a three-dimensional thermal-electrochemical coupled model ... · porous electrode model of li -ion...

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A Three-Dimensional Thermal-Electrochemical Coupled Model for Spirally Wound Large-Format

Lithium-Ion Batteries

Kyu-Jin Lee*, Kandler Smith, Gi-Heon KimNREL/PR-5400-51151

Space Power Workshop

April 18, 2011

Los Angeles, CA

This research activity is funded by the US Department of Energy (Dave Howell)

Innovation for Our Energy Future2

Objectives• Develop thermal and electrochemical models resolving

3-dimensional spirally wound structures of cylindrical cells

• Understand the mechanisms and interactions between local electrochemical reactions and macroscopic heat and electron transfer

• Develop a tool and methodology to investigate macroscopic designs of cylindrical Li-ion battery cells


Physics of Li-Ion Battery Systems in Different Length Scales

Li diffusion in solid phaseInterface physicsParticle deformation & fatigueStructural stability

Charge balance and transportElectrical network in composite electrodesLi transport in electrolyte phase

Electronic potential &current distributionHeat generation and transferElectrolyte wettingPressure distribution

Atomic Scale

Particle Scale

Electrode Scale Cell Scale

System ScaleSystem operating conditionsEnvironmental conditionsControl strategy

Module ScaleThermal/electricalinter-cell configurationThermal managementSafety control

Thermodynamic propertiesLattice stabilityMaterial-level kinetic barrierTransport properties

Multi-Scale Physics in Li-Ion Battery Systems


Porous Electrode Model of Li-ion Battery• Pioneered by Newman group (Doyle, Fuller,

and Newman 1993)• Captures lithium diffusion dynamics and

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

kinetics, and transport across electrodes

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

r Capacity [Ah]

Volta

ge [V

]

TimeCap

acity

[Ah/

m2 ]


Computational Cost of Modeling Large Li-ion Cell

•Characteristic length of electrodes: Lelec•Grids for the porous

electrode model: Nelec

Characteristic length of a cell: Lcell

Number of grids for a full 3-D electrode porous model:Ncell ~ (Lcell / Lelec *Nelec)3

Liu and Siddique, 218th ECS , 2010 Micro-structure Reconstruction

Number of grids in a model resolving mesoscale geometry: ~ 102-3

A full 3-D mesoscale cell model is extremely expensive.


ξ1

ξ2ξ3

x1

x2x3

Ɵ1

Ɵ2Ɵ3

: particle domain : electrode domain : cell domain ξ x

Multi-Scale Multi-Dimensional (MSMD) Model

Ɵ

• Introduces separate computational domains for corresponding length scale physics

• Decouples geometry between the domains• Has independent coordinate systems for each domain• Uses two-way coupling of solution variables using multi-scale model

schemes

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

• Achieves high computational efficiency• Provides flexible & expandable modularized framework

Description

Advantage


Large Cell Design DifferencesPrismatic cells Cylindrical cells

• Stacking / folding / semi-winding• Complex and slow production

processes• Better packing efficiency for modules• Better heat transfer

• Winding• Simple and fast production processes• Low manufacturing cost

Photo Credit:http://en.wikipedia.org/wiki/List_of_battery_sizes

Photo Credit: NREL-Dirk Long


Large Cell Design can Lead to Large Temperature Difference

• Anisotropic thermal conductivity of electrodes coated on current collectors

Negative current collector

Positive current collector

SeparatorAnode electrode

Cathode electrode

Kin-plane 10-100W/mK

Kthrough-plane ~1W/mK

Prismatic cell Cylindrical cell

• Stacked electrodes • Thin and wide shape helps thermal

uniformity

Kthrough-plane

Kin-plane

Kthrough-plane

Kin-plane

Kin-plane

• Wound electrodes • Center region of cell heats up easily

due to the poor radial thermal conductivity


Prismatic cell Cylindrical cell

• Large number of small metal current collectors

• Electric current flows through small distance

• A pair of long continuous metal current collectors

• Electric current flows through long distance.• Tab design can critically impact on cell

performance

Example:Prismatic cell: 200 mm x 150 mm x 7 mmCylindrical cell: radius: 25.85 mm height: 100 mm Thickness of an electrode pair: 300 µm Length of current collectors: ~ 7 m

tab

Cell volume: 0.21 mL

Current

Large Cell Design can Lead to Large Electric Potential Difference

Unwinding electrodes


1-D spherical particle representation model

r

1-D porous electrode model

Sub-model choice for 2-D cylindrical cell model

2-D Cylindrical Cell Model

X

R

2-D axisymmetric cell model

Particle domain sub-model Electrode domain sub-model Cell domain sub-model

– Previous study

Applicable to continuous tab design

Continuous tab design

Extended foil

Axisymmetric assumption

Cylindrical cell Unwinding jellyrolls

Innovation for Our Energy Future

Continuous Tab 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

1470

1470

1470

Nominal D[mm]: 50 H[mm]: 107

2025

0 20 40 60 80 1005

10152025

X (mm)

0 20 40 60 80 1005

10152025

0 20 40 60 80 1005

10152025


Continuous Tab 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

12

∆i [%]V [V]T-Tavg [K]

1470

1470

1470

T-Tavg [K]

V [V]

∆i [%]

Nominal D[mm]: 50 H[mm]: 107

2025

0 20 40 60 80 1005

10152025

X (mm)

0 20 40 60 80 1005

10152025

0 20 40 60 80 1005

10152025

T-Tavg [K]

V [V]

∆i [%]


Present Study:

Current flows along the winding direction

3-D spiral wound cell model

tab

tab

• 2-D axisymmetric model is not applicable to a wound cell .

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

13

Electrical Design Issue-Tab Configuration

1-D spherical particle representation model

r

1-D porous electrode model

Sub-model choice for 3-D cylindrical cell model

Particle domain sub-model Electrode domain sub-model Cell domain sub-model


Cell Domain Model:

14

Unit structure: Double-paired electrodes on single-paired current collectors


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: Alternatively layered jelly roll



Anode electrodeSeparatorCathode electrode

Outer electrode pairInner electrode pair

A current collector has two electrode pairs in both sides


Spiral Cell Structures:

φ-i

φ-i+1

φ-i-1

φ+i

φ+i+1jLi,i

out

i+i+

i-i-

i-

Non-uniform potential along the current collectors occurs from electric current in the winding direction

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

Electrical potential fieldsand charge transfer reaction


Modeling Case Diameter 40 mm, inner diameter 8 mm, 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 = 25°C Tini = 25°C

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 pair


Inner electrode pair

Outer electrode pairNickel oxide-based cathodeGraphite-based anode


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

18

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

Inner electrode pair

Outer electrode pair



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

19

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

Outer electrode pair

Radial heat transfer from tabs Temperature difference is relatively

small

More usage of electrode near tabs


Modeling Results: Parametric Study

SOCini = 90%

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

Output voltage

10 tabs5 tabs2 tabs

2-D modelContinuous

tab


Modeling Results:

Temperature 2 tabs5 tabs

10 tabs

2-D model

Continuous tab

Natural convection:hinf = 5 W/m2K

Tamb = 25°C Tini = 25°C

Temperature

Parametric Study


Generated Heat

2 tabs5 tabs

10 tabs

2-D mode

Continuous tab

Natural convection:hinf = 5 W/m2K

Tamb = 25°C Tini = 25°C



High rate of discharge with a moderate heat transfer condition Heat generation dominates temperature distribution in the system

2 tabs5 tabs

10 tabsContinuous

tab

Rejected Heat



Electrochemical reaction rate comparison

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

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]

2 tabs

5 tabs

Continuous tab

10 tabs

in the inner electrode pair at 5 min

03

56

89

30

120

130

122

121

124

129

128

127

126

125

123

Δi”/ i”avga

32.2%

6.6%

2.2%

0.2%



-0.4

-0.3

-0.2

-0.1

00.1

0.20.3

0.4

25

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

0.1T-Tavg [°C]

Temperature deviation comparison

0.19°C

0.37°C

0.78°C

3.25°C

2 tabs

5 tabs

Continuous tab

10 tabs

ΔTat 5 min

-0.4

0.1

-0.3

-0.2

0

-0.1

0.2

0.3

0.4



Conclusions

26

• Used Multi-Scale Multi-Dimensional model to evaluate large-format cell designs by integrating micro-scale electrochemical processes and macro-scale heat and electrical current transport.

• Spatial non-uniformity of battery physics, which becomes significant in large batteries, requires 3 dimensional model.

• Developed macro-scale domain model resolved spirally wound structures of lithium-ion batteries.

• Modeled effects of tab configurations and the double-sided electrode structure.

• Increasing the number of tabs in spiral-wound cells would be preferable to manage internal heat and electron current transport, and to achieve uniform electrochemical kinetics.

• The spiral-wound cell model provides quantitative information regarding optimization of cell design including tab location and number.


US. Department of Energy, Vehicle Technology ProgramDave Howell, Hybrid Electric Systems Team LeaderBrian Cunningham, CAEBAT Coordinator

National Renewable Energy LaboratoryAhmad Pesaran, Energy Storage Team Leader

Acknowledgments

27

a three-dimensional thermal-electrochemical coupled model ... · porous electrode model of li -ion...

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