Three-Dimensional Numerical Simulation of Lead-Acid Battery

Size: px

Start display at page:

Download "Three-Dimensional Numerical Simulation of Lead-Acid Battery"

Randolf Lynch
6 years ago
Views:

1 1

2 Three--Dimensional Numerical Simulation Three of Lead Lead--Acid Battery Vahid Esfahanian Hamid Afshari Arman Pouyaei Amir Babak Ansari Vehicle, Fuel and Environment Research Institute (VFRI) Department of Mechanical Engineering University of Tehran Iran 2

3 The First Battery Made by Parthian Wilhelm Koning (1938) I = 250 ma V = Volt Time = 200 h 3

4 The first Lead Acid cell studied by Gaston Planté (1834 ( ) 1889) French physicist

5 Wh Modeling? M d li? Why pe e t Experiment 1 Practical and Valuable Time Consuming Expensive 5

6 Wh Modeling? M d li? Why pe e t Experiment Practical and Valuable Time Consuming Expensive 1 Simulation & Modeling 2 Available Fast Cheap Gives deep insight of phenomena 6

7 C l it off Battery B tt M d li Complexity Modeling 1 Various Involved Physical Phenomena 2 Complex Electrochemical Equations 3 Different Macroscopic and Microscopic Time Scales 4 M l i Ph Multi-Phase, M Multi-Component lic Fl Flow 5 Porous Media 6 Thermodynamics 7 Heat Transfer 7

8 Battery Model Positive Plate Separator Rib Separator Negative Plate 8

9 Lead-Acid Cell Model Negative Electrode discharge PbSO 4(s) +H + +2ePb(s) +HSO 4- charge discharge + - PbSO 4(s) +2H 2O Positive Electrode PbO 2(s) +HSO 4 +3H +2e charge 9

10 C i and Transport Processes iin LAB Coupled Electrochemical Conservation of Charge in Solid.( eff s ) Aj Conservation of Charge in Liquid.( eff l ).[ eff D (ln c)] Aj Conservation of Species (( c)) Aj eff v. c.(d c) a 2 t 2F Conservation of Momentum v 1 v. v p.( v) g[1 (c c0 )] ( v) K t Conservation of Mass.v 0 10

11 Mathematical Formulation The electrode porosity equations Aj a1 0 t 2F Anode M PbSO4 M PbO2 a1 PbSO PbO2 4 Cathode M Pb M PbSO4 a1 Pb PbSO4 The active surface equations in electrode Discharging process A A max SOC Charging process A A max (1 SOC ) Butler-Volmer equation af cf exp i i 0 exp RT RT 11

12 Boundary Conditions l 0 n I s eff discharging n I charging eff c 0 n l 0 n I discharging eff s I n charging eff c 0 n x=0 x=l s 0 n Coupled l 12

13 Initial Conditions Initial Acid Concentration c c0 Initial potential in solid and liquid 1) Solve steady state equations 0. eff s Aj and. eff l Aj. eff D ln c 2) Solve the whole system up to a small time step (i.e sec.) 13

14 Th M hs di off L d A id C ll The Most IImportant CFD R Research Studies Lead-Acid Cell Name Year Method Model Experiment p Newman and Tiedemann 1979 POD 1-D No H. Gu et al FDM 1-D No V. Esfahanian and F. Torabi 2006 FDM Keller-Box 1-D No V Esfahanian E f h i ett al. l V CFD/ECM 1D 1-D N No V. Esfahanian et al POD 1-D No 14

15 Th M hs di off L d A id C ll The Most IImportant CFD R Research Studies Lead-Acid Cell Name Year Method F. Alavyoon et al FDM 2-D Yes D.M. Bernardi et al FDM 2-D No W.B. Gu and C.Y. Wang 1997 FVM 2-D No 2011 Model Experiment p Theoretical Study and Formulation F Torabi T bi and d V. V Esfahanian Ef h i F. V. Esfahanian et al FVM 2-D No 2013 FLUENT 2-D No 15

16 R h Obj i Research Objective For the first time in the present model, full simulation of electrochemical-fluid lead-acid battery in three-dimensional has been done using fluent software, regardless of the thermal effects. effects 16

17 Validation C Comparison i off measured d vertical ti l velocity l it profiles fil att the th half h lf height h i ht off the th electrolyte reservoir after 60 minutes 17

18 Validation Comparison C i off measured d vertical ti l concentration t ti profiles fil att th the middle iddl off the electrolyte reservoir after 15 and 30 minutes 18

19 Results and Discussion C Comparison i off vertical ti l velocity l it profile fil in i width idth off the th reservoir i after ft 15 minutes 19

20 Results and Discussion Th vertical The ti l velocity l it in i the th middle iddl off the th cell ll after ft 15 minutes i t 20

21 Results and Discussion a) b) C Comparison i off velocity l it profile fil through th h cell ll length l th after ft 15 minutes i t a) L/2 b) L/32 21

22 C l i Conclusion According to the obtained three three-dimensional dimensional simulation results results, 2-D 2D and 3-D simulations have a good conformity with each other in some cases therefore 2 cases, 2-D D simulation can be used in order to decrease the solution time. 3-D simulation results is more closer to experimental p data than 2-D. In addition, in the three-dimensional simulation the stratification process is observed more precisely. Furthermore, the velocity field near the wall, shows some vortices which are caused by concentration gradient. 22

23 Thank you for your attention 23

NUMERICAL SIMULATION OF ACID STRATIFICATION IN LEAD-ACID BATTERIES

NUMERICAL SIMULATION OF ACID STRATIFICATION IN LEAD-ACID BATTERIES Vahid Esfahanian 1, Farschad Torabi 1 Professor, School of Mechanical Engineering, University of Tehran, Corresponding author Email: evahid@ut.ac.ir