Lithium-Ion Batteries: Thermal Behaviour Investigation of Unbalanced Modules
Abstract
:1. Introduction
2. Module Description
3. Mathematical Modelling of the Module
3.1. Governing Equations
3.1.1. Electrochemical Equations of the Cells
3.1.2. Electrochemical-Thermal Equations of the Cells
3.1.3. Thermo-Hydrodynamic Equations of the Module
3.2. Boundary Conditions
3.3. Numerical Solution and Validation
4. Results and Discussion
4.1. Module Design Considerations
4.1.1. Influence of the Cooling
4.1.2. Influence of the Air Flux
4.1.3. Influence of the Spacing
4.1.4. Validation of the Computational Fluid Dynamics Model
4.2. Unbalanced Battery Module
4.2.1. Voltage of the Cells
4.2.2. Temperature Distribution
4.2.3. Heat Generation
5. Conclusions
List of Symbols (Variables and Parameters)
Symbols | |
---|---|
as | Active surface area (1/m) |
c | lithium ions concentration (mol/m3) |
cp | Heat capacity (J/kg·K) |
d | Diameter at the start of the spiral or internal diameter of the cell (m) |
D | Diffusion coefficient (m2/s) |
D | Diameter taken at the end of the spiral or cell diameter (m) |
Ea | Activation energy (J/mol) |
F | Faraday constant, 96,485 C/mol |
h | Convection heat transfer coefficient W/m2·K |
i0 | Exchange current density of an electrode reaction (A/m2) |
jLi | Transfer current due to the intercalation or deintercalation of lithium ions (A/m3) |
k | Electrochemical reaction rate constant (m/s) |
k | Thermal conductivity (W/m·K) |
L | Total length of the spiral constituting the internal structure of the cell (m) |
L | Length of the cells in the vertical direction (i.e./height) (m) |
N | Total number of layers in the jelly roll structure of the cell (/) |
N | Total number of cells in the battery module (NT·NL) (/) |
NL | Number of cells in the longitudinal direction of the battery module (/) |
NT | Number of cells in the transverse direction of the battery module (/) |
Q | Heat generation (W/m3) |
r | Radius of the spherical particle (m) |
R | Universal gas constant, 8314 J/mol·K |
ST | Transverse distance between two consecutive cells on the same row (m) |
t | Time (s) |
t+ | Transference number of lithium ions (/) |
T | Temperature (°C) |
U | Open circuit voltage (V) |
v | Fluid velocity at the entrance of the module (m/s) |
V | Volume of layer (m3) |
w | Width of the different layers constituting the jelly roll (m) |
Greek letters | |
---|---|
α | Charge transfer coefficient (/) |
ϵ/Volume | fraction (/) |
η | Overpotential (V) |
κ | Ionic conductivity (S/m) |
ϕ | Potential (V) |
ρ | Density (kg/m3) |
σ | Electrical conductivity (S/m) |
Subscripts | |
---|---|
a | Anode |
c | Cathode |
e or l | Electrolyte phase |
eff | Effective |
f | Fluid |
i | Inlet |
max | Maximum |
measured | Measured by experiment |
model | Modeled by simulation |
o | Outlet |
s | Solid phase |
w | Wall |
Abbreviations | |
---|---|
DoD | Depth of discharge |
EV | Electric vehicle |
HEV | Hybrid electric vehicle |
LFP | Lithium iron phosphate |
MUMPS | Multifrontal Massively Parallel Solver |
SoC | State of charge |
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Physics | Governing Equations | Mathematical Expressions |
---|---|---|
Chemical kinetics | Butler–Volmer equation | |
Electrode overpotential | η=(ϕs−ϕe) – U | |
Exchange current density | ||
Charge conservation | Solid phase | |
Electrolyte phase | ||
Mass Transfer | Species conservation in solid phase | |
Species conservation in electrolyte |
Parameters | Anode | Separator | Cathode |
---|---|---|---|
Thickness [24], (m) | 3:4 ×10−5 | 2:5 × 10−5 | 8 × 10−5 |
Active material volume fraction [24], (/) | 0:58 | 0:55 | 0:374 |
Filler volume fraction [24], (/) | 0:0326 | – | 0:0535 |
Volume fraction electrolyte, (/) | 0:3874 | 0:45 | 0:5725 |
Particle radius [24], (m) | 5 × 10−6 | – | 5 × 10−8 |
Electrolyte phase Li+ diffusion [24], (m2/s) | 2 × 10−10 | ||
Initial electrolyte concentration [23], (mol/m3) | 2000 | ||
Maximum solid phase concentration [24], (mol/m3) | 30, 555 | – | 22, 806 |
Regions | cp (J/kg·K) | ρ (kg/m3) | kT (W/m·K) |
---|---|---|---|
Cell internal region | 1034:2 | 3345:5 | 0:33434 (kT;r) 57:515 (kTang) |
negative electrode [23] | 1437:4 | 1347:33 | 1:04 |
positive electrode [23] | 750 | 3600 | 0:20 |
separator electrode [23] | 1978:16 | 1008:98 | 0:344 |
negative current collector [23] | 385 | 8933 | 398 |
positive current collector [23] | 875 | 2770 | 170 |
Conservation Equations | Mathematical Expressions |
---|---|
Conservation of mass | |
Conservation of momentum | |
Conservation of energy |
Cases | ReD (/) | Present Study, NuD (/) | Zukauskas [32], NuD (/) | Deviation (%) |
---|---|---|---|---|
Figure 7a,b | 538 | 8.91 | 10.01 | 11 |
Figure 7c,d | 1229 | 21.32 | 19.81 | 7 |
Cell number | Initial Depth of Discharge |
---|---|
2 | 5% |
3 | 10% |
4 | 20% |
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Capron, O.; Samba, A.; Omar, N.; Coosemans, T.; Bossche, P.V.d.; Van Mierlo, J. Lithium-Ion Batteries: Thermal Behaviour Investigation of Unbalanced Modules. Sustainability 2015, 7, 8374-8398. https://doi.org/10.3390/su7078374
Capron O, Samba A, Omar N, Coosemans T, Bossche PVd, Van Mierlo J. Lithium-Ion Batteries: Thermal Behaviour Investigation of Unbalanced Modules. Sustainability. 2015; 7(7):8374-8398. https://doi.org/10.3390/su7078374
Chicago/Turabian StyleCapron, Odile, Ahmadou Samba, Noshin Omar, Thierry Coosemans, Peter Van den Bossche, and Joeri Van Mierlo. 2015. "Lithium-Ion Batteries: Thermal Behaviour Investigation of Unbalanced Modules" Sustainability 7, no. 7: 8374-8398. https://doi.org/10.3390/su7078374