! Test case for battery development. ! This is the discharge test case in Master's thesis. ! ! Here Solvers 1 & 2 are iterated until converged for each timestep, ! thereafter solver 3 & 4 are solved only once. ! ! It was difficult to obtain convergence. The following tricks are used: ! - Electrostatic equations only are iterated as coupled system $npass times ! - Concentration equations are only updated once for given potential ! - The equilibrium potentials are kept constant during concentration computations ! - The solid state concentration has a maximum allow change, $dcsmax ! - Currently 2nd order mesh is used, this enables use of strong form of diffusive source for Ce ! - Sensitivity of solution is used for linearization of Phis, Phie, Ce (but not of Cs) ! ! Notes on accuracy: ! - Even the current accuracy is not very good. One could increase $nss or decrease $sstol ! - There is a heavy computational cost in large number of iterations ! ! Peter Raback, CSC & Timo Uimonen, University of Vaasa. 15.8.2019 ! If you want to use this as part of your own research we would ! appreciated contacting. !--------------------------------------------------------------------- Check Keywords Warn $area = 1.0452 $currdens = 6.0 / area $p0 = 0.126 $p1 = 0.676 $q1 = 0.442 $q0 = 0.936 $prefix="a" $relax=0.4 ! relaxation factor, note (1-relax)^iter must be small $npass=5 ! how many ss iterations for electrostatics only $nss=20 ! how many ss iterations for full system $dcsmax=2.0 ! largest allowed change in concentration in one iteration $sstol=1.0e-6 ! ss convergence tolerance Header Mesh DB "." "battery1d" End Constants Faraday Constant = Real 96485.9 Gas Constant = Real 8.314 Transference Number = Real 0.363 Electrode Plate Area = Real $area Ambient Temperature = Real 288.0 Current Collector Resistance = Real 0.0020 End Simulation Max Output Level = 7 Coordinate System = Cartesian 2D Simulation Type = Transient Timestepping method = implicit euler ! 3600 s for a full hour, 3 s for testing Timestep Intervals(1) = 3 ! 3600 Timestep Sizes(1) = 1.0 Output Intervals(1) = 10 ! from um to m Coordinate Scaling = Real 1.0e-6 Steady State Min Iterations = $npass+nss Steady State Max Iterations = 200 End Body 1 Name = "Left_Anode" ! negative Target Bodies(1) = 1 Equation = 1 Material = 1 Initial condition = 1 Body Force = 1 End Body 2 Name = "Center" Target Bodies(1) = 2 Equation = 2 Material = 2 Initial condition = 2 Body Force = 1 End Body 3 Name = "Right_Cathode" ! positive Target Bodies(1) = 3 Equation = 1 Material = 3 Initial condition = 3 Body Force = 1 End Body Force 1 Name = "just save" Save Line = Logical True End Equation 1 Name = "SolidphaseEqs" ! We use this way to tell active solvers since it allows ! for renumering of the solver to test different orders. ElectrolytePot = Logical True ElectrolyteCons = Logical True SolidphasePot = Logical True SolidphaseCons = Logical True End Equation 2 Name = "ElectrolyteEqs" ElectrolytePot = Logical True ElectrolyteCons = Logical True End Solver 1 ! Phis Equation = SolidphasePot Procedure = "BatterySolver" "SolidphasePot" Linearize Flux = Logical True Linear System Solver = Direct Linear System Direct Method = UMFPack Nonlinear System Max Iterations = 10 Nonlinear System Relaxation Factor = $relax Nonlinear System Convergence Tolerance = 1.0e-7 Nonlinear System Convergence Measure = "solution" Steady State Convergence Tolerance = $sstol ! Nonlinear Post Solvers(1) = 2 Charge Controller = Logical True Cutoff voltage = Real 3.1 End Solver 2 ! Phie Equation = ElectrolytePot ! Exec Solver = always Procedure = "BatterySolver" "ElectrolytePot" Linearize Flux = Logical True ! Fixed Overpotential = Logical True ! Calculate Ce sensitivity = Logical True ! Ignore Electrolyte Diffusion = Logicalx True Quadratic Electrolyte Diffusion = Logical True Linear System Solver = Direct Linear System Direct Method = UMFPack Nonlinear System Max Iterations = 10 Nonlinear System Relaxation Factor = $relax Nonlinear System Convergence Tolerance = 1.0e-7 Nonlinear System Convergence Measure = "solution" Steady State Convergence Tolerance = $sstol End Solver 3 ! Ce Equation = ElectrolyteCons Procedure = "BatterySolver" "ElectrolyteCons" ! How many times visit the solver before going to work Number Of Passive Visits = Integer $npass Linearize Flux = Logical True Fixed Overpotential = Logical True ! Use Mean Flux = Logical True ! Correct Butler Volmer Fluxes = Logical True ! Also calculate sensitivity for solver '4' ! Calculate Cs sensitivity = Logical True ! Skip Butler Volmer = Logical True Linear System Solver = Direct Linear System Direct Method = UMFPack Nonlinear System Max Iterations = 1 Nonlinear System Convergence Tolerance = 1.0e-8 Nonlinear System Convergence Measure = "solution" Nonlinear System Relaxation Factor = $relax Steady State Convergence Tolerance = $sstol End Solver 4 ! Cs Equation = SolidphaseCons Procedure = "BatterySolver" "SolidphaseCons" Number Of Passive Visits = Integer $npass Linearize Flux = Logical False Fixed Overpotential = Logical True ! Note that we use "speed" hence the change is speed*dt Maximum Global Change Speed = Real $dcsmax Linear System Solver = Direct Linear System Direct Method = UMFPack ! These define the 1D mesh that is created on-the-fly for this solver ! Note that currently we use 2nd order mesh ! Using 1st order mesh allows more elements with same computational cost. 1D Mesh Create = Logical True 1D Element Order = Integer 2 1D Number Of Elements = Integer 50 1D Mesh Length = Real 1.0 1D Active Direction = Integer 1 1D Body Id = Integer 1 ! If we try to iterate the system further the global iteration suffers Nonlinear System Max Iterations = Integer 1 Nonlinear System Relaxation Factor = $relax Nonlinear System Convergence Tolerance = 1.0e-8 Save Solid Phase Average = Logical True Save Solid Phase Diff = Logical True Save State of Charge = Logical True ! This keywords allows use to the submodel solution (Cs OneDim), of given mesh ! Otherwise the last submodel is saved. ! Visualize Node Index = Integer 20 End Solver 5 ! Phie Equation = BatteryPost Exec Solver = "after timestep" Procedure = "BatterySolver" "BatteryPost" End Solver 6 Equation = SaveScalars Procedure = "SaveData" "SaveScalars" Exec Solver = after timestep Variable 1 = time Filename = f$prefix$.dat End Solver 7 Equation = SaveBatterProfile Procedure = "SaveData" "SaveLine" ! Exec Solver = after saving Exec Solver = never Filename = g$prefix$.dat Save Solver Mesh Index = Integer 1 End Solver 8 Equation = SaveSubmodel Procedure = "SaveData" "SaveLine" ! Exec Solver = after saving Exec Solver = never Filename = h$prefix$.dat Save Solver Mesh Index = Integer 4 End ! Material parameters from Table1 of Master's Thesis Material 1 Name = "Anode" ! left Anode = Logical True Particle Radius = Real 1.0e-6 Active Particle Volume Fraction = Real 0.58 Electrolyte Volume Fraction = Real 0.332 Maximum solid phase concentration = Real 16.1e3 Kinetic Constant = Real 1.38e-4 Anodic charge transfer coefficient = Real 0.5 Cathodic charge transfer coefficient = Real 0.5 Solid Phase Diffusion Coefficient = Real 2.0e-16 Electrolyte Diffusion Coefficient = Real 2.0e-10 Solid Phase Electrical Conductivity = Real 100.0 Stoichiometry at Full Charge = Real $p1 Stoichiometry at Nill Charge = Real $p0 End Material 2 Name = "Electrolyte" Electrolyte Volume Fraction = Real 0.5 Electrolyte Diffusion Coefficient = Real 2.0e-10 End Material 3 Name = "Cathode" ! right Cathode = Logical True Particle Radius = Real 1.0e-6 Active Particle Volume Fraction = Real 0.50 Electrolyte Volume Fraction = Real 0.330 Maximum solid phase concentration = Real 23.9e3 Kinetic Constant = Real 0.64e-4 Anodic charge transfer coefficient = Real 0.5 Cathodic charge transfer coefficient = Real 0.5 Solid Phase Diffusion Coefficient = Real 3.7e-16 Electrolyte Diffusion Coefficient = Real 2.0e-10 Solid Phase Electrical Conductivity = Real 10.0 Stoichiometry at Full Charge = Real $q1 Stoichiometry at Nill Charge = Real $q0 End Initial Condition 1 Name = "InitialCondition 1" Cs = Real $p1*16.1e3 Ce = Real 1205.0 Phie = Real 2.2 Phis = Real 2.0 Jli = Real 0.0 End Initial Condition 2 Name = "InitialCondition 2" Ce = Real 1205.0 Phie = Real 2.2 Jli = Real 0.0 End Initial Condition 3 Name = "InitialCondition 3" Cs = Real $q1*23.9e3 Ce = Real 1205.0 Phie = Real 2.2 Phis = Real 6.0 Jli = Real 0.0 End ! Note that in BCs all natural one are automatically satisfied (zero flux) Boundary Condition 1 Name = "0" Target Boundaries(1) = 1 current density = Real $ currdens End Boundary Condition 2 Name = "Lneg" Target Boundaries(1) = 2 End Boundary Condition 3 Name = "Lpos" Target Boundaries(1) = 3 End Boundary Condition 4 Name = "L" Target Boundaries(1) = 4 current density = Real $ -currdens End ! Currentle these imply consistency, not correctness! Solver 1 :: Reference Norm = 4.30264101E+00 Solver 2 :: Reference Norm = 2.14011214E+00 Solver 3 :: Reference Norm = 1.20488804E+03 Solver 4 :: Reference Norm = 1.08044183E+05 !End Of File
