Droplet-Laden Flows in Multistage Compressors: An Overview of the Impact of Modeling Depth on Calculated Compressor Performance †
Abstract
1. Introduction
- The majority of droplets, typical for high fogging in terms of diameter, hit the blades in the first stages (at least 25% and up to 98% of the injected water mass for droplet diameters between 5 and 30 µm).
- Droplet–wall interaction modeling is essential because deposition effectively decreases the droplet water mass available for evaporation.
- Partial deposition (splashing) was shown to be particularly relevant for intermediate and large droplets, as the resulting secondary droplets strongly enhance evaporation and were identified to be the main source of phase change for those cases.
2. Multiphase Flow Modeling
2.1. Gas Phase
2.2. Droplet Phase
- The parcel exits the computational domain through the compressor outlet,
- The parcel impacts the surface,
- The droplet diameter decreases below 1 × 10−9 m or
- The tracking time exceeds 20 s.
2.2.1. Heat Transfer
2.2.2. Mass Transfer
2.3. Droplet–Wall Interaction
2.4. Films
2.4.1. Casing Films
2.4.2. Film Re-Entrainment
3. Benchmark Compressor
4. Modeling Approach
4.1. Assumptions and Simplifications
4.2. Cases Studied
4.2.1. Case 1: Dry Flow
4.2.2. Case 2: Full Deposition
4.2.3. Case 3: Partial Deposition
4.2.4. Case 4: Partial Disintegration
4.2.5. Case 5. Full Disintegration
4.3. Properties of the Injector
4.3.1. Representative Diameter
4.3.2. Ligament Length
4.3.3. Droplet Temperature
4.3.4. Injector Position
5. Results
5.1. Overall Impact of Re-Entrainment Modeling
5.2. Spatial Distribution of Flow Quantities
6. Discussion of Modeling Assumptions
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
| Quantities | |||
| absolute velocity (m/s) | temperature (K) | ||
| mass flow rate (kg/s) | latent heat (J/kg) | ||
| pressure (Pa) | R | specific gas constant (J/kg/K) | |
| density (kg/m3) | D | droplet diameter (m) | |
| surface tension (N/m) | D | diffusivity (m2/s) | |
| h | thickness (m) | dynamic viscosity (Pa × s) | |
| specific compression work (J/kg) | ligament length (m) | ||
| r | radius (m) | n | rev per minute (1/min) |
| M | molar mass (g/mol) | critical temperature (K) | |
| s | specific entropy (J/kg/K) | Eötvös constant ( | |
| Numbers | |||
| relative film thickness | Reynolds number | ||
| splashing threshold | deviation | ||
| Weber number | polytropic efficiency | ||
| w | vapor mass per dry air mass | f | liquid mass per dry air mass |
| total pressure ratio | total temperature ratio | ||
| Rosin–Rammler function | |||
| Sub-/Superscripts | |||
| ideal mixture | liquid phase | ||
| pure air | parcel | ||
| pure vapor | Sauter mean | ||
| t | total | TE | trailing edge |
| sat | saturation | I | impact |
| ~ | modified | in | inlet |
| out | outlet | red | normalized |
| ax | axial direction | depos | deposited mass |
| tr | triple point value | s | static |
Appendix A
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| 1 | 5 | 10 | 25 | 50 | |
| Rel. ejected mass | 0.00 | 0.18 | 0.36 | 0.70 | 0.91 |
| τ [-] | n [1/min] | |||
| 1.85 | 5000 | 0.904 | 6.11 | |
| Π [-] | ||||
| 247.6 | 7.02 | 1013.25 | 288.15 | 0.0 |
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Geist, S.; Schatz, M. Droplet-Laden Flows in Multistage Compressors: An Overview of the Impact of Modeling Depth on Calculated Compressor Performance. Int. J. Turbomach. Propuls. Power 2025, 10, 36. https://doi.org/10.3390/ijtpp10040036
Geist S, Schatz M. Droplet-Laden Flows in Multistage Compressors: An Overview of the Impact of Modeling Depth on Calculated Compressor Performance. International Journal of Turbomachinery, Propulsion and Power. 2025; 10(4):36. https://doi.org/10.3390/ijtpp10040036
Chicago/Turabian StyleGeist, Silvio, and Markus Schatz. 2025. "Droplet-Laden Flows in Multistage Compressors: An Overview of the Impact of Modeling Depth on Calculated Compressor Performance" International Journal of Turbomachinery, Propulsion and Power 10, no. 4: 36. https://doi.org/10.3390/ijtpp10040036
APA StyleGeist, S., & Schatz, M. (2025). Droplet-Laden Flows in Multistage Compressors: An Overview of the Impact of Modeling Depth on Calculated Compressor Performance. International Journal of Turbomachinery, Propulsion and Power, 10(4), 36. https://doi.org/10.3390/ijtpp10040036
