Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 1: SinglePhase Ejectors
Abstract
:1. Introduction
 Ejector fundamentals’ discussion of conventional ejector types and extension to more recent concepts employing complex geometries for the nozzles and the mixing chambers.
 Treatment of singlephase and twophase ejector variants in separate developments for a full account and analysis of their progress.
 Inclusion of ejector operational features, conditions affecting stability and performance, such as external constraints, internal geometry, flow regimes as well as many other considerations, which are thoroughly described and discussed in detail.
 Existing and potential ejector applications, beyond conventional refrigeration systems and selected from different areas of specialties (buildings, transportation, industry and several other domains). Their discussion aims to trigger a better exchange of information and bridge between professionals of different backgrounds and objectives.
 Modeling methods, their types and particularities thoroughly dissected to provide guidance, depending on the research objectives pursued. Typical analytical and numerical (computational fluid dynamics, CFD) models to serve as a common basis for the vast majority of similar research are proposed.
 Provision of very detailed, abundantly discussed information on the fundamental elements serving as building blocks to help structure such models. Further, a thorough discussion of the modeling works available in the literature supported by visualization and experiments complements this information.
2. Ejector Fundamentals
2.1. Ejector Types
2.2. Ejector Geometry
2.2.1. Conventional Ejector
2.2.2. Other Geometry Concepts
3. Ejector Operation
3.1. Performance Coefficients
3.2. Operational Factors
3.2.1. Ejector Operation Curve
3.2.2. Effect of Inlet Pressures
3.3. Geometry Factors
3.3.1. The Nozzle Exit Position (NXP)
3.3.2. Primary Nozzle Exit Area Ratio
3.3.3. The Mixing Chamber Shape Effects
The Mixing Chamber Throat Ratio
The Mixing Chamber Throat Length
The Mixing Chamber Inlet Angle
3.3.4. Variable Geometry Ejector (VGE)
4. Flow Regimes and Internal Structure
4.1. Primary Nozzle Flow Regimes
 If the primary inlet pressure is insufficient, the jet will be supersonic in part of the divergent but leaves the nozzle in subsonic conditions due to a normal shock wave formation inside the divergent. This occurrence is a particular case of an overexpanded flow.
 When the primary pressure increases, the flow becomes an overexpanded jet of conic form with a succession of oblique shocks, generally occurring when the nozzle exit pressure is lower than the reigning ambient.
 If the primary pressure further increases, then the jet becomes underexpanded and will continue to expand past the nozzle to reach the ambient condition.
4.2. Ejector Internal Flow Structure
 Fully developed supersonic flow (Figure 17a): occurs for high inlet pressures and low induced flows. The primary jet is fully expanded in the mixing chamber and the induced flow is equally supersonic.
 Supersonic flow with secondary sonic throat (Figure 17b): the primary jet expansion is less important than in the preceding regime and the induced flow is higher, reaching sonic conditions in the mixing chamber at a location where the effective crosssection is minimum. Downstream of this point, both flows are supersonic.
 Supersonic saturated regime (Figure 17c): the primary jet is supersonic with moderately low pressure and the induced flow remains subsonic. A pseudoshock front sets somewhere between the primary nozzle outlet and the mixing throat inlet.
 Supersonic regime with double choking (Figure 17d): characterized by double choking, this flow exhibits two distinct pseudoshocks, the first behind the primary nozzle and the second before the diffuser inlet. This regime occurs for low geometric ratios, corresponding to small mixing chamber sections.
5. Application Potential of Ejectors
5.1. AirConditioning, Refrigeration and Heating
5.2. Automotive AirConditioning
5.3. Aeronautics and Space Applications
5.4. Vacuum Creation
5.5. Gas Turbine Performance Enhancement
5.6. Fluid Mixing and Separation
5.7. Fuel Cell Applications
5.8. Natural Gas Recompression Stations
5.9. Desalination Plants
5.10. Other Industrial Applications
6. Ejector Modeling Methods
6.1. Analytical Modeling
6.2. Numerical Ejector Modeling
6.2.1. Equations of Conservation
6.2.2. Parameters Selection
Mesh Sensitivity
Solvers
Computation and Discretization Schemes
Turbulence Modeling
7. Experimentation on Ejectors
7.1. Working Fluids
7.2. Parameters Measurements
7.3. Data for Model Validations
7.3.1. Global Validation
7.3.2. Local Validation
Pressure Distribution
Flow Visualization
8. Recent Ejector Refrigeration Systems (ERS) Studies
8.1. Conventional ERS
8.1.1. Conventional ERS Theoretical Studies
8.1.2. Conventional ERS Experimental Studies
8.2. Ejector Combinations with Conventional Technologies
8.2.1. Combined ERS Theoretical Studies
8.2.2. Combined ERS Experimental Studies
9. Conclusions
 The ejector as a component is presented as theoretically and experimentally tested in terms of performance and operation under a controlled environment in which inlet and outlet conditions are imposed.
 The conventional ERS tested and analysed in the context of refrigeration and airconditioning.
 More complex combined systems integrating ejectors and other technologies to work in complementarity.
Funding
Conflicts of Interest
Abbreviations
Nomenclature  
A  area  L  length 
CAM  Constant Area Mixing  M  Mach number 
CFD  Computational Fluid Dynamics  $\dot{\mathrm{m}}$  mass flow rate 
COP  Coefficient of performance  NXP  nozzle exit position 
C_{p}  Specific heat  P  pressure 
CPM  Constant Pressure Mixing  Q  capacity 
CRMC  Constant Rate of Momentum Change  R, r  ideal gas constant 
D  diameter  T  temperature 
E  total energy  t  time 
ERS  Ejector Refrigeration Systems  V, u, v  velocity components 
ESDU  Engineering Sciences Data Unit  VGE  Variable Geometry Ejector 
h  enthalpy  W  energy consumption 
k  conductivity  x_{i}  Cartesian coordinate 
Greek symbols  
α  nozzle convergent angle  μ  dynamic viscosity 
β  nozzle divergent angle  ρ  density 
δ  mixing length ratio $({\mathrm{L}}_{\mathrm{m}}/{\mathrm{D}}_{\mathrm{m}})$  τ  compression ratio, stress tensor 
η  diffuser angle, efficiency  ϕ  area ratio ${({\mathrm{D}}_{\mathrm{m}}/{\mathrm{D}}_{\mathrm{t}})}^{2}$ 
θ  nozzle area ratio ${({\mathrm{D}}_{\mathrm{x}}/{\mathrm{D}}_{\mathrm{t}})}^{2}$  φ  mixing convergent angle (degree) 
κ  gas constant  ω  entrainment ratio 
Subscripts/superscripts  
0  stagnation  m  mixing 
*  critical  me  mechanical 
b  back  n  nozzle 
c  condenser  p  primary 
dif  diffuser  pu  pump 
e  evaporator  s  secondary 
f  effective  t  throat, turbulent 
g  generator  th  thermal 
is  isentropic  x  nozzle outlet 
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References  Ejector Geometry  Application  Analysis  Remarks 

[13,14,15]  CAM/CPM  Refrigeration  Theor./Exp.  CAM offers higher entrainment but lower compression than CPM. 
[20,21,22,23]  CRMC  Refrigeration  Theor./Exp.  CRMC concept takes advantage of both CAM and CPM. Δω ≈ 37–40% than CPM. 
[17,18,19]  Twostage  Refrigeration  Theor.  Higher performance than CAM (Δτ ≈ 13%). 
[25]  Petal nozzle  Refrigerator  Exp.  Higher compression ratio than conical nozzle, especially for large aspect ratio. 
[33]  Lobed nozzle  Refrigeration  Theor.  Pressure recovery improved (≈60%) 
[35]  Tip ring version    Exp.  Δω ≈ 30% and Δτ ≈ 50% higher than conical nozzle. 
[34]  Chevron nozzle  Solar desalination  Theor.  Δω ≈ 14–22% and Δτ ≈ 8.5% higher than conical nozzle. 
[26,27,28,29,30]  Spinning rotor  Refrigeration  Theor./Exp.  Enhanced flow induction and mixing. Increased cost and complex manufacturing of the ejector. 
[31]  Rotating ejector  Refrigeration  Theor.  Lower secondary pressure for the rotating ejector than static ejector 
[36]  Bypass ejector    Theor./Exp.  Entrainment ratio increased by up to 31.5%. 
[37,38,39]  Ejector with auxiliary suction  Desalination  Theor./Exp.  Enhanced entrainment ratio (Δω ≈ 11–27%) 
[40]  Pulsed ejector    Theor./Exp.  Mixing is enhanced and entrainment is improved 
Author(s)  Working Fluid  Gas Properties  Mixing Model  Remarks  

Perfect  Real  
Keenan et al. [11]  Air  ✓    CAM  —Neglecting losses. —Without diffuser. 
Keenan et al. [12]  Air  ✓    CPM  —Neglecting losses. —Diffuser included. 
Khoury et al. [178]  Hexane, nButane  ✓    CAM  —Account molecular weights. 
Munday and Bagster [113]  steam  ✓    CPM  —Effective area concept introduced. 
Eames et al. [51]  steam  ✓    CPM  —Losses in nozzle, mixing and diffuser considered. 
Lallemand et al. [179]  R11R114 R113R142b  ✓    CPM  —2 fluids in one ejector. 
Grazzini and Mariani [17]  steam  ✓    CAM  —Twostage ejector configuration included. 
Huang et al. [70]  R141b  ✓    CPM  —Loss coefficients calibrated with experimental data. 
Eames [20]  steam  ✓      —New design method (CRMC). —Neglecting losses. 
Ouzzane and Aidoun [41]  R142b    ✓  CPM  —1D, incremental approach. 
Selvaraju and Mani [187]  R134a, R152a, R290, R600a, R717    ✓  CPM  —Friction factor considered in mixing chamber. 
Zhu et al. [188]  R141b, R11  ✓    CPM  —Shock circle model: boundary layer near wall considered. 
Zhu and Li [189]  steam, R11, R141b  ✓      —Radial velocity function imposed in mixing chamber. —Model for both wet and dry vapor fluids working. 
Cardemil and Colle [190]  steam, R141b, CO_{2}  ✓  ✓  CPM  —Model for both wet and dry vapor fluids working. —Speed of sound in 2 phase mixture evaluated. 
Chen et al. [182]  R236fa    ✓  CAM  —NXP considered. 
Ma et al. [183]  steam, R141b, R134a    ✓  CAM  —Empirical correlation for the hypothetical throat is used. 
Chen et al. [102]  R141b, R134a  ✓    CAM  —2D. —Characteristics method used. —Account for VGE. 
Croquer et al. [191]  CO_{2}, air, R141b, R134a, R245fa,    ✓  CAM  —Droplet injection in mixing section. 
Author(s)  Working Fluid  Solver  Turbulence Model  Remarks 

Riffat et al. [173]  R717, R134a, R290  Commercial software  kε  —Various nozzle geometries analyzed. 
Riffat and Omer [71]  methanol  Fluent  kε, RNG kε  —3D. 
Bartosiewicz et al. [207]  air  Fluent  kε realizable, RNG kε, kω, kω SST, RSM  —An axial capillary probe was introduced in the ejector. 
Alansary [147]  R134a  Fluent 6.2  RNG kε  —Ejector for cooling turbine inlet. 
Gawehn et al. [243]  air  ANSYSCFX CATUM  RSM  —Laval nozzles with parallel side walls. —CATUM: a CFD tool of Technical University of Munich. 
Yang et al. [32]  steam  Fluent V6.3.26  kε, kε realizable, RNG kε  —Conical, elliptical, square, rectangular and crossshaped nozzles tested. 
Yu et al. [244]  air  Fluent V6.3.26  SpalartAllmaras, kε, kε realizable, RNG kε, kω, kω SST, RSM  —RSM predicts more accurately the turbulent fluctuations. 
Zhu and Jiang [229]  N_{2}  ANSYS Fluent v13  kε, RNG kε, kω SST  —Bypass ejector with an annular cavity in the nozzle wall. 
Gagan et al. [245]  air  ANSYS Fluent v12  kε, kε realizable, RNG kε, kω, kω SST, RSM  —2Daxi and 3D. 
Bouhanguel et al. [246]  air  ANSYS Fluent  kω SST  —RANS vs. LES. 
Mazzelli et al. [209]  R245fa  ANSYS Fluent v14.5  kω SST  —Surface roughness investigated. 
García Del Valle et al. [203]  R134a  ANSYS Fluent v14.5  kε, kε realizable, RNG kε, kω SST  —Both kε and the kω SST turbulence models show good results. 
Besagni et al. [234]  air, exhaust gases  ANSYS Fluent v14.5.7  kε realizable, kω SST, RSM  —Ejector in blast furnace gas. 
HakkakiFard et al. [211]  R134a  PHOENICS  kε  —Design Optimization of ejector. 
Croquer et al. [247]  R134a  ANSYS Fluent v.15  kε, kε realizable, RNG kε, kω SST, RSM  —kω SST model with lowReynolds formulation appears very promising. 
Berzin et al. [226]  R245fa  StarCCM+ Fluent  kω SST  —Surface roughness effect. 
Wang et al. [85]  steam  ANSYS Fluent  RNG kε  —Surface roughness and area ratio effects on condensation primary nozzle. 
Zhang et al. [248]  R134a  Fluent  RNG kε  —Surface roughness effect. 
Expósito Carrillo et al. [227]  air, CO_{2}  ANSYS Fluent v.17.1  kω SST  —Performance optimization by multiobjective algorithm. 
Han et al. [249]  steam  ANSYS Fluent v.17.1  kε, kε realizable, RNG kε, kω SST  —Influence of boundary layer separation on ejector performance. 
Author(s)  Load (kW)  T_{e} or P_{e}  T_{c} or P_{c}  T_{g} or P_{g}  COP or (ω)  Comments 

Eames et al. [51]  1  5–10 °C  26–37 °C  120–140 °C  0.1–0.37  —Fixed geometry suitable for cooling. 
Chen and Sun [60]    7–14 torr  10–50 torr  83–187 torr  (0.1–1.3)  —Effects of nozzle exit Mach. —Operation map and correlation. 
Eames et al. [64]  2  0–10 °C  20–50 °C  100–132 °C  (0.3–0.8)  —3 nozzles and 3 diffusers tested. —NXP effects. 
Chang and Chen [25]  6  12–24 °C  12–27 °C  54–58 °C  (0.6–2.6)  —Different area ratios and nozzle geometries. 
Chunnanond and Aphornratana [49]  3  5–15 °C  29–40 °C  120–140 °C  0.25–0.5  —Test on 3 nozzles. —Internal pressure measurements. 
Zhang et al. [97]    0.08 MPa  0.11–0.3 MPa  0.4–0.6 MPa  (0.1–0.6)  —VGE experiments with 3 spindle positions. 
Reddick et al. [144]    50–90 kPa  100–170 kPa  350–550 kPa  (0.1–.65)  —Tests on steamCO_{2} mixture at the secondary. 
Kitrattana et al. [23]  1  7.5 °C  35–70 mbar  130–140 °C  (0.15–0.4)  —CPM vs. CRMC ejectors. 
Author(s)  Fluid  Load (kW)  T_{e} (°C)  T_{c} (°C)  T_{g} (°C)  ω  Comments 

Huang et al. [50]  R113  Up to 2  5–15  35–47  65–80  0.05– 0.27  —On and offdesign results —Performance map for design. 
Huang and Chen [52]  R113    15–25  22–50  70–90  0.1–1.2  —5 ejector geometries (NXP, throat area, mixing throat length variable). 
AlKhalidy and Zayonia [261,262,263]  R113  Up to 0.7  6.7  42.3  87.8  0.2–0.31  —Solar activated ejector. —Effect of boiler, condenser and evaporator on performance. 
Aphornratana et al. [13]  R11  Up to 1.7  –5–12  35–41  100–110    —2 mixing chambers tested —COP = 0.1–0.5. 
Eames et al. [21]  R236fa  1.5  4–12  27–33  60–100  0.3–0.6  —At design condition, COP = 0.35. 
Selvaraju and Mani [59]  R134a  0.5  2–13.5  26–38  65–90  0.1–0.4  —6 ejector geometries tested. —Optimal ω exists for each ejector. —COP = 0.1–0.5. 
Eames et al. [73]  R245fa  2  10–15  32–47  100–120  0.32–0.95  —CRMC based —Effect of nozzle size and NXP. —Performance maps, (COP = 0.25–0.7). 
Yapici and Yetişen [53]  R11  ≤ 1  0–16  27–34  88–102    —Fixed geometry ejector. —Effects of operating parameters on performance (COP = 0.02–0.35). 
Yapici et al. [67]  R123    10  34  83–103    —6 ejector geometries (area ratios 6.5–11.5) —COP = 0.29–0.41. 
Ablwaifa et al. [54]  R245fa  2  8–15  34–44  100–120  0.2–0.65  —Validation data for CFD. —NXP variation. 
Pereira et al. [264]  R600a  2  9  12–30  83  0.55–1  —VGE study (NXP, spindle control). —COP = 0.2–0.9. 
Butrymowicz et al. [118]  R600a    3.5–7  24–34  50–64  0.05–0.24  —On and offdesign results. —NXP: 5–7 mm. 
García Del Valle et al. [48]  R134a    10  26–36  84.39  0.02–0.5  —Data for 3 mixing chambers. —Variable NXP. 
Thongtip and Aphornratana [62]  R141b  2  –6–15  30–33  70–130  0–0.5  —3 nozzle sizes tested. —Analysis based on P_{e}* 
Shestopalov et al. [56]  R245fa  12  8–16  30–39  80–105  0–0.7  —3 nozzles and 3 mixing chambers tested. —On and offdesign results —Performance maps. 
Thongtip and Aphornratana [84]  R141b  2  –6–20  24–36  70–140  0–0.27  —6 nozzles tested. —Analysis on nozzle exit Mach 
Yan et al. [57]  R134a  1.5  1.5–24  12–24  72–90  0.03–0.85  —A correlation for P_{b}* was derived. 
Hamzaoui et al. [256]  R245fa  35  10–20.5  33– 41  74–90  0.1–0.27  —COP = 0.1–0.6. 
Author(s)  Analysis  Fluid(s)  Capacity [kW]  Activation Source  General Remarks 

Buyadgie et al. [294]  Theoretical  binary, multicomponent     

Fang et al. [271]  R1234yf R1234ze  3    
Diaconu [298]  Water  5  Solar  
Du et al. [300]  R245fa  153  Geothermal  
Sadeghi et al. [288]  R141b  6  Automotive  
Yan et al. [57]  Experiment  R134a  1.5    
Allouche et al. [301]  Water  5  solar  
Smierciew et al. [268]  Isobutane  2  solar  
Mazzelli and Milazzo [165]  R245fa  40  Industrial  
Zegenhagen and Ziegler [255]  R134a  6  Automotive  
Smierciew et al. [272]  HFO1234ze  30  Any heat source below 70 °C  
Hamzaoui et al. [256]  R245fa  6  Waste heat 
Author(s)  Analysis  Fluid(s)  Capacity [kW]  Application  General Remarks 

Ben Mansour et al. [315]  Theoretical  R134a  5  hybrid, cascades systems 

Xu et al. [317]  R152a  100  hybrid solarejectionmechanical compression  
Expósito et al. [318]  R134a, R1234yf, R600a  5  hybrid, multistage compression systems  
Bellos and Tzivanidis [325]  LiBrH_{2}O  100  Solarabsorptionejector system  
Petrenko et al. [328]  R600  10  Microtrigeneration system  
Ghaebi et al. [330]  ammoniawater  1133  Kalina cycleejector refrigeration  
Chen et al. [172]  R141b    twostage ejector refrigeration system  
Hao et al. [335]  zeotropic mixture R170/R600a  2.6  Hybrid autocascadeejector refrigeration system  
Yan et al. [155]  Experiment  R134a  8  Combined ejectorvapor compression cycle  
Huang et al. [338]  R245fa  5.6  Solarassisted ejectorvapor compression cycle  
Nesreddine et al. [339]  R245fa  15  Ejectorcompression cascade system  
He et al. [340]  R718  1  Twostage ejector refrigeration system  
Wang et al. [342]  R134a  1.5  Hybrid ejectorcompressor airconditioning system  
Li et al. [343]  R134a  2.5  Multievaporatorejector refrigeration system  
Abed et al. [344]  Ammoniawater  35  Solar ejectorabsorption cooling cycle  
Shi et al. [345]  LiBrH_{2}O  10  Ejectorabsorption refrigeration 
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Aidoun, Z.; Ameur, K.; Falsafioon, M.; Badache, M. Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 1: SinglePhase Ejectors. Inventions 2019, 4, 15. https://doi.org/10.3390/inventions4010015
Aidoun Z, Ameur K, Falsafioon M, Badache M. Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 1: SinglePhase Ejectors. Inventions. 2019; 4(1):15. https://doi.org/10.3390/inventions4010015
Chicago/Turabian StyleAidoun, Zine, Khaled Ameur, Mehdi Falsafioon, and Messaoud Badache. 2019. "Current Advances in Ejector Modeling, Experimentation and Applications for Refrigeration and Heat Pumps. Part 1: SinglePhase Ejectors" Inventions 4, no. 1: 15. https://doi.org/10.3390/inventions4010015