Determination of Hydrogen’s Thermophysical Properties Using a Statistical Thermodynamic Method
Abstract
:1. Introduction
2. Theoretical Model and Implementation
2.1. Statistical Thermodynamic Model for Hydrogen
2.1.1. Equilibrium Ortho-H2 Fraction
2.1.2. Para-Ortho H2 Conversion Heat
2.1.3. Isobaric Heat Capacity
2.1.4. Fundamental EOSs for Hydrogen
2.2. Implementation of Different Methods for Hydrogen’s Thermophysical Properties
2.3. Analytical Model for VCS-MLI Combined Structure
2.3.1. Physical Model for VCS-MLI
2.3.2. VCS-MLI Heat Transfer Model and Its Verification
3. Results and Discussion
3.1. Accuracy of Statistical Thermodynamic Method
3.1.1. Ortho-H2 Fraction and Conversion Heat
3.1.2. Isobaric Heat Capacity and Enthalpy
3.2. Convenience of the Statistical Thermodynamic Method
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Physical Parameters of VDMLI | Value |
---|---|
Material of Radiation Shields | Double-Aluminized Mylar |
Residual Gas Pressure, p | 0.001 Pa |
Accomodation Coefficient of Residual Gas, α | 0.9 |
Material of Spacers | Dacron Net |
Empirical Coefficient of Spacers, C2 | 0.008 |
Relative Density of Spacers, f | 0.02 |
Total Number of Radiation Shields, m | 43 |
Total Number of Spacers, n | 126 |
Total Thickness | 33.2 mm |
Warm Boundary Temperature, Th | 300 K |
Cold Boundary Temperature, Tc | 20 K |
Configuration Parameters of VDMLI | Value | |
---|---|---|
Layer Number of Radiation Shields | Low-Layer-Density Zone, m1 | 8 |
Medium-Layer-Density Zone, m2 | 14 | |
High-Layer-Density Zone, m3 | 21 | |
Layer Density | Low-Layer-Density Zone, d1 | 6.35 N·cm−1 |
Medium-Layer-Density Zone, d2 | 12.70 N·cm−1 | |
High-Layer-Density Zone, d3 | 19.35 N·cm−1 |
Pressure/Mpa | Maximum Deviation/% |
---|---|
0.5 | 0.0006 |
1 | 0.0021 |
2 | 0.0051 |
5 | 0.0271 |
10 | 0.2454 |
20 | 2.3129 |
Method | Average Running Time/s (14,001 Circulations) | Average Running Time/s (28,001 Circulations) |
---|---|---|
Spline Interpolation | 0.1735 | 0.3356 |
REFPROP Data | 1.6971 | 3.3626 |
Statistical Thermodynamic Calculation | 0.0716 | 0.1463 |
Case | Method | Average Running Time/s (10,001 Circulations) | Average Running Time/s (20,001 Circulations) |
---|---|---|---|
With Para-ortho Conversion | Spline Interpolation (1.1) | 0.3253 | 0.6562 |
REFPROP Data (1.2) | 56.8849 | 113.5774 | |
Statistical Thermodynamic Calculation (1.3) | 0.1077 | 0.2124 | |
Without Para-ortho Conversion | Spline Interpolation (2.1) | 0.1731 | 0.3384 |
REFPROP Data (2.2) | 1.2122 | 2.3988 | |
Integral of cp with Temperature (2.3) | 81.5196 | 163.1697 | |
Statistical Thermodynamic Calculation (2.4) | 0.0518 | 0.1039 |
Case | Method | Average Running Time/s | Number of Iterations |
---|---|---|---|
With Para-ortho Conversion | Spline Interpolation (1.1) | 0.2668 | 5198 |
REFPROP Data (1.2) | 37.0464 | 5224 | |
Statistical Thermodynamic Calculation (1.3) | 0.1030 | 5182 | |
Without Para-ortho Conversion | Spline Interpolation (2.1) | 0.1947 | 6108 |
REFPROP Data (2.2) | 1.0806 | 6137 | |
Integral of cp with Temperature (2.3) | 15.3030 | 6102 | |
Statistical Thermodynamic Calculation (2.4) | 0.0859 | 6090 |
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Xu, Z.; Tan, H.; Wu, H. Determination of Hydrogen’s Thermophysical Properties Using a Statistical Thermodynamic Method. Appl. Sci. 2023, 13, 7466. https://doi.org/10.3390/app13137466
Xu Z, Tan H, Wu H. Determination of Hydrogen’s Thermophysical Properties Using a Statistical Thermodynamic Method. Applied Sciences. 2023; 13(13):7466. https://doi.org/10.3390/app13137466
Chicago/Turabian StyleXu, Zhangliang, Hongbo Tan, and Hao Wu. 2023. "Determination of Hydrogen’s Thermophysical Properties Using a Statistical Thermodynamic Method" Applied Sciences 13, no. 13: 7466. https://doi.org/10.3390/app13137466