Thermodynamic Modeling and Exergy Analysis of A Combined High-Temperature Proton Exchange Membrane Fuel Cell and ORC System for Automotive Applications

A combined system consisting of a high-temperature proton exchange membrane fuel cell (HT-PEMFC) and an organic Rankine cycle (ORC) is provided for automotive applications in this paper. The combined system uses HT-PEMFC stack cathode exhaust gas to preheat the inlet gas and the ORC to recover the waste heat from the stack. The model of the combined system was developed and the feasibility of the model was verified. In addition, the evaluation index of the proposed system was derived through an energy and exergy analysis. The numerical simulation results show that the HT-PEMFC stack, cathode heat exchanger, and evaporator contributed the most to the total exergy loss of the system. These components should be optimized as a focus of future research to improve system performance. The lower current density increased the ecological function and the system efficiency, but reduced the system’s net out-power. A higher inlet temperature and higher hydrogen pressures of the stack and the lower oxygen pressure helped improve the system performance. Compared to the HT-PEFC system without an ORC subsystem, the output power of the combined system was increased by 12.95%.


Introduction
As the global energy crisis and environmental pollution problems become increasingly serious, it is essential to develop and utilize a clean, efficient, and sustainable source of energy [1][2][3][4][5][6]. Hydrogen energy is regarded as an indispensable energy carrier of the future owing to its high heat value, sustainability, and zero pollution [7]. Proton exchange membrane thermal cells (PEMFCs) can efficiently convert hydrogen energy to electricity through chemical reactions. In this context, PEMFCs are viewed to be one of the most promising power conversion devices for fuel cell vehicles (FCVs) because of their high energy efficiency and environmental friendliness [8][9][10][11][12][13][14]. Conventional low-temperature proton exchange membrane fuel cells (LT-PEMFCs) utilize Nafion and other polymer membranes and are limited to an operating temperature range of 333-353 K [15,16]. HT-PEMFCs with phosphoric-acid-doped polybenzimidazole (PA/PBI) membranes operate at higher temperatures and have excellent proton conductivity [17][18][19][20][21]. An HT-PEMFC operating at 393-473 K has significant advantages over an LT-PEMFC [22]: increased CO tolerance [23]; improved electrode reaction kinetics [24]; a simpler system for water and heat management [25]; and higher quality waste heat [26]. The higher quality waste heat produced by the stack offers more possibilities for vehicle energy recovery or other thermal systems [27,28].
In general, the electrical efficiency of the PEMFC is approximately 50%, which indicates that about half of the fuel energy is lost to the environment by way of heat [29].
The key to fuel cell thermal management is to keep the working temperature within a sensible variety as well as to fully utilize the exhaust heat from the stack to enhance the system's efficiency [30]. Waste heat recovery (WHR) technology offers an excellent solution characteristics of the system components and their connections. The analysis methods of energy and exergy were applied to evaluate the system performance. It is stressed that an exergy analysis is an effective method for the study of fuel cell systems. Unlike traditional energy analyses, an exergy analysis is used to determine the limits of system performance and the main sources of exergy loss, and to find the optimal operating conditions. Therefore, the exergy distribution in the combined system can be understood in-depth through an exergy analysis, which helps to better optimize the system. In addition, the performance of the HT-PEMFC system before and after the use of an ORC to recover waste heat was compared. This paper further explored and understood the potential and direction of system improvement based on the exergy analysis. The main work of the following sections is outlined as follows: Section 3.1 gives a schematic diagram of the proposed system; the system model is developed and the exergy analysis method is introduced in Section 3.2; and Section 2 provides a validation and simulation discussion of the model. The main conclusions of this study are presented in Section 4.

Results and Discussion
The input parameters of the single fuel cell in this study are referenced from [40]. The operating conditions of the ORC system in this paper can be found in [33].The data of the combined system model are presented in Table 1. The control variable method was used for the parametric studies of system performance. The inlet temperature of the fuel cell stack, T in , represents the inlet temperature of hydrogen, air, and coolant, T in = T 12 = T 4 = T 15 . Table 1. The input parameters of the combined system model.

Components Parameters Values
HT-PEMFC stack

Model Validation
The auxiliary equipment involved in the system is common in academic research and engineering practices, and the modeling formulas for these components have been widely validated and accepted [48]. Figure 1 shows the comparison between the HT-PEMFC single cell output voltage model, the experimental data in [49], and the modeling results for simulation conditions at 423 K and 448 K (p = 1 atm; DL = 5.6; RH = 0.38%). The comparison results showed that the proposed HT-PEMFC voltage model agreed well with the experimental data. Part of the error was due to the relationship between the limiting current density and the temperature, pressure, and concentration of reactants not being considered in the present model [50]. A comparison of the ORC model for this work and the previous simulation work in [30] is given in Figure 2. The comparison results show that the ORC model in this paper has a certain reliability.  The energy and exergy information of the system components under the defined work conditions are shown in Table 2. It can be seen that the AC was the component that consumed the greatest amount of power out of all the ancillary equipment. Therefore, it is crucial to decrease the power consumption of the AC for system optimization and further study. It is worth mentioning that this system utilized the exhaust and water preheating reaction gas from the fuel cell stack cathode outlet, which reduced the power of the ancillary equipment. Moreover, since the HT-PEMFC stack had a dominant role in causing exergy losses (75.46%), an improvement in the stack energy conversion efficiency is key to optimizing the overall system performance. The heat exchanger and evaporator were the components with the greatest energy loss in the auxiliary equipment, which was because the heat was not sufficiently utilized and was lost to the ambient environment during the heat exchange process. Therefore, it would be meaningful to improve the heat transfer efficiency and find ways to apply heat in future research.  previous simulation work in [30] is given in Figure 2. The comparison results show that the ORC model in this paper has a certain reliability.  The energy and exergy information of the system components under the defined work conditions are shown in Table 2. It can be seen that the AC was the component that consumed the greatest amount of power out of all the ancillary equipment. Therefore, it is crucial to decrease the power consumption of the AC for system optimization and further study. It is worth mentioning that this system utilized the exhaust and water preheating reaction gas from the fuel cell stack cathode outlet, which reduced the power of the ancillary equipment. Moreover, since the HT-PEMFC stack had a dominant role in causing exergy losses (75.46%), an improvement in the stack energy conversion efficiency is key to optimizing the overall system performance. The heat exchanger and evaporator were the components with the greatest energy loss in the auxiliary equipment, which was because the heat was not sufficiently utilized and was lost to the ambient environment during the heat exchange process. Therefore, it would be meaningful to improve the heat transfer efficiency and find ways to apply heat in future research. The energy and exergy information of the system components under the defined work conditions are shown in Table 2. It can be seen that the AC was the component that consumed the greatest amount of power out of all the ancillary equipment. Therefore, it is crucial to decrease the power consumption of the AC for system optimization and further study. It is worth mentioning that this system utilized the exhaust and water preheating reaction gas from the fuel cell stack cathode outlet, which reduced the power of the ancillary equipment. Moreover, since the HT-PEMFC stack had a dominant role in causing exergy losses (75.46%), an improvement in the stack energy conversion efficiency is key to optimizing the overall system performance. The heat exchanger and evaporator were the components with the greatest energy loss in the auxiliary equipment, which was because the heat was not sufficiently utilized and was lost to the ambient environment during the heat exchange process. Therefore, it would be meaningful to improve the heat transfer efficiency and find ways to apply heat in future research.  Figure 3 depicts the variation in different system performances with current density. Referring to Figure 3a, the system output power achieved a maximum at the high current density area, but the energy efficiency and exergy efficiency of the system decreased with a rise in the current density. When the current density j was 8000 A·m 2 , the net output power of the combined system using ORC to recover exhausted heat improved by 12.92%. Furthermore, the energy and exergy efficiency of the combined system increased compared to the HT-PEMFC system alone. It can be observed from Figure 3b that the combined HT-PEMFC and ORC system had a higher energy destruction rate and a lower ecological function in the high current density region. This was mainly because the HT-PEMFC stack generated more heat at high current densities, which resulted in more exergy loss during heat exchange in the evaporator for the combined system. For improved output performance and exergy efficiency of the combined system, it is key to improve the heat transfer efficiency of the evaporator. However, the COP of the combined system was higher than that of the HT-PEMFC system alone. Therefore, waste heat recovery with ORC helps improve the system's performance. The ecological function and exergy destruction rate of the system deteriorated with the growth of the current density. It should be pointed out that the current density j is supposed to be kept small to ensure the good condition of the system performance indicators. In practice, this is often limited by power density requirements, especially for power systems in FCVs where installation space is limited.   Figure 3 depicts the variation in different system performances with current density. Referring to Figure 3a, the system output power achieved a maximum at the high current density area, but the energy efficiency and exergy efficiency of the system decreased with a rise in the current density. When the current density was 8000 A • m , the net output power of the combined system using ORC to recover exhausted heat improved by 12.92%. Furthermore, the energy and exergy efficiency of the combined system increased compared to the HT-PEMFC system alone. It can be observed from Figure 3b that the combined HT-PEMFC and ORC system had a higher energy destruction rate and a lower ecological function in the high current density region. This was mainly because the HT-PEMFC stack generated more heat at high current densities, which resulted in more exergy loss during heat exchange in the evaporator for the combined system. For improved output performance and exergy efficiency of the combined system, it is key to improve the heat transfer efficiency of the evaporator. However, the COP of the combined system was higher than that of the HT-PEMFC system alone. Therefore, waste heat recovery with ORC helps improve the system's performance. The ecological function and exergy destruction rate of the system deteriorated with the growth of the current density. It should be pointed out that the current density is supposed to be kept small to ensure the good condition of the system performance indicators. In practice, this is often limited by power density requirements, especially for power systems in FCVs where installation space is limited.

Effect of Current Density
(a) (b) Figure 3. Effect of current density on system performance. (a) Out-power, energy efficiency, and exergy efficiency; (b) ecological function, , and exergy destruction rate. Figure 3. Effect of current density on system performance. (a) Out-power, energy efficiency, and exergy efficiency; (b) ecological function, COP, and exergy destruction rate.

Influence of Inlet Temperature
The effects of inlet temperature on the output performance for different systems are presented in Figure 4. Figure 4a shows that the system output power increased slightly with an increase in the operating temperature. This was caused by a reduction in the ohmic overvoltage, resulting in higher fuel cell voltage values and thus an increment in the output power. The trend in the energy and exergy efficiency is similar to the output power behavior with a constant input fuel flow rate during temperature variations. The output power and efficiency of the combined system at different operating temperatures were higher compared to the HT-PEMFC standalone system. According to Figure 4b, the performance coefficient of the system COP slightly increased by recovering the exhaust heat from the stack at different temperatures using ORC. In addition, the increase in the inlet temperature contributed to the reduction in the energy destruction rate of the system, which led to a reduction in the energy loss of the system. From Equation (37), the ecological function E increased with a rise in the inlet temperature. Therefore, the system performance can be effectively improved by increasing the stack inlet temperature within a reasonable range.

Influence of Inlet Temperature
The effects of inlet temperature on the output performance for different systems are presented in Figure 4. Figure 4a shows that the system output power increased slightly with an increase in the operating temperature. This was caused by a reduction in the ohmic overvoltage, resulting in higher fuel cell voltage values and thus an increment in the output power. The trend in the energy and exergy efficiency is similar to the output power behavior with a constant input fuel flow rate during temperature variations. The output power and efficiency of the combined system at different operating temperatures were higher compared to the HT-PEMFC standalone system. According to Figure 4b, the performance coefficient of the system slightly increased by recovering the exhaust heat from the stack at different temperatures using ORC. In addition, the increase in the inlet temperature contributed to the reduction in the energy destruction rate of the system, which led to a reduction in the energy loss of the system. From Equation (37), the ecological function increased with a rise in the inlet temperature. Therefore, the system performance can be effectively improved by increasing the stack inlet temperature within a reasonable range.   Figure 5 presents the variations in the output power, energy efficiency, and exergy efficiency with the cathode inlet pressure for different systems. It can be observed from Figure 5a that with an increment in the cathode inlet pressure, the system output power and efficiency decreased. The reasons for this were mainly due to the increased power consumption of the AC, caused by the increase in cathode pressure. According to Table 2, the air compressor was the component with the greatest power consumption, so it is essential to increase the efficiency of the AC and reduce the cathode inlet pressure. As represented in Figure 5b, the decrease in the system's and with increasing cathode inlet pressure was due to the decrease in the net system's output power. Meanwhile, the increase in the cathode inlet pressure also increased the system's exergy destruction rate, which caused an increase in the system's exergy loss. Therefore, the cathode pressure should be lower for both HT-PEMFC systems and combined systems to achieve higher power generation and energy conversion efficiency.  Figure 5 presents the variations in the output power, energy efficiency, and exergy efficiency with the cathode inlet pressure for different systems. It can be observed from Figure 5a that with an increment in the cathode inlet pressure, the system output power and efficiency decreased. The reasons for this were mainly due to the increased power consumption of the AC, caused by the increase in cathode pressure. According to Table 2, the air compressor was the component with the greatest power consumption, so it is essential to increase the efficiency of the AC and reduce the cathode inlet pressure. As represented in Figure 5b, the decrease in the system's COP and E with increasing cathode inlet pressure was due to the decrease in the net system's output power. Meanwhile, the increase in the cathode inlet pressure also increased the system's exergy destruction rate, which caused an increase in the system's exergy loss. Therefore, the cathode pressure should be lower for both HT-PEMFC systems and combined systems to achieve higher power generation and energy conversion efficiency.  Figure 6 displays the variation in the evaluation indexes with the anode inlet pressure for different systems. According to Figure 6a, the output power and efficiency of the system increased with an increase in the cathode inlet pressure. This was because an increase in the cathode inlet pressure was beneficial for increasing the output power of an HT-PEMFC single cell and the pressure regulator for hydrogen without power consumption. It can be seen in Figure 6b that an increment in the anode inlet pressure led to an increase in the ecological function and a reduction in exergy destruction. Therefore, it is essential to keep the anode pressure as high as possible during the operation of the system to achieve better output performance. The combined system had a higher at different anode pressures than the HT-PEMFC system alone.  Figure 7 shows the schematic diagram of the proposed HT-PEMFC and ORC combination system. The system consists of an HT-PEMFC subsystem for generating electrical power and an ORC subsystem for exhaust heat utilization and recovery. The two  Figure 6 displays the variation in the evaluation indexes with the anode inlet pressure for different systems. According to Figure 6a, the output power and efficiency of the system increased with an increase in the cathode inlet pressure. This was because an increase in the cathode inlet pressure was beneficial for increasing the output power of an HT-PEMFC single cell and the pressure regulator for hydrogen without power consumption. It can be seen in Figure 6b that an increment in the anode inlet pressure led to an increase in the ecological function and a reduction in exergy destruction. Therefore, it is essential to keep the anode pressure as high as possible during the operation of the system to achieve better output performance. The combined system had a higher COP at different anode pressures than the HT-PEMFC system alone.  Figure 6 displays the variation in the evaluation indexes with the anode inlet pressure for different systems. According to Figure 6a, the output power and efficiency of the system increased with an increase in the cathode inlet pressure. This was because an increase in the cathode inlet pressure was beneficial for increasing the output power of an HT-PEMFC single cell and the pressure regulator for hydrogen without power consumption. It can be seen in Figure 6b that an increment in the anode inlet pressure led to an increase in the ecological function and a reduction in exergy destruction. Therefore, it is essential to keep the anode pressure as high as possible during the operation of the system to achieve better output performance. The combined system had a higher at different anode pressures than the HT-PEMFC system alone.  Figure 7 shows the schematic diagram of the proposed HT-PEMFC and ORC combination system. The system consists of an HT-PEMFC subsystem for generating electrical power and an ORC subsystem for exhaust heat utilization and recovery. The two  Figure 7 shows the schematic diagram of the proposed HT-PEMFC and ORC combination system. The system consists of an HT-PEMFC subsystem for generating electrical power and an ORC subsystem for exhaust heat utilization and recovery. The two subsystems are connected by a common evaporator, and each subsystem has a fluid flow diagram.

System Description
The state of the fluid in the combined system is represented by the numbers in Figure 7, and the arrows represent the flow direction of the fluid. In the HT-PEMFC subsystem, the hydrogen comes out of the hydrogen tank and is regulated to the operating pressure required for operation using a pressure regulator. In practice, the amount of delivered hydrogen ought to be greater than the demand in the stack reaction to ensure fuel cell stability. The unreacted hydrogen in the stack is pressurized by a hydrogen compressor (HC) and recombined with hydrogen from the hydrogen tank, which will not only improve hydrogen utilization, but also increase the temperature and humidity of the mixed hydrogen. The anode heat exchanger (AHE) then preheats the hydrogen mixture to the operating temperature and flows it into the anode inlet of the stack. The cathode inlet of the stack is mainly air from the ambient. The air passes through the air compressor (AC) and the cathode heat exchanger (CHE) to achieve the required pressure and temperature of the fuel cell stack. The energy required to heat the hydrogen and air comes from the excess air and water generated at the cathode outlet, which helps to decrease the power consumption of the accessory devices and improve the overall system efficiency. The combined system uses a coolant (tri-ethylene glycol) to bring out the excess heat produced by the fuel cell stack, after which it flows into the evaporator [45]. Finally, the coolant is pressurized by pump 1 and reflows into the stack.
In the ORC subsystem, the organic working fluid absorbs the excess heat generated by the electric stack in the evaporator to become superheated vapor. The superheated steam passes through the expander (Exp) and reaches a low-pressure superheated state, where the generator is driven to produce electric power. Then, the organic working vapor is exothermically condensed to the low-pressure liquid state through the condenser (Con). Finally, after pump 2 is pressurized, the working fluid flows into the evaporator to complete the whole cycle.

Thermodynamic Modeling
To simplify the system model and calculations, the following sensible assumptions were made: • The combined system operated in a stable working condition [51]. The dynamic model for studying the control strategy was not considered due to the focus of this paper on the performance evaluation and parametric study of the proposed system. In the HT-PEMFC subsystem, the hydrogen comes out of the hydrogen tank and is regulated to the operating pressure required for operation using a pressure regulator. In practice, the amount of delivered hydrogen ought to be greater than the demand in the stack reaction to ensure fuel cell stability. The unreacted hydrogen in the stack is pressurized by a hydrogen compressor (HC) and recombined with hydrogen from the hydrogen tank, which will not only improve hydrogen utilization, but also increase the temperature and humidity of the mixed hydrogen. The anode heat exchanger (AHE) then preheats the hydrogen mixture to the operating temperature and flows it into the anode inlet of the stack. The cathode inlet of the stack is mainly air from the ambient. The air passes through the air compressor (AC) and the cathode heat exchanger (CHE) to achieve the required pressure and temperature of the fuel cell stack. The energy required to heat the hydrogen and air comes from the excess air and water generated at the cathode outlet, which helps to decrease the power consumption of the accessory devices and improve the overall system efficiency. The combined system uses a coolant (tri-ethylene glycol) to bring out the excess heat produced by the fuel cell stack, after which it flows into the evaporator [45]. Finally, the coolant is pressurized by pump 1 and reflows into the stack.
In the ORC subsystem, the organic working fluid absorbs the excess heat generated by the electric stack in the evaporator to become superheated vapor. The superheated steam passes through the expander (Exp) and reaches a low-pressure superheated state, where the generator is driven to produce electric power. Then, the organic working vapor is exothermically condensed to the low-pressure liquid state through the condenser (Con). Finally, after pump 2 is pressurized, the working fluid flows into the evaporator to complete the whole cycle.

Thermodynamic Modeling
To simplify the system model and calculations, the following sensible assumptions were made:

•
The combined system operated in a stable working condition [51]. The dynamic model for studying the control strategy was not considered due to the focus of this paper on the performance evaluation and parametric study of the proposed system.

•
The pressure drop in the heat exchanger, evaporator, and condenser can be ignored [51]. The pressure drop in the heat exchanger, evaporator, and compressor has little influence on the performance of the overall system. • The temperature rise in the coolant and reaction gas passing through the stack was set to 5 K and the pressure drop was set to 0.2 atm. Since temperature and pressure changes are inevitable when reactants and coolants pass through the fuel cell stack, the temperature rise and pressure drop of reactants and coolants should be set within a reasonable range.

•
The energy loss when connecting single cells in a series was neglected, and the performance of the fuel cell stack was the same as that of a single cell [52][53][54]. In practice, there are energy losses and inconsistent performance between single cells in a stack. To simplify the analysis, the energy losses and inconsistencies between cells were ignored. • Changes in the potential and kinetic energies of fluids were neglected [55].

•
The air entering the system was composed of 79% nitrogen and 21% oxygen [53]. The ambient temperature and pressure were 298.15 K and 1 atm, respectively. The relative humidity of the reactants was considered as 7.6% [56]. • Energy losses and isentropic efficiencies exist in compressors, pumps, and turbines [55].

Thermodynamic Model HT-PEMFC Subsystem
The fuel cell generates electricity by the electrochemical reactions of hydrogen and oxygen in the anode and cathode catalyst layers. The reactions of the anode and cathode are The stack model investigated in this study was composed of a series of connections of HT-PEMFC single cells, and the thermodynamic model of a single cell can be referred to in our previous study [57,58]. The HT-PEMFC single cell voltage can be obtained by using the following equation [57][58][59][60]: where U cell is the output voltage of the HT-PEMFC; E rev is the reversible cell voltage; and E act , E ohm , and E conc represent the activation overpotential, ohmic overpotential, and concentration overpotential, respectively. α is the charge transfer coefficient; j represents the current density; j leak , j 0 , and j L represent leakage current density, exchange current density, and limit current density, respectively; t mem and σ mem are the thickness and proton conductivity of the membrane, respectively; F is the Faraday constant; and n e is the number of electrons.
The output power and the generated heat of the HT-PEMFC stack were obtained by using the following equations [61]: where W stack and Q stack are the output power and the heat generated by the stack; N cell is the number of single cells; and A is the effective electrode area. The mass flow rate of air and hydrogen can be determined by the following [46]: .
where . m is the mass flow rate; λ is the stoichiometry; M is the relative molecular mass; g is the mass fraction; and J is the operating current.
The mass flow rate of the fluid at the outlet of the fuel cell stack can be calculated by the following equation [47]: .
The compression process can be considered an isentropic compression process. The power consumption by the HC and the AC can be obtained by the following equations [35]: where W AC and W HC are the power consumption of the air compressor and the hydrogen compressor, respectively; C p is the specific heat at a constant pressure; p and T are the pressure and temperature, respectively; and γ is the adiabatic coefficient. The numbers in the subscripts correspond to the different states of the working fluid in Figure 7.
After pressurization by the hydrogen compressor and air compressor, the gas temperature is [46]: According to the conservation of energy, the process of hydrogen mixing can be expressed as [46]: . m 3 C p,3 T 8 = . m 2 C p,2 T 2 + . m 6 C p,6 T 6 (12) In addition, the heat exchange process in the CHE and AHE follows the principle of energy conservation [47]: . m 10 C p,10 (T 10 − T 12 ) = .
where T 12 and T 4 are the inlet temperatures of hydrogen and air at the inlet of the stack, respectively. The power consumption of pump 1, W pump1 , is [35]: The mass flow rate of the coolant . m 13 is determined by the following [35]: .
ORC Subsystem According to the principle of ORC operation, the relationship between the pressure and entropy of the working fluid at different state points can be expressed as: p 19 = p 16 , p 17 = p 18 , S 16 = S 17 , and S 18 = S 19 . Different organic fluids have certain impacts on the output power and efficiency of the system. Based on the findings of the authors of [35,56], R245fa was selected as the organic fluid for the ORC since it possesses good thermodynamic properties for recovering heat produced by the fuel cell stack and its ozone depletion potential (ODP) is 0.
The mass flow rate of the organic fluid in the evaporator is determined by the following [35]: The power generated by the expander W Exp can be expressed as [30]: The heat dissipated through the condenser Q Con is [33]: The power consumed by pump 2 W pump2 is [33]: The ORC subsystem output power W orc and efficiency η orc can be calculated by the following [62]:

Energy Analysis
When the HT-PEMFC subsystem is not considering the ORC recovery waste heat, the output power for the HT-PEMFC system, W HT−PEMFC , can be obtained by the following: The output power for the HT-PEMFC and ORC combined system, W HT−PEMFC/ORC , is given by the following: The output power of the system can be calculated by the following: The coefficient of performance (COP) in a system is described as the total output power to the total generated power ratio [63]:

Exergy Analysis
The exergy efficiency based on the second law of thermodynamics is the ratio of the electrical power output of the system to the maximum possible work done, which reflects the maximum potential of the proposed system. Figure 8 illustrates the exergy classification and exergy analysis model. The mass flow exergy primary includes physical exergy and chemical exergy [43]. Since the potential and kinetic energies of the fluid were ignored, the potential and kinetic exergies were not considered in this system analysis. The energy flow exergy primary includes the exergy of work and the exergy of heat. The exergy analysis model can be obtained by calculating the different exergy types of each facility.

Exergy Analysis
The exergy efficiency based on the second law of thermodynamics is the ratio of the electrical power output of the system to the maximum possible work done, which reflects the maximum potential of the proposed system. Figure 8 illustrates the exergy classification and exergy analysis model. The mass flow exergy primary includes physical exergy and chemical exergy [43]. Since the potential and kinetic energies of the fluid were ignored, the potential and kinetic exergies were not considered in this system analysis. The energy flow exergy primary includes the exergy of work and the exergy of heat. The exergy analysis model can be obtained by calculating the different exergy types of each facility.

Exergy
where is the specific exergy, and and are the chemical and physical exergies of the flows, respectively. The physical exergy and the chemical exergy of the flows can be determined by the following [65]: where ℎ and are are the specific enthalpy and entropy of the substances, respectively; is the mole fraction of a single chemical species; and is the standard chemical exergy. The chemical exergy is relevant to the chemical composition, molar fraction, and environment of the fluid in the system. The standard chemical exergy of the reactants that appeared in the present study can be obtained from [46].
The exergy of work, , is the same as the power generated or consumed by the facility [46]: The exergy of heat, , observes the Carnot cycle, so it can be expressed as [46]: To achieve an exergy performance evaluation for different facilities, the exergy balance of the facility can be obtained by the following [66]: m· ex ch + ex ph (26) where ex is the specific exergy, and ex ch and ex ph are the chemical and physical exergies of the flows, respectively. The physical exergy and the chemical exergy of the flows can be determined by the following [65]: where h and s are are the specific enthalpy and entropy of the substances, respectively; χ i is the mole fraction of a single chemical species; and e ch i is the standard chemical exergy. The chemical exergy is relevant to the chemical composition, molar fraction, and environment of the fluid in the system. The standard chemical exergy of the reactants that appeared in the present study can be obtained from [46].
The exergy of work, Ex w , is the same as the power generated or consumed by the facility [46]: The exergy of heat, Ex Q , observes the Carnot cycle, so it can be expressed as [46]: To achieve an exergy performance evaluation for different facilities, the exergy balance of the facility can be obtained by the following [66]: The definitions of fuel exergy, product exergy, and exergy loss for all system components are presented in Table 3. The exergy efficiency of each component can be determined by the following [43]: The exergy destruction ratio of different components, ε d,k , can be calculated by the following [43]: The ratio between the exergy loss of a device and the overall system exergy loss is [67]: The exergy destruction rate of the system, ε d,system , can be expressed as [43]: ε d,system = Ex loss,system Ex F,system = Ex loss,system Ex 2 + Ex 7 − Ex 12 (35) The exergy efficiency of the systems, η Ex,system , can be obtained by the following [68]: The ecological function E is described as the difference between the net output power and the exergy loss for the system, which is an evaluation index aimed at increasing the net output power and reducing the exergy loss. The ecological function, E system , of the system can be obtained by the following [35]:

Conclusions
In this paper, a combined system model of HT-PEMFC and ORC was proposed, in which the ORC subsystem could recover the waste heat produced by the stack for power generation, and the fluid at the PEMFC cathode outlet was also used to preheat the inlet reaction gas. The thermodynamic model of the combined system was developed and validated with experimental data according to the proposed design. In addition, energy and exergy analyses were conducted on the system. The main conclusions of this work are summarized as follows: (1) The results of the energy and exergy analyses show that the air compressor is the component with the largest power consumption in the system. The HT-PEMFC stack is the dominant component with the biggest exergy loss. The cathode heat exchanger and evaporator represent the largest exergy losses in the auxiliary components. Therefore, priority should be given to improving these components to improve the system performance.
(2) Compared to the HT-PEMFC subsystem, the net output power of the combined HT-PEMFC and ORC system increased by 12.92%. The energy efficiency, exergy efficiency, and COP of the system can be effectively improved by using ORC to recover the waste heat.
(3) When the current density increased, the system's net output power increased, but all the other system performance indicators deteriorated. Therefore, the current density of the stack should be as low as possible when the system output power and power density meet the required design.
(4) The system's performance can be improved by increasing the stack inlet temperature and anode inlet pressure within a certain range. The cathode inlet pressure should be reduced to decrease the power consumption of the air compressor and improve the system's output performance.