Optimum Placement of Heating Tubes in a Multi-Tube Latent Heat Thermal Energy Storage
Abstract
:1. Introduction
2. Model and Governing Equations
3. Numerical Method, Mesh Study, and Validation
3.1. Numerical Method
3.2. Mesh and Time-Step Size Study
3.3. Validation
4. Results and Discussion
5. Conclusions
- Based on the Taguchi design, the first row of the HTF tubes should be placed at the lowest possible point while the other tubes should be distributed evenly in the enclosure.
- The charging time of the LHTES unit could be changed by about 76% by just changing the location of tubes in the enclosure.
- From the streamlines and melting interfaces, it can be concluded that the formation of streamlines and free-convection flow circulation in each step of the melting process are the key points in the design of LHTES. Special attention should be paid to the streamline at the final stages of the charging process. A general uniform large circulation flow in the enclosure was much better than several small and week circulation flows.
- The Taguchi method could be used to effectively propose the optimum design of an LHTES unit with few simulations. Thus, this approach seems useful in the future design of energy storage systems.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Am (kg m−3 s−1) | mushy zone constant | tm (s) | melting/solidification time |
Cp (J kg−1 K−1) | specific heat | T (K) | temperature |
g (ms−2) | gravity | Te (K) | mean temperature after the phase change process |
k (W m−1 K−1) | thermal conductivity | Ti (K) | initial temperature |
Lf (J kg−1) | latent heat of fusion | ||
LF | the normal total amount of melted phase change mateial | ||
m (kg) | mass | Greek symbols | |
P (Pa) | pressure | β (K−1) | expansion coefficient |
Q (J) | thermal storage/recovery capacity | λ | local liquid fraction |
(W) | thermal storage/recovery rate | μ (kg m−1 s−1) | dynamic Viscosity |
TL (K) | liquidus temperature | ρ (kg m−3) | density |
Ts (K) | solidus temperature | ΔH (J kg−1) | latent heat of fusion |
(m s−1) | velocity |
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Property | ρ (kg m−3) | Lf (kJ kg−1) | Cp (kJ kg−1 K) | k (W m−1 K) | μ (N s m−2) | TL (°C) | TS (°C) | β (1 K−1) |
---|---|---|---|---|---|---|---|---|
Values | 815 | 170 | 2.0 | 0.2 | 0.023 | 35 | 29 | 0.0006 |
Factors | Description | Level 1 | Level 2 | Level 3 | Level 4 |
---|---|---|---|---|---|
A | HL0/D (height of the first tube) | 1.2 | 1.8 | 2.4 | 3.0 |
B | HL1/D (height of the second tube) | 1.2 | 1.8 | 2.4 | 3.0 |
C | HL2/D (height of the fourth tube) | 1.2 | 1.8 | 2.4 | 3.0 |
Experiment Number | Design Parameters | Time (s) for LF = 0.75 | Signal-to-Noise (S/N) Ratio | ||
---|---|---|---|---|---|
HL0/D | HL1/D | HL2/D | |||
1 | 1.2 | 1.2 | 1.2 | 13,633 | −82.6918 |
2 | 1.2 | 1.8 | 1.8 | 13,613 | −82.6791 |
3 | 1.2 | 2.4 | 2.4 | 9025 | −79.1089 |
4 | 1.2 | 3.0 | 3.0 | 8205 | −78.2816 |
5 | 1.8 | 1.2 | 1.8 | 11,977 | −81.5670 |
6 | 1.8 | 1.8 | 1.2 | 13,850 | −82.8290 |
7 | 1.8 | 2.4 | 3.0 | 9161 | −79.2389 |
8 | 1.8 | 3.0 | 2.4 | 9206 | −79.2814 |
9 | 2.4 | 1.2 | 2.4 | 14,742 | −83.3711 |
10 | 2.4 | 1.8 | 3.0 | 9374 | −79.4385 |
11 | 2.4 | 2.4 | 1.2 | 11,096 | −80.9033 |
12 | 2.4 | 3.0 | 1.8 | 10,332 | −80.2837 |
13 | 3.0 | 1.2 | 3.0 | 12,603 | −82.0095 |
14 | 3.0 | 1.8 | 2.4 | 10,710 | −80.5958 |
15 | 3.0 | 2.4 | 1.8 | 12,379 | −81.8537 |
16 | 3.0 | 3.0 | 1.2 | 10,104 | −80.0899 |
Level | HL0/D | HL1/D | HL2/D |
---|---|---|---|
1 | −80.69 | −82.41 | −81.63 |
2 | −80.73 | −81.39 | −81.60 |
3 | −81.00 | −80.28 | −80.59 |
4 | −81.14 | −79.48 | −79.74 |
Delta | 0.45 | 2.93 | 1.89 |
Rank | 3 | 1 | 2 |
Optimum Factors | Charging Time of LF = 0.75 | |||
---|---|---|---|---|
HL0/D | HL1/D | HL2/D | Taguchi Prediction | Tested Case |
1.2 | 3.0 | 3.0 | 7915 | 8205 |
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Ghalambaz, M.; Mohammed, H.I.; Naghizadeh, A.; Islam, M.S.; Younis, O.; Mahdi, J.M.; Chatroudi, I.S.; Talebizadehsardari, P. Optimum Placement of Heating Tubes in a Multi-Tube Latent Heat Thermal Energy Storage. Materials 2021, 14, 1232. https://doi.org/10.3390/ma14051232
Ghalambaz M, Mohammed HI, Naghizadeh A, Islam MS, Younis O, Mahdi JM, Chatroudi IS, Talebizadehsardari P. Optimum Placement of Heating Tubes in a Multi-Tube Latent Heat Thermal Energy Storage. Materials. 2021; 14(5):1232. https://doi.org/10.3390/ma14051232
Chicago/Turabian StyleGhalambaz, Mohammad, Hayder I. Mohammed, Ali Naghizadeh, Mohammad S. Islam, Obai Younis, Jasim M. Mahdi, Ilia Shojaeinasab Chatroudi, and Pouyan Talebizadehsardari. 2021. "Optimum Placement of Heating Tubes in a Multi-Tube Latent Heat Thermal Energy Storage" Materials 14, no. 5: 1232. https://doi.org/10.3390/ma14051232
APA StyleGhalambaz, M., Mohammed, H. I., Naghizadeh, A., Islam, M. S., Younis, O., Mahdi, J. M., Chatroudi, I. S., & Talebizadehsardari, P. (2021). Optimum Placement of Heating Tubes in a Multi-Tube Latent Heat Thermal Energy Storage. Materials, 14(5), 1232. https://doi.org/10.3390/ma14051232