Large Eddy Simulation of Conjugate Heat Transfer in a Ribbed Channel: Reynolds Number Effect
Abstract
:1. Introduction
2. Numerical Methods and Code Validation
2.1. Numerical Methods
2.2. Code Validation
3. Results and Discussion
3.1. Effect of Reynolds Number on the Isothermal Ribbed Channel
3.2. Time-Averaged Thermal Fields in the Conducting Ribbed Channel
3.3. Turbulent Heat Transfer Statistics
3.4. Thermal Performance
4. Conclusions
- In pure convection, when the Reynolds number is lowered from 30,000 to 7000, the heat transfer increases by 5% on the channel wall, but decreases by 20% on the rib.
- When the thermal conductivity ratio is more than 10, the Reynolds number effect is stronger in the rib than in the wall. When Re = 7000, the heat transfer coefficient ratio in the rib is larger than that when Re = 30,000.
- Compared with the turbulent flow, the effect of conduction in the laminar flow is observed at a low thermal conductivity ratio, and the effect of heat transfer promotion is not large in the typical ribbed channel geometry of the gas turbines.
- In the turbulent flow, when K* = 100 or more, the heat transfer promotion effect of the ribbed channel can be expected even at a low Reynolds number. If K* = 10 or less, then the heat transfer promotion performance of the rib becomes worse than that in the laminar flow, and thus, the effect of the rib cannot be expected under these conditions.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Ac:b | cross-sectional area at the base |
Arib | rib surface area |
Bi | Biot number (=hd/ks) |
C* | heat capacity ratio (=(ρ cp)f/(ρ cp)s) |
d | thickness of the channel wall |
f | frication factor |
fi | momentum forcing |
k | thermal conductivity |
K* | thermal conductivity ratio (=ks/kf) |
ms | mass source/sink |
Nu | Nusselt number (=hDh/kf) |
q” | heat flux |
q | heat transfer rate |
qf | heat transfer rate through a fin |
Re | bulk Reynolds number (=UbDh/ν) |
t | time |
T | temperature |
Tb | bulk temperature |
Tw | wall temperature |
Ub | bulk velocity |
Greek symbols | |
εf | fin effectiveness |
ηf | fin efficiency |
ν | kinematic viscosity |
θ | dimensionless temperature (=(T − Tb)/(Tw − Tb)) |
Θ | time-averaged dimensionless temperature |
ω | index function between the solid and the fluid |
Subscripts | |
f | fluid or fin |
rms | root-mean-square value |
s | solid |
0 | fully developed value in a smooth pipe |
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Ahn, J.; Song, J.C.; Lee, J.S. Large Eddy Simulation of Conjugate Heat Transfer in a Ribbed Channel: Reynolds Number Effect. Processes 2022, 10, 1928. https://doi.org/10.3390/pr10101928
Ahn J, Song JC, Lee JS. Large Eddy Simulation of Conjugate Heat Transfer in a Ribbed Channel: Reynolds Number Effect. Processes. 2022; 10(10):1928. https://doi.org/10.3390/pr10101928
Chicago/Turabian StyleAhn, Joon, Jeong Chul Song, and Joon Sik Lee. 2022. "Large Eddy Simulation of Conjugate Heat Transfer in a Ribbed Channel: Reynolds Number Effect" Processes 10, no. 10: 1928. https://doi.org/10.3390/pr10101928