Conservative Analysis of Transient Heat Transfer in Thermal Protection Systems with Interval Parameters
Abstract
:1. Introduction
2. Transient Heat Transfer Equations with Interval Parameters
3. Affine Interval Finite Element Method
4. Numerical Examples
4.1. Plate Model
4.2. TPS Model
4.3. Comparison of Computing Efficiency between AIFEM and MCM
5. Conclusions
- (1)
- The uncertainty of the TPS in the transient heat transfer analysis had a significant impact on its temperature response, so it is necessary to analyze the uncertainty of TPSs.
- (2)
- The temperature response bounds obtained by the AIFEM were wider than those obtained by the MCM, and the AIFEM can generally obtain a more conservative temperature response. The conservative AIFEM is a safe approach in uncertain TPS designs under transient heat transfer conditions.
- (3)
- The temperature response bounds provided by the MCM offered a real solution, but their calculation was very time-consuming. The AIFEM effectively improved the calculation efficiency. From the perspective of calculation efficiency, the AIFEM is a reasonable method to predict the temperature response of uncertain TPSs under transient heat transfer.
- (4)
- Given the uncertainty of TPS design under transient heat transfer conditions, the AIFEM can be used as an efficient and safe method. Next, the authors will try to study the conservatism of uncertain TPS thermal stress based on the AIFEM, and when conservative analysis is needed in other fields, try to use this method for research.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Uncertainty Level (%) | Bound | c (J/(kg·°C)) | λ (W/(m·°C)) |
---|---|---|---|
5 | UB | 210 | 10.5 |
LB | 190 | 9.5 | |
10 | UB | 220 | 11 |
LB | 180 | 9 |
Uncertain Level (%) | Time (s) | Bound | AIFEM (°C) | MCM (°C) | Error (%) |
---|---|---|---|---|---|
5 | 100 | UB | 101.71 | 99.90 | 1.81 |
LB | 83.52 | 85.14 | 1.90 | ||
200 | UB | 179.61 | 176.42 | 1.81 | |
LB | 156.16 | 159.11 | 1.85 | ||
10 | 100 | UB | 110.26 | 107.61 | 2.46 |
LB | 76.08 | 78.02 | 2.49 | ||
200 | UB | 190.43 | 185.26 | 2.79 | |
LB | 146.33 | 150.59 | 2.83 |
Uncertainty Level (%) | Bound | c (J/(kg·°C)) | λ (W/(m·°C)) | qs (W/m2) | Ta (°C) |
---|---|---|---|---|---|
5 | UB | 641.55 | 7.14 | 1.05 × 105 | −76 |
LB | 580.45 | 6.46 | 0.95 × 105 | −84 | |
10 | UB | 672.10 | 7.48 | 1.1 × 105 | −72 |
LB | 549.90 | 6.12 | 0.9 × 105 | −88 |
Uncertain Level (%) | Time (s) | Bound | AIFEM (°C) | MCM (°C) | Error (%) |
---|---|---|---|---|---|
5 | 300 | UB | 263.38 | 257.72 | 2.20 |
LB | 205.23 | 209.73 | 2.15 | ||
600 | UB | 378.41 | 368.87 | 2.59 | |
LB | 308.91 | 317.68 | 2.76 | ||
10 | 300 | UB | 292.03 | 283.80 | 2.90 |
LB | 181.18 | 186.48 | 2.84 | ||
600 | UB | 406.84 | 394.97 | 3.01 | |
LB | 283.73 | 292.75 | 3.08 |
Method | Plate Model | TPS Model |
---|---|---|
AIFEM | 0.021 s | 1.208 s |
MCM | 120.4 s | 13,246.9 s |
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Feng, X.; Shi, Z.; Yang, Z. Conservative Analysis of Transient Heat Transfer in Thermal Protection Systems with Interval Parameters. Appl. Sci. 2024, 14, 9446. https://doi.org/10.3390/app14209446
Feng X, Shi Z, Yang Z. Conservative Analysis of Transient Heat Transfer in Thermal Protection Systems with Interval Parameters. Applied Sciences. 2024; 14(20):9446. https://doi.org/10.3390/app14209446
Chicago/Turabian StyleFeng, Xuelei, Zhiyu Shi, and Zheng Yang. 2024. "Conservative Analysis of Transient Heat Transfer in Thermal Protection Systems with Interval Parameters" Applied Sciences 14, no. 20: 9446. https://doi.org/10.3390/app14209446
APA StyleFeng, X., Shi, Z., & Yang, Z. (2024). Conservative Analysis of Transient Heat Transfer in Thermal Protection Systems with Interval Parameters. Applied Sciences, 14(20), 9446. https://doi.org/10.3390/app14209446