A Thermodynamic-Based Black-Box Modeling Approach for the Comprehensive Analysis of Vortex Tube Applications
Abstract
:1. Introduction
- Fluid mechanical approaches;
- Thermodynamic black-box approaches.
2. Methodology
2.1. Review of the Available Vortex Tube Modeling Approaches
2.2. Derivation of New Black-Box Modeling Approach
2.3. Evaluation of Measured Data
- Neglect of the inequality of the energy balance;
- Correction of the entropy balance by means of heat flow;
- Correction of one output flow enthalpy and adiabatic entropy balance.
3. Results
3.1. Cold Gas Mass Fraction Influence
- A maximum turning point;
- A steady increase.
3.2. Pressure Influence
3.3. Further Influences of the Vortex Tube Efficiency
4. Discussion
5. Conclusions
- For the derivation of using experimental data, it is necessary to consider heat transfer to and from the ambient.
- The literature data do not provide a clear and comprehensive trend for the developed expression of , especially for the influence of the pressure ratio or the geometric influence.
- A simple conservative yet physical-based formulation of is capable of depicting the vortex tube behavior for air in alignment with measurement data.
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Symbols | ||
Symbol | Unit | Description |
A | Area | |
c | m/s | Velocity |
J/(kg K) | Specific heat capacity at constant pressure | |
d | m | Diameter |
f | - | Function |
- | Empirical constant | |
- | Empirical constant | |
h | J/kg | Specific enthalpy |
J/kg | Corrected specific enthalpy | |
H | - | Vortex tube coefficient |
L | m | Length |
kg/s | Mass flow | |
M | kg/mol | Molar mass |
p | Pa | Pressure |
- | Pressure ratio | |
J/kg | Specific heat flow | |
R | J/(mol K) | Ideal gas constant |
- | Rossby number | |
s | J/(kg K) | Specific entropy |
J/(kg K) | Corrected specific entropy | |
T | K | Temperature |
K | Corrected temperature | |
X | - | De-dimensionalized pressure difference |
y | - | Cold gas mass fraction |
Greek symbols | ||
Symbol | Unit | Description |
- | Isentropic exponent | |
- | Difference between two values | |
- | Efficiency | |
kg/ | Density | |
- | Mass fraction |
Indices and abbreviations | ||
Note: Indices which belong to one specific symbol (e.g., ) are not shown in this table. | ||
Symbol | Description | |
A | Component A of a binary mixture | |
B | Component B of a binary mixture | |
c | Cold outlet | |
Corr | Correction | |
h | Hot outlet | |
h-c | Difference between hot and cold outlet | |
i | Component i of a mixture | |
in | Inlet | |
irr | Irreversible | |
mix | Mixutre | |
out | Outlet | |
p | Constant pressure | |
ref | Reference | |
rel | Relative | |
sep | Separation | |
th | Theoretically | |
throt | Throttling valve | |
T | Constant temperature | |
V1 | Variant 1 | |
V2 | Variant 2 | |
VT | Vortex tube |
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Author | Advantages | Disadvantages |
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Shannak [19] |
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Mansour et al. [20] |
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Mischner and Bespalov [21] |
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Keller et al. [3] |
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Liu et al. [22] |
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Assumptions |
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Sager, R.; Petersen, N.H.; Wirsum, M. A Thermodynamic-Based Black-Box Modeling Approach for the Comprehensive Analysis of Vortex Tube Applications. Energies 2024, 17, 4180. https://doi.org/10.3390/en17164180
Sager R, Petersen NH, Wirsum M. A Thermodynamic-Based Black-Box Modeling Approach for the Comprehensive Analysis of Vortex Tube Applications. Energies. 2024; 17(16):4180. https://doi.org/10.3390/en17164180
Chicago/Turabian StyleSager, Robert, Nils Hendrik Petersen, and Manfred Wirsum. 2024. "A Thermodynamic-Based Black-Box Modeling Approach for the Comprehensive Analysis of Vortex Tube Applications" Energies 17, no. 16: 4180. https://doi.org/10.3390/en17164180