1 Introduction
2 Method
2.1 Heat Transfer
2.2 Chemical Kinetics
Chemical mechanisms | Eq. | |
---|---|---|
SEI decomposition | \(R_{\text{sei}} = - \frac{{{\text{d}}c_{\text{sei}} }}{{{\text{d}}t}} = A_{\text{sei}} \exp \left[ { - \frac{{E_{\text{sei}} }}{RT}} \right]\) \(c_{\text{sei}}^{{n_{\text{sei}} }}\) | 7 |
\(q_{\text{sei}}^{'''} = \Delta H_{\text{sei}} W_{\text{n}} R_{\text{sei}}\) | 8 | |
Negative-electrode reaction | \(R_{\text{n}} = - \frac{{{\text{d}}c_{\text{n}} }}{{{\text{d}}t}} = A_{\text{n}} { \exp }\left[ { - \frac{z}{{z_{0} }}\left] { \exp } \right[ - \frac{{E_{\text{n}} }}{RT}} \right]c_{\text{n}}\) | 9 |
\(\frac{{{\text{d}}z}}{{{\text{d}}t}} = A_{\text{n}} { \exp }\left[ { - \frac{z}{{z_{0} }}\left] { \exp } \right[ - \frac{{E_{\text{n}} }}{RT}} \right]c_{\text{n}}\) | 10 | |
\(q_{\text{n}}^{'''} = \Delta H_{\text{n}} W_{\text{n}} R_{\text{n}}\) | 11 | |
Positive-electrode reaction | \(R_{\text{p}} = \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = A_{\text{p}} \alpha \left( {1 - \alpha } \right){ \exp }\left[ { - \frac{{E_{\text{p}} }}{RT}} \right]\) | 12 |
\(q_{\text{p}}^{'''} = \Delta H_{\text{p}} W_{\text{p}} R_{\text{p}}\) | 13 | |
Electrolyte decomposition | \(R_{\text{e}} = - \frac{{{\text{d}}c_{\text{e}} }}{{{\text{d}}t}} = A_{\text{e}} { \exp }\left[ { - \frac{{E_{\text{e}} }}{RT}} \right]c_{\text{e}}^{{n_{\text{e}} }}\) | 14 |
\(q_{\text{e}}^{'''} = \Delta H_{\text{e}} W_{\text{e}} R_{\text{e}}\) | 15 |
2.3 Experimental Validation for a Single Cell
Symbol | Description | Value | Unit |
---|---|---|---|
Asei | SEI decomposition frequency factor | s−1 | |
An | Negative-solvent frequency factor | 1.67E6 [36] | s−1 |
Ap | Positive-solvent frequency factor | s−1 | |
Ae | Electrolyte decomposition frequency factor | 5.14E25 [27] | s−1 |
Esei | SEI-decomposition activation energy | J mol−1 | |
En | Negative-solvent activation energy | 7.72E4 [36] | J mol−1 |
Ep | Positive-solvent activation energy | J mol−1 | |
Ee | Electrolyte decomposition activation energy | 2.74E5 [27] | J mol−1 |
∆Hsei | SEI-decomposition heat release | J kg−1 | |
∆Hn | Negative-solvent heat release | J kg−1 | |
∆Hp | Positive-solvent heat release | J kg−1 | |
∆He | Electrolyte decomposition heat release | 1.55E5 [27] | J kg−1 |
Wn | Specific negative active content | 363 [26] | kg m−3 |
Wp | Specific positive active content | 726 [26] | kg m−3 |
We | Specific electrolyte content | 407 [27] | kg m−3 |
msei | Reaction order for SEI decomposition | – | |
me | Reaction order for electrolyte decomposition | 1 [27] | – |
csei0 | Initial value of csei | – | |
cn0 | Initial value of cn | – | |
α0 | Initial value of α | – | |
z0 | Initial value of z | – | |
ce0 | Initial value of ce | 1 [27] | – |
T0 | Initial temperature | 301.15 [26] | K |
h | Convection heat transfer coefficient | 7.17 [27] | W m−2 K−1 |
ε | Surface emissivity | 0.8 [27] | – |
Materials | ρ (kg m−3) | cp (J kg−1 K−1) | k (W m−1 K−1) |
---|---|---|---|
Battery cells [26] | 2580 | 830 | 3.4 |
Bubble wrap* [40] | 1.2 | 1007 | 0.025 |
Molded polystyrene [41] | 19 | 1280 | 0.036 |
Polyurethane Board [41] | 28 | 1537 | 0.024 |
2.4 Mesh Independence Analysis
Number of elements | t = 2 h | t = 5 h | t = 10 h | |||
---|---|---|---|---|---|---|
Tcentral (°C) | Qtot (J s−1) | Tcentral (°C) | Qtot (J s−1) | Tcentral (°C) | Qtot (J s−1) | |
3872 | 76.2 | 0.627 | 123.3 | 0.583 | 126.9 | 0.260 |
5150 | 75.9 | 0.589 | 122.8 | 0.582 | 126.8 | 0.259 |
7480 | 76.0 | 0.596 | 122.9 | 0.582 | 126.4 | 0.259 |