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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,168 @@ | ||
| from firedrake import * | ||
| from echemfem import EchemSolver, NavierStokesBrinkmanFlowSolver, NavierStokesFlowSolver | ||
| import argparse | ||
| parser = argparse.ArgumentParser(add_help=False) | ||
| parser.add_argument("--family", type=str, default='CG') | ||
| parser.add_argument("--vel_file", type=str, default=None) | ||
| args, _ = parser.parse_known_args() | ||
| if args.family == "CG": | ||
| SUPG = True | ||
| else: | ||
| SUPG = False | ||
|
|
||
| #flow_rate = 2.4 * 5/3 * 1e-8 # m3/s -> x ml/min | ||
| #area = 4e-4 # m2 -> 4 cm2 | ||
| #v_avg = flow_rate/area | ||
| v_avg = 1e-10# | ||
| print(v_avg) | ||
|
|
||
| current_density = 50 * 10 # A/m2 -> 50 mA/cm2 | ||
| current_density = 1e-1 # A/m2 -> 50 mA/cm2 | ||
|
|
||
| electrode_thickness = 500e-6 # m | ||
| electrode_length = 500e-6#2e-3 # m | ||
| inlet_length = electrode_length/4 | ||
| outlet_length = electrode_length/4 | ||
| mesh = RectangleMesh(50, 50, electrode_length, electrode_thickness, quadrilateral=True) | ||
| if False: | ||
| x, y = SpatialCoordinate(mesh) | ||
| V1 = FunctionSpace(mesh, "HDiv Trace", 0) | ||
| f3 = Function(V1).interpolate(conditional(And(And(y < 1e-16, | ||
| x <= electrode_length - outlet_length), | ||
| x >= inlet_length), 1., 0.)) | ||
| f5 = Function(V1).interpolate(conditional(And(y < 1e-16, x < inlet_length), 1., 0.)) | ||
| f6 = Function(V1).interpolate(conditional(And(y < 1e-16, x > electrode_length - outlet_length), 1., 0.)) | ||
| mesh = RelabeledMesh(mesh, | ||
| [f3, f5, f6], | ||
| [3, 5, 6]) | ||
|
|
||
| """ | ||
| Schematic of the domain: | ||
| _____4_____ | ||
| | | | ||
| 1 2 | ||
| | | | ||
| |_5_._3_._6_| | ||
| """ | ||
|
|
||
| class BortelsSolver(EchemSolver): | ||
| def __init__(self): | ||
| conc_params = [] | ||
|
|
||
| conc_params.append({"name": "V2", | ||
| "diffusion coefficient": 2.4e-10, # m^2/s | ||
| "bulk": 1000., # mol/m^3 | ||
| }) | ||
|
|
||
| conc_params.append({"name": "V3", | ||
| "diffusion coefficient": 2.4e-10, # m^2/s | ||
| "bulk": 1000., # mol/m^3 | ||
| }) | ||
|
|
||
| #physical_params = {"flow": ["advection", "diffusion", "porous"], | ||
| physical_params = {"flow": ["advection", "diffusion", "poisson", "porous"], | ||
| "F": 96485.3329, # C/mol | ||
| "R": 8.3144598, # J/K/mol | ||
| "T": 273.15 + 25., # K | ||
| "solid conductivity": 1e4, # S/m | ||
| "liquid conductivity": 40, # S/m | ||
| "specific surface area": 8e4, # 1/m | ||
| "porosity": 0.68, | ||
| "U_app": 0., # ground U_solid = 0 | ||
| "applied current density": Constant(current_density), | ||
| } | ||
|
|
||
| def reaction(u): | ||
| # Butler-Volmer | ||
| V2 = u[0] | ||
| V3 = u[1] | ||
| Phi2 = u[2] | ||
| Phi1 = u[3] | ||
| #Phi2 = -0.2499 | ||
| #Phi1 = 0 | ||
| Cref = 1. # mol/m3 | ||
| J0 = 0.016 # A/m^2 | ||
| U0 = -0.25 | ||
| F = physical_params["F"] | ||
| R = physical_params["R"] | ||
| T = physical_params["T"] | ||
| beta = 0.5 * F / R / T | ||
| eta = Phi1 - Phi2 - U0 | ||
| return J0 / Cref * (V2 * exp(beta * eta) | ||
| - V3 * exp(-beta * eta)) | ||
| #def reaction(u): | ||
| # return 1e-1 | ||
|
|
||
|
|
||
|
|
||
| echem_params = [] | ||
| echem_params.append({"reaction": reaction, | ||
| "electrons": 1, | ||
| "stoichiometry": {"V2": 1, | ||
| "V3": -1}, | ||
| }) | ||
| #echem_params = [] | ||
| super().__init__( | ||
| conc_params, | ||
| physical_params, | ||
| mesh, | ||
| echem_params=echem_params, | ||
| family=args.family, | ||
| SUPG=SUPG) | ||
|
|
||
| def set_boundary_markers(self): | ||
| self.boundary_markers = {"inlet": (1,), | ||
| "outlet": (2,), | ||
| "applied": (3,), # U_solid = 0 | ||
| "applied liquid current": (4,), | ||
| } | ||
|
|
||
| def set_velocity(self): | ||
| boundary_markers = {"no slip": (3,4,1,2,), | ||
| #"inlet velocity": (5,), | ||
| #"outlet velocity": (6,), | ||
| "outlet pressure": (6,), | ||
| "inlet pressure": (5,), | ||
| } | ||
| boundary_markers = {"no slip": (3,4,), | ||
| #"inlet velocity": (5,), | ||
| #"outlet velocity": (6,), | ||
| "outlet pressure": (2,), | ||
| "inlet pressure": (1,), | ||
| } | ||
|
|
||
| #vel = as_vector([Constant(0), Constant(v_avg)]) | ||
| #vel_out = as_vector([Constant(0), Constant(-v_avg)]) | ||
| x, y = SpatialCoordinate(self.mesh) | ||
| vel = as_vector([Constant(0), 4 * Constant(v_avg) * x * (Constant(inlet_length) - x)/Constant(inlet_length**2)]) | ||
| vel_out = as_vector([Constant(0), 4 * Constant(-v_avg) * (x - Constant(electrode_length-outlet_length)) * (Constant(electrode_length) - x)/Constant(outlet_length**2)]) | ||
| flow_params = {"inlet velocity": vel, | ||
| "outlet pressure": 0., | ||
| "inlet pressure": 4e-3, | ||
| "outlet velocity": vel_out, | ||
| "density": 1e3, # kg/m3 | ||
| "dynamic viscosity": 8.9e-4, # Pa s | ||
| "permeability": 5.53e-11 # m2 | ||
| } | ||
| NS_solver = NavierStokesBrinkmanFlowSolver(mesh, flow_params, boundary_markers) | ||
| #NS_solver = NavierStokesFlowSolver(mesh, flow_params, boundary_markers) | ||
| NS_solver.setup_solver() | ||
| NS_solver.solve() | ||
| self.vel = NS_solver.vel | ||
|
|
||
|
|
||
| solver = BortelsSolver() | ||
| solver.setup_solver(initial_solve=False) | ||
| solver.solve() | ||
| us = solver.u.subfunctions | ||
| i_n = Function(solver.V, name="Current Density").interpolate(solver.echem_params[0]["reaction"](solver.u)) | ||
| File("results/current_density.pvd").write(i_n) | ||
| Vec = VectorFunctionSpace(solver.mesh, "CG", 1) | ||
| kappa_0 = solver.physical_params["liquid conductivity"] | ||
| kappa = solver.physical_params["porosity"]**1.5 * kappa_0 | ||
| i_l = Function(Vec, name="ionic current").interpolate(kappa * grad(us[solver.i_Ul])) | ||
| File("results/current.pvd").write(i_l) | ||
| av = solver.physical_params["specific surface area"] | ||
| print(assemble(av * i_n * dx)/assemble(Constant(1) * dx(domain=solver.mesh))) | ||
| print(current_density/electrode_length) |