State of the Art of Modelling and Design Approaches for Ejectors in Proton Exchange Membrane Fuel Cell

Antetomaso, Christian

doi:https://doi.org/10.1155/2024/7931501

Modelling and Simulation in Engineering

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Abstract Introduction Literature Review Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Review Article | Open Access

Volume 2024 | Article ID 7931501 | https://doi.org/10.1155/2024/7931501

State of the Art of Modelling and Design Approaches for Ejectors in Proton Exchange Membrane Fuel Cell

Christian Antetomaso^1,2

Academic Editor: Vijayanandh Raja

Received03 Oct 2023

Revised17 Jan 2024

Accepted18 Mar 2024

Published05 Apr 2024

Abstract

Proton exchange membrane fuel cell (PEMFC) has a promising future in the power generation and transportation fields. Recirculation of unused anodic gases is fundamental to achieve a high-performance energy system, and this is usually attained employing ejectors or pumps. With respect to the latter, ejectors present no moving parts, thus resulting in both higher overall efficiency of the system and lower maintenance cost. Their main drawback is represented by the narrow optimal operative range: the entrainment ratio (ER) greatly depends on primary pressure, working pressure, and operative condition in general. In the last decade, numerous authors focused their efforts on fully comprehending and correctly simulating their working principles and analyzing how geometrical parameters influence ER and design different geometries to enlarge the operative range. The aim of this paper is to present in an ordered and clear manner the state of the art of ejector design, both from simulative (turbulence model, single or multiphase stream, etc.) and empirical (commonly used “rule of thumb”) points of view.

1. Introduction

PEMFC has been proven to be a possible solution for a green future in both transportation [1] and static power production [2]. It is a common practice to supply reaction gas with excess stoichiometric ratio to ensure high performance [3] of the cell and purge forming water droplets and impurities [4, 5]; thus, several researchers focused their effort on investigating various gas management strategies, with the predominant ideas being dead-end anode [6, 7] and excessive gas recirculation [8, 9]. In operating with a dead-end configuration, the cell presents good performance and high hydrogen utilization rate; however, employing this strategy for a prolonged period led to accumulation of inert gas and water, hence degrading cell over time. On the other hand, anodic gas recirculation system (ARS) requires the design, installation, and maintenance of an additional component, being it a pump or an ejector. Pumps have a wide operating range and relatively easy control but will increase power consumption and overall complexity of the system [10, 11]. Ejectors present themselves as an interesting option to play that role, given their advantages with respect to pumps: lower installation and maintenance cost, no moving parts, and no noise [12, 13].

Figure 1 shows a simplified scheme for an ARS that employs an ejector. The hydrogen is primarily supplied to the PEMFC from the high-pressure hydrogen tank; the gas travels through the serpentine, and then, the exceeding part is recovered in a secondary circuit. It is worth noting that the nature of this “recovered” flow, two-phase multispecies, poses one of the major issues with ejector simulation [14].

The ejector is essentially a device that uses the high pressure of a fluid to pump a low-pressure one.

Figure 2 shows the geometry of a simple ejector. The motive or primary fluid is the one at high pressure (), while the secondary fluid resides at low pressure () are in a toroidal space. The motive fluid is initially accelerated through a nozzle (, ) and thus creates a low-pressure region nearby its exit; this region is often referred to as suction chamber since the low-pressure fluid tends to move towards the motive fluid due to the pressure gradient. At this point, fluids start to mix in the mixing chamber (, ) and finally expand in the divergent section (, ) to recover kinetic energy and reach the required working pressure. An experimental schlieren visualization of this process is presented by Rao and Jagadeesh [15]. All the parameters shown in Figure 2 (and even more if we consider different geometries, e.g., convergent-divergent nozzle and multistage ejector) are fundamental during the design process, since they play an important role in determining the ER provided by the ejector, its optimal operative range, and critical condition. The ER is evaluated through the following formula: where and are the primary and secondary mass flow, respectively. Another important parameter to characterize ejectors is the range coefficient (); it indicates the percentage of working condition that the designed ejector can cover with respect to the whole operative range of the system. In PEMFC system, it is usually in the range 65-80% [16]. It is calculated as follows: where and are the maximum and minimum operating power and is the power peak of the fuel cell stack.

Figure 3 is useful to better understand how ER changes in the working range of the ejector. At fixed and , it is stable on its maximum value as increases since both flows are chocked. This is the range for which the ejector was originally designed. As the backpressure surpasses a certain threshold, only the motive fluid is chocked, and the ER sharply decreases. If the backpressure continues to rise even further from the design point, reverse flow mode is reached. This means that the useful operative range of an ejector is quite narrow. Several authors investigated through experimental and simulative studies the effects of geometrical parameters, some even proposed novel ejector concepts (multinozzle, variable area, and so on). Deciding which model and thus which rule follow in designing an ejector for a specific purpose is quite tortuous due to the abundance of empiric rules that are presented in the literature. In this paper, the state of the art from both experimental and simulation point of view is presented and commented with the aim to provide an overlook on the most commonly used models.

2. Ejector Simulation

Due to the reciprocal influences of the various geometrical parameters of an ejector, the optimization of its design could be a long and expensive process. Proper modelling could be an invaluable tool to optimize this device and bring down prototyping costs. The first distinction that has to be made when talking about ejector modelling is whether to consider a constant pressure mixing (CPM) or constant area mixing (CAM) device. The substantial difference lays on the geometry of the designed suction chamber. Figure 4 visualizes these design concepts. Their models were early developed by Keenan et al. [17] and still today represent the basis for ejector analysis and performance evaluation. CPM ejectors are considered more favourable for most applications since, even though they provide lower mass flow rate, they have the advantages of operating in a wider range of backpressures, thus showing higher working stability [18, 19]. At present, the two most adopted modelling approaches are the lumped parameter model (LPM) and computational fluid dynamics (CFD) model. The former is faster, but its prediction capability strongly depends on the parameter choice and how those are able to summarize local phenomena. On the other hand, CFD approach is far more time-consuming, and it has not a defined methodology. Historically speaking, density-based (DB) solver was used for its high-speed compressible flow [20], but it requires attention in imposing Courant-Friedrichs-Lewy (CFL) condition [21]. However, Van Vu and Kracik [22] compared DB and pressure-based (PB) solvers with a real gas model, evaluating a 1% discrepancy for ER, but also observing that PB resulted less time-consuming and more stable. Even more troubling is the simulation of turbulence inside this device. Reynolds-averaged Navier-Stokes (RANS) approach is generally used, but studies presented from different authors show contradictory results over which turbulence model should be adopted: even though global parameter (e.g., ER) can be similarly predicted with different turbulence model, the local flow phenomena may differ [23]. Mazzelli et al. [24] conducted numerical analysis using 4 different turbulence models (–, – realizable, – SST, and the stress– Reynolds Stress), noticing that the best solution varies with the operative condition. In particular “ models” are more accurate with low primary pressure, whereas – SST showed the best overall performance. Besagni and Inzoli [25] confirmed that – SST performs better than other models, showing good agreement in both global and local parameters. However, in the case of fuel cell ejector, Chen et al. [26] concluded that – model is more accurate for low and medium flow rate, while – realizable shows better agreement with experimental results at large flow rate. Xiao et al. [27] performed a comparative study varying solver, turbulence model, near-wall treatment, and spatial discretization scheme. They concluded that the results from PB solver are slightly closer to the experimental data with respect to the ones from DB. The standard – model resulted very sensitive to the near-wall treatment; thus, the – SST and the – realizable (with standard wall function or enhanced wall treatment) are recommended. A different concern in simulating these devices lays on whether to consider a 2D axisymmetric or 3D domain. Both Pianthong et al. [28] and Gagan et al. [29] compared a 2D and 3D ejector model, concluding that, even though the 3-dimensional approach led to better accuracy, the axisymmetric assumption had a marginal influence on the model prediction capabilities, since it just slightly influenced axial velocity and pressure in the divergent region. However, Mazzelli et al. [24] noted that this effect may lead to large errors when operating in the off-design zone. It is worth noting that, when considering rectangular ejector cross-section, using the 2D or 3D approach may cause big discrepancies [30, 31]. One last concern regards the nature of the recirculating fluid, since it presents water vapor and thus condensation may occur inside the component. A commonly made assumption neglects the effect of this state-shift phenomenon, or even neglects the presence of water vapor at all, considering a dry hydrogen flux due to the complexity of this multiphase problem. However, both Wang et al. [32] and Ariafar et al. [33] confirmed that the wet steam model is able to better capture flow patterns inside the ejector. Han et al. [14, 34] performed two-phase simulations to weigh the effect of liquid water on the ejector efficiency. In [14], results showed an increase in temperature (due to latent heat of vaporization), lower velocity, and higher pressure of the gas phase due to condensation, resulting in a lower entrainment performance and better agreement with experimental results. In [34], the authors took into account both the homogeneous and the heterogeneous condensation. The two crucial factors that seem to influence the most droplet size were residence time and subcooling degree. Condensation process led to a mean efficiency reduction of 1.42%. From the experimental point of view, some studies have been conducted to visualize flow morphology and droplet distribution [35–37]; however, these studies often offer only a qualitative analysis of the phenomenon due to both visualization difficulties and hydrogen safety hazard.

3. Literature Review

Defining the optimal nozzle geometry is a fundamental step since it affects both entrainment ratio and critical backpressure. Metin et al. [38] used ANSYS Fluent to model an ejector under the single-phase axisymmetric flow assumption, concluding that the ER of the ejector could be increased up to 6% varying the primary nozzle position. It is worth noting that they also observed a critical point where while increasing NXP, the ER starts decreasing. Chen et al. [39] proposed an annular mixing layer theory: the idea is that the primary and secondary flow mix in an annular layer that grows as flow moves towards the ejector axis. The developed model is in good agreement with the experimental data and confirmed that the optimal nozzle exit position depends on the expansion ratio, thus on the working condition. Poirier [40] performed an extensive experimental campaign to verify the effect of working condition on nozzle optimal position. In one of the analyzed cases, the critical entrainment ratio improved by 34% just by moving the nozzle. Moreover, he also observed multiple “optimal” value, up to four peaks. Also, Rand et al. [41] experimentally and numerically investigated the presence of these suboptimal nozzle position points using the compound choking indicator: for a given operative point, this criterion highlights the location where the secondary flow is choked and allows to individuate the variation of choking position for several values of . However, also the mixing chamber layout plays an important role in the ejector’s overall performance. As a matter of fact, Pei et al. [42] proposed a CFD single-phase ideal gas model to perform a parametric study on the measures of interest of an ejector. In particular, they determined an optimal range for the ratio between mixing chamber and nozzle out diameter () and between mixing chamber length and diameter (). Ma et al. [43] performed a 3D CFD simulation and, at set operative conditions, considered 4 geometrical parameters to be optimized with a user-defined priority: nozzle diameter, nozzle position, secondary inlet diameter, and mixing chamber diameter. It is clear by now that the design geometry strongly depends on the defined criterion; therefore, more complex and comprehensive optimization algorithms [44–50] are needed.

Table 1 reports a summary of the type of study performed, modelling adopted, and key findings for several literature papers.

4. Alternative Geometries

From the literature review presented in Table 1, it is clear that simulation and optimization led to an increase in ejector performance, but the narrow operational range issue still remains. Therefore, some researchers focused their efforts on investigating novel approach on ejector design: multistage, multinozzle, moving nozzle, nested nozzle, bypass circuit, and other solutions are hereby presented.

A simple solution is the introduction of a moving needle in the nozzle, allowing for operation with variable nozzle diameter and with the possibility to better control motive flow direction as it enters the suction chamber (see Figure 5). This solution needs a control strategy that properly set the correct nozzle effective area with respect to operative condition considered, but it is able to enlarge the range coefficient of the ejector [63–66]. However, the sealing, manufacturing costs, precise control, and long-time reliability are significant challenges.

Another conceptually simple solution is the usage of multiple ejectors [67–70], and the ad hoc control strategy realized by Chen et al. [71] for a 70 kW PEMFC using two identical ejectors was able to cover the stack’s minimum 8% to maximum 100% power output.

Other authors investigated deeper change in ejector geometry. Chen et al. [72] observed a low-pressure zone in between mixing and diffuser section and proposed a motive fluid bypass to enlarge ER. The proposed solution (see Figure 6) showed good performance when compared to the original design: larger ER and lower critical backpressure.

Song et al. [73] simulated and experimentally investigated the performance of a twin-nozzle ejector, compared to the traditional one that improved the hydrogen recirculation under low load condition. The geometry proposed by Xue et al. [74] also employs a modified version of a nozzle which was divided into four small nozzles, as per Figure 7. The total mass flow rate passing through the novel nozzles is equal to the original one. In choosing the number, they had to consider the fact that, even though more nozzles lead to more flow rate step, it may also lead to malfunctioning in the single node operational mode. Simulation results confirmed that the multinozzle ejector expands the operating range by switching the working condition with different coactive nozzle strategies, thus effectively increasing the range coefficient. Another study [75] introduced a nested nozzle (see Figure 8), in which geometry was optimized through CFD in order to cover the whole operative range, from idle condition to full power. On a similar note, Du et al. [76] and Han et al. [77] investigated the performance of a coaxial nozzle, confirming the extension of operative range with respect to the default one. A different take on multistage ejectors is the one offered by Wang et al. [78] and shown in Figure 9: it is a geometry not as compact as the one shown in Figure 8 but still offers an increase in ER of around 30%.

5. System Integration and Control

Other than the ejector itself, the whole PEMFC energy system must be considered when designing this component [16]. First, the anodic side usually requires the presence of a gas-water separator in order to remove most of the humidity from the recirculating circuit. The three mainly used separator types are presented in Figure 10. Even though cyclone and filter separator are characterized by a high-phase separation efficiency, they also cause larger pressure drop with respect to baffle one; regardless from the selected ARS, a lower recirculating pressure implies overall worst operative condition for the system. Han et al. [79] focused their efforts on optimizing a baffle separator through CFD simulations. In particular, three different structures were developed for a 75 kW PEMFC and analyzed both experimentally and numerically. For a comparable pressure drop, the optimum geometry ensures better separation efficiency.

On a different note, Ma et al. [80] designed a novel cyclone water separator system for a 40 kW PEMFC and investigated the flow field characteristics through CFD simulations. The new concept was designed with a volute inlet to boost the swirling effect, leading to enhanced centrifugal effect and steadier performance throughout the flow rate range. However, even in the presence of this component, a suitable purging phase has to be carefully chosen to fulfil two main functions: it removes inert gases that may accumulate in the anode due to membrane permeability and eliminates impure hydrogen [81]. Nitrogen may cross from cathode to anode through membrane due to the concentration gradient, and its accumulation negatively impacts the ER [62]. At the same time, a high purging frequency increases hydrogen consumption and leads to pressure fluctuations that may damage the membrane [82, 83]: keeping the pressure difference within the threshold with fast transient responses is a crucial issue for the safe operation of PEM fuel cell system [84]. For what regards ejector integration in the overall energy system, as shown in the previous chapter, different geometries have been proposed through years since the simple design suffers of low range coefficient. In [69], a comparative study was performed between single- and dual-ejector layouts, with the latter being able to cover the whole PEMFC-operating range. However, the authors noted that during the switching phase, pressure oscillations may undermine the lifetime of the membrane; thus, adequate control strategies are required. Thompson et al. [85] performed an analysis cost for an 80 kW light duty vehicle. They considered dual static ejectors (and relative control valves) for the ARS; nevertheless, they hinted to the fact that, according to their model, a single pulsed ejector may represent a valid solution: it shows the lower volume, lower power request, and lower production cost. Singer et al. [86] designed and performed numerical and experimental investigations on a pulsed injector-ejector unit. Ejectors are usually designed to work at full load, but the pulsed one is a very promising approach to cover the highly dynamic load of the automotive market. A solenoid valve just before the ejector nozzle can be opened for a desired period and frequency, ensuring proper stoichiometric value at anode inlet even at low load.

In this context, control strategies are of fundamental importance [87, 88]. As a matter of fact, the needle position in a variable area nozzle, the activation in a multiejector layout, and the opening in a multinozzle ejector all require an ad hoc control to cover low to medium system load. Qin et al. [89] proposed a classic PID to control the hydrogen mass flow by regulating a proportional valve just before the ejector body; the study reported a regulating time below 4.5 seconds under several load conditions. In [63], a variable geometry ejector is responsible for recirculating hydrogen in the cell, a stepper motor-leadscrew-based linear actuator control needle positioning, thus changing the effective nozzle diameter. Experiments suggested that the implemented PID algorithm produced considerable unnecessary motion of the needle. To overcome this issue, the derivative part of the controller was removed and a dead-band was added to the calculated pressure error. The new PI controller was able to provide the required hydrogen stoichiometry. Moreover, the ejector showed a good tolerance to liquid water, experiencing only momentary pressure drops. In [90], a common rail hydrogen injection+ejector system is implemented, and a Mamdani fuzzy controller is designed to regulate the hydrogen pressure. The controller evaluates the error between the hydrogen pressure setpoint and its actual value and also the error change rate, giving as output the change of the pulse width of the injection phase. Sankar and Jana [91] proposed a multi-input multioutput (MIMO) sliding mode controller with the aim of maximizing membrane lifetime. Selected inputs were anode source pressure, compressor motor voltage, and cooling water flow; measured outputs were output cell voltage, compressor airflow, and system temperature. An adaptive supertwisting (ASTW) sliding mode algorithm is developed for the cooperative control of fuel and air feeding in PEMFC by Yin et al. [92]. Hydrogen excess ratio was aimed to a constant 1.5, while optimal oxygen excess ratio was taken from the literature table, given the current. It is worth noting that, since the air compressor has to dynamically adjust to the controller request, the membrane may suffer efficiency/useful life loss; thus, this value has to be monitored with caution. Reported results show an improved regulation time and smaller overshoot for an ASTW controller with respect to a conventional PID one.

6. Summary

Fuel cell systems can represent a step forward in the direction of cleaner and greener future, but the technology itself is still not mature. The design of an effective and efficient ARS could help its spread. In this work, a literature review on ejector modelling, geometry optimization, and possible alternative configurations is presented. The following conclusions can be drawn: (i)There are lots of papers that investigate the optimization of ejector geometrical features with different modelling approaches (thermodynamic model, CFD 2D axisymmetric/3D, etc.) and different optimization rules (single-object, multiobject, adjoint method, etc.), but the reported results show sometimes contradictory findings. The reason of this inconsistency is due to the great influence that both working fluid and working conditions have on the optimal geometry. A robust workflow for ejector simulation is still to be developed. As a matter of fact, the chosen turbulence model influences the simulation behavior in the region near the jet core and there is no defined recommended model. Moreover, most of the reported literature focused their efforts on simulating the simple ejector geometry; thus, it is recommended to perform those simulations also for alternative geometries and/or different ARS layouts(ii)Flow condensation phenomena inside the ejector are usually neglected, but some studies have been conducted both from experimental and numerical points of view; given the lack of a sturdy workflow, it is recommended to conduct numerical simulations of this two-phase flow varying the adopted turbulence model. This may give some insight on what could be the best way to simulate ejectors(iii)Even though there are some differences in the adopted methodology, researchers seem to agree that the dimensionless ratios / and /, the nozzle diameter , and its position are the most important geometrical parameters in the ejector design. Some studies even reported the presence of multiple suboptimal nozzle position; thus, it is of focal importance to correctly chose this value(iv)Some alternative geometries and control strategy are reported in the last part of the paper. It is worth noting that the simplicity of the ejector was one of its best “selling point”; however, its implementation in real working system requires some tweaks; the sealing and manufacturing cost for a variable ejector nozzle, or the proper control of pressure oscillation during switching phase for a twin ejector layout, are still significant challenges

Acronyms

ARS:	Anodic gas recirculation system
ASTW:	Adaptive supertwisting
CAM:	Constant pressure mixing
CFD:	Computational fluid dynamics
CFL:	Courant-Friedrichs-Lewy
CPM:	Constant area mixing
DB:	Density based
ER:	Entrainment ratio
LPM:	Lumped parameter model
MIMO:	Multi-input multioutput
PB:	Pressure based
PEMFC:	Proton exchange membrane fuel cell
RANS:	Reynolds-averaged Navier-Stokes.

Symbols

:	Primary/motive pressure
:	Secondary pressure
:	Outlet pressure
:	Nozzle angle
:	Nozzle outlet diameter
:	Nozzle position
:	Mixing chamber length
:	Mixing chamber diameter
:	Divergent angle
:	Divergent outlet diameter
:	Secondary mass flow
:	Primary mass flow.

Data Availability

The numeric results and experimental data presented in this review are from previously reported studies and datasets, which have been cited.

Conflicts of Interest

The author declares that he has no conflict of interests regarding the publication of this paper.

Acknowledgments

The author gratefully acknowledges the partial financial support of the European Union, NextGenerationEU—in the framework of the National Sustainable Mobility Center—MOST (CN00000023) and Italian Ministry of University and Research Decree no. 1033 (17/06/2022, Spoke 12).

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