Keywords

1 Introduction

In recent years, hydrogen energy with high energy density and no pollution has gradually become an object of interest for researchers in various countries due to the increasingly severe problems of global warming and oil scarcity. Proton exchange membrane fuel cell (PEMFC) is an ideal power source for electric vehicles and household distributed power generation devices because of its fast start-up at conventional temperature, high efficiency (40–60%) and ability to quickly adjust output power according to power demand [1, 2]. With the application of electrolytic water for hydrogen production, it also results in a large amount of oxygen not being fully utilised. If this oxygen could be utilised, it would effectively improve the efficiency of distributed power generation units.

Based on the above ideas, the topology of a new fuel cell cathode gas supply system with oxygen and air mixing is proposed in this paper, and a simulation platform is built to study it.

2 Structure and System Model Building

2.1 Introduction of Topology of Cathode Gas Supply System

The topology of the new fuel cell cathode gas supply system with oxygen and air mixing proposed in this paper are shown in Fig. 1. Compared with the conventional air supply systems, this topology mixes the oxygen supplied by the oxygen source with the gas in the mixing cavity to a preset oxygen concentration and feeds it to the stack via ejector. The gas in the mixing cavity is a mixture of saturated water vapor discharged from the stack and dry air fed by an air compressor. At the same time the humidity of the gas is controlled by the air compressor.

Fig. 1.
figure 1

The topology of the new fuel cell cathode gas supply system with oxygen and air mixing

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2.2 Voltage Model of the PEMFC

The voltage model is based on the operating conditions of the stack and the cell voltage \(V_{cell}\) is calculated from the Nernst voltage \(E\), activation loss \(\eta_{act}\), ohmic loss \(\eta_{ohm}\) and concentration loss \(\eta_{conc}\) respectively, as shown in the following equations [3]:

$$ V_{cell} = E - \eta_{act} - \eta_{ohm} - \eta_{conc} $$
(1)

The Nernst voltage can be expressed as follows [4]:

$$ E = 1.229 - 2.302 \times 10^{ - 4} (T^{st} - 298.15) + 4.308 \times 10^{ - 5} T^{st} \ln \left( {\left( {p_{{{\text{O}}_{2} }}^{{}} } \right)^{\frac{1}{2}} p_{{{\text{H}}_{2} }}^{{}} } \right) $$
(2)

where \(T^{st}\) is the temperature of the stack, \(p_{{{\text{O}}_{2} }}^{{}}\) is the partial pressure of oxygen at the cathode and \(p_{{{\text{H}}_{2} }}\) is the partial pressure of hydrogen at the anode.

The \(\eta_{act}\) is obtained by solving the following simplified Tafel equation:

$$ \eta_{act} = \frac{{RT^{st} }}{2\alpha F}\ln \left( {\frac{j}{{j^{0} }}} \right) $$
(3)

where \(j\) is the current density and \(j^{0}\) is the reference current density.

The \(\eta_{ohm}\) due to the resistance to proton transport within the proton exchange membrane can therefore be expressed as [5]:

$$ \eta_{ohm} = j \times ASR $$
(4)

where \(ASR\) is the surface resistance, which depends mainly on the thickness of the film \(\delta_{mem}\) and its conductivity \(\sigma_{mem}\).

The \(\eta_{conc}\) caused by the consumption of reactants in the catalytic layer is expressed as follow [4]:

$$ \eta_{conc} = \frac{{RT^{st} }}{2\alpha F}\ln \left( {\frac{{c_{{{\text{O}}_{2} }}^{0} }}{{c_{{{\text{O}}_{2} }}^{st\_cgdl} }}} \right) $$
(5)

where \(c_{{{\text{O}}_{2} }}^{0}\) is the reference oxygen concentration within the catalytic layer.

2.3 Modeling the Gas Situation in the Stack

The molar flow rate of each component gas \(\dot{n}_{{x_{2} }}^{{}}\) (\(x_{2} = \{ {\text{O}}_{2} ,{\text{H}}_{2} ,{\text{N}}_{2} \}\)) in the stack can be obtained according to the mass conservation equation as follows:

$$ \dot{n}_{{x_{2} }}^{ca/an} = \dot{n}_{{x_{2} }}^{ca/an\_i} - \dot{n}_{{x_{2} }}^{ca/an\_e} - \dot{n}_{{x_{2} }}^{ca/an\_react} $$
(6)

Part of the gas entering the stack is consumed by the electrochemical reaction and the flow rate can be expressed as:

$$ \dot{n}_{{x_{2} }}^{react\_ca/an} = \left\{ {\begin{array}{*{20}c} {\frac{{n_{cell} I^{st} }}{nF}} & {x_{2} = \{ {\text{H}}_{2} ,{\text{O}}_{2} \} } \\ 0 & {x_{2} = \{ {\text{N}}_{2} \} } \\ \end{array} } \right. $$
(7)

where \(n_{cell}\) is the number of cells, \(I^{st}\) is the output current, \(n\) is the number of participating electrons, and \(F\) is Faraday constant.

According to the mass conservation equation can be obtained separately from the cathode and anode within the molar flow of gaseous water:

$$ \dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{ca} = \dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{ca\_i} - \dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{ca\_e} + \dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{ca\_react} - \dot{n}_{{{\text{H}}_{2} {\text{O}}(l)}}^{ca\_e} $$
(8)
$$ \dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{an} = \dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{an\_i} - \dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{an\_e} - \dot{n}_{{{\text{H}}_{2} {\text{O}}(l)}}^{an\_e} $$
(9)

The flow rate of liquid water at the cathode and anode is:

$$ \dot{n}_{{{\text{H}}_{2} {\text{O}}(l)}}^{ca/an\_e} = \dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{ca/an\_e} \times \frac{{p_{{{\text{H}}_{2} {\text{O}}(l)}}^{ca/an} }}{{p_{{{\text{H}}_{2} {\text{O}}}}^{ca/an} }} $$
(10)

where \(p_{{{\text{H}}_{2} {\text{O}}(l)}}^{st\_ca}\) is the equivalent pressure under the same temperature conditions assuming that all liquid water in the cathode flow channel is converted to water vapor.

The channel pressure model uses a general gas cavity model with molar flow as input and pressure as output. The component pressures are calculated as shown below:

$$ p_{{x_{2} }}^{ca/an} = \frac{{\left( {\int\limits_{0}^{t} {\dot{n}_{{x_{2} }}^{ca/an} d\tau } } \right) \times R \times T^{st} }}{{V^{st\_ca} }} $$
(11)

Assuming that the water vapor in the channel reaches the saturation vapor pressure, the subsequent generation of water is all liquid water, water vapor partial pressure and the equivalent pressure of liquid water all converted to water vapor is shown below:

$$ p_{{{\text{H}}_{2} {\text{O}}}}^{ca/an} = \min \left( {\frac{{\left( {\int\limits_{0}^{t} {\dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{ca/an} d\tau } } \right) \times R \times T^{st} }}{{V^{ca/an} }},p_{sat} \left( {T^{st} } \right)} \right) $$
(12)
$$ p_{{{\text{H}}_{2} {\text{O}}(l)}}^{ca/an} = \frac{{\left( {\int\limits_{0}^{t} {\dot{n}_{{{\text{H}}_{2} {\text{O}}}}^{ca/an} d\tau } } \right) \times R \times T^{st} }}{{V^{st\_ca/an} }} - p_{{{\text{H}}_{2} {\text{O}}}}^{ca/an} $$
(13)

The total pressure in the cathode and anode are shown below:

$$ p_{total}^{ca} = p_{{{\text{O}}_{2} }}^{ca} + p_{{{\text{N}}_{2} }}^{ca} + p_{{{\text{H}}_{2} {\text{O}}}}^{ca} $$
(14)
$$ p_{total}^{an} = p_{{{\text{H}}_{2} }}^{an} + p_{{{\text{H}}_{2} {\text{O}}}}^{an} $$
(15)

3 Results and Discussion

In this work, a stack rated at 75 kW in the conventional topology was chosen as the object of simulation analysis, and its main parameters are shown specifically in Table 1. On the other hand, in the new topology, the oxygen concentration \(\eta_{{{\text{in}}}} = 40\%\), the lead ratio \(\mu = 2.86\) and the opening of the electron tee \(\theta = 0.2\).

Table 1. Characteristic parameters of the stack
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3.1 Comparative Performance Analysis of New Topologies

Figure 2 shows that the new topology can effectively increase the output power of the stack because the increase in oxygen partial voltage effectively increases the Nernst voltage, reduces the activation loss and concentration loss, which ultimately increases the output power of the fuel cell. At the same time, as the current increases, the concentration loss is further reduced and the net power of the system is further increased. Overall, the increase is above 10% when the stack is at high current output. Figure 2(b) shows that the power consumption of the compressor in the new topology is reduced by nearly 50% compared to the conventional topology.

Fig. 2.
figure 2

The characteristic curves of the two topologies

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3.2 The Analysis of System Performance at Different Oxygen Excess Ratios

Figure 3 shows the variation of stack output power and system net power with Oxygen excess ratio \(\lambda\), when \(\eta_{{{\text{in}}}} = 40\%\), \(I = 300\,A\), the output power of the stack increases as \(\lambda\) increases, but the growth rate gradually decreases. Meanwhile, the consumption of the air compressor increases with the increase of \(\lambda\). This leads to the decrease of the net power of the system from \(\lambda\) = 2.0, and the molar fraction of oxygen \(\eta_{out}\) at cathode outlet is greater than 21%, the phenomenon of oxygen wastage occurs.

Fig. 3.
figure 3

The characteristic curves at different oxygen excess ratio

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3.3 The Analysis of System Performance at Different Molar Fraction of Oxygen at the Cathode Inlet

Figure 4(a) shows the variation of stack output power and net power of system with different \(\eta_{{{\text{in}}}}\), when \(\lambda = 2.0\), \(I = 300\,A\), as the \(\eta_{{{\text{in}}}}\) increases, the power consumption of the compressor decreases proportionally, and the net power growth rate of the system eventually decreases due to the decrease in the power growth rate of the stack output. Figure 4(b) shows that when the \(\eta_{{{\text{in}}}}\) ≥ 40%, the phenomenon of oxygen wastage occurs.

Fig. 4.
figure 4

The characteristic curves at different oxygen concentration

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4 Conclusion

In this work, a new fuel cell cathode gas supply system is proposed and mathematically modeled for study. Simulation and theoretical analysis show that this topology can effectively increase the output power of the stack and reduce the power consumption of the air compressor, which can eventually increase the net power of the system up to more than 10%. This provides a solid theoretical basis and guiding direction for fuel cell system performance optimization research and design development.