2.1. Injector in PEMFC working principle
An anode hydrogen recirculation system with a single nozzle injector is shown in Figure 1. A diagram of an anode hydrogen recirculation system with a single nozzle injector. The injector consists of a nozzle, a suction chamber, a constant pressure, constant area mixing chamber and a diffusion chamber. The pressure reducing valve reduces the high pressure hydrogen from the hydrogen tank. Next, the low-pressure hydrogen gas (primary flow (PF)) expands through the nozzle, converting the hydrogen’s pressure potential energy into kinetic energy. The secondary flow (unreacted hydrogen (SF)) from the PEMFC stack anode is drawn into the injector’s suction chamber. Afterwards, SF and PF are mixed in the mixing chamber. The mixed gas enters the fuel cell anode after passing through the diffusion chamber.
During the recovery process, the injector improves fuel utilization while also releasing fuel cell anode water. In a fuel cell system, the relationship between different hydrogen mass flow rates around the injector is expressed as: is the mass of hydrogen entering the fuel cell, and are the mass of hydrogen recycled (unreacted) and consumed in the fuel cell, respectively.
The mass of hydrogen entering the fuel cell in the fuel cell system is greater than the mass of hydrogen that should theoretically respond.The hydrogen excess coefficient can be expressed by the following formula
represents the actual mass of hydrogen entering the fuel cell:
2.2. Structural design of PNFN injector
The power rating, mass flow rate, cell voltage, and other geometric parameters of the PEMFC are important for injector design.
According to the fuel cell parameters, the hydrogen PF mass flow rate
The calculation is as follows:
Where is the rated power of the fuel cell, is the molar mass of hydrogen, and are the single cell voltage and Faraday’s constant respectively.
Nozzle structure design is a key step for the injector.The following formula is used to calculate the nozzle throat area
:
Where is the critical speed, is the ratio of gas specific heat, is relative pressure, is PF pressure, is the gas critical pressure, is the gas constant, and is the gaseous critical temperature.
For 170 kW (Pe) high-power fuel cells, this study proposes a new four-nozzle injector. Traditional single-nozzle injectors are designed at certain operating points of the fuel cell. When the fuel cell power changes significantly, the performance of traditional single-nozzle injectors will drop sharply and cannot meet the flow requirements. Therefore, we designed multi-nozzle injectors to improve injector performance over the full operating range. We chose four types of nozzles (10%, 20%, 20% and 50% of the fuel cell rated power) because this type can meet the overall power requirements by combining nozzles with different operating modes. If the number of nozzles is less than four, the injector cannot operate within the entire power range of the fuel cell, and when the number of nozzles is greater than four, the structure of the injector will be too complex.
The nozzle that meets 10% of the rated power is called the first nozzle (N1). The second nozzle (N2) and the third nozzle (N3) are the same nozzles applying 20% of the rated power. The nozzle with 50% rated power is called the fourth nozzle (N4). In combination with different power nozzles, PNFN injectors can operate throughout the entire power range of the fuel cell. The working modes of injectors with different power according to the number of working nozzles are shown in Table 1.
In a four-nozzle injector, the hydrogen supply flow rate of each nozzle is equal to the percentage of the hydrogen supply flow rate of the fuel cell under rated operating conditions, and the throat area of each nozzle is equal to the percentage area of the total throat area. Combining the above formula, the throat area of each nozzle is calculated as follows:
Where is the nozzle (X) diameter, X = 1, 2, 3, 4.
The injector design process is shown in Figure 2.
Table 2 shows the diameters of the four nozzles obtained through the above iterative calculation process.
PEMFC systems use recirculation rates () to evaluate the performance of the injector, which is defined as: here is PF mass flow rate, is the SF mass flow rate.
Recirculation rate (
) of a PNFN injector can be calculated using the following formula:
Where, , , and are the mass flow rates of N1, N2, N3 and N4 respectively.
In addition to the injector nozzle, the performance and mass flow of the injector are significantly affected by other structural factors, such as NXP, mixing chamber diameter, diffusion chamber length, etc. These values are determined through multiple simulations.When the minimum recirculation ratio If it exceeds 0.50, the injector design process ends, otherwise, the injector structure is redesigned. Table 3 shows other geometric parameter values of the PNFN injector.
The PNFN injector structural diagram and 3D model diagram are shown in Figure 3a and Figure 3b respectively.