Recent Advances in Numerical Simulation of Ejector Pumps for Vacuum Generation—A Review
Abstract
:1. Introduction
2. Fundamental of Ejectors
- The primary fluid’s pressure energy is converted into kinetic energy within the nozzle.
- The low-velocity secondary fluid is entrained and mixed with the high-velocity primary fluid in the mixing throat, driven by viscous friction and the suction created by the pressure drop at the nozzle exit.
- The combined fluid’s kinetic energy is transformed back into pressure energy within the diffuser.
2.1. Entrainment Ratio
2.2. Pressure Ratio
2.3. Efficiency of Ejector
2.4. Subsonic Ejectors
2.5. Supersonic Ejectors
2.6. Vacuum Ejectors
- Response Time: The vacuum response time is the time at which the vacuum level reaches 63 % of the maximum vacuum level. Response time is crucial for system efficiency. A longer response time can decrease overall work efficiency and increase air consumption. Therefore, minimizing is essential for optimal performance.
- Vacuum Holding Time: This stage represents a significant portion of the work cycle, typically accounting for 50–80% of the total time. During this period, high-pressure air is continuously supplied to make up for leakage and maintain the desired vacuum level.
2.7. Applications
2.7.1. Single-Phase and Two-Phase Ejectors
2.7.2. Geography of Ejectors Research
3. Computational Fluid Dynamics Modeling of Ejectors
3.1. Single-Phase Ejector CFD Simulation
3.2. Two-Phase Ejectors CFD Simulation
- Volume of fluid (VOF): Suitable for simulating fluids with a sharp interface, such as liquid–gas flows.
- Mixture model: often used for simulating homogeneous multiphase flows or when the interface is not of primary interest.
- Lagrangian–Eulerian model: Suitable for particle-scale phenomena which can be modeled using fundamental principles of physics.
3.3. Numerical Methods
3.4. Geometry and Mesh
3.5. Boundary Conditions
3.6. Solvers and Software
3.7. Turbulence Modeling
3.8. Validation and Verification
3.9. Parametric Study
3.9.1. Nozzle Exit Position
3.9.2. Nozzle Area Ratio
3.9.3. Mixing Throat Diameter
3.9.4. Other Geometric Aspects
3.9.5. Operating Conditions
3.10. Optimization
Single-Factor and Multi-Factor Analyses of Vacuum Ejectors
3.11. Entropy Loss
- Entropy generation through viscous dissipation caused by average velocity gradients.
- Entropy generation through heat conduction resulting from average temperature gradients.
- Entropy generation through viscous dissipation caused by fluctuating velocity gradients (turbulent dissipation).
- Entropy generation through heat conduction due to fluctuating temperature gradients (turbulent heat transfer).
3.12. Entrainment Ratio Behavior
- Implementing advanced turbulence models.
- Optimizing geometry; involving nozzle design, mixing chamber shape, diffuser design.
- Adjusting operating conditions.
- Utilizing adjoint optimization.Additional factors can also be added to this list, such as:
- Incorporation of real gas effects.
- Boundary layer control involving wall treatments.
3.13. Internal Flow Visualization
3.13.1. Mixing Characteristics
3.13.2. Shock Structure
3.14. Investigation into the Properties of Heat and Mass Transfer
3.14.1. Condensation Effect
3.14.2. Nucleation
3.14.3. Droplet Growth
3.14.4. Condensing Nozzle
4. Limitations of Multiphase Flow Simulation in Ejectors
5. Conclusions
- Computational fluid dynamics (CFD) is a powerful tool for modeling and understanding complex flow phenomena in ejectors, including shock waves, mixing processes, and phase transitions.
- The accuracy of numerical predictions heavily depends on appropriate turbulence models, multiphase flow modeling, and consideration of non-equilibrium effects.
- Significant progress has been made in modeling condensation phenomena, leading to improved understanding and optimization of ejector performance parameters.
- Challenges remain in accurately modeling real gas effects, phase change kinetics, and coupled heat and mass transfer processes.
- Further validation against experimental data is needed, particularly for complex multiphase flow scenarios.
- Developing more robust multiphase flow models, incorporating advanced turbulence modeling techniques.
- Exploring adjustable, multi-nozzle designs, and specific operation conditions for practical multi-factor optimization of vacuum ejectors.
- Investigating various working fluids (e.g., real gas air, , , ) and materials (e.g., glass, wood, sponge, PVC pipes) to assess performance and applicability of vacuum ejectors.
- Integrating machine learning-based optimization methods. Exploring novel ejector configurations and applications in emerging technologies like energy storage and waste heat recovery systems.
Funding
Conflicts of Interest
References
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Paper | Primary–Secondary Flow | Fluid Flow | Geometry | Elements No. |
---|---|---|---|---|
Niu and Zhang 2024 [18] | Air–air (both ideal gas) single-phase | supersonic | 2D | 44,400 |
Chai et al., 2024 [42] | Saturated steam–water two-phase | supersonic | 3D | 294,480 |
Li et al., 2024 [41] | Nitrogen–air single-phase | Supersonic | 2D for single nozzle and 3D for 4-nozzles | 374,000 for single nozzle 16 million for 4-nozzles |
Talebiyan et al., 2024 [35] | Gas–gas (both ideal gas) single-phase | supersonic | 2D with rectangular cross-section | 430,000 |
Singer et al., 2024 [40] | Pure hydrogen-mixed H2/N2 single-phase | supersonic | 2D axis-symmetric | 330,000 |
Feng et al., 2024 [43] | Steam–water two-phase | supersonic | 2D axis-symetric | 140,000 |
Kus and Madejski 2024 [44] | water–CO2 two-phase | subsonic | 2D axis-symetric | 28,299 |
Tavakoli et al., 2023 [36] | Air–air (both ideal gas) single-phase | subsonic | 2D without and with fluidic oscillator | 50,000 |
Hou et al., 2022 [38] | Steam–steam (both ideal saturated steam) single-phase | supersonic | 3D | 982,362 |
Dadpour et al., 2022 [45] | Wet steam–wet steam two-phase | supersonic | 2D | 40,000 |
Koirala et al., 2022 [46] | Sub-cooled water–vapor two-phase | subsonic | 3D | 1.8 million |
Wen et al., 2020 [47] | Vapor–liquid two-phase | supersonic | 2D | 73,000 |
Macia et al., 2019 [37] | Air–air (both ideal gas) single-phase | supersonic | 2D axisymmetric | 20,300 |
Han et al., 2019 [48] | Steam–steam (both ideal gas) single-phase | supersonic | 2D axisymmetric | 46,352 |
Banu and Mani 2019 [39] | Steam–steam (both ideal gas) single-phase | - | 3D | 700,000 |
Giacomelli et al., 2016 [49] | wet steam–wet steam two-phase | supersonic | 2D axis-symmetric | 45,000 |
Ariafar et al., 2014 [50] | wet steam nozzle (of an ejector) two-phase | supersonic | 2D axis-symmetric with rectangular cross-section | 6510 |
Paper | Two-Phase Model | Best Turbulence Model Reported | Entrainment Ratio Remarks | Heat and Mass Transfer Model and Parameters |
---|---|---|---|---|
Niu and Zhang 2024 [18] | - | - | Was analyzed using both single-factor and multi-factor approaches | - |
Chai et al., 2024 [42] | Heterogeneous two-fluid (Eulerian) model | - | - | Non-equilibrium condensation model |
Li et al., 2024 [41] | - | - | Reported versus compression ratio, non-mixing length | - |
Talebiyan et al., 2024 [35] | - | k- SST | The adjoint optimization method notably improved entrainment ratio by around 20.8%, 15.3%, and 16.5% for different operating modes | - |
Singer et al., 2024 [40] | - | RSM with adjusted GEKO parameters | Reported versus the percentage of the fuel cell stack’s maximum load point/ Generalized k- turbulence model decreases overprediction of entrainment ratio by 25% | - |
Feng et al., 2024 [43] | Eulerian–Eulerian | - | Reported versus liquid mass fraction, droplet number/increase in droplet mass fraction led to a 9.15% decrease in M | classical homogeneous nucleation theory |
Tavakoli et al., 2023 [36] | - | k- SST k- | Reported versus pressure ratio/Ejector with oscillator improved entrainment ratio by 38.3% | |
Kus and Madejski 2024 [44] | Not available | - | - | Direct contact condensation and Mixture multiphase mode (MMP) |
Hou et al., 2022 [38] | - | - | Reported versus oultlet back pressure | - |
Dadpour et al., 2022 [45] | Eulerian-Eulerian | - | Reported versus back pressure/injection leads to a decrease in M by approximately 22.93% | - |
Koirala et al., 2022 [46] | Eulerian multiphase model | - | Back pressure ratio on entrainment ratio Primary flow temperature on entrainment ratio Entrainment pressure on entrainment ratio Time on entrainment ratio Condensation on entrainment ratio/ | Direct contact condensation resistance models for heat transfer interaction Ranz–Marshall to zero-resistance |
Wen et al., 2020 [47] | Not available | k- SST | Reported versus inlet pressure of suction chamber on entrainment ratio/ M grows as the pressure in the suction chamber increases | Non-equilibrium condensation model |
Macia et al., 2019 [37] | - | - | - | - |
Han et al., 2019 [48] | - | realizable k- | Reported versus primary fluid temperature, Back pressure, Throat diameter, NXP/ | |
Banu and Mani 2019 [39] | - | - | Reported versus pressure drive ratio and for different sweep angles of cavity type swirl generator/ | - |
Giacomelli et al., 2016 [49] | Eulerian multiphase model | - | Reported versus outlet pressure/HEM predicts a lower value of M | Non-equilibrium condensation model Homogeneous Non-equilibrium model |
Ariafar et al., 2014 [51] | Eulerian–Eulerian approach | - | described without curves | - |
Paper | Boundary Conditions | Solver and Software | Turbulence Modeling and Wall Function | Validation and Verification |
---|---|---|---|---|
Niu and Zhang [18] | MPa, MPa, MPa | Implicit pressure-based Ansys Fluent 19.0 | k- SST, Standard wall function | Experimental |
Chai et al., 2024 [42] | Inlet: mass flow rate for primary and secondary, 0.6–2.9 MPa, Outlet: 500 kPa | Pressure-based Ansys CFX 18.0 | k-,Scalable wall function | - |
Li et al., 2024 [41] | 6.84 kg/s, 316.2 K, 0.61 kg/s, K, kPa, K | coupled implicit density-based, FLUENT 19.0 | k- SST | Experimental |
Talebiyan et al., 2024 [35] | Inlet: kPa, K, kPa, K, Outlet: kPa, K | Pressure-based Ansys Fluent 2022 R2 | k- SST | Karthick et al., 2016 (exp) [55], Samsam-Khayani et al., 2022 (Num) [56] |
Singer et al., 2024 [40] | Inlet: , kPa Outlet: kPa with variation of pure hydrogen and mixed volume percentage | pressure-based using pressure–velocity coupling, Ansys Fluent 2023 R1 | Spallart allmaras, Standard k- wall function: Enhanced Wall Treatment, RNG k-, Realizable k-, k-, SST k-, Generalized k- (GEKO), RSM stress-BSL | Experimental |
Feng et al., 2024 [43] | Inlet: Pa, K, kPa, K Outlet: kPa, K | density-based implicit, FLUENT 19.2 | k- SST | Experimental and CFD by Sriveerakul [57] |
Kus and Madejski 2024 [44] | Inlet: m/s, bar, C, g/s, bar, C Outlet: bar | Segregated flow model, Siemens StarCCM+ 2022.1.1 | Realizable k- | - |
Tavakoli et al., 2023 [36] | Inlet: kg/s, 99,961.75 Pa, Outlet: 102,161 Pa | URANS equations (unsteady) Ansys Fluent 2022 R2 | k- and k- SST | - |
Hou et al., 2022 [38] | Inlet: 27,100 Pa, , , Outlet: : an independent variable, : saturated steam temperature corresponding to the | Pressure-based (steady state) Fluent | Realizable k-,standard wall function | Numerical |
Dadpour et al., 2022 [45] | B-Moore nozzle: kPa, K, , K, Ejector: kPa, , kPa, K Outlet: , K | Using Gauss–Seidel method coupled with implicit scheme, Open FOAM | k- model | B-Moore nozzle |
Koirala et al., 2022 [46] | Inlet: MPa, , MPa, Outlet: MPa | Pressure-based (steady and unsteady) Ansys Fluent 2019 R2 | k- model | Zhang et al., 2012 [58] |
Wen et al., 2020 [47] | Total pressure and total temperature for the entrances and exit | URANS equations (unsteady) Ansys Fluent 19 | k- SST | Sharifi and Boroomand 2013 (exp) [59] Laval nozzle Moses and Stein (exp) 1978 [60] Starzman et al., 2018 [61] |
Macia et al., 2019 [37] | Inlet: bar, Neumann condition for velocity, bar, Outlet: | Density-based explicit (rhoCentralFoam) implicit (HiSA) solvers OpenFOAM 6 | k- SST | Experimental |
Han et al., 2019 [48] | Inlet: 310–390 kPa, 2330–3170 Pa, Outlet: 3500–7000 Pa | ANSYS Fluent 17 | Standard k-, RNG k-, realizable k-, with Standard Wall Function and Enhanced Wall Function, and k- SST | Experimental |
Banu and Mani 2019 [39] | Inlet: , bar | Density-based (steady) Ansys Fluent 15.0 | k- SST | Experimental Banu et al., 2016 [62] as well as PIV study |
Giacomelli et al., 2016 [49] | Inlet: , ; primary and secondary pressures are the saturation pressures corresponding to | Ansys Fluent 16.2 | - | WS model in Fluent 16.2 |
Ariafar et al., 2014 [50] | kPa, K, Outlet: kPa | Coupled implicit solver Ansys Fluent 14.5 | Realizable k- | Two experimental cases by Moor et al. [63] and Bakhtar et al. [64] |
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Sadeghiseraji, J.; Garcia-Vilchez, M.; Castilla, R.; Raush, G. Recent Advances in Numerical Simulation of Ejector Pumps for Vacuum Generation—A Review. Energies 2024, 17, 4479. https://doi.org/10.3390/en17174479
Sadeghiseraji J, Garcia-Vilchez M, Castilla R, Raush G. Recent Advances in Numerical Simulation of Ejector Pumps for Vacuum Generation—A Review. Energies. 2024; 17(17):4479. https://doi.org/10.3390/en17174479
Chicago/Turabian StyleSadeghiseraji, Jaber, Mercè Garcia-Vilchez, Robert Castilla, and Gustavo Raush. 2024. "Recent Advances in Numerical Simulation of Ejector Pumps for Vacuum Generation—A Review" Energies 17, no. 17: 4479. https://doi.org/10.3390/en17174479
APA StyleSadeghiseraji, J., Garcia-Vilchez, M., Castilla, R., & Raush, G. (2024). Recent Advances in Numerical Simulation of Ejector Pumps for Vacuum Generation—A Review. Energies, 17(17), 4479. https://doi.org/10.3390/en17174479