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A model predicting performance of proton exchange membrane fuel cell stack thermal systems
Applied Thermal Engineering 24 (2004) 501–513 www.elsevier.com/locate/apthermeng
A model predicting performance of proton exchange membrane fuel cell stack thermal systems Yangjun Zhang *, Minggao Ouyang, Qingchun Lu, Jianxi Luo, Xihao Li Department of Automotive Engineering, Tsinghua University, Beijing 100084, China Received 1 May 2003; accepted 17 October 2003
Abstract A technique for modeling proton exchange membrane (PEM) fuel cell stack thermal systems is presented to determine the fundamental thermal–physical behavior of the thermal systems, and to investigating the system parameters. The fuel cell stack is represented by a lumped thermal mass model. The model allows an assessment of the effect of operating parameters (stack power output, cooling water flow rate, air flow rate, and environmental temperature) and parameter interactions on the system thermal performance. The model represents a useful tool to determine the operating temperatures of the various components of the thermal system, and thus to fully assess the performance of the thermal system, especially when investigating applications that have highly dynamic operating conditions, such as automobiles. The model has been applied to determine the thermal performance of an experimental PEM fuel cell stack thermal system. The model is validated by comparing model results with experimental measurements. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Proton exchange membrane fuel cells; Thermal systems; Mathematical modeling
1. Introduction Fuel cells have emerged as a potential replacement for the internal combustion engine in vehicles because they are clean, energy efficient, fuel flexible. The proton exchange membrane (PEM) fuel cell is the focus of current development efforts because it is capable of higher power density and faster start-up than other fuel cells [1–5].
*
Corresponding author. Tel.: +86-10-62792333; fax: +86-10-62785708. E-mail address: [email protected] (Y.J. Zhang).
1359-4311/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2003.10.013
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Nomenclature A C cf D e H h I k M m_ n p Pe Pe;sys q_ T u V Vc Greek e q n DTm
surface area, m2 average specific heat capacity, J/(kg K) skin friction coefficient diameter, m internal energy per unit mass, J/kg total enthalpy, J convective heat transfer coefficient, W/(m2 K) stack current output, A overall heat transfer coefficient, W/(m2 K) mass, kg mass flow rate, kg/s number of cells in a fuel cell stack pressure, Pa stack power output, W stack system net power output, W heat rate, W temperature, K velocity, m/s volume, m3 average voltage of one cell in a stack, V letters thermal coefficient fluid density, kg/m3 pressure loss coefficient overall temperature difference, K
Subscripts a air env environment f final value following a step change I value immediately after a step change rad radiator w water 1, 3 inlet 2, 4 outlet A PEM fuel cell is an electrochemical device in which the energy of a chemical reaction is converted directly into electricity. By combining hydrogen fuel with oxygen from air, electricity is formed, without combustion of any form [6]. Water and heat are the only by-products when hydrogen is used as the fuel source. PEM fuel cells operate at low temperatures (less than 100 °C), allowing faster start-ups and immediate responses to changes in the demand for power. PEM fuel
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cells have been demonstrated in systems ranging in size from 1 W to 250 kW. The first practical application for PEM fuel cells was in the Gemini space program [7]. They are ideally suited to transportation applications. With demonstration programs underway and intensive development programs at vehicle manufacturers, research institutes and universities, significant progress has been made in the development of PEM fuel cell stack systems over the past years [8–10]. However, key technical challenges still remain for PEM fuel cell stack systems to be viable for transportation applications. One of the technical issues in fuel cell stack system development is thermal management [11,12]. Proper thermal management is essential for maximizing the performance of a fuel cell stack system. Essentially, one can view the issue of thermal management in automotive fuel cell stack systems at two levels––at the cell level to ensure proper membrane hydration and thereby ensure good conductivity of the membrane, and at the system level to keep the stack from heating up of the fuel cell stack system. Obviously, the requirements at one level play into the requirements at the other level. Many parameters are associated with automotive fuel cell stack system thermal management; parameters are anything that affects the design or performance of the thermal system. To understand the relative importance of the parameters and parameter interactions an investigation of the parameters is needed [13]. For automotive use, if start-up, shut-down or control processes are considered, the knowledge of the transient behaviour becomes important. An investigative technique that is well suited for these tasks is mathematical modeling. This is because a model can be developed that is easily changed, allowing different configurations of a system to be simulated. This reduces the time and cost associated with parameter and transient behaviour investigations. Several attempts have been made to develop mathematical models for PEM fuel cells (e.g., Refs. [14–16]). Their main focus is to investigate electrochemical processes of single fuel cells. These models model physical processes using equations derived from basic principles and experimentally determined constants. There exist some thermal models of PEM fuel cell stacks [17–22]. These models typically treat the cell stack as a process unit, trying to develop models based on electrical performance and the inlet–outlet stream physical characteristics. The calculations required for these models are too extensive to be used in a comprehensive model of a complete stack. A need exists for a technique for determining PEM fuel cell stack thermal performance that does not require a large number of calculations. In addition, the technique needs to be able to be integrated into a numerical model of complete fuel cell stack thermal system so that complete fuel cell stack thermal systems may be modeled. The information will be provided about heat transfer through the various thermal system components and the interactions between them. Thus, it is possible to determine the operating temperatures of the various components of the thermal system, and thus to fully assess the performance of the thermal system, especially when investigating applications that have highly dynamic operating conditions, such as automobiles. Consequently the objective of this investigation was to develop such a technique.
2. Thermal system models The PEM fuel stack thermal system typically consists of a PEM fuel cell stack, a radiator, a fan, coupled by a circulating flowstream with pump and water tank. The system is used for transferring
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the fuel cell stack heat indirectly from a hot coolant flow stream to a cold airflow stream. The schematic of the fuel cell stack thermal system is shown in Fig. 1. A technique for numerically modeling the PEM fuel stack thermal performance, developed specially to be implemented as part of a numerical model of a complete fuel cell stack thermal system, is presented. And a suite of dynamic models are presented to describe the behavior of the other thermal system components, such as radiator, pipes, and flowspits, etc. All of the modules are independent of each other so components can be changed without rewriting an entire model. This makes a model developed using this technique easy to change, an asset when used for parameter investigations and when modifications to a model are required to account for technical advances in thermal systems. 2.1. Fuel cell stack Assuming that the temperature and pressure distributions etc., are uniform in the space of the fuel cell stack, the fuel cell stack is represented by lumped thermal mass model, which has the heat transfer and pressure loss characteristics of the elements. Heat is produced when a fuel cell stack operates. If all the enthalpy of reaction of a hydrogen fuel cell were converted into electrical energy, then the output voltage would be 1.48 V if the water product were in liquid form, or 1.25 V if the water product were in vapour form [10]. It clearly follows that the difference between the actual cell voltage and this voltage represents that the energy that is not converted into electricity––i.e., the energy that is converted into heat instead. m W,2 T W,2 P W,2
m W,1 T W,1 P W,1
Stack Pump
Tank
circulating water flowstream
external air flowstream m W,4 T W,4 P W,4
ma,1 T a,1 P a,1
m W,3 T W,3 P W,3
Radiator m a,2 T a,2 P a,2 Fig. 1. Schematic diagram of a fuel stack thermal system.
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During fuel cell operation, especially at high current densities, liquid water is likely to appear in the cathode, resulting in two-phase transport phenomena. However, in our test activities, the cases where water finally ends in liquid form are few. Here just consider the vapour case for simple. And this means the cooling effect of water evaporation has been taken into account. It also means that energy is leaving the fuel in three forms, electricity, ordinary ‘‘sensible’’ heat, and in the latent heat of the water vapour. For a stack of n cells at current I, the heat generated is thus q_ ¼ nIð1:25 Vc Þ In terms of electrical power, Eq. (1) becomes 1:25 1 q_ ¼ Pe Vc
ð1Þ
ð2Þ
Neglecting the heat loss from the stack surface to the environment, thermal energy balances around the fuel cell stack, in a steady-state, can be written as: ð3Þ
q_ ¼ q_ w The heat delivered by the cooling water is, q_ w ¼ ðhAÞw ðTstack 0:5ðTw;1 þ Tw;2 ÞÞ
ð4Þ
Here the arithmetic mean temperature difference may be substituted by the log mean temperature difference for more effective. The physical principle of mass flow applied to the fuel cell stack model, we have the continuity equation m_ w;1 ¼ m_ w;2 ¼ m_ w
ð5Þ
The pressure loss through the fuel cell stack is considered by an automatically calibrated orifice at the exit of the element block. The momentum equation can be written as pw;1 pw;2
qu2w;1 ¼n 2
ð6Þ
Eqs. (1)–(6) describe the steady-state equilibrium conditions of the fuel cell stack. An unsteadystate energy balance is the extension of the steady-state thermal model by addition of an accumulation term, such that dTstack ð7Þ MC ¼ q_ q_ w dt where M is the total mass of the fuel cell stack, C is the average specific heat of the stack, and dTstack =dt is the temperature change with respect time. The estimated value of MC in the accumulation term may be determined by using the summed Mi Ci values of the individual components of the fuel cell stack such as the graphite and stainless steel. And the MC value may also be measured using an experimental approach by rearranging Eq. (7):
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q_ f q_ w;f MC ¼ dTstack dt i
ð8Þ
where the subscript i represents values immediately after a step change in power and the subscript f represents the final values following a step change in power. The transient model may be obtained by coupling the steady-state thermal model as a function of time with the new accumulation term from Eq. (7) giving: dTstack 1 ðq_ q_ w Þ ¼ MC dt
ð9Þ
2.2. Radiator Since the radiator simulation will be applied to system cycle simulations, the main concern of the radiator simulation is predicting the water outlet conditions given the water and air inlet conditions. In the steady-state, the radiator has four temperature variables. These are shown in Fig. 1. Two of these variables (Tw;3 and Ta;1 ) correspond to the entry temperatures of the hot water and cold air streams and two of them to the output of the exchanger (Tw;4 and Ta;2 ). The heat transfer equation for the radiator may be expressed as ð10Þ
q_ ¼ kA DTm
The temperature difference DTm is an overall difference between the temperature of the circulating water and the air temperature, which is averaged over the radiator. The overall temperature difference depends on the radiator configuration. The physical principle of mass flow applied to the radiator model, we have the continuity equation m_ w;3 ¼ m_ w;4 ¼ m_ w ;
m_ a;1 ¼ m_ a;2 ¼ m_ a
ð11Þ
The radiator energy balance, in a steady-state, can be written as q_ ¼ m_ w Cw ðTw;3 Tw;4 Þ ¼ m_ a Ca ðTa;2 Ta;1 Þ
ð12Þ
The pressure loss through the radiator is considered by an automatically calibrated orifice at the exit of the element block. The momentum equation can be written as pw;3 pw;4 ¼ n
qu2w;3 2
ð13Þ
An unsteady-state energy balance is the extension of the steady-state thermal model by including the effects of the radiator wall capacitance MC, dTrad 1 ðm_ w Cw ðTw;3 Tw;4 Þ m_ a Ca ðTa;2 Ta;1 ÞÞ ¼ MC dt
ð14Þ
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2.3. Flow network simulation This section describes the method of flow solution used in pipes and flowspits. The internal network of the whole thermal management system is discretized into many volumes, where each flowspit is represented by a single volume, and every pipe is divided into one or more volumes. These volumes are connected by boundaries. The scalar variables (pressure, temperature, density, etc.) are assumed to be uniform over each volume. The vector variables (mass flux, velocity, mass fraction fluxes, etc.) are calculated for each boundary. The flow calculation involves the solution of the continuity, momentum and energy equations: Continuity: Z Z
qu dA ¼ 0
ð15Þ
boundaries
Momentum: dðquAÞ ¼ dt
dpA þ
qu2 dxA 1 2 n qu A qu dA 4cf boundaries 2 2 D dx
RR
2
ð16Þ
Energy: dðqeV Þ dV ¼p þ dt dt
Z Z
quH dA hAðT Twall Þ
ð17Þ
boundaries
Here assumes that the pipe is round and straight. Flow losses on pipes due to friction along the walls are calculated by considering the Reynolds number and the surface roughness of the walls. The pressure loss coefficient is defined as n¼
p2 p1 1 qu21 2
ð18Þ
where p1 , p2 stand for static pressure at pipe inlet, outlet respectively.
3. Results and discussions The modeling technique described above was specifically designed to aid investigating the parameters and parameter interactions of a fuel cell stack thermal system. The fuel cell stack used in this study was used as the test stack for the electric hybrid power system of Tsinghua Fuel Cell City Bus. The series of experimental runs performed on the stack were done with air and hydrogen in the Fuel Cell Engine Test Facility at Tsinghua University. The design target of the fuel cell stack system net power output is 50 kW. The design specifications of the thermal system are listed in Table 1.
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Table 1 List of parametric coeffiecients for the fuel cell stack thermal system Parameter
Value
Stack Stack system net power output, Pe;sys Output voltage, Vc Heat transfer parameter, ðhAÞw Environmental temperature, Tenv Heat capacity, MC
50 kW 0.625 V 181.8 W/K 30 °C 35.12 kJ/K
Radiator Heat transfer parameter ðhAÞw ðhAÞa Overall heat coefficient, K Heat capacity, MC
1089 W/K 939.9 W/K 288.25 W/(m2 K) 9.17 kJ/K
Others Circulating flow rate, m_ w Airside flow rate, m_ a
3.11 kg/s 1.165 kg/s
3.1. Steady-state behaviour To study the thermal performance of the thermal system, a thermal coefficient e has been defined by means of system thermal efficiency. The system thermal effectiveness e, represents the ratio of the actual heat load to the maximum load that is thermodynamically possible. From this definition it can be shown that the system thermal effectiveness e can be represented by the ratio of the temperature difference that the circulating water stream undergoes, to the maximum temperature driving force that exists in the radiator. The latter term is the difference between stream inlet temperatures. This is defined as Tw;3 Tw;4 ð19Þ e¼ Tw;3 Ta;1
Fig. 2. Thermal coefficient e as a function of air and water flow ratios, for ðm_ max Þwater ¼ 4:55 kg/s, ðm_ max Þair ¼ 3:86 kg/s.
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Fig. 3. Influence of environmental temperature in thermal efficiency for different air and water mass flow rates.
The thermal efficiency is a function of three parameters: airflow rate, cooling water flow rate and the environmental temperature. Fig. 2 shows the thermal efficiency values for different air and water rates, for the same environmental temperature. As expected, the efficiency increases with air flow rate and decreases with an increase in water flow rate (due to a decrease in water temperature). The environmental temperature has an influence in system efficiency which is shown in Fig. 3. At a relative airflow rate of ðm_ =m_ max Þair ¼ 0:27, the efficiency decreases slightly with environmental temperature for different water flow rates, and the decrease is linear. However, at a relative airflow rate of ðm_ =m_ max Þair ¼ 1:00, the efficiency decreases steeply for different water flow rates. It also indicates the increased influence of environmental temperature with decreasing water flow rate. 3.2. Transient behaviour The transient behavior is studied for the thermal system shown in Fig. 1. The system has three input signals and one output signal. The one output signal is radiator outlet temperature of coolant flow stream, and the three input signals are: (1) flow rate perturbation of water stream (i.e., perturbation of pump flow rate); (2) flow rate perturbation of radiator airside flow stream (i.e., perturbation of fan flow rate); (3) fuel stack perturbation of fuel cell stack power output. For control applications disturbances occurring during steady-state operation are of great importance. Therefore a steady-state operating condition is chosen as the initial state. Fig. 4 shows the system response to a flow rate step increasing perturbation of the circulating fluid. The water flow rate step up from 2 to 4 kg/s. The radiator outlet temperature of water flow stream Tw;4 increases until a new steady-state is reached. Fig. 5 shows the radiator airside flow rate step up from 1.0 to 1.5 kg/s, Tw;4 decreases until a new steady-state is reached. Fig. 6 shows the fuel cell stack power step up from 40 to 50 kW/s. For vehicle use, the fuel cell stack is tested with a test cycle in the Fuel Cell Engine Test Facility at Tsinghua University. The test cycle includes several engine work conditions, such as idle, part load, full load, etc. Fig. 7(a) shows the stack power output during a test cycle. At the full load of
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Fig. 4. Transient plot for stack cooling water flow rate step up from 2 to 4 kg/s.
Fig. 5. Transient plot for radiator airside flow rate step up from 1.0 to 1.5 kg/s.
Fig. 6. Transient plot for fuel cell stack power step up from 40 to 50 kW.
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fuel cell engine condition, the fuel cell system net power output is near 50 kW, and the fuel cell stack output is about 70 kW. During the test cycle, the circulating flow rate keeps constant, m_ w ¼ 3:11 kg/s. However, the radiator airside cooling flow rate is changed by turn on/off the cooling fan, or controlling the fan speed during the test cycle. Fig. 7(b) gives out the controlled airside flow during the test cycle. The experimental and calculated stack outlet water temperatures are shown in Fig. 8. A comparison of the trends predicted by the model to the trends associated with the experimental results showed that the model predictions matched the experimental results. Further analysis of the calculational results indicates that the influence of system heat capacity in the system transient behaviour is significant, which means that the stack structure, and materials are the key factors to the transient thermal performance of the system.
Fig. 7. The stack power output and the radiator airside flow rate during a test cycle: (a) stack power output, (b) radiator airside flow rate.
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Fig. 8. Transient plot for stack outlet water temperature during the test cycle.
4. Conclusions In this paper a model of the thermal behaviour of the PEMFC stack thermal system, i.e., the PEMFC stack coupled with radiator, pump, fan, etc., is developed. It will enable the variation of the temperature of the PEMFC stack as well as the other components of the thermal system. The model allows to study the influence of working parameters on the system thermal performance. The model can be used to predict the steady-state performance of the thermal system for different combinations of operating conditions. The model has been applied to determine the thermal performance of an experimental fuel cell stack thermal system. The thermal efficiency increases with air flow rate, decreases with an increase in water flow rate, and decreases slightly with environmental temperature. If the system undergoes a perturbation, such as the stack initial start-up, a large step in power output, shut-down, or the fan start-up, shut-down, etc., the model will be able to generate transient information such as stack outlet cooling water temperature as a function of time, etc. The model is validated by comparing model results with experimental measurements.
Acknowledgements This work was supported by a grant 2001AA501100, 863-project from the Department of Science & Technology of China. References [1] T. Yokoyama, Y. Naganuma, K. Kuriyama, M. Arimoto, Development of fuel-cell bus, SAE Paper 2003-01-0417. [2] M. Ogburn, D.J. Nelson, W. Luttrell, B. King, S. Postle, R. Fahrenkrog, Systems integration and performance issues in a fuel cell hybrid electric vehicle, SAE Paper 2000-01-0376.
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[3] J.K. Seong, O.B. Soo, Fuel economy and life-cycle cost analysis of a fuel cell hybrid vehicle, Journal of Power Sources 105 (1) (2002) 58–65. [4] E. Per, R. Monika, The fuel cell vehicle analysis of energy use, emissions and cost, International Journal of Hydrogen Energy 23 (5) (1998) 381–385. [5] J.M. Ogden, M.M. Steinnbugler, T.G. Kreutz, A comparison of hydrogen, methanol and gasoline as fuels for fuel cell vehicles: implications for vehicle design and infrastructure development, Journal of Power Sources 79 (2) (1999) 143–168. [6] J. Larminie, A. Dicks, Fuel Cell Systems Explained, John Wiley & Sons, Ltd, 2002. [7] M. Warshay, P.R. Prokopius, The fuel cell in space: yesterday, today and tomorrow, Journal of Power Sources 29 (1–2) (1990) 193–200. [8] US Department of Energy, 2000 Transportation Fuel Cell Power Systems Annual Progress Report, October 2000. [9] US Department of Energy, 2001 Transportation Fuel Cell Power Systems Annual Progress Report, December 2001. [10] M. Nadal, F. Barbir, Development of a hybrid fuel cell/battery powered electric vehicle, International Journal of Hydrogen Energy 21 (6) (1996) 497–505. [11] Y.J. Zhang, M.G. Ouyang, J.X. Luo, Z. Zhang, Y.J. Wang, Mathematical modeling of vehicle fuel cell power system thermal management, SAE Paper 2003-01-1146. [12] R. Andrew, X.G. Li, Mathematical modeling of proton exchange membrane fuel cells, Journal of Power Sources 102 (1–2) (2001) 82–96. [13] J.C. Amphlett, R.M. Baumert, R.F. Mann, B.A. Peppley, P.R. Roberge, Parametric modeling of the performance of a 5-kW proton exchange membrane fuel cell stack, Journal of Power Sources 49 (1994) 349–356. [14] J.C. Amphlett, R.F. Mann, B.A. Peppley, P.R. Roberge, A. Rodrigues, A model predicting transient responses of proton exchange membrane fuel cells, Journal of Power Sources 61 (1996) 183–188. [15] J.H. Lee, T.R. Lalk, A.J. Appleby, Modeling electrochemical performance in large scale proton exchange membrane fuel cell stacks, Journal of Power Sources 70 (1998) 258–268. [16] J.H. Lee, T.R. Lalk, Modeling fuel cell stack systems, Journal of Power Sources 73 (1998) 229–241. [17] G. Maggio, V. Recupero, C. Mantegazza, Modeling of temperature distribution in a solid polymer electrolyte fuel cell stack, Journal of Power Sources 62 (1996) 167–174. [18] T.V. Nguyen, R.E. White, A water and heat management model for proton exchange membrane fuel cells, Journal of the Electrochemical Society 140 (8) (1993) 2178–2186. [19] N. Djilali, D.M. Lu, Influence of heat transfer on gas and water transport in fuel cells, International Journal of Thermal Sciences 41 (2002) 29–40. [20] M. Ogburn, D.J. Nelson, W. Luttrell, et al., Systems integration and performance issues in a fuel cell hybrid electric vehicle, SAE Paper 2000-01-0376. [21] N.S. Ap, Influence of front end vehicle, fan and fan shroud on the cooling system of fuel cell electric vehicle (FCEV), EVS 18, Berlin, 2001. [22] M.H. Fronk, D.L. Wetter, D.A. Masten, A. Bosco, PEM fuel cell system solutions for transportation, SAE Paper 2000-01-0373.
A model predicting performance of proton exchange membrane fuel cell stack thermal systems Yangjun Zhang *, Minggao Ouyang, Qingchun Lu, Jianxi Luo, Xihao Li Department of Automotive Engineering, Tsinghua University, Beijing 100084, China Received 1 May 2003; accepted 17 October 2003
Abstract A technique for modeling proton exchange membrane (PEM) fuel cell stack thermal systems is presented to determine the fundamental thermal–physical behavior of the thermal systems, and to investigating the system parameters. The fuel cell stack is represented by a lumped thermal mass model. The model allows an assessment of the effect of operating parameters (stack power output, cooling water flow rate, air flow rate, and environmental temperature) and parameter interactions on the system thermal performance. The model represents a useful tool to determine the operating temperatures of the various components of the thermal system, and thus to fully assess the performance of the thermal system, especially when investigating applications that have highly dynamic operating conditions, such as automobiles. The model has been applied to determine the thermal performance of an experimental PEM fuel cell stack thermal system. The model is validated by comparing model results with experimental measurements. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Proton exchange membrane fuel cells; Thermal systems; Mathematical modeling
1. Introduction Fuel cells have emerged as a potential replacement for the internal combustion engine in vehicles because they are clean, energy efficient, fuel flexible. The proton exchange membrane (PEM) fuel cell is the focus of current development efforts because it is capable of higher power density and faster start-up than other fuel cells [1–5].
*
Corresponding author. Tel.: +86-10-62792333; fax: +86-10-62785708. E-mail address: [email protected] (Y.J. Zhang).
1359-4311/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2003.10.013
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Y.J. Zhang et al. / Applied Thermal Engineering 24 (2004) 501–513
Nomenclature A C cf D e H h I k M m_ n p Pe Pe;sys q_ T u V Vc Greek e q n DTm
surface area, m2 average specific heat capacity, J/(kg K) skin friction coefficient diameter, m internal energy per unit mass, J/kg total enthalpy, J convective heat transfer coefficient, W/(m2 K) stack current output, A overall heat transfer coefficient, W/(m2 K) mass, kg mass flow rate, kg/s number of cells in a fuel cell stack pressure, Pa stack power output, W stack system net power output, W heat rate, W temperature, K velocity, m/s volume, m3 average voltage of one cell in a stack, V letters thermal coefficient fluid density, kg/m3 pressure loss coefficient overall temperature difference, K
Subscripts a air env environment f final value following a step change I value immediately after a step change rad radiator w water 1, 3 inlet 2, 4 outlet A PEM fuel cell is an electrochemical device in which the energy of a chemical reaction is converted directly into electricity. By combining hydrogen fuel with oxygen from air, electricity is formed, without combustion of any form [6]. Water and heat are the only by-products when hydrogen is used as the fuel source. PEM fuel cells operate at low temperatures (less than 100 °C), allowing faster start-ups and immediate responses to changes in the demand for power. PEM fuel
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cells have been demonstrated in systems ranging in size from 1 W to 250 kW. The first practical application for PEM fuel cells was in the Gemini space program [7]. They are ideally suited to transportation applications. With demonstration programs underway and intensive development programs at vehicle manufacturers, research institutes and universities, significant progress has been made in the development of PEM fuel cell stack systems over the past years [8–10]. However, key technical challenges still remain for PEM fuel cell stack systems to be viable for transportation applications. One of the technical issues in fuel cell stack system development is thermal management [11,12]. Proper thermal management is essential for maximizing the performance of a fuel cell stack system. Essentially, one can view the issue of thermal management in automotive fuel cell stack systems at two levels––at the cell level to ensure proper membrane hydration and thereby ensure good conductivity of the membrane, and at the system level to keep the stack from heating up of the fuel cell stack system. Obviously, the requirements at one level play into the requirements at the other level. Many parameters are associated with automotive fuel cell stack system thermal management; parameters are anything that affects the design or performance of the thermal system. To understand the relative importance of the parameters and parameter interactions an investigation of the parameters is needed [13]. For automotive use, if start-up, shut-down or control processes are considered, the knowledge of the transient behaviour becomes important. An investigative technique that is well suited for these tasks is mathematical modeling. This is because a model can be developed that is easily changed, allowing different configurations of a system to be simulated. This reduces the time and cost associated with parameter and transient behaviour investigations. Several attempts have been made to develop mathematical models for PEM fuel cells (e.g., Refs. [14–16]). Their main focus is to investigate electrochemical processes of single fuel cells. These models model physical processes using equations derived from basic principles and experimentally determined constants. There exist some thermal models of PEM fuel cell stacks [17–22]. These models typically treat the cell stack as a process unit, trying to develop models based on electrical performance and the inlet–outlet stream physical characteristics. The calculations required for these models are too extensive to be used in a comprehensive model of a complete stack. A need exists for a technique for determining PEM fuel cell stack thermal performance that does not require a large number of calculations. In addition, the technique needs to be able to be integrated into a numerical model of complete fuel cell stack thermal system so that complete fuel cell stack thermal systems may be modeled. The information will be provided about heat transfer through the various thermal system components and the interactions between them. Thus, it is possible to determine the operating temperatures of the various components of the thermal system, and thus to fully assess the performance of the thermal system, especially when investigating applications that have highly dynamic operating conditions, such as automobiles. Consequently the objective of this investigation was to develop such a technique.
2. Thermal system models The PEM fuel stack thermal system typically consists of a PEM fuel cell stack, a radiator, a fan, coupled by a circulating flowstream with pump and water tank. The system is used for transferring
504
Y.J. Zhang et al. / Applied Thermal Engineering 24 (2004) 501–513
the fuel cell stack heat indirectly from a hot coolant flow stream to a cold airflow stream. The schematic of the fuel cell stack thermal system is shown in Fig. 1. A technique for numerically modeling the PEM fuel stack thermal performance, developed specially to be implemented as part of a numerical model of a complete fuel cell stack thermal system, is presented. And a suite of dynamic models are presented to describe the behavior of the other thermal system components, such as radiator, pipes, and flowspits, etc. All of the modules are independent of each other so components can be changed without rewriting an entire model. This makes a model developed using this technique easy to change, an asset when used for parameter investigations and when modifications to a model are required to account for technical advances in thermal systems. 2.1. Fuel cell stack Assuming that the temperature and pressure distributions etc., are uniform in the space of the fuel cell stack, the fuel cell stack is represented by lumped thermal mass model, which has the heat transfer and pressure loss characteristics of the elements. Heat is produced when a fuel cell stack operates. If all the enthalpy of reaction of a hydrogen fuel cell were converted into electrical energy, then the output voltage would be 1.48 V if the water product were in liquid form, or 1.25 V if the water product were in vapour form [10]. It clearly follows that the difference between the actual cell voltage and this voltage represents that the energy that is not converted into electricity––i.e., the energy that is converted into heat instead. m W,2 T W,2 P W,2
m W,1 T W,1 P W,1
Stack Pump
Tank
circulating water flowstream
external air flowstream m W,4 T W,4 P W,4
ma,1 T a,1 P a,1
m W,3 T W,3 P W,3
Radiator m a,2 T a,2 P a,2 Fig. 1. Schematic diagram of a fuel stack thermal system.
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During fuel cell operation, especially at high current densities, liquid water is likely to appear in the cathode, resulting in two-phase transport phenomena. However, in our test activities, the cases where water finally ends in liquid form are few. Here just consider the vapour case for simple. And this means the cooling effect of water evaporation has been taken into account. It also means that energy is leaving the fuel in three forms, electricity, ordinary ‘‘sensible’’ heat, and in the latent heat of the water vapour. For a stack of n cells at current I, the heat generated is thus q_ ¼ nIð1:25 Vc Þ In terms of electrical power, Eq. (1) becomes 1:25 1 q_ ¼ Pe Vc
ð1Þ
ð2Þ
Neglecting the heat loss from the stack surface to the environment, thermal energy balances around the fuel cell stack, in a steady-state, can be written as: ð3Þ
q_ ¼ q_ w The heat delivered by the cooling water is, q_ w ¼ ðhAÞw ðTstack 0:5ðTw;1 þ Tw;2 ÞÞ
ð4Þ
Here the arithmetic mean temperature difference may be substituted by the log mean temperature difference for more effective. The physical principle of mass flow applied to the fuel cell stack model, we have the continuity equation m_ w;1 ¼ m_ w;2 ¼ m_ w
ð5Þ
The pressure loss through the fuel cell stack is considered by an automatically calibrated orifice at the exit of the element block. The momentum equation can be written as pw;1 pw;2
qu2w;1 ¼n 2
ð6Þ
Eqs. (1)–(6) describe the steady-state equilibrium conditions of the fuel cell stack. An unsteadystate energy balance is the extension of the steady-state thermal model by addition of an accumulation term, such that dTstack ð7Þ MC ¼ q_ q_ w dt where M is the total mass of the fuel cell stack, C is the average specific heat of the stack, and dTstack =dt is the temperature change with respect time. The estimated value of MC in the accumulation term may be determined by using the summed Mi Ci values of the individual components of the fuel cell stack such as the graphite and stainless steel. And the MC value may also be measured using an experimental approach by rearranging Eq. (7):
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q_ f q_ w;f MC ¼ dTstack dt i
ð8Þ
where the subscript i represents values immediately after a step change in power and the subscript f represents the final values following a step change in power. The transient model may be obtained by coupling the steady-state thermal model as a function of time with the new accumulation term from Eq. (7) giving: dTstack 1 ðq_ q_ w Þ ¼ MC dt
ð9Þ
2.2. Radiator Since the radiator simulation will be applied to system cycle simulations, the main concern of the radiator simulation is predicting the water outlet conditions given the water and air inlet conditions. In the steady-state, the radiator has four temperature variables. These are shown in Fig. 1. Two of these variables (Tw;3 and Ta;1 ) correspond to the entry temperatures of the hot water and cold air streams and two of them to the output of the exchanger (Tw;4 and Ta;2 ). The heat transfer equation for the radiator may be expressed as ð10Þ
q_ ¼ kA DTm
The temperature difference DTm is an overall difference between the temperature of the circulating water and the air temperature, which is averaged over the radiator. The overall temperature difference depends on the radiator configuration. The physical principle of mass flow applied to the radiator model, we have the continuity equation m_ w;3 ¼ m_ w;4 ¼ m_ w ;
m_ a;1 ¼ m_ a;2 ¼ m_ a
ð11Þ
The radiator energy balance, in a steady-state, can be written as q_ ¼ m_ w Cw ðTw;3 Tw;4 Þ ¼ m_ a Ca ðTa;2 Ta;1 Þ
ð12Þ
The pressure loss through the radiator is considered by an automatically calibrated orifice at the exit of the element block. The momentum equation can be written as pw;3 pw;4 ¼ n
qu2w;3 2
ð13Þ
An unsteady-state energy balance is the extension of the steady-state thermal model by including the effects of the radiator wall capacitance MC, dTrad 1 ðm_ w Cw ðTw;3 Tw;4 Þ m_ a Ca ðTa;2 Ta;1 ÞÞ ¼ MC dt
ð14Þ
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2.3. Flow network simulation This section describes the method of flow solution used in pipes and flowspits. The internal network of the whole thermal management system is discretized into many volumes, where each flowspit is represented by a single volume, and every pipe is divided into one or more volumes. These volumes are connected by boundaries. The scalar variables (pressure, temperature, density, etc.) are assumed to be uniform over each volume. The vector variables (mass flux, velocity, mass fraction fluxes, etc.) are calculated for each boundary. The flow calculation involves the solution of the continuity, momentum and energy equations: Continuity: Z Z
qu dA ¼ 0
ð15Þ
boundaries
Momentum: dðquAÞ ¼ dt
dpA þ
qu2 dxA 1 2 n qu A qu dA 4cf boundaries 2 2 D dx
RR
2
ð16Þ
Energy: dðqeV Þ dV ¼p þ dt dt
Z Z
quH dA hAðT Twall Þ
ð17Þ
boundaries
Here assumes that the pipe is round and straight. Flow losses on pipes due to friction along the walls are calculated by considering the Reynolds number and the surface roughness of the walls. The pressure loss coefficient is defined as n¼
p2 p1 1 qu21 2
ð18Þ
where p1 , p2 stand for static pressure at pipe inlet, outlet respectively.
3. Results and discussions The modeling technique described above was specifically designed to aid investigating the parameters and parameter interactions of a fuel cell stack thermal system. The fuel cell stack used in this study was used as the test stack for the electric hybrid power system of Tsinghua Fuel Cell City Bus. The series of experimental runs performed on the stack were done with air and hydrogen in the Fuel Cell Engine Test Facility at Tsinghua University. The design target of the fuel cell stack system net power output is 50 kW. The design specifications of the thermal system are listed in Table 1.
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Table 1 List of parametric coeffiecients for the fuel cell stack thermal system Parameter
Value
Stack Stack system net power output, Pe;sys Output voltage, Vc Heat transfer parameter, ðhAÞw Environmental temperature, Tenv Heat capacity, MC
50 kW 0.625 V 181.8 W/K 30 °C 35.12 kJ/K
Radiator Heat transfer parameter ðhAÞw ðhAÞa Overall heat coefficient, K Heat capacity, MC
1089 W/K 939.9 W/K 288.25 W/(m2 K) 9.17 kJ/K
Others Circulating flow rate, m_ w Airside flow rate, m_ a
3.11 kg/s 1.165 kg/s
3.1. Steady-state behaviour To study the thermal performance of the thermal system, a thermal coefficient e has been defined by means of system thermal efficiency. The system thermal effectiveness e, represents the ratio of the actual heat load to the maximum load that is thermodynamically possible. From this definition it can be shown that the system thermal effectiveness e can be represented by the ratio of the temperature difference that the circulating water stream undergoes, to the maximum temperature driving force that exists in the radiator. The latter term is the difference between stream inlet temperatures. This is defined as Tw;3 Tw;4 ð19Þ e¼ Tw;3 Ta;1
Fig. 2. Thermal coefficient e as a function of air and water flow ratios, for ðm_ max Þwater ¼ 4:55 kg/s, ðm_ max Þair ¼ 3:86 kg/s.
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Fig. 3. Influence of environmental temperature in thermal efficiency for different air and water mass flow rates.
The thermal efficiency is a function of three parameters: airflow rate, cooling water flow rate and the environmental temperature. Fig. 2 shows the thermal efficiency values for different air and water rates, for the same environmental temperature. As expected, the efficiency increases with air flow rate and decreases with an increase in water flow rate (due to a decrease in water temperature). The environmental temperature has an influence in system efficiency which is shown in Fig. 3. At a relative airflow rate of ðm_ =m_ max Þair ¼ 0:27, the efficiency decreases slightly with environmental temperature for different water flow rates, and the decrease is linear. However, at a relative airflow rate of ðm_ =m_ max Þair ¼ 1:00, the efficiency decreases steeply for different water flow rates. It also indicates the increased influence of environmental temperature with decreasing water flow rate. 3.2. Transient behaviour The transient behavior is studied for the thermal system shown in Fig. 1. The system has three input signals and one output signal. The one output signal is radiator outlet temperature of coolant flow stream, and the three input signals are: (1) flow rate perturbation of water stream (i.e., perturbation of pump flow rate); (2) flow rate perturbation of radiator airside flow stream (i.e., perturbation of fan flow rate); (3) fuel stack perturbation of fuel cell stack power output. For control applications disturbances occurring during steady-state operation are of great importance. Therefore a steady-state operating condition is chosen as the initial state. Fig. 4 shows the system response to a flow rate step increasing perturbation of the circulating fluid. The water flow rate step up from 2 to 4 kg/s. The radiator outlet temperature of water flow stream Tw;4 increases until a new steady-state is reached. Fig. 5 shows the radiator airside flow rate step up from 1.0 to 1.5 kg/s, Tw;4 decreases until a new steady-state is reached. Fig. 6 shows the fuel cell stack power step up from 40 to 50 kW/s. For vehicle use, the fuel cell stack is tested with a test cycle in the Fuel Cell Engine Test Facility at Tsinghua University. The test cycle includes several engine work conditions, such as idle, part load, full load, etc. Fig. 7(a) shows the stack power output during a test cycle. At the full load of
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Fig. 4. Transient plot for stack cooling water flow rate step up from 2 to 4 kg/s.
Fig. 5. Transient plot for radiator airside flow rate step up from 1.0 to 1.5 kg/s.
Fig. 6. Transient plot for fuel cell stack power step up from 40 to 50 kW.
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fuel cell engine condition, the fuel cell system net power output is near 50 kW, and the fuel cell stack output is about 70 kW. During the test cycle, the circulating flow rate keeps constant, m_ w ¼ 3:11 kg/s. However, the radiator airside cooling flow rate is changed by turn on/off the cooling fan, or controlling the fan speed during the test cycle. Fig. 7(b) gives out the controlled airside flow during the test cycle. The experimental and calculated stack outlet water temperatures are shown in Fig. 8. A comparison of the trends predicted by the model to the trends associated with the experimental results showed that the model predictions matched the experimental results. Further analysis of the calculational results indicates that the influence of system heat capacity in the system transient behaviour is significant, which means that the stack structure, and materials are the key factors to the transient thermal performance of the system.
Fig. 7. The stack power output and the radiator airside flow rate during a test cycle: (a) stack power output, (b) radiator airside flow rate.
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Fig. 8. Transient plot for stack outlet water temperature during the test cycle.
4. Conclusions In this paper a model of the thermal behaviour of the PEMFC stack thermal system, i.e., the PEMFC stack coupled with radiator, pump, fan, etc., is developed. It will enable the variation of the temperature of the PEMFC stack as well as the other components of the thermal system. The model allows to study the influence of working parameters on the system thermal performance. The model can be used to predict the steady-state performance of the thermal system for different combinations of operating conditions. The model has been applied to determine the thermal performance of an experimental fuel cell stack thermal system. The thermal efficiency increases with air flow rate, decreases with an increase in water flow rate, and decreases slightly with environmental temperature. If the system undergoes a perturbation, such as the stack initial start-up, a large step in power output, shut-down, or the fan start-up, shut-down, etc., the model will be able to generate transient information such as stack outlet cooling water temperature as a function of time, etc. The model is validated by comparing model results with experimental measurements.
Acknowledgements This work was supported by a grant 2001AA501100, 863-project from the Department of Science & Technology of China. References [1] T. Yokoyama, Y. Naganuma, K. Kuriyama, M. Arimoto, Development of fuel-cell bus, SAE Paper 2003-01-0417. [2] M. Ogburn, D.J. Nelson, W. Luttrell, B. King, S. Postle, R. Fahrenkrog, Systems integration and performance issues in a fuel cell hybrid electric vehicle, SAE Paper 2000-01-0376.
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