3D Thermal and Electrochemical Model for Spirally Wound ... · lithium diffusion dynamics and...

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3D Thermal and Electrochemical Model for Spirally Wound Large Format Lithium-ion Batteries

Kyu-Jin Lee*, Gi-Heon Kim, Kandler Smith

NREL/PR-5400-49795

218th ECS Meeting, Las Vegas, NVOct 14, 2010

Innovation for Our Energy Future2

Objectives of this Study

• To develop thermal and electrochemical models resolving 3 dimensional spirally wound structures of cylindrical cells.

• To understand the mechanisms and interactions between local electrochemical reactions and macroscopic heat and electron transfers.

• To develop a tool and methodology to support macroscopic designs of cylindrical Li-Ion battery cells.

Behaviors of spirally wound large format Li-Ion batteriesare affected by macroscopic designs of cells.


“Requirements” are usually defined in a macro-scale domain and terms

Requirements & Resolutions

Multi-Scale Physics in Li-Ion Battery

• Wide range of length and time scale physics • Design improvements required at different scales• Need for better understanding of interaction among varied scale physics

PerformanceLifeCostSafety


Multi-Physics InteractionComparison of two 40 Ah

flat cell designs

This cell is cycled more uniformly, can therefore use less active material ($) and

has longer life.

2 min 5C discharge

working potential working potential

transfer current generation

temperature temperature

socsoc

transfer current generation

High temperature promotes faster electrochemical reactionHigher localized reaction causes more heat generation

Larger over-potential promotes faster discharge reactionConverging current causes higher potential drop along the collectors

- Previous study


Charge Conservation

r

( ) Ues −−= φφη

Porous Electrode Model

( ) qTktTcp ′′′+∇⋅∇=∂∂ρ

• Pioneered by Newman group (Doyle, Fuller, and Newman 1993)

• Captures lithium diffusion dynamics and charge transfer kinetics

• Predicts current/voltage response of a battery• Provides design guide for thermodynamics, kinetics,

and transport across electrodes

eeeffDee

effss

effes

Li cTUTUjq φκφφκφφσφφ ∇⋅∇+∇⋅∇+∇⋅∇+

∂∂

+−−=′′′ ln

Charge Transfer Kinetics at Reaction Sites

Species Conservation

Energy Conservation • Difficult to resolve heat and electron current transport in large cell systems


ξ1

ξ2ξ3

x1

x2x3

Ɵ1

Ɵ2Ɵ3

: particle domain dimension : electrode domain dimension :cell domain dimensionξ x

Multi-Scale Multi-Dimension (MSMD) Model

Ɵ

• Introducing separate computational domains for corresponding length scale physics

• Geometry decoupling between the domains• Using independent coordinate systems for each domain• Two-way coupling of solution variables using multi-scale model schemes

• Selectively resolve higher spatial resolution for smaller characteristic length scale physics

• Achieve high computational efficiency• Provide flexible & expandable modularized framework


Large Cell Design IssuesPrismatic cell Cylindrical cell

•Stacking electrodes coated on metal current collectors•Less efficient manufacturing

processes for mass production

•Rolling electrodes coated on metal current collectors•Well established manufacturing process

for small batteries•More difficulties for large cell design (cf.

tap design, heat management, etc)


1D spherical particle representation model

r

1D porous electrode model

Sub-model choice for spirally wound continuous tab cells

Previous Development of Wound Cell Model

X

R

2D axisymmetric cell model

Applicable to continuous tab design

continuous tab design

Extended Foil

Axisymmetric assumption

Cylindrical cell Unwinding jellyrolls

: particle domain sub-model : electrode domain sub-model :cell domain sub-model

- Previous study

Innovation for Our Energy Future

Tab-less Wound Cell Design Evaluation

Large H D[mm]: 14 H[mm]: 350 Nominal D[mm]: 50 H[mm]: 107

Large D D[mm]: 115 H[mm]: 20

40

110

90

60

50

100

80

70

120

30

27

73

60

40

33

67

53

47

80

2010 20 30 8040 50 60 9070

SOC (%)

Dis

char

ge P

ower

(kW

)

Cha

rge

Pow

er (k

W)

HPPC, BSF = 78

• Large H design has almost 10% less power capability.

10s pulse power capability comparison

X (mm)

0 20 40 60 80 1005

10152025

X (mm)

0 20 40 60 80 1005

10152025

0 20 40 60 80 1005

10152025

∆i [%]

V

T-Tavg

0 50 100 150 200 250 300468101214

0 50 100 150 200 250 300468101214

∆i [%]

0 50 100 150 200 250 300468101214

V

T-Tavg

X (mm)

0 105

10

15

20

25

30

35

40

45

50

55

X (mm)

0 105

10

15

20

25

30

35

40

45

50

55

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

X (mm)

0 105

10

15

20

25

30

35

40

45

50

55

3.318

3.32

3.322

3.324

3.326

3.328

∆i [%]VT-Tavg

9 min 5C discharge

Effects of “Aspect Ratio” of a Cylindrical Cell - Previous study

11


Present StudyTab configuration: number & size

Current flows along the winding direction 3 dimensional spiral wound geometry

Cylindrical cell Unwinding jellyrolls

tab

tab

• 2D axisymmetric model is not applicable to a wound cell with a finite number of current tabs where lateral electric current is not negligible in current collector foils.

• Geometries and materials of electric current paths in spirally wound layer structure should be properly resolved.

12


New Development of Cell Domain Model

13

Unit structure: Double Paired Electrodes on Single-Paired Current Collectors

Negative current collector

Positive current collectorSeparator

Winding: Alternating Radial Placement of Double Paired-Electrodes

Two electrode pairs are formed when the unit structure is wound.

Double sided anode electrode

Double sided cathode electrode

Spirally Wound Cell Model:

Outer electrode

pair

Inner electrode

pair

Outer electrode

pair

Two points with a distance of a winding cycle of outer electrode pair are matched in the wound structure


Spiral cell structures

Positive current collectorNegative current collector

Anode electrode

SeparatorCathode electrode

A current collector has two electrode pairs in both sides.

Alternatively layered jelly roll

Outer electrode pair

Inner electrode pair


Spiral cell structures

jLi,iin

φ-i

φ-i+1

φ-i-1

φ+i

φ+i+1

jLi,iout

We cannot expect uniform potential along the current collectors due to inevitable electric current in winding direction.

Non-uniform electrical potential along current collectorsNon-uniform charge transfer reaction

i+i+

i-i-

i-


Modeling case Diameter 40mm, inner diameter 8mm, height 100 mm form factor Positive tabs on the top side, negative tabs on the bottom side 10 Ah capacity

5C constant current dischargesocini = 90%Natural convection :

hinf = 5 W/m2KTamb = 25oC Tini = 25oC

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

X [m]

]m[

Y

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

X [m]

]m[

Y

Tab locations for 5 tab case


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

X [m]

]m[

Y

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.05

0.1

X [m]

]m[

Y

Tab configuration of each electrode pairs

Positive current collector




X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

122124126128

17

Modeling results

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

0

0.01

0.02

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.05

0.1

122124126128

Electrochemical reaction rate

Electric potential

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

-0.02

-0.01

5 tabs in each current collector 5C discharge for 5 min



Positive current collector


0 2 4 6 83

3.2

3.4

3.6

3.8

Time [min]

V out [V

]

Topview

Bottomview

- Current mainly flows in the winding direction

- High generation rate of transfer current near tabs


0 2 4 6 825

30

35

40

45

50

Time [min]

Tem

pera

ture

[o C]

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

0.3

0.3

18

State of charge

TemperatureX [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.05

0.1

0.32

0.34

Modeling resultsInner electrode pair


High rate discharge with a moderate heat transfer condition

Heat generation dominates temperature distribution in the system.

Temperature difference in the system is relatively small yet.

- More usage of electrode near tabs


Modeling results

0 1 2 3 4 5 6 7 825

30

35

40

45

Time [min]

T avg [o C

]

Parametric study

Cells with fewer tabs …• lower output voltage• higher average temperature

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.93

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

SOC

Vou

t [V]

2D modelTapless10 taps5 taps2 taps

2D modelcontinuous

tab 10 tabs5 tabs2 tabs

socini = 90%Natural convection :

hinf = 5 W/m2KTamb = 25oC Tini = 25oC

2 tabs

10 tabs

continuous tab

5 tabs

Different tab numbers (2,5,10 and continuous tab ) on cell performance 10 Ah capacity, 5C discharge


Electrochemical reaction rate comparison

- Parametric studyModeling results

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

120 121 122 123 124 125 126 127 128 129 130

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

i” [A/m2]

0.2%

2.2%

6.6%

32.2%

Δi”/ i”avg

2 tabs

5 tabs

Continuous tab

10 tabs

in the inner electrode pair at 5 min


- Parametric studyModeling results

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

X [m]

Y [m

]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.05

0.1

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4T-Tavg [oC]

Temperature deviation comparison

0.19oC

0.37oC

0.78oC

3.25oC

2 tabs

5 tabs

Continuous tab

10 tabs

ΔT

at 5 min


Conclusion

22

• A Multi-Scale Multi-Dimension model was used for evaluating large format automotive cell designs by integrating micro-scale electrochemical process and macro-scale heat and electrical current transports.

• Spatial non-uniformity of battery physics, which becomes significant in large batteries, cause unexpected performance in spiral wound lithium-ion batteries.

• A macro-scale domain model based on spirally wound structures of lithium-ion batteries was developed to understand effects of tab configurations and the double sides electrodes structure.

• Spiral wound cells with more tabs would be preferable to manage cell internal heat and electron current transport, and consequently to achieve uniform electrochemical kinetics over a system.

• The spiral wound cell model can provide quantitative data in terms of finding the optimum number of tabs to battery manufacturers.


US. Department of Energy, Vehicle Technology ProgramDave Howell, Hybrid Electric Systems Team Lead

National Renewable Energy LaboratoryAhmad Pesaran, Energy Storage Team Lead

Acknowledgments

23

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