Numerical Investigation on Thermally Induced Self-Excited Thermoacoustic Oscillations in the Pipelines of Cryogenic Storage Systems
Abstract
1. Introduction
2. CFD Methodology
2.1. Model Description
2.2. Simplifications and Assumptions
2.3. Solution of the Governing Equations
2.4. Simulation Strategy and Boundary Conditions
2.5. Sensitivity Studies
2.6. Comparison with Existing Literature
3. Acoustic and Flow Characteristics of the Cryogenic Helium Pipe
3.1. Transient Growth of Self-Excited Thermoacoustic Oscillations
3.2. Velocity and Temperature Profiles at Steady State
4. Impact on the Dynamic Behavior of Taconis Oscillations
4.1. Position of Temperature Gradient
4.2. Magnitude of Temperature Gradient
5. Conclusions
- (1)
- CFD simulations on the benchmark cryogenic helium pipe indicate that when ε = 1 and Γ = 14,500 K/m, large-amplitude Taconis oscillations occur. These oscillations exhibit two distinct frequencies: a first-mode frequency of 60 Hz with an amplitude of 213 kPa and a second-mode frequency of 121 Hz with a significantly lower amplitude. The velocity profile in the y direction follows a Poiseuille pattern, whereas the helium temperature is more uniform away from the walls.
- (2)
- The position of the temperature gradient significantly affects the stability of the cryogenic helium pipe. When ε = 1, the onset temperature gradient for Taconis oscillations is relatively low, approximately 7000 K/m. This suggests that, to prevent the occurrence of Taconis oscillations, the transition between the warm and cold sections should be away from one-quarter of the cryogenic pipe. When ε = 0.5, although the pressure amplitude is lower, higher-order acoustic modes are more easily excited within the helium pipeline, leading to the coexistence of multiple acoustic modes. The natural frequencies of acoustic modes increase as ε increases due to increased average temperature as a result of a larger proportion the hot section.
- (3)
- The magnitude of the temperature gradient also has a significant impact on the dynamic behavior of Taconis oscillations. As Γ increases, the cryogenic helium tube becomes more susceptible to instability and easier to excite, resulting in a shorter time to reach steady-state periodic oscillations. In addition, the oscillation frequency of the cryogenic helium pipe rises with increasing Γ due to the increased sound speed at higher temperatures.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters | Symbols | Values and Units |
---|---|---|
Hot-section temperature | Th | Values: 150 K to 900 K; increment: 50 K |
Cold-section temperature | Tc | Fixed at 10 K |
Temperature ratio | Γ | Values: 7000 K/m to 44,500 K/m; baseline value: 14,500 K/m |
Length of hot section | l | 1/6L, 1/4L, and 1/3L; |
Length ratio | ε | Values: 0.5, 1, and 2; baseline value: 1 |
Steps | Hot Section | Cold Section | Transition Section | Left End (x = 0) | Right End (x = L) |
---|---|---|---|---|---|
Step 1: Steady calculation | Rigid wall, T = Th | Rigid wall, T = Tc | Rigid wall, linear decrease from Th to Tc | Pressure inlet, p = 10 Pa, T = Th | Pressure outlet, p = 0 Pa, T = Th |
Step 2: Transient calculation | Rigid wall, T = Th | Rigid wall, T = Tc | Rigid wall, linear decrease from Th to Tc | Rigid wall, u = 0, T = Th | Rigid wall, u = 0, T = Th |
Grid Node | 91,563 | 142,531 | 241,520 | Timestep Size | 1.5 × 10−5 s | 1 × 10−5 s | 0.5 × 10−5 s |
---|---|---|---|---|---|---|---|
f (Hz) | 60.8 | 60 | 59.1 | f (Hz) | 58.4 | 60 | 61.3 |
ER | 2.9% | 1.5% | N/A | ER | 4.7% | 2.1% | N/A |
CPUhs | 431 | 545 | 631 | CPUhs | 270 | 545 | 675 |
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Liu, L.; Zhuo, C.; Liu, Y.; Chen, G. Numerical Investigation on Thermally Induced Self-Excited Thermoacoustic Oscillations in the Pipelines of Cryogenic Storage Systems. Symmetry 2025, 17, 1361. https://doi.org/10.3390/sym17081361
Liu L, Zhuo C, Liu Y, Chen G. Numerical Investigation on Thermally Induced Self-Excited Thermoacoustic Oscillations in the Pipelines of Cryogenic Storage Systems. Symmetry. 2025; 17(8):1361. https://doi.org/10.3390/sym17081361
Chicago/Turabian StyleLiu, Liu, Cong Zhuo, Yongqing Liu, and Geng Chen. 2025. "Numerical Investigation on Thermally Induced Self-Excited Thermoacoustic Oscillations in the Pipelines of Cryogenic Storage Systems" Symmetry 17, no. 8: 1361. https://doi.org/10.3390/sym17081361
APA StyleLiu, L., Zhuo, C., Liu, Y., & Chen, G. (2025). Numerical Investigation on Thermally Induced Self-Excited Thermoacoustic Oscillations in the Pipelines of Cryogenic Storage Systems. Symmetry, 17(8), 1361. https://doi.org/10.3390/sym17081361