Hybrid cooling-based lithium-ion battery thermal management for electric vehicles

Abstract

The use of rechargeable lithium-ion batteries in electric vehicles is one among the most appealing and viable option for storing electrochemical energy to conciliate global energy challenges due to rising carbon emissions. However, a cost effective, efficient and compact cooling technique is needed to avoid excessive temperature build up during discharging of these batteries to maintain its performance and longevity. In this work, phase change material (PCM)-based hybrid cooling system is proposed for the battery thermal management system consisting of 25 commercial Sony-18650 cells arranged in a cubical battery pack. Air was chosen as an active cooling agent and PCM as a passive cooling agent. The coupling between the 1D electrochemical model and the 2D thermal-fluid model was developed using COMSOL Multiphysics solver for the discharging cycle of the cells. The combined effects of different air inflow velocities (U₀ = 0–0.1 m/s) and PCM layer thickness over the cells (t = 0–3 mm) have been delineated at various discharge rates (1C, 3C and 5C). Extensive results have been reported in terms of discharge curve, temperature fields, average and maximum cell temperature and PCM melt fraction. Obviously, an increasing airflow is seen to lower the temperature of the cells up to ~ 25 K. In addition, the presence of a thin PCM layer over the cells shows a remarkable improvement in heat removal due to the latent heat energy storage in the melted (charged) PCM. However, beyond a certain thickness of PCM layer, the heat removal efficiency becomes constant. Lastly, comparing the thermal performance predictions by the three different cell spacing of 24 mm, 28 mm and 32 mm, we observed that an increased cell spacing shows a better heat removal only in the absence of any PCM layer on the cells.

Appendices

Appendix 1:

Governing equations for the 1D electrochemical model (Doyle & Newman, 1996; Srinivasan & Wang, 2003).

Macroscale

$$ {\text{Charge}}\,{\text{ in}}\,{\text{solid }}\,{\text{phase}}\quad \quad \nabla .i_{s} = - J({\text{ne, pe, cc}}) $$

$$ {\text{Charge}}\,{\text{in}}\,{\text{liquid}}\,{\text{phase}}\quad \quad \quad \nabla .i_{l} = J\left( {\text{ne, pe, cc}} \right) $$

$$ {\text{Species }}\,{\text{in}}\,{\text{ liquid}}\,{\text{phase}}\quad \quad \quad \varepsilon_{l} \frac{{\partial c_{l} }}{\partial t} + \nabla .N_{l} = \frac{J}{F}\left( {\text{ne, pe, el}} \right) $$

$$ {\text{Energy}}\quad \quad \quad \left( {\rho C_{P} } \right)^{eff} \frac{\partial T}{{\partial t}} + \nabla .q \, = \, Q \, \left( {{\text{all}}\,{\text{ layers}}} \right) $$

Microscale

$$ {\text{Species}}\,{\text{in}}\,{\text{solid }}\,{\text{phase}}\quad \quad \left\{ \begin{gathered} \frac{Ds}{{ls}}(Cs^{{{\text{surf}}}} - \, Cs^{{{\text{surf}}}} ) = - \frac{{i_{{{\text{fara}}}} }}{F} \hfill \\ \frac{{{\text{d}}cs^{{{\text{avg}}}} }}{{{\text{d}}t}} = - \frac{{i_{{{\text{fara}}}} }}{FRs} \hfill \\ \end{gathered} \right.\left( {\text{ne, pe}} \right) $$

Flux

$$ i_{s} = - \sigma_{s}^{{{\text{eff}}}} \nabla \phi_{s} $$

$$ i_{l} = - \sigma_{s}^{{{\text{eff}}}} \nabla \phi_{l} + \frac{{2RT\sigma_{l}^{{{\text{eff}}}} }}{F}(1 - t_{0}^{ + } )\nabla \left( {{\text{ln}}c_{l} } \right) $$

$$ Nl = - D_{l}^{{{\text{eff}}}} \nabla c_{l} \, + \, \frac{{i_{l} t_{0}^{ + } }}{F} $$

$$ q = - k^{{{\text{eff}}}} \nabla T $$

Boundary conditions

$$ {\text{At}}\,{\text{the}}\,{\text{negative}}\,{\text{end}}\quad \quad \phi_{s} = 0, \, q_{x} = \, 0 $$

$$ {\text{Collector/electrode}}\,{\text{interface}}:i_{{\left. {sx} \right| + }} = \, i_{{\left. {sx} \right| - }} , \, q_{\left. x \right| + } = \, q_{\left. x \right| - } , \, i_{lx} = N_{lx} = \, 0 $$

$$ {\text{Electrode}}/{\text{separator}}\,{\text{ interface}}:i_{sx} = 0, \, q_{\left. x \right| + } = q_{\left. x \right| - } , \, i_{{\left. {lx} \right| + }} = i_{{\left. {lx} \right| - }} ,N_{{\left. {lx} \right| + }} = N_{{\left. {lx} \right| - }} $$

$$ {\text{At}}\,{\text{the}}\,{\text{positive}}\,{\text{end}}:i_{sx} = - i_{{{\text{app}}}} ,\, \, q_{x} = 0 $$

Initial conditions

$$ c_{s} = c_{s}^{avg} = c_{s}^{0} ,\quad c_{l} = c_{l}^{0} $$

$$ \phi_{s} = \left\{ \begin{gathered} 0,{\text{ (ne)}} \hfill \\ \phi_{s}^{0} ,{\text{ (pe)}} \hfill \\ \end{gathered} \right.,\quad \quad \phi_{l} = \phi_{l}^{0} {\text{, (ne, pe, el)}} $$

$$ T = T_{0} $$

Appendix 2:

Constitutive relations: (Doyle & Newman, 1996; Srinivasan & Wang, 2003) (Table 2 )

Table 2 Parameters of battery cells (Ye et al., 2012; Tong et al., 2016)

$$ J = \left\{ {\begin{array}{*{20}l} {A_{s} i_{{{\text{fara}}}} } \hfill & {\text{(ne, pe)}} \hfill \\ 0 \hfill & {\text{(cc)}} \hfill \\ \end{array} } \right. $$

$$ i_{{0,{\text{fara}}}} = Fk_{o} c_{l}^{{\alpha_{a} }} \left( {c_{s}^{\max } - c_{s}^{{{\text{surf}}}} } \right)^{{\alpha_{a} }} \left( {c_{s}^{{{\text{surf}}}} } \right)^{{\alpha_{c} }} {\text{ (ne, pe)}} $$

$$ i_{{{\text{fara}}}} = i_{{0,{\text{fara}}}} \left\{ {\exp \left( {\frac{\alpha a\eta F}{{RT}}} \right) - \exp \left( { - \frac{{\alpha_{c} \eta F}}{RT}} \right)} \right\}\,{\text{(ne,}}\,{\text{ pe)}} $$

$$ \eta = \phi_{s} - \phi_{l} - U_{{{\text{ref}},i}}^{{{\text{eff}}}} \, (i = {\text{ne, pe}}) $$

$$ A_{s} = \frac{{3(1 - \varepsilon_{l} - \varepsilon_{f} - \varepsilon_{p} )}}{{R_{s} }} \, ({\text{ne, pe}}) $$

$$ U_{{{\text{ref}},i}}^{{{\text{eff}}}} = U_{{{\text{ref}},i \, }} + \, (T - T_{{{\text{ref}}}} )\frac{{\partial U_{{{\text{ref}},i}} }}{\partial T} \, (i \, = {\text{ne,pe}}) $$

$$ U_{{{\text{ref}},i}} = \left\{ \begin{gathered} - 0.16 + 1.32\exp ( - 3\theta_{{{\text{ne}}}} ) + 10\exp ( - 2000\theta_{{{\text{ne}}}} ) \hfill \\ 4.1983 + 0.0565\,\tanh ( - 14.554\theta_{{{\text{pe}}}} + 8.6094) - 0.0275\left( {\frac{1}{{(0.9984 - \theta_{{{\text{pe}}}} )^{0.4924} }} - 1.9011} \right) \hfill \\ - 0.1571\exp ( - 0.0474\theta_{{{\text{pe}}}}^{8} ) + 0.8102\exp ( - 40(\theta_{{{\text{pe}}}} - 0.1339) \hfill \\ \end{gathered} \right. $$

$$ \theta_{i} = \frac{{c_{s}^{{{\text{surf}}}} }}{{c_{s}^{\max } }} \, (i \, = {\text{ ne, pe}}) $$

$$ Q = \left\{ \begin{gathered} J\eta + JT\frac{{\partial U_{{{\text{ref}},i}} }}{\partial T} + \sigma_{{\text{s}}}^{{{\text{eff}}}} (\nabla \phi_{l} )^{2} + \frac{{2RT\sigma_{{\text{l}}}^{{{\text{eff}}}} }}{F}\left( {1 - t_{ + }^{0} } \right)\nabla (\ln c_{{\text{l}}} ).\nabla \phi_{{\text{l}}} \, ({\text{ne,}}\,{\text{ pe}}) \hfill \\ \sigma_{{\text{l}}}^{{{\text{eff}}}} (\nabla \phi_{l} )^{2} + (1 - t_{ + }^{0} )\nabla (\ln \,c_{l} ).\nabla \phi_{l} \, (el) \hfill \\ \sigma_{s}^{{{\text{eff}}}} (\nabla \phi_{s} )^{2} \, (cc) \hfill \\ \end{gathered} \right. $$

$$ \frac{{\partial U_{{{\text{ref}},i}} }}{\partial T} = \left\{ \begin{gathered} \frac{{344.1347\exp (8.3167 - 32.9633\theta_{{{\text{ne}}}} )}}{{1 + 749.0756\exp (8.8871 - 34.7909\theta_{{{\text{ne}}}} )}} - 0.852\theta_{{{\text{ne}}}} + 0.3622\theta_{{{\text{ne}}}}^{2} + 0.2698 \hfill \\ - 4.1453 + 8.147\theta_{{{\text{pe}}}} - 26.0645\theta_{{{\text{pe}}}}^{2} + 12.766\theta_{{{\text{pe}}}}^{3} + 4.3127\exp (0.5715\theta_{{{\text{pe}}}} ) - 0.1842\exp \left( { - \frac{{\theta_{{{\text{pe}}}} - 0.5169}}{0.0462}} \right)^{2} \hfill \\ + 1.2816\,\sin ( - 4.9916\theta_{{{\text{pe}}}} ) - 0.0904\,\sin ( - 20.9669\theta_{{{\text{pe}}}} - 12.5788) + 0.0313\,\sin (31.7663\theta_{{{\text{pe}}}} - 22.4295) \hfill \\ \end{gathered} \right. $$

$$ D_{l}^{{{\text{eff}}}} = D_{l} \varepsilon_{l}^{\gamma } $$

$$ \sigma_{l}^{{{\text{eff}}}} = \sigma_{l} \varepsilon_{l}^{\gamma } $$

$$ \left. {\sigma_{l} } \right|_{{T_{{{\text{ref}}}} }} = - 1.172 \times 10^{ - 14} c_{l}^{4} + 1.3605 \times 10^{ - 10} c_{l}^{3} - 5.2245 \times 10^{ - 7} c_{l}^{2} + 6.7461 \times 10^{ - 10} c_{l} + 1.0793 \times 10^{ - 2} $$

$$ \sigma_{s}^{{{\text{eff}}}} = \sigma_{s} (1 - \varepsilon_{l} - \varepsilon_{f} - \varepsilon_{p} ){\text{ (ne,}}\,{\text{pe)}} $$

$$ k^{{{\text{eff}}}} = k(1 - \varepsilon_{l} ) + k\varepsilon_{l} \, ({\text{ne, }}\,{\text{pe,}}\,{\text{ sp}}) $$

$$ (\rho C_{{\text{p}}} )^{{{\text{eff}}}} = (\rho C_{{\text{p}}} )(1 - \varepsilon_{{\text{l}}} ) + (\rho C_{{\text{p}}} )\varepsilon_{l} \, ({\text{ne, }}\,{\text{pe,}}\,{\text{ sp}}) $$

$$ \Theta (T) = \left. \Theta \right|_{{T_{{{\text{ref}}}} }} \exp \left[ {\frac{{E_{a,\Theta } }}{R}\left( {\frac{1}{{T_{{{\text{ref}}}} }} - \frac{1}{T}} \right)} \right](\Theta = D_{{\text{s}}} ,D_{{\text{l}}} ,\sigma_{{\text{l}}} ) $$

$$ l_{{\text{s}}} = \frac{{R_{{\text{s}}} }}{5}{\text{ (ne,pe)}} $$

$$ \phi_{s}^{0} = U_{{\text{ref,pe}}} (\theta_{{{\text{pe}}}}^{{0}} ) - U_{{\text{ref,ne}}} (\theta_{{{\text{ne}}}}^{{0}} ) $$

$$ \phi_{l}^{0} = - U_{{\text{ref,ne}}} (\theta_{{{\text{ne}}}}^{0} ) $$