Thermodynamic Modeling of Multilayer Insulation Schemes Coupling Liquid Nitrogen Cooled Shield and Vapour Hydrogen Cooled Shield for LH2 Tank
Abstract
1. Introduction
2. LH2 Storage Tank and Insulation System
3. Thermodynamic Model and Experimental Verification
3.1. Assumptions
- (1)
- The absorption effect of spacers in MLI materials on radiative heat transfer was neglected.
- (2)
- Due to the high vacuum level within the MLI, convection caused by residual gas was neglected.
- (3)
- Thermal expansion and delamination between the MLI materials were not considered.
- (4)
- The internal pressure of the LH2 storage tank was maintained at 0.1 MPa with a temperature stabilized at 20 K.
- (5)
- The paper mainly focused on the condition where the ACS and coil reach steady state; that is, the temperature of the ACS was equal everywhere, without considering the temperature difference in ACS.
3.2. Thermodynamic Model of MLI and MLI-ACS
3.2.1. Thermodynamic Model of MLI
- (1)
- Heat transfer model of tank wall
- (2)
- Heat transfer model of MLI
- -
- Radiative heat transfer
- -
- Solid conduction
- -
- Residual gas conduction
- (3)
- Heat transfer model of interlayer
3.2.2. Thermodynamic Model of MLI-LNCS/MLI-VHVCS
- (1)
- Heat transfer in OMLI
- (2)
- Heat leakage through IMLI
- (3)
- Heat absorption by LNCS
- (4)
- Heat absorption by VHVCS
3.2.3. Thermodynamic Model of Thermal Bridge
- (1)
- Thermal bridge model of support system
- (2)
- Thermal bridge model of piping system
3.3. Boundary Conditions and Calculation Procedure
3.4. Experimental Validation
4. Results and Discussion
4.1. Heat Transfer in MLI
4.1.1. Temperature Distribution and Heat Leakage
4.1.2. Heat Leakage Distribution and Proportion in MLI
4.2. Co-Optimization of MLI-LNCS Scheme
4.2.1. Optimization of IMLI-Layer Count Based on Initial LNCS Position
4.2.2. Optimization of LNCS Position Based on IMLI Layer Count
4.2.3. Co-Optimization of IMLI Layer Count and LNCS Position
4.3. Co-Optimization of MLI-VHVCS Scheme
4.3.1. Iterative Co-Optimization of VHVCS Position and IMLI Layer Count
- (1)
- First iteration step
- (2)
- Second iteration step
- (3)
- Iteration steps three to seven
4.3.2. Convergence Characteristics of Co-Optimization Process
4.3.3. Evolution of Heat Leakage and MLI Temperature Distribution
4.4. Comparison of Three Insulation Schemes
5. Conclusions
- (1)
- The established model demonstrated good performance in predicting the thermal performance of MLI insulation under LH2 temperature conditions. The relative deviations between the calculated values and experimental values are within 5%. The thermal resistance of the insulation scheme gradually decreases from the inner side to the outer side. A significant temperature gradient is observed near the cold boundary, while the gradient becomes more moderate near the warm boundary.
- (2)
- For the MLI-LNCS scheme, the optimal number of IMLI layers is 36, with the optimal LNCS position installed at 49% of the interlayer space. For the MLI-VHVCS scheme, the optimal number of IMLI layers is 21, and the corresponding optimal VHVCS installation position is identified at 39%.
- (3)
- Compared to the conventional MLI scheme, the MLI-LNCS scheme reduces heat leakage by 88.09%. However, the LN2 circulation system results in high operational costs. The MLI-VHVCS scheme achieves a 62.74% reduction in heat leakage, demonstrating that harnessing the sensible cooling capacity of cryogenic vapor effectively enhances the thermal insulation performance of LH2 storage tanks. Although the MLI-LNCS scheme provides a 68.04% reduction in heat leakage compared to the MLI-VHVCS scheme, the latter proves more favorable when considering economic considerations.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
LT | length of the tank, m | Q* | dimensionless heat leakage |
QMLI | heat leakage through the MLI, W | m* | dimensionless mass flow rate |
σ | Stephan–Boltsman constant | η | dimensionless evaluation parameter |
ε(T) | emissivity of the radiation shield | λH | conductivity at hot boundary, W/(m·K) |
T1 | inner-surface temperature of inner tank, K | λL | conductivity at cold boundary, W/(m·K) |
T2 | outer-surface temperature of inner tank, K | TACS | ACS temperature, K |
Tn−1 | inner-surface temperature of outer tank, K | λACS | conductivity of acs, W/(m·K) |
Tn | outer-surface temperature of outer tank, K | λamb | conductivity of air, W/(m·K) |
C | empirical constant, 0.008 | Nu | Nusselt number |
f | relative solid density | Re | Reynolds number |
k | conductivity of spacer, W/(m·K) | Pr | Prandtl number |
Ta | ambient temperature, 300 K | ψ | daily boil-off rate |
p | vacuum pressure, Pa | ρ | LH2 density, kg/m3 |
γ | specific heat ratio, γ = cp/cv | V | tank capacity, m3 |
α | accommodation coefficient, 0.9 | LH2 | liquid hydrogen |
RT | total thermal resistance, K/W | LN2 | liquid nitrogen |
QOMLI | heat leakage through OMLI, W | MLI | multilayer insulation |
QIMLI | heat leakage through IMLI, W | OMLI | outer-multilayer insulation |
QACS | heat absorbed by ACS, W | IMLI | inner-multilayer insulation |
m | mass flow rate, kg/s | ACS | active cooled shield |
∆H | latent heat of vaporization, kJ/kg | LNCS | liquid-nitrogen cooled shield |
QSEN | sensible heat of cryogenic vapor, J/kg | VHVCS | vapor-hydrogen cooled shield |
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Basic Parameters | Cold-Boundary Temperature (K) | Hot-Boundary Temperature (K) | Wind Speed (m/s) | MLI Layer Count (Layers) | MLI Layer Density (Layers/cm) |
---|---|---|---|---|---|
20 | 300 | 7.717 | 80 | 25 |
Path | Literature—Chen | Emissivity: 0.05 | Emissivity: Exponential Equation |
---|---|---|---|
Insulation heat leakage (%) | 29.92 | 30.43 | 39.21 |
Support-structure heat leakage (%) | 68.59 | 68.11 | 59.52 |
Pipeline-system heat leakage (%) | 1.49 | 1.46 | 1.27 |
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Lu, J.; Chen, L.; Zhou, X. Thermodynamic Modeling of Multilayer Insulation Schemes Coupling Liquid Nitrogen Cooled Shield and Vapour Hydrogen Cooled Shield for LH2 Tank. Processes 2025, 13, 2574. https://doi.org/10.3390/pr13082574
Lu J, Chen L, Zhou X. Thermodynamic Modeling of Multilayer Insulation Schemes Coupling Liquid Nitrogen Cooled Shield and Vapour Hydrogen Cooled Shield for LH2 Tank. Processes. 2025; 13(8):2574. https://doi.org/10.3390/pr13082574
Chicago/Turabian StyleLu, Jingyang, Liqiong Chen, and Xingyu Zhou. 2025. "Thermodynamic Modeling of Multilayer Insulation Schemes Coupling Liquid Nitrogen Cooled Shield and Vapour Hydrogen Cooled Shield for LH2 Tank" Processes 13, no. 8: 2574. https://doi.org/10.3390/pr13082574
APA StyleLu, J., Chen, L., & Zhou, X. (2025). Thermodynamic Modeling of Multilayer Insulation Schemes Coupling Liquid Nitrogen Cooled Shield and Vapour Hydrogen Cooled Shield for LH2 Tank. Processes, 13(8), 2574. https://doi.org/10.3390/pr13082574