humidifier 97
• 3.2.3.1. Transport equations of shell and tube side bulk streams 97
• 3.2.3.2. Heat transport through the shell and tube side boundary layer 101
• 3.2.3.3. Heat transport across the membrane 103
• 3.2.3.4. Mass transport through the shell and tube side boundary layer 104
• 3.2.3.5. Mass transport across the membrane: solution-diffusion model 106
• 3.2.3.6. Estimation of the model parameters 108
• 3.2.4. Coolant and radiator fan pump 109
• 3.2.5. Radiator 110
• Chapter 4. Results and discussions 111
• 4.1. Analysis of water transport properties 111
• 4.1.1. Water diffusion coefficient 112
• 4.1.2. Electro-osmotic drag coefficient 115
• 4.1.3. Ionic conductivity 119
• 4.1.4. Comparison with Nafion-based properties 123
• 4.2. System-level performance analysis: PEMFC single-cell to stack 126
• 4.2.1. Analysis on PEMFC single-cell performance 126
• 4.2.1.1. Effects of operating conditions 128
• 4.2.1.2. Spatial variations on the through-plane 134
• 4.2.2. Validation of the stack model in a fuel cell electric vehicle 137
• 4.2.3. Dynamic behavior under transient states 140
• 4.2.3.1. Transient response of temperature and stack voltage 142
• 4.2.3.2. Transient response of water transport 145
• 4.3. Analysis of balance of plant (BOP) system 148
• 4.3.1. Air supply system: air compressor and intercooler 148
• 4.3.2. Membrane humidifier 155
• 4.3.2.1. Characteristics of polysulfone membrane 155
• 4.3.2.2. Parametric study: steady-state results 159
• 4.3.2.3. Dynamic behavior under transient states 171
• 4.3.3. Thermal management system (TMS) 174
• 4.3.4. Analysis of vehicle system efficiency in FCEV 179
• Chapter 5. Conclusions 182
• Bibliography 188
• 국문 초록 203