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Thermal Modeling of Vanadium Redox Flow Battery Student: Jia Junduo Supervisor: Asst Prof Zhao Jiyun Co-Supervisor: Mr. Ng Kian Wee Examiner: Assoc Prof Ali I. Maswood
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• Thermal Modeling of Vanadium Redox Flow Battery

Student: Jia Junduo

Supervisor: Asst Prof Zhao Jiyun

Co-Supervisor: Mr. Ng Kian Wee

Examiner: Assoc Prof Ali I. Maswood

• 1. Introduction

Tank

Catholyte

Tank

Anolyte

PUMP PUMP

Cation Exchange Membrane

ELECTR

OD

E

ELECTR

OD

E Cell

STACK

• 1. Introduction

elec

tro

de

elec

tro

de

dis

char

ge

dis

char

ge

char

ge

char

ge

reduction

reduction

oxidation

oxidation

mem

bra

ne

• 1. Introduction

Positive: 𝑉𝑂 + 2𝐻 + 𝑒 ↔ 𝑉𝑂 +

𝐻 𝑂

Negative: 𝑉 ↔ 𝑉 + 𝑒

The overall equation is:

𝑉 + 𝑉𝑂 + 2𝐻 ↔ 𝑉𝑂 + 𝑉 +

𝐻 𝑂

• 1. Introduction

Objective: Construct a thermal model

Influencing factors: Flow rate, currents and surrounding temperature vs Stack/Tank temperature

• 2. Literature Review

W.Skyllas-Kazacos, C.Menictas, M.Kazacos, J Electrochem Soc, 143 (1996) LB6-L88

In the negative half-cell, the V(2+) and V(3+) ions will start to precipitate at a temperature lower than about 10 degree Celsius. For V(4+) and V(5+) ions in the positive half-cell, they will start to precipitate at a temperature above about 50 degree Celsius.

• 2. Literature Review A.Tang, S.M.Ting, J. Bao, M.Skyllas-Kazacos, J Power Sources, 203 (2012) 165-176

𝐶𝑝𝜌𝑉𝑠𝑑𝑇𝑠

𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑡+ − 𝑇𝑠 + 𝑄 𝐶𝑝𝜌 𝑇𝑡− − 𝑇𝑠 +

𝑈𝑠𝐴𝑠 𝑇𝑎𝑖𝑟 − 𝑇𝑠 + 𝐼 𝑅

𝐶𝑝𝜌𝑉𝑡 𝑑𝑇𝑡+

𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑠 − 𝑇𝑡 + 𝑈 𝐴𝑡 𝑇𝑎𝑖𝑟 − 𝑇𝑡

𝐶𝑝𝜌𝑉𝑡 𝑑𝑇𝑡−

𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑠 − 𝑇𝑡 + 𝑈 𝐴𝑡 𝑇𝑎𝑖𝑟 − 𝑇𝑡

• 3. Methodology

𝐶𝑝𝜌𝑉𝑠𝑑𝑇𝑠

𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑡+ − 𝑇𝑠 +

𝑄 𝐶𝑝𝜌 𝑇𝑡− − 𝑇𝑠 + 𝑈𝑠𝐴𝑠 𝑇𝑎𝑖𝑟 − 𝑇𝑠 +

𝑃𝑅 + 𝑃𝑐ℎ

𝐶𝑝𝜌𝑉𝑡 𝑑𝑇𝑡+

𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑠 − 𝑇𝑡 +

𝑈 𝐴𝑡 𝑇𝑎𝑖𝑟 − 𝑇𝑡 + 𝑃𝑝𝑢𝑚𝑝

𝐶𝑝𝜌𝑉𝑡 𝑑𝑇𝑡−

𝑑𝑡= 𝑄 𝐶𝑝𝜌 𝑇𝑠 − 𝑇𝑡 +

𝑈 𝐴𝑡 𝑇𝑎𝑖𝑟 − 𝑇𝑡 + 𝑃𝑝𝑢𝑚𝑝

• 3.1 power losses due to the internal resistance

𝑃𝑅 = 𝐼 𝑅

Charging or Discharging: Different currents and internal resistance

• 3.2 Chemical Power Loss

q = T∆S = T 𝑆𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 − 𝑆𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠

𝑃𝑐ℎ = 𝑞𝑛 = 𝑇∆𝑆𝑛

C.Blanc, Modeling of a vanadium redox flow battery electricity storage system, Phd thesis, Ecole polytech Fed Lausanne, 2009.

• 3.3 Pump Power Loss

Friction loss

Form loss

𝑃𝑝𝑢𝑚𝑝 = ∆𝑝 × 𝑄

∆p = ∆𝑝𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 + ∆𝑝𝑓𝑜𝑟𝑚

∆𝑝𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 = 𝑓𝐿

𝐷ℎ

𝜌𝑉𝑚2

∆𝑝𝑓𝑜𝑟𝑚 = 𝐾𝜌𝑉𝑚

2

• 3.3 Pump Power Loss

2 parts: Stack and Hydraulic Structure

To calculate friction loss in stack:

• 3.4 State Space Model

𝑥 = 𝐴𝑥 + 𝐵𝑢

y = Cx + Du

𝑑𝑇𝑠

𝑑𝑡= −

𝑄+ 𝑄−

𝑉𝑠−

𝑈𝑠𝐴𝑠

𝐶𝑝𝜌𝑉𝑠𝑇𝑠 +

𝑄+

𝑉𝑠𝑇𝑡 +

𝑄−

𝑉𝑠𝑇𝑡 +

𝑈𝑠𝐴𝑠

𝐶𝑝𝜌𝑉𝑠𝑇𝑎𝑖𝑟 +

1

𝐶𝑝𝜌𝑉𝑠𝑃𝑅 +

1

𝐶𝑝𝜌𝑉𝑠𝑃𝑐ℎ

𝑑𝑇𝑡+

𝑑𝑡=

𝑄+

𝑉𝑡+𝑇𝑠 + −

𝑄+

𝑉𝑡+−

𝑈+𝐴𝑡

𝐶𝑝𝜌𝑉𝑡+𝑇𝑡 +

𝑈+𝐴𝑡

𝐶𝑝𝜌𝑉𝑡+𝑇𝑎𝑖𝑟 +

1

𝐶𝑝𝜌𝑉𝑡+𝑃𝑝𝑢𝑚𝑝

𝑑𝑇𝑡−

𝑑𝑡=

𝑄−

𝑉𝑡−𝑇𝑠 + −

𝑄−

𝑉𝑡−−

𝑈−𝐴𝑡

𝐶𝑝𝜌𝑉𝑡−𝑇𝑡 +

𝑈−𝐴𝑡

𝐶𝑝𝜌𝑉𝑡−𝑇𝑎𝑖𝑟 +

1

𝐶𝑝𝜌𝑉𝑡−𝑃𝑝𝑢𝑚𝑝

• 3.4 State Space Model

The state vector x =

𝑇𝑠𝑇𝑡 𝑇𝑡

, input u =

𝑃𝑅𝑇𝑎𝑖𝑟𝑃𝑝𝑢𝑚𝑝𝑃𝑐ℎ

A =

−𝑄+ 𝑄−

𝑉𝑠−

𝑈𝑠𝐴𝑠

𝐶𝑝𝜌𝑉𝑠

𝑄+

𝑉𝑠

𝑄−

𝑉𝑠

𝑄+

𝑉𝑡+−

𝑄+

𝑉𝑡+−

𝑈+𝐴𝑡

𝐶𝑝𝜌𝑉𝑡+0

𝑄−

𝑉𝑡−0 −

𝑄−

𝑉𝑡−−

𝑈−𝐴𝑡

𝐶𝑝𝜌𝑉𝑡−

B =

1

𝐶𝑝𝜌𝑉𝑠

𝑈𝑠𝐴𝑠

𝐶𝑝𝜌𝑉𝑠0

1

𝐶𝑝𝜌𝑉𝑠

0𝑈+𝐴𝑡

𝐶𝑝𝜌𝑉𝑡+

1

𝐶𝑝𝜌𝑉𝑡+0

0𝑈−𝐴𝑡

𝐶𝑝𝜌𝑉𝑡−

1

𝐶𝑝𝜌𝑉𝑡−0

C =1 0 00 1 00 0 1

D = 0

• 4. Simulations and Results

MATLAB is used to perform the simulation

• 4.1 Chemical power loss and power loss due to internal resistance

• 4.2 Pump power loss

• 4.3 Simulations of stack temperature with various flow rate

(𝐼𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔 = 𝐼𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔 = 30𝐴, surrounding temperature

25 constant)

𝑄 = 30𝑐𝑚 𝑠 1

𝑄 = 60𝑐𝑚 𝑠 1

• 𝑄 = 120𝑐𝑚 𝑠 1

𝑄 = 180𝑐𝑚 𝑠 1

𝑄 = 240𝑐𝑚 𝑠 1

• 4.4 Simulation of stack temperature with various flow rate

(𝐼𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔 = 30𝐴, 𝐼𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔 = 100𝐴, surrounding

air temperature 25 constant)

𝑄 = 30𝑐𝑚 𝑠 1

𝑄 = 60𝑐𝑚 𝑠 1

• 𝑄 = 120𝑐𝑚 𝑠 1

𝑄 = 180𝑐𝑚 𝑠 1

𝑄 = 240𝑐𝑚 𝑠 1

• 4.5 Simulations of stack temperature with various charging and discharging currents

(𝑄𝑠𝑡𝑎𝑐𝑘 = 4 × 𝑄𝑚𝑖𝑛, surrounding air temperature 25 constant)

I=40A

I=60A

• I=80A

I=100A

I=120A

• 4.6 Simulations of stack temperature with changing flow rate

(I=30A, surrounding air are varying between 15℃ to 35℃)

𝑄 = 30𝑐𝑚 𝑠 1

𝑄 = 60𝑐𝑚 𝑠 1

• 𝑄 = 120𝑐𝑚 𝑠 1

𝑄 = 180𝑐𝑚 𝑠 1

𝑄 = 240𝑐𝑚 𝑠 1

• 4.7 Simulations of stack temperature with various charging/discharging current (𝑄 = 120𝑐𝑚 𝑠 1, surrounding air are varying between 15℃ to 35℃)

• I=80A

I=100A

I=120A

• 4.8 Simulation of stack temperature and tank temperature I=30A, 𝑄 = 120𝑐𝑚 𝑠 1 and constant surrounding air temperature.

• 5. Future improvement

Self-discharging and the side reactions will also contribute to heat generation so that the temperature of stack will increase more. Especially, when the battery is standing by, the self-discharging characteristic has to be investigated.

• 6. Conclusion

a dynamic thermal model based on conservation of energy is developed

friction power loss and form power loss are not negligible

chemical power and internal resistance loss

Factors: flow rate of electrolyte, currents and surrounding air temperature

• Acknowledgement

Q&A

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