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

Load

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 =

𝑃𝑅𝑇𝑎𝑖𝑟𝑃𝑝𝑢𝑚𝑝

𝑃𝑐ℎ

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