# Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 2: Two-Phase Ejectors

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## Abstract

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## 1. Introduction

_{2}heat pumps occupies an important place among the available works. Sarkar [6] compared several important such cycles with transcritical CO

_{2}for the purpose of expansion recovery. Elbel [7], building on previous work [1], provided a detailed account of the transcritical CO

_{2}ejector application in air-conditioning, in addition to analytical and experimental results on system performance improvements. Further work by Sumeru et al. [3] extended the investigation to issues like thermodynamic modeling and comparison with the conventional cycle, irrespective of the refrigerant type. Around the same time, Sarkar [8] also proposed a review of ejector expansion cycle including geometric parameters, refrigerant and operating considerations. This work included a good description of various cycle configurations as well as performance characteristics of both subcritical and transcritical systems. A recent paper by Besagni [11], gives a concise rundown of last two-year achievements in areas of ejector-based refrigeration, power conversion and chemical processes, with future research and development perspectives.

_{2}ejector passages by means of validated CFD modeling. The recent work of Elbel and Lawrence [10] provided more information on emerging CFD efforts, new control measures, alternate cycle configurations and progress towards the development of applications based on ejectors for expansion recovery in cooling-refrigeration setups.

## 2. Two-Phase Ejector Characteristics

#### 2.1. Ejector Types

#### 2.1.1. Gas–Liquid Injectors

#### 2.1.2. Liquid–Gas Ejectors

#### 2.2. Ejector Geometry

_{m}) as defined in Figure 2. The mixing chamber and the diffuser angles (respectively φ and η) as well as the angle of the primary nozzle divergent β, also are sometimes considered.

_{m}. It generally has an effect on both the entrainment and the compression ratios of ejectors.

_{2}under transcritical conditions. A maximum COP value was reached when the motive nozzle exit positioned before the mixing chamber inlet was three times the diameter of the constant-area mixing section. Hu et al. [29] experimented a two-phase ejector with the refrigerant R410A, in an air-conditioning system. The distance between the nozzle outlet and the constant section mixing chamber was varied from 0 to 9 mm. An optimal position of the nozzle for system capacity and performance was found to be 3 mm. Experimental results obtained by Wang and Yu [30] with R600a two-phase ejector showed no optimal position for the nozzle. A slight increase of entrainment ratio with NXP was observed, but at 6 mm upstream of the mixing chamber, the entrainment ratio tended to remain constant. Unlike this trend, experiments of Ameur and Aidoun [31] with R134a two-phase ejector have shown an optimal position of the primary nozzle in the ejector, and this position was not very sensitive to operational conditions. The authors noticed a sharp drop in performance of the ejector when the nozzle was placed close to the inlet of the constant-area section.

_{e}= 5 °C and T

_{c}= 40 °C), isobutane yielded maximum COP improvement of 21.6% followed by propane (17.9%) and ammonia (11.9%), for area ratios of 10, 7.7 and 5.7 respectively.

_{m}/D

_{m}ratios ranged from 4 to 21. However, no significant improvement in pressure recovery was observed beyond L

_{m}/D

_{m}= 16.

_{2}two-phase ejector with rectangular cross-section. Three mixing lengths were experimented (5 mm, 15 mm, and 25 mm); the 15 mm case yielded the highest ejector efficiency and COP in all tested conditions. Along the same lines of investigations with transcritical CO

_{2}two-phase ejector, Banasiak et al. [37] tested three mixing section length (L

_{m}/D

_{m}= 5, 10 and 20); the ratio L

_{m}/D

_{m}= 10 was associated with the highest ejector efficiency. In a recent study, Jeon et al. [38], investigated the effects of D

_{t}and D

_{m}on the performance of an ejector expansion air conditioner using R410A, under various climatic conditions. D

_{t}was varied from 1.04 to 1.21 mm, and D

_{m}from 7 to 13 mm, while the ratio L

_{m}/D

_{m}was fixed at 10. At the smallest D

_{t}, the maximum COP increase was observed. The optimum D

_{m}was determined to be 9 mm. D

_{m}was optimized based on the climatic conditions. The optimum D

_{m}increased with an increase in the average annual outdoor temperature.

_{2}, such that the pressure profiles did not correspond to the predictions of the isentropic homogeneous equilibrium model because the flow was in a non-equilibrium and supersaturated state.

_{2}ejector refrigeration system [42].

_{2}with a bypass on the suction nozzle duct (Figure 4). The study assessed numerically the bypass positioning and its angle of incidence under several working conditions. Encouraging preliminary results in the order of 22.4% to 30.4% efficiency improvement at low-pressure conditions were obtained but more work is needed for higher pressures.

#### 2.3. Ejector Performance

#### 2.3.1. Ejector Efficiency

_{2}air-conditioning system model to estimate ejector component efficiencies at different ejector geometries and operating conditions [52].

#### 2.3.2. Second Law Analysis of Ejectors

_{2}ejectors by introducing a new factor to evaluate performance, based on the reference entropy increase in a classic expansion valve. The parameter ς

_{ej}introduced by the authors quantifies the entropy increase avoided with the use of an ejector relative to a reference process:

_{ej}and ΔS

_{ref}are the generated entropies across the ejector and reference process respectively. In the case of an EERC, ΔS

_{ref}represents the throttling stage of a standard refrigeration cycle under the same operating conditions.

_{2}, Banasiak et al. [54] observed ς

_{ej}in the range (−0.062; 0.223). Negative ς

_{ej}values mean that more irreversibilities were generated across the ejector than the reference did. In addition, the influence of the diameter and length of the mixing chamber was shown to significantly affect performance. In the conditions considered in this study, an enlargement of the mixing cross section area by 17.4% and shortening the mixing length by 33.3% resulted in an increase of the overall entropy growth rate by 8.9% and 5.4%, respectively.

_{χ}, defined as the ratio of outlet to input exergy flow rates:

_{χ}represents the amount of potential work recovered using an ejector.

_{ej}≈ 98% for an EERC with R134a. The exergy efficiency of the whole EERC system was on average 18%, always two points over that of the standard refrigeration system without ejector tested under the same operating conditions.

#### 2.4. Internal Flow Structure

_{2}ejectors, the scarcity of experimental identification or classification of flow patterns for the two-phase CO

_{2}ejector passages. In this respect and for two-phase ejector internal flow structures in general, visualization methods with high resolution are needed to capture shock phenomena in specially limited component sizes such as found in two-phase ejectors operating with common and natural refrigerants. Schlieren visualization and PIV techniques applied in single-phase devices are also progressively introduced to capture two-phase flow structures and velocity effects.

_{2}in transcritical conditions. Images of flashing CO

_{2}flow were captured for both under-expanded and over-expanded flow by using an analog microscope and a camera. The flows could be observed through the transparent polycarbonate wall on one side of the nozzle.

_{2}cycle was based on a shadowgraph visualization approach. The study concerned the mixing chamber and focused on suction and mixing processes as well as configuration variations in flow structure with operational parameters or geometry features such as primary pressure conditions, cross-section area mixing and the primary nozzle divergent length. Images of the mixing process showed that these parameters played an important role in premixed vortex formations, their size and their location in the suction chamber. The geometry features in particular, seemed to substantially influence the stream mixing and the flow homogeneity, a condition that affects performance.

_{2}two-phase ejector operating in transcritical flow conditions, relying of visualization experiments by direct photography. The method used a single lens reflex camera and a light film for uniform light and more brightness adjustment to better distinguish vapor and liquid droplets in the flow medium.

_{2}and oil droplets in the flow. The results of the investigations have shown the influence of parameters such as the inlet pressures and the expansion angle at the nozzle exit.

#### 2.5. Applications Potential of the Two-Phase Ejector

_{2}cycle [48,81]. The performances of the transcritical CO

_{2}cycles are generally superior to the other refrigerants.

## 3. Two-Phase Ejector Modeling

#### 3.1. Thermodynamic and Analytical Modeling

_{2}by Banasiak and Hafner [95], who investigated the influence of the phase transition model on the mass flow rate prediction. The delayed equilibrium model with homogeneous nucleation, superimposed to homogeneous and heterogeneous nucleation was used for the purpose of the metastable state analysis of a transcritical flow with delayed flashing over the motive nozzle.

_{0}. At choking conditions, the mass flux G is maximized. There is therefore less need to determine the local speed of sound for this particular purpose and the mass flux approach can be easily applied in two-phase flows, where critical conditions lie mostly over the saturation line. The model of Ameur et al. [18,25] employs this approach to compute the thermodynamic properties of liquid–vapor in the primary nozzle in critical conditions. In the application to ejectors for EERCs, deviations of up to 7–14% and 6–14% were respectively observed in the primary jet critical mass flow rate and the compression ratios.

_{2}EERC.

_{2}flow with delayed flashing over the motive nozzle.

_{2}expansion process in ejectors was proposed. Zhu and Jiang [87], in a study of transcritical CO

_{2}ejector expansion refrigeration cycle proposed an analytical model taking into account non-equilibrium effects by means of a correlation based on experimental data of several case studies and capable of predicting primary and secondary mass flow rates. A further correlation simplifying computations at the ejector throat was developed for the primary mass flow rate. Accounting for non-equilibrium was to be important when the liquid mass fraction at the nozzle throat was higher than 0.65. A number of analytical and thermodynamic ejector models are reported in Table 1.

#### 3.2. CFD Modeling of Two-Phase Ejectors

#### 3.2.1. Treatment of Two-Phase CO_{2} Ejectors

_{2}transonic ejector flow by using homogeneous and heterogeneous flow models in order to account for non-equilibrium effects. They then compared the predictions of both approaches in terms of pressure distribution in the mixing chamber, which were well predicted by both approaches. Unfortunately, this partial validation was insufficient since the heterogeneous approach predicted the lowest pressure by an order of magnitude right after the nozzle throat. In addition, according to the authors, entrainment ratio predictions were also different.

_{2}as the working fluid were based on Nakagawa et al. [36] for validation in terms of pressure recovery. Even though the trends of the results were comparable, the discrepancies between simulations and experiments were important. The authors attributed this poor concordance to the challenges of modeling two-phase, turbulent non-equilibrium flow and the selection of the turbulence model.

_{2}ejector-expander applications for refrigeration and heat pumps. It is a non-homogeneous mixture model, including several sub-models for local interphase energy and mass transfer, two-phase velocity of sound formulation and real fluid properties of the refrigerant. The turbulence model formulation used was the k-ω SST type and the thermophysical properties of CO

_{2}were obtained from the NIST-REFPROP database. The simulations indicated that the ejector performance was only slightly influenced by the inclusion of the slip model. The cavitation portion of phase change was generally small but could be dominant near the walls and at the motive nozzle throat. Compression and entrainment ratios were predicted to within 10% of experimental data and there was a threshold diameter at which performance was characterized with a gentle shock in the mixing zone. In a subsequent investigation, Yazdani et al. [111] put more focus on the flow process of transcritical and subcritical cases of CO

_{2}in converging–diverging nozzles. This study showed that phase change is generally small but can be dominant near the walls and at the motive nozzle throat. Choking occurred downstream of the throat, where void generation promoted flow acceleration while leading to a drop in the sound speed. The nozzle configuration and the upstream operating conditions were found to shape the two-phase jet and affect the void generation rate.

_{2}ejector was developed on the assumption of homogeneous equilibrium flow. An enthalpy-based formulation, in which the specific enthalpy, instead of the temperature, as an independent variable was employed. Gas–liquid mechanical and thermal equilibrium between phases was assumed for two-phase flow and the turbulence effects were modeled by the RNG k-ε turbulence model. In addition, NIST-REFPROP database was again used for the extraction of the fluid properties. Maximum discrepancies on the prediction of primary and secondary flows were respectively 14% and 19.7%.

_{2}operations. The comparison of the experimental and computational results showing accurate results could be obtained when operating near or above the critical point. The model accuracy decreased with the decreasing temperature and decreasing distance to the saturation line [114].

_{2}two-phase ejectors. The predictive accuracy of the motive nozzle mass flow rate improved, in comparison to currently available numerical models for subcritical regimes. For operating regimes in transcritical conditions, comparable high accuracy to the HEM model was found. Further, the authors reported that HRM application for motive pressures above 59 bar predicted motive flow within 15% accuracy. Below 59 bar, the motive mass flow rate prediction was 5% to 10% more accurate than with HEM formulation.

_{2}ejectors by introducing a new factor to evaluate the ejector performance based on the reference entropy increase in a classic expansion valve. They found that the shock train at the primary nozzle outlet and the turbulent interaction process in the mixing chamber were a major source of irreversibility. Moreover, and based on the model predictions, the authors recommend that all ejector dimensions must be optimized simultaneously, otherwise, the irreversibility reduction in one ejector section may translate into an increase in the next section, thus neutralizing the overall gain. In addition, the influence of the diameter and length of the ejector mixing chamber was shown to significantly affect performance.

_{2}ejectors for refrigeration systems. They worked on ejector geometries to adjust several parameters for maximized performance. The optimization of the results showed that the ejector efficiency could be improved by up to 6%. A recently published paper by Haida et al. [117] numerically assessed the effects of heat transfer on the wall of a CO

_{2}ejector in the context of air-conditioning. The results indicated the reduction of the mass entrainment ratio could be as high as 13%, as a result of the non-adiabatic assumption condition.

#### 3.2.2. Phase Change in the Motive Nozzle

## 4. Experiments on Ejectors

_{2}was expanded. The decompression pressure profile was recorded. It was found that the optimum supersonic decompression before shock waves occurrence obeyed the homogeneous equilibrium model, while behind the shock, the pressure profile displayed no equilibrium condition as indicated by the thickness of the shock waves and the subsonic flow behind them. These measurements indicated that the decompression process in the motive nozzle divergent could not be correctly predicted by the IHE model, which hinted to a thermal and mechanical non-equilibrium state. In a subsequent work, Nakagawa et al. [41] observed and experimentally addressed the CO

_{2}decompression phenomena in the nozzle divergent when metastable fluid flashes to low quality two-phase flow. As was previously established, the fluid in the nozzle was in temperature and pressure equilibrium, in accordance with the experimental measurements. Two-phase flow results through converging–diverging nozzles with divergence angles ranging from 0.07° and 0.612° at inlet pressure and temperature conditions of 6 to 9 MPa and about 20 to 37 °C, respectively were gathered. The authors confirmed by both calculation and experiment that optimum decompression for the largest divergent angles (>0.306°) and inlet temperature above 35 °C, was in homogeneous equilibrium condition. Similar experimental observations were reported by Berana et al. [59] who also measured the wall pressure along the nozzle divergent in an attempt to trace the shock wave occurrence.

_{2}, in view of the growing interest for this refrigerant. Berana et al. [59] investigated the two-phase flow field in a converging–diverging nozzle with transcritical pressure CO

_{2}. This work concerned a flashing flow with different lengths but with the same divergence angle and in the presence of shocks and non-equilibrium effects measurements.

_{2}by Zhu et al. [67]. The flow structure was recorded by means of direct photography under various operating conditions in the zones of suction and mixing after the primary nozzle exit. Observations highlighted the effect of inlet pressures on the primary mass flow rate. The primary flow angle at the nozzle exit decreased with increasing secondary pressures. Large expansion angles of the primary flow reduced the entrainment of the secondary stream. It was also observed that both primary and the secondary flows mix over short mixing region in the chamber and the resulting stream became rapidly uniform.

## 5. Two-Phase Ejector Cycles and Systems

_{2}as a natural refrigerant with good thermophysical properties and performance potential in transcritical cycles [133]. Relevant theoretical and experimental developments in two-phase ejector treating these aspects are briefly presented in the next subsections.

#### 5.1. The Conventional Ejector Expansion Refrigeration Cycle

#### 5.1.1. EERC Theoretical Studies

_{e}= 5 °C and T

_{c}= 40 °C) with the use of the ejector as an expansion device, isobutene yielded maximum COP improvement of 21.6% followed by propane (17.9%) and ammonia (11.9%).

_{2}) due to its favorable thermophysical properties generally and more particularly as a working fluid in EERC cycles under transcritical operating conditions. In air-conditioning system applications, the use of transcritical CO

_{2}in two-phase ejectors as expanders presents advantageous features. The pressure difference across the compressor is very high in comparison to ordinary refrigerants, thus representing a high source potential for work in ejectors which otherwise will not be recovered. Moreover, the compression ratio remains moderate, which means more reliable compressor operation and reasonable electricity consumption.

_{2}cycle for air-conditioning was investigated. It was found that the COP of EERC could be improved by more than 16% over the conventional compression CO

_{2}cycle working in the same conditions.

_{2}and R134a. It was found that the COP of the ejector expansion transcritical CO

_{2}cycle could be improved by more than 15% compared to the conventional transcritical reference. Furthermore, a comparison of R-134a and CO

_{2}based refrigeration cycles showed a better performance with CO

_{2}.

_{2}refrigeration application by Deng et al. [146] provided performance improvements in terms of system COP and capacity of 18.5% and 8.2% respectively over the conventional case with an internal heat exchanger and 22% and 11.5% respectively without the internal heat exchanger.

_{2}heat pumps, showing that the use of ejector as an alternative improved the energetic and exergy performances, while significantly reducing the optimum high side system pressure. He also proposed a correlation for the optimum pressure discharge of the system. A thermodynamic analysis of transcritical CO

_{2}refrigeration cycles performed by Perez-Garcia et al. [148] compared three configurations: with internal heat exchanger, ejector (EERC) or turbine, as alternative replacement devices to the conventional expansion valve. COP based estimations indicated that the turbine-using cycle generally outperformed the other configurations under the same conditions. However, outlet gas-cooler temperatures above 27 °C favor the ejector configuration over the internal heat exchanger one, for entrainment ratios higher than 0.5. Further, increasing the evaporation temperature from −10 °C to 0 °C results in the highest COP improvement in comparison to the IHX and turbine configurations (35.85%, 25.4%, and 24.21%, respectively).

_{2}cycle for air-conditioning purposes. They evaluated losses in different parts of the cycle, the effect of ejector operation on overall performance and compared the EERC and the expansion valve compression cycle. It was found that for any given running condition there was a critical point for which the operating parameters corresponded to the optimized operation of the cycle. At this point, the use of ejector instead of a throttling valve could reduce by more than 25% exergy losses and increase COP by more than 30%.

_{2}ejector expansion cycles was studied by Zhang et al. [150]. In their paper they reported simulations on the effect of IHX on the performance of the ejector expansion refrigeration cycle. They found that unlike in a conventional throttle valve cycle, the addition of an IHX in the CO

_{2}ejector refrigeration cycle did not always improve the system performance but rather depended on the isentropic efficiency level of the ejector.

_{2}EERC performance. Results from this study indicated that maximum COP could be up to 45.1% higher than that of the conventional cycle. In addition, exergy losses of the ejector-expansion could be reduced by about 43.0% in the same conditions.

_{2}. This model helps monitoring changes in the expansion valve openings or the ejector area ratio variations and understand the EERC operational characteristics. As such, this tool can serve as a guide for better system control.

_{2}ejector-expansion heat pump. Dynamic optimization control strategy by genetic algorithm was used to obtain the optimal setting points. Results indicated the overall performances during the charging process can be increased, the energy consumption and the charging time can be reduced significantly.

#### 5.1.2. EERC Experimental Studies

_{2}.

_{2}, more specifically R134a and its potential substitute, R1234fa, showing that higher COPs were achieved with R1234fa and R134a, respectively 12% and 8% over the same cycle with CO

_{2}. Yet, the latter is more popular given its higher work recovery rate. Ersoy and Bilir [162] generated further experimental results showing that the R134a refrigeration system with an ejector as the expander could reach a COP between 6.2% and 14.5% higher than that of the conventional system.

_{2}EERC could increase COP by up to 22% over a conventional CRC working in similar conditions. The author confirmed that this increment in performance varied, depending on the operating temperature, ejector flow ratio, nozzle and diffuser efficiencies. Elbel and Hrnjak [48] then generated experimental data in a transcritical CO

_{2}ejector system which they then compared to conventional expansion valve system test results. Ejector integration in the cycle indicated that both the COP and the cooling capacity were improved by up to 7% and 8%, respectively.

_{2}EERC with or without an IHX, which they compared to the conventional system in the same conditions. The results indicated that an optimum length existed, for which performance in terms of ejector efficiency and cycle COP was maximized irrespective of the use of IHX. In this condition, a COP improvement of up to 26% over the conventional system was attained. Away from this optimum length, COP decreased by as much as 10% [165].

_{2}air-conditioning system in both expansion valve and ejector based configurations was assessed. The ejector design accounted for the non-equilibrium state in the evaluation of the sonic velocity and the critical mass flux in the motive nozzle. The variation of ejector geometry such as the motive nozzle throat and the mixing section diameters, NXP as well as the separator volume were carried out. The system configuration included an internal heat exchanger for heat recovery in all cases. Experimental results showed that there exist optimum design parameters in each test. Comparison between the conventional air-conditioning system with a throttle valve and an ejector-based configuration revealed that the COP of this latter was superior by 15% approximately.

_{2}EERC used a controllable ejector. At constant compressor speed, COP and capacity were enhanced by 60% and 40% respectively at optimum nozzle throat, D

_{t}and NXP. The variable speed compressor was found to significantly increase COP and cooling capacity in comparison to conventional compression cycle.

_{2}and the corresponding cycle performance which they compared to a conventional cycle with an expansion valve in terms of the ejector efficiency, the entrainment ratio, and the pressure recovery. Investigations were for constant evaporation pressures of 26 bar and 34 bar (respectively −10 °C and −1 °C), gas cooler outlet temperatures of 30 °C, 35 °C and 40 °C and nozzle inlet suction superheat about 4 °C. Maximum ejector efficiency as defined by Koehler et al. [49] was up to 22% and COP improvement over the conventional cycle with expansion valve in similar conditions was up to 17% with respect to the high side pressure.

_{2}ejector cycle to predict the experimental data within 10% for ejector efficiency and the mass flow rate within 5%.

_{2}configurations, which represent an interesting performance improvement potential. In this respect, Guangming et al. [171] conducted a theoretical analysis and experimentation with CO

_{2}on two-phase ejectors for water heating applications. Their theoretical predictions were in good agreement with the experiments. The system was tested in both on-design and off-design conditions.

_{2}heat pump equipped with an ejector, were performed by Minetto et al. [172] showing improved circulation of refrigerant in the evaporator. The heat pump was both tested for water and space heating. The comparison to a conventional heat pump employing an expansion valve was favorable according to the authors but no explicit performance comparison was provided. Recently, Zhu et al. [133] investigated the effects of working conditions on the performance of transcritical CO

_{2}ejector-expansion heat pump water heater system. Results showed a COP = 4.6 when the tap water outlet temperature was 70 °C, corresponding to an improvement of 10.3% over the basic cycle.

_{2}heat pump for space heating under partial and full-load conditions. The authors evaluated individual components and overall heat pump performance, varied the ejector area ratio and the compressor frequency to adjust to ambient conditions from −15 to 12 °C. Optimal COP was possible by varying the ejector area, regulated to match with the pressures at the inlet and outlet of the compressor. Optimal ejector performance does not necessarily match with optimal system operation.

_{2}EERC. Significantly higher oil circulation rate was observed at the evaporator inlet of the ejector cycle than at the high-pressure side. To reduce the negative impact of evaporator oil circulation, the influence of compressor speeds, ejector motive nozzle needle positions and evaporator inlet metering valve openings were considered.

#### 5.2. Miscellaneous Two-Phase Ejector Cycles

#### 5.2.1. Theoretical Studies

_{2}. In this respect, a transcritical CO

_{2}two-stage refrigeration cycle integrating a two-phase ejector, an internal heat exchanger and an inter-cooler was analyzed on the basis of the first and second laws of thermodynamics by Yari and Sirousazar [188]. Compared to the conventional two-stage cycle in the same conditions, the new configuration performance’s increase in terms of COP and second law efficiency was about 55.5% and 26%, respectively for typical air-conditioning conditions (Figure 18).

_{2}refrigeration cycle, shown in Figure 19. This is a modified multi-inter-cooling configuration of the previously proposed cycle by Manjili and Yavari [190] with an ejector expansion system.

_{2}cascade layouts (Figure 20) theoretically evaluated by Yari and Mahmoudi [191], yielding COP values in the respective ranges of 10.8–17.2% and 18–31.5% compared to a reference cascade cycle.

_{2}/NH

_{3}cascade cycle based on the thermodynamics first and second laws. The results indicated that COP and second law efficiency of this system were found to be 5–7% higher on average than the conventional cycle and exergy destruction rates roughly 8% lower as compared to the conventional cycle.

_{2}refrigeration cycle with two-stage ejector and an ejector enhanced vapor injection transcritical CO

_{2}heat pump cycle with sub-cooler, respectively. COP theoretical improvements over single ejector in CO

_{2}dual-temperature refrigeration and conventional vapor injection heat pump cycles were respectively up to 37.61% and 7.7%.

_{2}multi-ejector system and its comparison to a reference CO

_{2}booster system. The analysis demonstrated that for different climatic conditions, efficiencies and capacities of a system layout with ejectors and heat recovery, relevant improvements of up to 30% could be expected (Figure 21).

_{2}ejectors installed in a multi-ejector module to be integrated with supermarket refrigeration systems. The proposed model was generated by use of experimental data together with CFD model results. The developed mapping allowed determining the motive nozzle mass flow rate, entrainment ratio, pressure lift and ejector efficiency at the operating conditions typical for supermarket refrigeration, air-conditioning and a heat pump system.

_{2}supermarket refrigeration systems in countries with higher ambient temperatures, Huang et al. [198] modified a conventional booster refrigeration system by means of two-phase ejector, which they simulated under various conditions. Results indicated potential efficiency improvements of up to 11% in COP when ambient temperature is high. At low ambient temperatures, performance decreased below that of the conventional booster.

_{2}refrigeration system for fishing vessels, to operate in warmer climates without the need for an additional compressor unit. Results showed the multi-ejector system is the only solution which ensures no necessity for an additional compressor in warmer climates while still maintaining the designed cooling capacity. In this approach, the ejectors are used as a booster for the parallel compressors. Some miscellaneous theoretical cycles of the two-phase ejector are summarized in Table 8.

#### 5.2.2. Experimental Studies

## 6. General Remarks and Challenges

## 7. Conclusions

## Funding

## Conflicts of Interest

## Abbreviation

A | area |

CAM | Constant Area Mixing |

CFD | Computational Fluid Dynamics |

COP | Coefficient of performance |

CPM | Constant Pressure Mixing |

D | diameter |

EERC | Ejector Expansion Refrigeration Cycle |

ERC | Ejector recirculation cycle |

ERS | Ejector Refrigeration System |

G | mass flow rate |

h | enthalpy |

HEM | Homogeneous Equilibrium Model |

HRM | Homogenous Relaxation Model |

IHE | Isentropic Homogeneous Equilibrium |

IHX | Internal Heat Exchanger |

L | length |

$\dot{\mathrm{m}}$ | mass flow rate |

NXP | nozzle exit position |

P | pressure |

PIV | Particle Image Velocimetry |

Q | capacity |

T | temperature |

W | energy consumption |

Greek | |

x | vapor quality |

α | nozzle convergent angle |

β | nozzle divergent angle |

Δ | difference; improvement |

η | diffuser angle; efficiency |

θ | nozzle area ratio ${\left({\mathrm{D}}_{\mathrm{x}}/{\mathrm{D}}_{\mathrm{t}}\right)}^{2}$ |

ξ | exergy efficiency |

ρ | density |

ς | entropy increase avoided |

τ | compression ratio $\left({\mathrm{P}}_{\mathrm{b}}/{\mathrm{P}}_{\mathrm{s}}\right)$ |

ϕ | area ratio ${\left({\mathrm{D}}_{\mathrm{m}}/{\mathrm{D}}_{\mathrm{t}}\right)}^{2}$ |

φ | mixing convergent angle |

ω | entrainment ratio $\left({\dot{\mathrm{m}}}_{\mathrm{s}}/{\dot{\mathrm{m}}}_{\mathrm{p}}\right)$ |

$\dot{\mathsf{\chi}}$ | exergy flow rate |

Subscripts | |

0 | stagnation |

amb | ambient |

b | back |

c | condenser |

com | compressor |

dif | diffuser |

e | evaporator |

ej | ejector |

gc | gas cooler |

m | mixing |

n | nozzle |

p | primary |

ref | reference |

s | secondary |

sub | sub-cooling |

sup | superheating |

t | throat |

w | water |

x | nozzle outlet |

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**Figure 1.**Typical geometry of two-phase ejectors: (

**a**) vapor–liquid ejector; (

**b**) liquid–vapor ejector.

**Figure 3.**Dual-nozzle ejector [43].

**Figure 4.**Ejector with a bypass [44].

**Figure 6.**Condensation wave structure [62].

**Figure 7.**Motive jet condensation in mixing chamber inlet [64].

**Figure 8.**Refrigeration cycles with two-phase ejector: (

**a**) ejector-expander (EERC); (

**b**) ejector-recirculator (ERC).

**Figure 10.**Pressure distribution along the nozzle centerline with condensation shock [120].

**Figure 11.**EERC with internal heat recovery [36].

**Figure 12.**Variant of EERC cycle [178].

**Figure 14.**Ejector application in domestic refrigeration and freezing [180].

**Figure 15.**Schematic diagram of ejector-sub-cooled EERC [182].

**Figure 16.**Solar-powered bi-ejector refrigeration system [184].

**Figure 17.**Ejector-enhanced absorption system [186].

**Figure 19.**Two-stage multi-inter-cooling transcritical EERC [189].

**Figure 20.**Ejector-expansion based cascade refrigeration cycle layout [191].

**Figure 22.**Two-phase ejector auto-cascade refrigeration system [205].

**Figure 23.**Modified EERC system with two-phase injector [200].

Author(s) | Fluid(s) | Boundary | Ejector Component Efficiencies | Validation | Remarks |
---|---|---|---|---|---|

Kornhauser, 1990 [97] | R11, R12, R22, R113, R114, R500, R502, R717 | T_{e}: −15 °CT _{c}: 30 °C | -η_{p}: 0–1-η _{s}: 0–1-η _{dif}: 0–1 | - | Neglecting losses in mixing process. |

Menegay and Korhauser, 1994 [102] | R134A | T_{e}: −15 °CT _{c}: 30 °CΔT _{sup}: 5 °CΔT _{sub}: 5 °C | -η_{p}: 0.75–1-η _{s}: 0.9–1 | - | Extension of Kornhauser model, accounting for flow under-expansion and efficiencies. |

Liu and Groll, 2008 [103] | CO_{2} | P_{gc}: 9.5 MPaT _{gc}: 30 °CP _{s}: 3.7 MPa | -η_{p}: 0.986-η _{s}: 0.972-η _{dif}: 0.882 | -Efficiencies adjusted to reflect the experiments. -Uncertainty <5.9%. | -Correlation of Attou [103], for the speed of sound. -Correlation of Owen [104] for the diffuser. |

Sarkar, 2010 [33] | Isobutane, Propane, Ammonia | T_{c}: 35–30 °CT _{e}: −5 to 15 °C | -η_{p}: 0.8-η _{s}: 0.8-η _{dif}: 0.8 | - | Correlations of optimal ϕ for each refrigerant in terms of T_{e} and T_{c}. |

Kwidinski, 2010 [106] | Water–steam | Steam: 85–130 kg/h and 3.9 bar (ΔT _{sup}: 0–40 °C)Water: 1–6 m ^{3}/h | -Nozzle (velocity coefficient): 0.9 -Diffuser (resistance coeff.): 0.1–0.2 | P_{b} within 15% and T_{b} 1 K of experiments. | Steam injector model for pressure discharge prediction. |

Banasiak et al., 2011 [107] | CO_{2} | P_{gc}: 9.94–11.1 MPaP _{e}: 3.68–4.6 Mpa | -Friction factor considered. | Discrepancies less than 5% on ΔPs and m_{p}. | -Hybrid method (0D + 1D). -Delayed Equilibrium Model. |

Liu & Groll, 2012 [51] | CO_{2} | P_{gc}: 4.5 MPaP _{e}: 3.8 MPa${\dot{\mathrm{m}}}_{\mathrm{e}}$: 0.07 kg/s | -η_{p}: 0.7–0.9-η _{s}: 0.8–0.9-η _{mix}: 1 | Predictions within 7.6% on COP and 11.23% on Q_{e}. | Efficiency coefficients correlations provided. |

Hassanian et al., 2015 [86] | R134a | P_{c}: 1.4–1.65 MPaP _{e}: 0.37–0.43 MPaΔT _{sup}: 14.1–0.6ΔT _{sub}: 1.38–2.25 | -η_{p}: 0.5–1-η _{s}: 0.5–1-η _{dif}: 0.5–1 | Errors on COP less than 3%. | Design procedure using Henry-Fauske to evaluate the critical mass flux. |

Ameur et al., 2016 [25] | R134a, R410A, CO _{2} | CO_{2}: P_{p}: 6.1–9.1 MPaT _{p}: 21.8–35.8 °CR410A: P _{p}: 2.9–3.0 MPaP _{s}: 0.97–1.19 MPaR134a: P _{p}: 15.3 MPaP _{s}: 0.35 MPa | -η_{p}: 0.85-η _{s}: 0.85-η _{mix}: 0.97-η _{dif}: 0.7 | -Error on P_{th}:0.21–14.2% -Error on ΔP: 0.63–2.26% (R410a) 0.09–6.14%(R134a) | Design nozzle performed by maximizing the mass flow at the throat. |

Zhu & Jiang, 2018 [87] | CO_{2} | P_{gc}: 8–10.3 MPaT _{gc}: 32–43 °CP _{e}: 2.6–4.3 MPaT _{e}: 22 °C. | -η_{p}: 0.95-η _{mix}: $\mathrm{f}\left({\dot{\mathrm{m}}}_{\mathrm{p}},{\dot{\mathrm{m}}}_{\mathrm{s}}\right)$-η _{dif}: 0.9 | Error on mass flow rate: ${\dot{\mathrm{m}}}_{\mathrm{p}}$: ±3.5% ${\dot{\mathrm{m}}}_{\mathrm{s}}$: ±15% | Primary flow: use of correlation accounts for non-equilibrium when x > 0.65 |

Author(s) | Fluid(s) | Solver | Turbulence Model(s) | Boundary Conditions | Validation | Remarks |
---|---|---|---|---|---|---|

Burlinski et al., 2010 [110] | CO_{2} | ANSYS Fluent | RNG k-ε | - | High discrepancies in the entrainment ratio prediction. | Homogeneous/heterogeneous model for non-equilibrium effects. |

Colarossi et al., 2012 [13] | CO_{2} | Open-FOAM | k-ε | P_{gc}: 9.5–10.5 MPaT _{gc}: 42°C, T_{e}: 2 °C | Average error on pressure recovery: 18.6%. | -Assumed non-equilibrium state. -Nucleation delay treatment by HRM. |

Yazdani et al., 2012 [12] | CO_{2} | ANSYS Fluent V12.0 | k-ω SST | P_{p}: 12.33 MPaT _{p}: 313.1 KP _{b}: 3.71 MPaT _{s}: 268.2 K | Within 10% of own data of ω and τ. | Used a non-homogeneous mixture model and NIST Refprop. |

Yazdani et al., 2014 [111] | CO_{2} | ANSYS Fluent V12 | k-ω SST | Used data from Nakagawa et al., 2009 [40] | Fairly good concordance simulations-experiments | Phase change on walls and throat. Non-homogenous model + drift flux model for slip of phases. |

Smolka et al., 2013 [112] | R141B, CO_{2} | ANSYS Fluent V12.0 | k-ε RNG | P_{p}:8.4–9.9 MPaT _{p}:30–36 °CP _{s}: 3.5–5.1 MPaT _{s}:6–20 °CP _{b}: 3.8–5.5 MPa | -Average discrepancies for ${\dot{\mathrm{m}}}_{\mathrm{p}}$ and ${\dot{\mathrm{m}}}_{\mathrm{s}}$: 5.6% and 10.1%. | HEM assumption. Phases in thermal and mechanical equilibrium. |

Lucas et al., 2014 [113] | CO_{2} | Open-FOAM | k-ω SST | T_{gc}: 36.3–29.9 °CT _{e}: 20.7–6.6 °C | Error max on ${\dot{\mathrm{m}}}_{\mathrm{p}}$ and ${\dot{\mathrm{m}}}_{\mathrm{s}}$: 8% and 6.4%. | Assumption of homogeneous equilibrium. |

Banasiak et al., 2014 [54] | CO_{2} | ANSYS Fluent | k-ε RNG | P_{p}: 8–8.5 MPaT _{gc}: 303 KP _{s}: 3.5 MPa | Prediction error on ${\dot{\mathrm{m}}}_{\mathrm{gc}}$ and ${\dot{\mathrm{m}}}_{\mathrm{e}}$: 7.4% and 13%. | Performance and entropy generation in the flow was proposed for analysis. |

Palacz et al., 2015 [114] | CO_{2} | ANSYS Fluent | realizable k-ε | P_{p}: 4–9.5 MPaT _{p}: 6–36 °CP _{s}: 2.7–3.2 MPaT _{s}: 3–21 °C | Accuracy of mass flow rate predictions are highly variable. | -HEM approach. -Model generally accurate close to saturation line but deteriorates with the temperature decrease. |

Palacz et al., 2017 [116] | CO_{2} | ANSYS Fluent | realizable k-ε | P_{p}: 7.2–9.8 MPaT _{p}: 26.8–38.7 °CP _{s}: 2.5–2.9 MPaT _{s}: −2 + 3 °C | - | -HEM approach. -Genetic algorithm used for optimization (efficiency increase of up to 6%). |

Haida et al., 2018 [115] | CO_{2} | ANSYS Fluent | k-ω SST | P_{gc}: 50–95 barP _{e}: −10 to −6 °C. | Error on ${\dot{\mathrm{m}}}_{\mathrm{p}}$< 15% (for P_{p} > 59 bar) | -Improvement of HRM. -Influence of relaxation time on the flow by using a correlation. |

Baek et al., 2018 [88] | R134a | ANSYS Fluent V16.1.0 | Realizable k-ε | P_{p}: 10.3–10.7 barT _{p}: 40–41 °CP _{s}: 2.75–3.87 barT _{p}: 18–20 °C | Error on m_{s} ≤ 8.47%. | Evaporation-condensation model of the phase transition calibrated with experimental data of Lawrence, 2012 [100]. |

Author(s) | Fluid(s) | Capacity | Operating Conditions | Performance | Remarks |
---|---|---|---|---|---|

Starkman et al., 1964 [90] | Steam–water | Flow rates up to 2.5 lbs/s | P_{p} < 1000 psiaT _{p} < 580 °Fx _{p} < 20% | Weak shocks at overexpansion. | -Convergent–divergent nozzles. -Satisfactory for HEM except near saturation where other models apply. |

Menegay and Kornhauser, 1996 [80] | R12 | 3.5 kW | -EERC standard operation. | Experiments not conclusive | -Oversized nozzle design, mainly due to non-equilibrium effects. -Bubble formation in size and quantity controlled. |

Nakagawa, Berana et al., 2008–2009 [41,59,128] | CO_{2} | 1.3–2 kW | P_{p}: 9–10 MPaT _{p}: 37–50 °C | Thick shock in divergent. Increase in amplitude with temperature. | -Experiments on ejector nozzles. -Shock-wave behavior assessment in accordance with geometry and temperature. |

Wang and Yu, 2016 [53] | R600A | - | P_{p}: 100–200 kPaP _{s}: 50–70 kPax _{p}: 0.313–0.531 | - | Correlations for ejector component efficiency established. |

Zhu et al., 2017 [67] | CO_{2} | 5 kW | P_{p}: 7–9 MPaT _{p}: 30–35 °CP _{s}: 3–4.5 MPa. | The expansion angle and ω were measured for varying conditions. | -Visualization study highlighting internal flow structure of CO_{2}. |

Ameur et al., 2016, 2017 [18,93] | R134A | 5 kW | P_{p}: 7.7–16.8 barT _{p}: 30–56°CΔT _{sub}: 0.7–55 °CP _{b}: 3–7.5 bar | The critical mass flow rate significantly depends on the level of the degree of sub-cooling. | -Ejector operated with no induced flow. -Experimental critical flow rate compared with different models. |

Ameur et al., 2018 [46] | R134A | 5 kW | P_{p}: 8.8–14.9 barT _{p}: 30–56°CΔT _{sub}: 0.2–45 °CP _{s}: 3–4.44 barΔT _{sup}: 6–13 °CP _{b}: 3.1–4.8 bar | Performance curves established for P_{p}: 14.9 bar and P_{s}: 3–4.4 bar. | -Ejector operated with induced flow. -Pressure variation inside the ejector monitored. |

Author(s) | Fluid | Operating Conditions | Performance | Remarks |
---|---|---|---|---|

Li et al., 2014 [140] | R1234yf | T_{c}: 30–55 °CT _{e}: −10 to +10 °C | -ΔCOP, up to 13%, ΔQ_{e} up to 12% (at T_{c} = 50 °C, T_{e} = 5 °C, and same ΔP in suction nozzle.) -An optimum ΔP in suction nozzle exist for maximized performance. | R1234yf EERC has a better performance than R134a. |

Zhao et al., 2015 [141] | Mixture R134a/R143a | T_{c}: 30–50 °CT _{e}: −15 to −10 °C | With mixture 0.9/0.1, ΔCOP = 10.47% (compared to system with pure R143a). | EERC using zeotropic mixtures, fluid composition and working conditions effects investigated. |

Luo, 2017 [142] | R32 | T_{c}: 45 °CT _{e}: −25 to +5 °C | -ΔCOP ≈ 4.3%. -Expected improvement in COP of 8.5% with addition of IHX. | EERC with injecting oil into the compressor to approach a more isothermal compression process (oil-flooded compression cycle). |

Rodríguez-Muñoz et al., 2018 [143] | R134a, R1234ze(E), R290 | Air-conditioning conditions | IHX presence promotes a decrease in COP. | Effects of heat recovery by IHX in EERC |

Khosravi et al., 2018 [136] | R134A R407C R410A | T_{c}: 50–63 °C T _{e}: 20 °CQ: 1631 kW | Fuel consumption reduced by 22% and total cost of EERC system 15.2% less than conventional refrigeration with IHX. | -Application of a large scale industrial EERC for process water-cooling in an oil refinery. -Energy, exergy and economic analyses showed EERC as the best choice. |

Author(s) | Operating Conditions | Performance | Remarks |
---|---|---|---|

Deng et al., 2007 [146] | P_{gc}: 7.5–12.5 MPaT _{e}: 0–10 °C | -ΔCOP = 18.6%. ΔQ_{e} = 8.2% (with IHX).-ΔCOP = 22%, ΔQ _{e} = 11.5% (without IHX). | Exergy analysis showed that EERC greatly reduces the throttling losses. |

Fangian and Yitai, 2011 [149] | P_{gc}: 8–9.2 MPaT _{gc}: 312–318 KT _{e}: 267–290 KΔT _{sub}: 5 K | Ejector instead of throttling valve can reduce 25% of exergy losses and increase COP by 30%. | Effects of working conditions on COP and exergy loss. |

Sarkar and Bhattacharyya, 2012 [154] | T_{gc,w,in}: 30–40 °C T _{e,w,in}: 25–35 °C${\dot{\mathrm{m}}}_{\mathrm{gc},\mathrm{w}}$: 0.7–2 kg/min Q _{ev}: 1.5–2.3 kWQ _{gc}: 2.8–4 kW | -The effect of ${\dot{\mathrm{m}}}_{\mathrm{e},\mathrm{w}}$ on system performances is more pronounced compared to ${\dot{\mathrm{m}}}_{\mathrm{gc},\mathrm{w}}$. -The effect of T _{gc,w,in} is more significant compared to T_{e,w,in}. | Theoretical and experimental investigations on the water-side operating conditions of heat pump for water cooling and heating. |

Zhang et al., 2013 [150] | P_{gc}: 8.5–13 MPaT _{gc}: 40–50 °C T _{e}: 0–10 °C | IHX inclusion in EERC: -increases ω and ejector efficiency. -Pressure recovery decreases under the same gas cooler pressures. | IHX is only applicable with low ejector isentropic efficiencies or high gas cooler exit/evaporator temperatures for the EERC system from the view of energy efficiency. |

Zhang and Tian, 2014 [151] | P_{gc}: 8.5–11 MPaT _{gc}: 40–50 °C T _{e}: 0–10 °C | -ΔCOP up to 45%. -Exergy loss reduction up to 43%. | ΔP suction nozzle impact on ω is small but exist an optimum value for which COP and recovered pressure are maximized. |

Zheng et al., 2015 [152] | P_{gc}; 8–9 MPaP _{e}: 3.2–3.6 MPaω: 0.48–0.57 | Pressure predictions in gas cooler, evaporator and separator within 1.8%, 4.2% and 6.7%, respectively. | The dynamic behaviors of the EERC system undergoing the change of expansion valve opening and ejector area ratio are predicted by the developed model. |

Author(s) | Fluid | Operating Conditions | Performance | Remarks |
---|---|---|---|---|

Pottker et al., 2010 [163] | R410A | T_{c}: 40–60 °C T _{e}: 0–15 °CQ _{e}: 1.5–2.5 kW | -ΔCOP up to 14.8% over conventional system. -ΔCOP up to 8.4% over flash gas bypass system. -ω: 0.62–0.71, τ: 1.04–1.11. | The two benefits effects of EERC system (flash gas separation and work recovery) were investigated and quantified. |

Ersoy and Bilir, 2014 [162] | R134a | T_{c}: 52–60 °C T _{e}: 10 °CQ _{e}: 4.47 kW | -ΔCOP: 6.2–14.5% over conventional, depending on operating conditions. -ω: 0.63–0.65, τ: 1.063. | Under same external conditions, overall ΔP (in the evaporator particularly) is higher in conventional cycle. |

Hu et al., 2014 [29] | R410A | P_{c}: 1.9–2.4 MPa P _{e}: 1.05–1.28 MPa Q _{e}: 4.2 kW | -ΔCOP: up to 9.1% over conventional system. -ω: 0.58–0.78 | Adjustable ejector investigated under different conditions. |

Bilir-Sag et al., 2015 [55] | R134a | T_{c}: 40 °CT _{e}: 5 °CQ _{e}: 4.5 kW | Over a conventional system: -ΔCOP up by 7.34–12.24%. -Exergy efficiency up by 6.6%–11.24%. -ω: 0.73–0.83 | The irreversibility and efficiency of each cycle component determined and compared with those of a vapor compression refrigeration system. |

Pottker and Hrnjak, 2015 [134] | R410A | T_{c}: 40–60 °CT _{sink}: 38–52 °CT _{e}: 0–15 °CT _{source}: 10–27 °C | -ΔCOP: 12.2–19.2%. -ω: 0.62–0.71, τ: 1.04–1.11. | Work recovery and liquid-fed evaporator in EERC separately quantified. |

Wang and Yu, 2016 [30] | R600a | P_{p}: 1–2.6 bar x _{p}: 0.3–0.6P _{s}: 0.4–0.7 bar | ω: 0.18–0.33, τ: 1.01–1.30. | τ increases and ω decreases with increasing the quality of the primary fluid. |

Jeon et al., 2018 [38] | R410A | P_{c}: 24–31 bar P _{e}: 10–14 bar Q _{e}: 7.5 kW | -ΔCOP: 7.5% over the base line cycle. -ω: 0.6–0.95, τ: 1.02–1.07. | Effects of ejector geometries on the performance of an ejector expansion air conditioner. |

Author(s) | Operating Conditions | Performance | Remarks |
---|---|---|---|

Nakagawa et al., 2011, [36,165] | P_{gc}: 9–10.5 MPaT _{gc}: 41–47 °CT _{e}: 0–8 °CQ _{e}: 0.4–2.7 kW | - ΔCOP: up to 27% over base case when IHX is properly sized. - ω: 0.1–0.7, τ: 1.04–1.13 | -Effect of IHX size on EERC performance. -Effect of the mixing length on the performance investigated. |

Banasiak et al., 2012 [37] | T_{gc}: 30–70 °CT _{e}: 20 °CQ _{gc}: 5–13 kW | -ΔCOP: 8%. -ω: 0.41–0.7. | Effects of different ejector geometries on performance were examined. |

Lucas and Koehler, 2012 [169] | P_{gc}: 71–103 barT _{gc}: 30–40 °CP _{e}: 26–34 barT _{e}: −10 to −1 °C | -ΔCOP: 17%. -ω: 0.38–0.65, τ: 1.05–1.14. | Investigation of the working conditions on the performance. |

Minetto et al., 2013 [172] | P_{gc}: 100 barT _{gc}: 35 °C, T_{e}: 0 °CQ _{gc}: 5 kW | -ΔCOP: 7.5–23.3%. -ω: 0.8–1.6, τ: 1–1.143. | Technological issues related to lubricant recovery were faced. |

Lee et al., 2014 [167] | T_{gc}: 30–40 °CT _{e}: 27 °CQ _{e}: 3–5.7 kW | Depending on converter frequency adjustment, -ΔCOP: 6–9%. -ΔQ: 5%. | ω and the temperature of external fluid in the gas cooler were among the main controlling factors. |

Haida et al., 2016 [175] | T_{gc}: 26–36 °CP _{e}: 28 bar T _{e}: −8 °CQ _{e}: 46 kW | -COP improved up to 7% over parallel compression system. -ω: 0.15–0.4, τ: 1–1.4 | -Performance of multi-ejector expansion work recovery module compared to parallel compression system. |

Boccardi et al., 2017 [81] | P_{gc}: 80–100 barT _{gc}: 40–60 °CP _{e}: 20–30 barT _{e}: −5 to 12 °CQ _{gc}: 29–36 kW | -ΔCOP: 13.8%. -ΔQ _{gc}: 20%.when proper configuration of multi-ejector is used. -ω: 0.35–0.52, τ: 1.06–1.14. | -Heat pump system with multi-ejector pack and IHX for space heating. -There is a threshold value of the ambient temperature to switch from an ejector to another one in order to maximize the performance. |

He et al., 2017 [42] | P_{gc}: 90–114 barNozzle throat area: 0.638–1.217 m ^{2} | A controller based on a dynamic model tracking the optimal gas cooler pressure in real time to increase the system performance. | Improving the operating performance of the transcritical CO_{2} EERC by controlling the nozzle throat area. |

Zhu et al., 2018 [133] | P_{gc}: 81–121 barT _{gc}: 35–55 °CP _{e}: 50 bar (T_{air}: 22 °C), Q_{gc}: 5 kWT _{w,in}: 20 °C, T _{w,out}: 50–90 °C | -COP improvement of 10.3% over the basic cycle. -ω: 0.5–0.9, τ: 1.1. | Effects of working conditions on the performance of transcritical CO_{2} ejector-expansion heat pump water heater system. |

Author(s) | Application | Fluid | Operating Conditions | Performance | Remarks |
---|---|---|---|---|---|

Balamurugan et al., 2008 [77] | Liquid–gas contactor | Air-water | -Fixed water- and airflows. -Ejector outlet open to the atmosphere. | Optimum area ratio for highest liquid rate of entrainment was determined numerically. | -Theory and experiments of gas—liquid ejectors for use as contactors in industrial and process applications. - Validated CFD model. |

Dokandari et al., 2014 [192] | Ejector expansion cascade absorption cycle with two-phase ejector in each loop. | CO_{2}/NH_{3} | T_{c}: 30–40 °C, T_{e}: −55 to −45°C, Q_{e}: 175 kW | With respect to conventional cycle: -ΔCOP up by 7%. - Exergy destruction reduced by 8%. | Experiments required for validation and economic analysis for cost effectiveness, considering additional hardware and controls. |

Zhu et al., 2014 [179] | Two-phase ejector with 2 nozzles in a vapor-compression cycle for solar assisted air-source heat pump systems | R410A | T_{c}: 40 °C, T_{e1}: −5 °C, T_{e2}: −18 °C, ΔT_{sup}: 0°C | Improvement over conventional EERC: -ΔCOP: 4.6–34%. -ΔQ: 7.8–51.9%. | -Good potential of using simultaneously two energy sources for heat pumps. -Need to be experimentally validated |

Boumaraf et al., 2014 [176] | EERC with 2 evaporators | R134a, R1234yf | T_{c}: 40 °C, T_{e1}: −5 °C, T_{e2}: 0 °C | ΔCOP: more than 17% over conventional cycle for both refrigerants. | R134a performance somewhat higher than for R1234yf but improvement is comparable especially at high T_{C}. |

Wang et al., 2014 [180] | Modified EERC | R600A | T_{c}: 40 °C, ΔT_{sub}: 10 °C, T _{e1}: −5 °C, T_{e2}: −25 °C | -ΔCOP: 11.4%. -ΔQ: 22%. | Application of EERC concept to refrigerator-freezers. |

Unal and Yilmaz, 2015 [177] | EERC with two evaporators (air-conditioner for buses) | R134a | T_{c}: 48–48.8 °C, T_{e1}: 1.3–6.3 °C T _{e2}: −1.6–7.2 °C, Q: 2–2.52 kW | -ΔCOP: less than 15%. -ω: 0.06–0.59. | The heat transfer surface areas of the condenser and evaporator can be reduced 5% and 51%, respectively. |

Liu et al., 2015 [178] | A modified vapor refrigeration cycle with a two-phase ejector for applications in domestic refrigerator freezers | R290/ R600A | Tc: 35–55 °C, ΔTsub: 5–30 °C T _{e}: −35 to −25 °C, ΔT_{sup}: 10 °Cm _{comp}: 1 g/s | -ΔCOP: 16.7%. -ΔQ _{e}: 34.9%.-Exergy efficiency: 6.71%. -Exergy destruction reduced by 24.4% | -Using zeotropic mixture was investigated in terms of performances. -An optimal mixture composition can further be found for maximizing system performance. |

Xing et al., 2015 [182] | Two-phase ejector specifically assigned to provide mechanical sub-cooling to vapor-compression refrigeration cycle. | R410A, R290 | T_{c}: 45 °C, T_{e}: −40 °C to −10 °C | R410a: ΔQ: 11.7%. ΔCOP: 9.5%. R290: ΔQ: 7.2%. ΔCOP: 7%. | Need for experiments to confirm theoretical predictions for the real potential of the system and under which conditions. |

Goodarzi et al., 2015 [189] | Transcritical two-stage mechanical-EERC system with multi-cooling and IHX. | CO_{2} | P_{gc}: 80–120 barsT _{gc}: 36–44 °C, T_{e}: −30 to −5 °C | Potential increase of COP, in particular for low gas cooler pressures | The model used was validated by data from similar setup, without IHX. |

Bai et al., 2015 [193] | Vapor-injection in transcritical ejector heat pump cycle for cold climates. | CO_{2} | P_{gc}: 8.55 MPaT _{gc}: 35–50 °C, T_{e}: −25 to −5 °C | ΔCOP up to 7.7%, ΔQ_{gc} up to 9.5%ω: 0.75–1.13, τ: 1.06–1.12 | -Vapor injection with sub-cooler for lower discharge temperature and higher capacity. -Exergy destruction showed gas cooler and evaporator as main contributors. |

Bai et al., 2015 [194] | CO_{2} transcritical refrigeration cycle with bi-evaporator and with two-stage ejector. | CO_{2} | T_{gc}: 35–50 °C, T_{e1}: −5 to 5 °CT _{e2}: −35 to −15 °C | Improvement over conventional dual-evaporator cycle: -ΔCOP: 37.61% -Exergy efficiency: 31.9%. | Need for experiments to confirm theoretical predictions for the real potential of the system and under which conditions |

Smirciew et al., 2015 [200] | Two-phase injector as a feeding pump of the vapor generator in ejector refrigeration cycle. | Isobutane | P_{p}: 1.08–1.64 MPa; T_{p}: 70–90 °C P _{s}: 0.404 MPa; T_{s}: 15 °C (liquid)ΔT _{sub}: 15 °C | ω: 18–28, τ: 2.7–4.2 (condensation shock wave captured by calculations) | The replacement of the mechanical pump by a two-phase injector inside a conventional supersonic ejector cycle system leads to decrease the COP of the system. |

Sarkar, 2017 [181] | Multi-evaporator EERC systems. | R32, Propane | T_{c}: 40 °CT _{e}: 5, −20, −40 °C (multi-level evaporators) | ΔCOP: 20% over basic valve expansion two-stage mechanical cycle, 117% over single-stage and 67% over EERC. | More studies (theory and experiments) for data on the potential of these concepts are needed. |

Lawrence and Elbel, 2018 [196] | The ejector recirculation cycle and the conventional EERC. | R410A, CO_{2} | Q_{e}: 1 kWR410A, T _{c}: 45 °C, ΔT_{sub}: 1 KCO _{2} P_{gc}: 100 bar T_{gc}: 44 °C | Ejector recirculation cycle expected to perform more favorably at lower ambient temperature or with an ejector with low-pressure lift. | -Effect of microchannel heat exchangers design and operation on ejector cycles. -CO _{2} ejector cycle performance is much less sensitive to evaporator design. |

Author(s) | Application | Fluid | Operating Conditions | Performance | Remarks |
---|---|---|---|---|---|

Man et al., 2007 [201] | Refrigeration cycle with two-phase ejector for recirculation (ERC) | R404A | T_{c}: 50 °CT _{e}: −10 to 0 °C | -ΔCOP: 10% compared to conventional cycle. -ω: 0–0.98. | Vapor quality and refrigerant mass flow rate increase at the evaporator inlet. |

Lawrence and Elbel, 2012, 2014 [101,161] | Refrigeration cycle with two-phase ejector without separator and with two evaporators (COS). | R134a, R1234yf | T_{p}: 45 °CT _{s}: 6–12.5 °C | -ΔCOP: 10% for R134a 12% for R1234yf -ω: 0.05–0.7. | COS cycle had a slight performance advantage over typical EERC. |

Minetto et al., 2014 [209] | Three Evaporators overfeeding by means of ejector recirculator. | CO_{2} | T_{amb}: 16 °CT _{e}: −6 °CΔT _{sup}: 6 KQ _{e1,2}: 3.1 kWQ _{e3}: 5.5 kW | The compressor energy saving was about 13% of the case of thermostatic control. | Method for feeding flooded evaporators arranged in parallel in CO_{2} (subcritical) plants. |

Banasiak et al., 2015 [208] | Multi-ejector compressors system, typical supermarket application. | CO_{2} | T_{gc}: 35 °C,T _{e1}: −3 °CT _{e2}: −30 °CCapacity: 70 kW (at MT) 23 kW (at LT) | At specific subcritical condition, ΔCOP: 9.8% Δξ: 13.1% | Obtained low efficiency due to system design for performance mapping, nor representative of a complete supermarket installation. |

Lawrence and Elbel, 2016 [204] | ERC system. Refrigeration cycle with two-phase ejector for recirculation. | R410A | T_{c}: 35 °CT _{e}: 4–9 °CQ _{e}: 1 kW | -ΔCOP up to 16% for the ERC system and 9% with the standard EERC. -ω: 0.7–1.1, τ: 1.05. | The COP of each tested cycle is very dependent on evaporator design. |

Li et al., 2017 [83] | A falling-film water chiller with ejector for recirculation. | R134a | T_{amb}: 35 °CT _{e}: 4.8 °CQ _{e}: 55 kW | Evaporating capacity increases 9.5% with appropriate liquid recirculating ratio (1.21). | Using liquid recirculating ratio larger than 1.2 is not significant for enhancing the performance of falling-film heat transfer. |

Jeon et al., 2017–2018 [202,210] | COS cycle. | R600a | P_{c}: 500 kPaP _{e}: 70 kPaQ _{e}: 0.3 kW | -ΔCOP: 6.8–11.4% over the baseline cycle. -ω: 0–0.6, τ: 1–1.09. | Effects of operating conditions and ejector geometries on the performance of a small-sized household refrigeration cycle. |

Kim et al., 2017 [211] | COS cycle. | R410A | P_{c}: 25–31 barT _{c}: 41–51 °CP _{e}: 10.2–14.6 barT _{e}: 8–20 °CQ _{e1,2}: 12 kW | -ΔCOP: 14% over the baseline cycle (at ω = 0.1). -ω: 0–0.6, τ: 1–1.2. | No improvement of the performance was noted for an entrainment ratio larger than 0.3 |

Bai et al., 2018 [205] | Two-phase ejector auto-cascade refrigeration system. | R134a/ R23 | T_{amb}: 15–27 °CT _{e}: −50 to −40 °CQ _{e}: 100 W | -ΔCOP: 9.6% and Δξ: 25.1% over the conventional cycle. -ω: 0.5–1.3, τ: 1.19–1.22. | The refrigerant R134a/R23 with the optimal mass fraction ratio of 0.70/0.30 was proposed to get the maximum system exergy efficiency |

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**MDPI and ACS Style**

Aidoun, Z.; Ameur, K.; Falsafioon, M.; Badache, M.
Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 2: Two-Phase Ejectors. *Inventions* **2019**, *4*, 16.
https://doi.org/10.3390/inventions4010016

**AMA Style**

Aidoun Z, Ameur K, Falsafioon M, Badache M.
Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 2: Two-Phase Ejectors. *Inventions*. 2019; 4(1):16.
https://doi.org/10.3390/inventions4010016

**Chicago/Turabian Style**

Aidoun, Zine, Khaled Ameur, Mehdi Falsafioon, and Messaoud Badache.
2019. "Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 2: Two-Phase Ejectors" *Inventions* 4, no. 1: 16.
https://doi.org/10.3390/inventions4010016