1. Introduction
Proton exchange membrane fuel cells (PEMFCs) rely on the accurate control and continuous supply of hydrogen fuel (H2) and oxidant air (O2) to produce electricity with byproducts of heat and water. PEMFC and green hydrogen from renewable energies present a promising technological solution to substitute for internal combustion engines (ICEs) as a highly efficient, zero-emission energy converter. The combination can address the issues of air pollution, global warming, and fluctuating petroleum fuel supply for transportation and power generation.
The anode H
2 supply and circulation system of a PEMFC provides excessive fuel and recycles the unused hydrogen from the fuel cell stack back to the hydrogen supply stream to help maintain the ideal temperature, humidity, and quality of the hydrogen fuel. The compressed H
2 in storage tanks must be regulated to the targeted pressure (usually 1.5 MPa) and the required H
2 mass flow rate using pressure regulators, proportional valves, or injector(s) [
1]. A mechanical pump is traditionally used to recirculate the unconsumed hydrogen, as in the PEMFC system of the world’s first mass-produced fuel cell vehicle (FCV), the Toyota Mirai [
2]. Although reliable, mechanical pumps or blowers may corrode over time, and pump lubricant is a potential source of membrane poisoning, in addition to the parasitic power consumption by the pump. An ejector, if properly designed, can perform the circulation task with a reduced parasitic power consumption for the PEMFC system, as well as system weight and volume. Multiple ejectors can effectively circulate the unconsumed hydrogen over a broader range of the PEMFC system’s power output. Ejectors have been widely applied in many industries, such as air conditioning and refrigeration systems, to replace mechanical compressors since their introduction in the early 1900s [
3]. A typical ejector adopts a Venturi nozzle to create a high-speed stream with low pressure to suck another stream and reinject it to the main stream [
4]. H
2 ejectors used in the PEMFC system take advantage of the considerable H
2 pressure potential energy between the fuel tank and the stack (i.e., the primary flow) to create a pressure drop through a nozzle to suck the unused gas (i.e., the secondary flow) with no power consumption. However, the ejector’s hydrogen entrainment capability is restricted by its geometry, gas flow rate, and pressure drop. Due to the system’s advantages of a simple structure, no moving components, and zero energy consumption, other automotive manufacturers, such as Honda [
5,
6] and Hyundai [
7], have adopted ejectors in the PEMFC system of their FCVs.
Gas ejector design is challenging, especially for a PEMFC system, due to the broad range of a PEMFC’s power output and the resulting wide variation in the hydrogen flow rate. Many researchers have studied the ejector’s hydrogen entrainment ratio using numerical analysis [
8,
9]. A significant issue of the ejector with fixed geometries is that the ejector’s pressure is limited due to PEMFC stack anode system conditions. As a result, the hydrogen entrainment ratio of the ejector falls rapidly when the primary gas flow rate deviates from the design points, resulting in a narrow operating power range. Three different solutions have been suggested to address this problem [
9]: (i) variable-flow ejectors with a changeable nozzle diameter, (ii) multi-ejectors with more than one constant ejector, and (iii) a combination of an ejector and a pump. The ejectors proposed in [
10,
11], which used a needle inside the small nozzle opening to change its size, can provide a considerable range of primary mass flow rate and improve overall entrainment performance. To accurately control the needle position, diaphragms [
11] and electronically controlled motors [
10] were applied and tested. The diaphragms’ positions were adjusted by the pressure difference between the oxidizing gas and supplied fuel. The movement of the needle attached to the diaphragms was then changed during different operating conditions [
11]. A stepper motor can also perform this task by precisely controlling the needle’s displacement.
However, the needle sealing at elevated pressures and the central alignment of the actuator shaft are major concerns for the variable flow ejector, provoking significant challenges for real-life and long-duration applications. Two or more ejectors working in parallel were also proposed to better suit the rapid change operations of fuel cell vehicles. Compared to a single ejector, multi-ejector performance is better in the overall operating range. However, previous studies that employed a double ejector for a PEMFC simply multiplied the results of the single ejector by two [
12], and the proposed multi-ejectors did not show an excellent performance improvement without a systematical design and optimal control. Using the combination of an ejector and a pump for a PEMFC stack fuel-delivery system was also proposed [
13]. However, taking advantage of these two devices also will result in encountering drawbacks and increasing control difficulties and design complexities.
So far, no reported work has demonstrated the ability to support the full-power operation range of large PEMFC stacks using only ejectors. Even with variable ejectors proposed in previous studies, their performance and coverage are still minimal. The authors of [
8] compared three different ejector solutions for a 12.5 kW PEMFC stack used in a forklift system: (i) a single ejector covering the operating range of about 85–180 A (or 6.7–12.5 kW), (ii) dual ejectors covering 60–180 A (or 4.9–12.5 kW), and (iii) a variable nozzle geometry solution also covering 60–180 A. These solutions could not fully cover the full range of the PEMFC stack operation between 15 and 180 A. In [
9], the researchers designed an ejector with fixed geometries for a 5 kW stationary PEMFC system and compared it with different simulation models. A variable multi-ejector consisting of two constant nozzle ejectors and one solenoid valve was proposed in [
12] for a minibus PEMFC system, demonstrating a practical entrainment ratio lower than one for the operation range. An electronically controlled variable flow ejector using needles in the nozzle throat could perform the gas recirculation for a Ballard Mark 9 stack between 7 and 17 kW [
10]. Ejectors were also adopted in the H
2/O
2 PEMFC stack; e.g., using a dual-ejector system with one ejector to recirculate H
2 and one to recirculate O
2. They showed potential benefits for water management and performance improvement in closed-space or environment applications such as crewless underwater vehicles and spacecraft [
14].
This paper focused on the optimal design and operation control of two ejectors for H2 supply/circulation over the entire operating range of a PEMFC system, covering the stack’s minimum 8% to maximum 100% power output. The design could effectively support full-range PEMFC system operation, given that the PEMFC system’s parasitic power consumption was about 8–15%.
This work did not use ejectors with a changeable nozzle geometry [
10,
15] to avoid their control complexity, reliability issues, and high manufacturing cost. Instead, it used two ejectors with different nozzle dimensions to cover different PEMFC power output sections in the full range. The design optimization best distributed these ranges with no gaps and useless overlaps. On the other hand, the optimal operation control ensured smooth transitions between these two ejectors when the power output of the PEMFC system dramatically increased or decreased. These ejectors with optimally designed geometries, in cooperation with electronically controlled mass flow rate regulators, adjusted the primary flow to achieve a high hydrogen entrainment ratio and a wide operation range.
Specifically, this study modeled, simulated, designed, and tested a dual-ejector system for a PEMFC stack with maximum output power (
) of 70 kW. With the optimal control of the dual-ejector system, it could satisfy the stack operation conditions from the idle 6 kW to the maximum 70 kW power, ranging from 8% to 100% of
. The H
2 supply and circulation system using dual ejectors for the PEMFC stack are presented in
Section 2. The optimal design of each ejector’s geometrical parameters are introduced in
Section 3, based on the computational fluid dynamics (CFD) simulation and analysis, the test results for each ejector, and the comparisons to the CFD results.
Section 4 presents the optimal control and test of the dual-ejector system, which could fulfill the required stack H
2 stoichiometric ratio during the entire operating range. The anode gas pressure fluctuation was also studied and analyzed when shifting between different ejectors during operation. Conclusions regarding key findings are presented in
Section 5.
2. Anode Hydrogen Supply System Design with Two Ejectors
The PEMFC stack of the targeted anode hydrogen supply and recirculation system had a maximum output power of 70 kW. The stack operation current was from 40 A to 600 A, corresponding to a total stack voltage ranging from 158 V to 115 V, providing 6 kW of idle power and 70 kW of maximum power. The anode inlet and outlet pressure, mass flow rate, temperature, and required hydrogen stoichiometric ratio
are critical parameters in anode hydrogen supply and recirculation system design, with some of these parameters plotted in
Figure 1. The stoichiometric ratio of H
2 defines the total requested H
2 delivered to the stack over the theoretical reacted H
2. The unconsumed hydrogen from the stack anode outlet must be recirculated back to the primary stream to facilitate the ideal hydrogen fuel temperature and relative humidity (RH). The hydrogen gas temperature in the primary ejector inlet was assumed to be 293.15 K, and the anode outlet mixture was between 327.15 K and 348.15 K with 100% RH. Therefore, depending on the operation conditions, the required RH of anode inlet gas was between 40% and 80%.
2.1. Design of Dual-Ejector System
A dual-ejector gas recirculation device was designed to cover a wide range of operations from 40 to 600 A. Ejector A and Ejector B, as shown in
Figure 2, each had a unique, optimized geometric parameter to cover a specific range of the PEMFC system’s operation. A three-way ball valve was used to switch flows between the two different paths. One or two proportional valves (PVs) could control the dual-ejector’s pressure and mass flow rate. One PV could satisfy the functional requirements, but also could induce system pressure fluctuation during the transition process when the three-way valve shifted the hydrogen path from Ejector A to B or backward. Therefore, two PVs, with each PV corresponding to one ejector, were proposed, as shown in
Figure 2b. The dynamic pressure response and anode inlet pressure changes between the two ejectors were investigated and tested, the results of which are presented in a later section.
The compressed H2 from the fuel tank was reduced to 15 bara (absolute pressure) using pressure regulators before entering the mass/pressure control valves. Depending on the PEMFC operation status, the mass/pressure control valve had to adjust the H2 pressure and mass flow rate and inject high-pressure gas into the ejector to pump the unused gas. Finally, the two flows were mixed and ejected to the PEMFC anode with a low pressure between 1.5 and 2.7 bara based on the stack requirement. During the mixing process in the ejector, the dry primary hydrogen gas flow was humidified by the circulated used-hydrogen gas mixture; therefore, there no humidifier was needed in this system.
This integrated dual-ejector hydrogen supply and recirculation system’s optimal design had to rely on the specific PEMFC stack requirements. The main steps included:
- (i)
Calculating the minimum and maximum fuel mass flow rate and pressure drops for the wide-range operating conditions;
- (ii)
Choosing the appropriate fuel injector or pressure/mass flow rate regulator;
- (iii)
Optimal design of each ejector’s geometric parameters to enlarge its entrainment capability to fulfill the requested fuel stoichiometric ratio during the minimum and maximum operating conditions;
- (iv)
Optimal control of the integrated hydrogen supply system using successively or simultaneously working injectors to cover the full range of dynamic fuel cell power changes.
To achieve these goals, a CFD simulation of the ejectors and the optimal control methods, as well as the ejector sample tests, validation, and performance analysis, were carried out step by step.
2.2. Hydrogen Gas Pressure and Flow Rate Control
The anode hydrogen gas pressure and mass flow rate control rely on the accurate gas injection from a high-pressure tank. The mainstream of high-pressure H2 from this injection system usually adopts electronically controlled devices, such as injectors or proportional valves. They are crucial in ensuring fuel mass and pressure supply to the anode side.
Both H2 injectors and proportional valves rely on the electric current to generate magnetic forces to open and close the valve by lifting the plunger against the spring force and letting the gas flow. Advanced proportional control solenoid valves can precisely change the intensity of the coil current or the magnetic power to influence the valve’s opening degree. As a result, the flow rate can be freely controlled in proportion to the control signal. The control signal is usually converted into a pulse-width modulation (PWM) signal to eliminate hysteresis effects to prevent the static friction generated during the plunger’s movement. By adjusting the PWM frequency and duty cycle, the variable coil current can control the flow rate precisely in a proportional solenoid valve.
A proportional control solenoid valve was chosen in this study for the H
2 supply system, since it could operate at a higher pressure and sustain a wide range of inlet/outlet pressure differences. The proportional valve’s orifice design was essential for the continuous and smooth control of the variable flow rate. The most important parameters for selecting a correct solenoid valve are the flow coefficient (the
value in
or
value in
), the maximum operating pressure range (i.e., the pressure before and after the valve
and
), and the requested maximum flow rate. This paper took
values measured with the water’s flow rate at 293.15 K and 1 bar relative pressure at the valve inlet, compared with 0 bar at the valve outlet. For gases, the standard flow rate
was calculated depending on the low and high flow pressure drops through the valve orifice. The flow characteristics could change if the differential pressure between inlet and outlet pressure exceeded half the inlet pressure value. Specifically, the calculation of the standard flow rate for subcritical conditions; i.e.,
, is:
For critical flow, where
, the standard flow rate is determined by:
where
and
are the standard flow rate and gas density at 0 °C and 1 atm, respectively;
is the flow coefficient determined by the proportional valve;
and
are the temperature and pressure, respectively; and subscripts
and
represent the inlet and outlet of the valve, respectively.
The characteristic curves of a proportional valve with constant inlet pressure of 15 bara are plotted in
Figure 3. The hydrogen volume flow rate (
in NLPM, or normal liter per minute) of different valve lift at temperature 293.15 K versus the pressure differences (
were adjustable with different
values. The
value could be controlled by the PWM control signal, where the position of the plunger was determined by the coil current.
The PWM-controlled proportional valve offered a flexible range of pressure outlets at different mass flow rates. In this test, the downstream pressure could range from 14.5 to 1 bara by adjusting the duty cycle and value, allowing the optimal control to achieve a variable flow rate in a wide range of operations.
4. Optimal Control and Test of Dual-Ejector System
The control of ejectors with fixed dimensions relies on the accurate pressure and flow-rate adjustment of the primary inlet flow through proportional valves. Meanwhile, the secondary and outlet flows are connected to the fuel cell anode outlet and inlet. For this reason, the control of the hydrogen proportional valve is significant in achieving the best performance of the ejector. In the dual-ejector hydrogen supply and circulation system, each ejector has a proportional control valve with an electric actuator that can flexibly control the primary flow stream. In addition, a three-way valve can switch the gas flow path from either one of the dual-ejector to the fuel cell stack based on control policies.
The optimal operation control of the designed dual-ejector hydrogen system aimed at continuously supplying and effectively circulating fuel gas to the fuel cell stack for requested power at any time (
). The smaller ejector (Ejector A) was activated during the lower power output from the stack. In contrast, the larger one (Ejector B) was responsible for the higher stack power. It was critical to identify the appropriate switching power (
) at which the three-way valve was activated to shift gas flow from one to another. Depending on stack power output, the optimized operation control was conducted as shown in
Figure 8.
4.1. Dual-Ejector System Analysis and Discussion
The test results of the designed dual-ejector system demonstrated an effective gas recirculation during a wide range of gas flow rates, covering the PEMFC operating from 40 A to 600 A. Specifically, Ejector A could cover the PEMFC stack operation from 6 kW to 27 kW, and Ejector B could cover it from 27 kW to 70 kW. Due to the limitation of the air compressor’s maximum inlet pressure on the test bench, the ejector performance above 10 bara of primary inlet pressure was not verified. The designed dual-ejector system was optimized to fully cover the PEMFC operation from 8% to 100% of stack power. Based on the test results, which only covered up to 55 kW, the remaining range from 55 to 70 kW can be anticipated to have good consistency with the CFD simulation.
The gas, when changing from air to hydrogen, can affect the entrainment ratio of ejectors. The CFD simulations using hydrogen gas for Ejectors A and B are shown in
Figure 9. Both ejectors showed a higher entrainment ratio when hydrogen was used instead of air. Even when considering the MAPE of the air entrainment ratio, the hydrogen entrainment capability (
) of both ejectors satisfied the stack hydrogen stoichiometric ratio requirement.
In
Figure 9, the yellow line and blue lines indicate the CFD simulation of Ejectors A and B, respectively, using hydrogen. A high entrainment capability could be effectively achieved to fulfill the requirement of a hydrogen stoichiometric ratio from 8% to 100% of the PEMFC anode inlet gas (shown by the red dashed line). However, the entrainment capabilities of Ejectors A and B were slightly decreased, as shown by the red and purple dashed lines, when considering the MAPE generated from the simulation and test results using air. Nevertheless, both ejectors could still provide a high enough hydrogen stoichiometry to the system.
4.2. Discussion of Pressure Disturbances Using Dual Ejectors
The pressure fluctuation influenced by the transit process of changing hydrogen paths in a dual-ejector system is a primary concern. As required, the stack’s hydrogen inlet pressure should be maintained stable, and the pressure differences between the anode and cathode should be adequately controlled. Drastic pressure fluctuation of hydrogen inlet may cause accumulated damage to the membrane and degrade its performance. Compared to a single-ejector system, a dual-ejector system has two different gas paths, and each path is equipped with an ejector suitable for a specific range of stack power output. In this work, Ejector A was optimally designed for the PEMFC’s lower-power output, while Ejector B was for the high-power output. When the PEMFC output power exceeded the capacity of Ejector A, the hydrogen injection and circulation paths were shifted to the flow paths associated with Ejector B.
The three-way control valve in the system switched the gas circulation path between Ejector A and Ejector B back and forth, depending on the dual-ejector system’s operation control strategies. The different sizes of the flow chambers led to flow-rate variation during the switching process. As a result, pressure disturbances occurred due to the variant gas pressure and volume between the two paths.
As mentioned previously, using one proportional valve (shown in
Figure 2a) could successfully control the primary inlet pressure and mass flow rate for both ejectors, since there was only one ejector at work each time the injection valve served. The dual-ejector system’s three-way valve selected the stack’s hydrogen-feeding path. When the gas path was switched from Ejector A to Ejector B, the proportional valve had to reduce pressure while maintaining the same mass flow rate. Therefore, the proportional and three-way valves were actuated simultaneously; the pressure and mass flow rate of the three ports were measured and plotted in
Figure 10. We focused on the maximum absolute pressure variance of the discharged gas from the dual-ejector system (
) and the primary inlet pressure (
) response time
after switching the ejector. The
was limited to a specific value to reduce the pressure impact on the PEMFC membrane. In addition, the system response time of
had to be as fast as possible.
The ejector’s primary inlet pressure was required to be reduced from 10 to 4 bara instantly while the three-way valve switched the gas path from the smaller Ejector A to the larger Ejector B. Meanwhile, the stack inlet mass flow rate had to be kept the same to maintain the hydrogen flow rate for the stack. The sudden change in gas paths induced a surge in the mass flow rate at the dual-ejector outlet and caused the pressure fluctuation of the discharged gas. The maximum difference in the outlet pressure
with a simple switch was an unacceptable 94.8 kPa, as shown in
Figure 10a. The response time of the primary inlet pressure change (
) was also very slow with only one proportional valve controlling the inlet pressure. By shifting the gas pathways, the sudden overflow of gas caused an increment in the mass flow rate in Path B, which induced the increased discharge mass flow (
) that cause the rise in pressure (
). Due to the increased pressure drop between the second inlet and outlet, the ejector entrainment capacity was decreased, as indicated by the reduced secondary inlet mass
.
To better understand and control the dynamic ejector-switching process, a system dynamics model was introduced to reflect the dynamic behavior of the system pressure variation and identify the switching process’s ideal operation parameters. A second-order system dynamic model was built in MATLAB/Simulink, and the transfer function was produced using experimental data of the switching process:
where
,
and
are constants identified using the system dynamic response experimental data.
For this system, the natural frequency
and the damping ratio
could also be obtained. Therefore, the transfer function can be written as:
The objective of optimal operation control in the dual-ejector system was to maintain a constant pressure at the anode inlet (i.e., the pressure of the ejector’s discharged port (
)) during the back-and-forth shifting of the gas path from Ejector A to Ejector B. A smooth increase and decrease in the total flow mass in the chamber during the switching process was vital to achieving this goal. However, the difference in chamber volume inherently caused sharp pressure disturbances, as illustrated in
Figure 10. Therefore, optimal operation control during ejector switching was needed to address the issue.
The control variables for the dual-ejector system were the PWM control signals of the mass/pressure control valves that adjusted the ejector primary inlet conditions. When the dual-ejector hydrogen supply and circulation system used only one proportional valve, the operation control was accomplished by adjusting the timing of the pressure change. Using two proportional valves in the dual-ejector hydrogen supply and circulation system (
Figure 2b), one for each path, could reduce the system pressure fluctuation more effectively. The two proportional valves opened and closed following different and coordinated rates during the switching process to ensure the total mass of the gas in the chamber remained almost constant, eliminating pressure variation. Moreover, more dynamic and accurate control could significantly reduce the system’s response time.
This optimal switching process control problem can be formulated as:
where
is the control variable (i.e., the PWM valve signals to adjust the proportional valve’s pressure and mass);
is limited to the lower and upper boundary conditions (
and
); and
is the objective function, which was to minimize the pressure disturbance (
) and the system’s response time (
).
Based on the dynamic model, a PID controller was added to the system to elicit a quick response to pressure changes. The ejector’s primary inlet pressure responded faster to the PID controller, as shown in
Figure 11.
With each ejector controlled by an individual gas-injecting valve, the pressure and mass flow rate were adjusted using PWM control signals. In this work, we compared the maximum pressure fluctuation (
) caused by shifting the ejectors using only one inlet proportional valve (
Figure 2a) vs. using two inlet proportional valves (
Figure 2b). The results were tested and plotted below. The resulting pressure variations and response times were measured experimentally, as shown in
Figure 12.
Figure 12a shows the measured stack inlet pressure fluctuation when switching from the small ejector to the large ejector, controlling one inlet proportional valve and two inlet proportional valves. With optimal control and using two proportional valves, the system response time was reduced from 13 s to 0.25 s, and the pressure fluctuation was significantly reduced from 95 kPa to 44 kPa.
Figure 10b shows the measured pressure fluctuation when switching from the large ejector to the smaller one. Again, using two proportional valves could reduce the pressure fluctuation from a maximum of 24 kPa to 12 kPa and the response time from 3 s to 0.15 s.
The measured pressure disturbance and the predicted distribution from the Simulink models during the ejector switching were consistent, proving that the developed optimal control strategies for the proportional valves’ operation could effectively minimize the anode side pressure disturbance. By reducing the dual-ejector hydrogen supply and circulation system’s pressure variation, the impact on the PEMFC operational life was greatly reduced.