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Journal of Materials Science

, Volume 53, Issue 15, pp 10987–11001 | Cite as

A coupled electrochemical–thermal–mechanical model for spiral-wound Li-ion batteries

  • Xiting Duan
  • Wenjuan Jiang
  • Youlan Zou
  • Weixin Lei
  • Zengsheng Ma
Computation
  • 427 Downloads

Abstract

In order to clarify the interaction of electrochemistry, thermal and diffusion-induced stress, in this work, we present a coupled electrochemical–thermal–mechanical model for spiral-wound Li batteries by coupling the mass, charge, energy and mechanics conservations as well as the electrochemical kinetics. A series of temperatures and Li concentration parameters on the reaction rate and Li+ transport are employed in this model. The results show that this model is validated for both the electrochemical performances and thermal behaviors at a constant discharge current by finite element simulation. Furthermore, the heat generation of three thermal sources and stress analysis are also discussed. This work is helpful to the battery structural design and battery thermal management.

List of symbols

\( c_{2} \)

Li-ion concentration in the electrolyte (mol m−3)

\( c_{1} \)

Concentration of Li in the active material (mol m−3)

\( c_{1}^{0} \)

Initial concentration of Li in the active material (mol m−3)

\( c_{1}^{\text{surf}} \)

Li-ion concentration on the surface of the active particle

\( c_{1}^{ \hbox{max} } \)

Maximum concentration of Li in the active material (mol m−3)

\( c_{2}^{0} \)

Initial electrolyte concentration (mol m−3)

\( \Delta c \)

Li concentration change (mol m−3)

C

Normalized concentration

Cp

Heat capacity [J (kg K)−1]

D1

Diffusion coefficient of lithium in the active material (m2 s−1)

D2

Diffusion coefficient of electrolyte (m2 s−1)

\( E_{\text{cell}} \)

Working voltage of the battery (V)

E1,k

Diffusion activation energy (J mol−1)

E1,D

Reaction activation energy (J mol−1)

E

Young’s modulus (GPa)

F

Faraday’s constant (96487/C mol−1)

h

Convective heat transfer coefficient [W (m2 K)−1]

iapp

Applied current density (A m−2)

\( i_{1} \)

Solid-phase current density (A m−2)

\( i_{2} \)

Current density in the electrolyte (A m−2)

j0

Exchange current density (A m−2)

jn

Charge transfer current density at the interface (A m−2)

\( J_{2} \)

Molar flux of Li ions (mol m−2 s−1)

k

Thermal conductivity [W (m2 K)−1]

\( k_{0} \)

Reaction rate of active material

\( Q \)

Heat generation rate per unit volume (J m−3)

\( Q_{\text{act}} \)

Active heat generation (J m−3)

\( Q_{\text{ohm}} \)

Ohmic heat generation (J m−3)

\( R_{0} \)

Radius of electrode particles (m)

r

Radial coordinate inside a spherical particle (m)

R

Gas constant [8.314/J (K mol)−1]

\( \Delta S \)

Entropy change (J mol−1 K−1)

Sa

Specific surface area of the electrode (m−1)

SOC

State of charge

t

Time (s)

t+

Transport number of Li+

T

Temperature (K)

Tamb

Ambient temperature (K)

\( \Delta T \)

Temperature variation (K)

\( U_{\text{eq}} \)

Open circuit potential of the electrode (V)

\( U_{{{\text{eq}},{\text{ref}}}} \)

Open circuit potential under the reference temperature (V)

u

Displacement (m)

Greek letters

v

Poisson’s ratio

\( \varepsilon_{\text{p}} \)

Volume fraction of polymer phase

\( \varepsilon_{\text{l}} \)

Volume fraction of electrolyte

\( \varepsilon_{\text{f}} \)

Volume fraction of conductive filler additive

η

The local surface overpotential

\( \alpha_{\text{a}} \)

Anodic transfer coefficient

\( \alpha_{\text{c}} \)

Cathodic transfer coefficient

\( \phi_{2 } \)

Liquid-phase potential (V)

\( \phi_{1 } \)

Solid-phase potential (V)

\( \phi_{2}^{0} \)

Initial liquid-phase potential (V)

\( \phi_{1}^{0} \)

Initial solid-phase potentia (V)

\( \sigma_{1} \)

Solid-phase conductivity of electrodes (S m−1)

\( \sigma_{2} \)

Effective ionic conductivity of electrolyte (S m−1)

\( \sigma_{\text{c}} \)

Effective electrical conductivity of current collectors (S m−1)

\( \rho \)

Density (kg m−3)

\( \sigma_{\text{h}} \)

Hydrostatic stress (GPa)

\( \varOmega \)

Partial molar volume (m3 mol−1)

εij

Strain components

σij

Stress components (GPa)

\( \delta_{ij} \)

Dirac delta function

\( \sigma_{\text{r}} \)

Radial stress (GPa)

\( \sigma_{\theta } \)

Hoop stress (GPa)

\( \alpha \)

Coefficient of thermal expansion (K−1)

\( \xi \)

Emissivity of the outer can material

\( \beta \)

Stefan–Boltzmann constant (5.670400 × 10−8 W m−2 K−4)

Subscripts and superscripts

0

Initial or equilibrated state

1

Solid phase

2

Liquid phase

Amb

Ambient temperature

n

Negative electrode

p

Positive electrode

s

Separator

irr

Irreversible

re

Reversible

ei_T

Eigen strain due to thermal expansion

ei_c

Eigen strain due to intercalation

me

Mechanical

Notes

Acknowledgements

This study was funded by the National Natural Science Foundation of China (Grant Nos. 11702234 and 11602213), Natural Science Foundation of Hunan Province (Grant No. 2017JJ3301) and Key Fund Project of Hunan Provincial Department of Education (Grant No. 17A206).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National-Provincial Laboratory of Special Function Thin Film Materials, School of Materials Science and EngineeringXiangtan UniversityXiangtanChina

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