def DeclareEquations(self):
dae.daeModel.DeclareEquations(self)
ndD = self.ndD
N = ndD["N"] # number of grid points in particle
T = self.ndD_s["T"] # nondimensional temperature
r_vec, volfrac_vec = geo.get_unit_solid_discr(ndD['shape'], N)
# Prepare the Ideal Solution log ratio terms
self.ISfuncs = None
if ndD["logPad"]:
self.ISfuncs = np.array([
extern_funcs.LogRatio("LR", self, dae.unit(), self.c(k))
for k in range(N)
])
# Prepare noise
self.noise = None
if ndD["noise"]:
numnoise = ndD["numnoise"]
noise_prefac = ndD["noise_prefac"]
tvec = np.linspace(0., 1.05 * self.ndD_s["tend"], numnoise)
noise_data = noise_prefac * np.random.randn(numnoise, N)
# Previous_output is common for all external functions
previous_output = []
self.noise = [
extern_funcs.InterpTimeVector("noise", self, dae.unit(),
dae.Time(), tvec, noise_data,
previous_output, _position_)
for _position_ in range(N)
]
# Figure out mu_O, mu of the oxidized state
mu_O, act_lyte = calc_mu_O(self.c_lyte, self.phi_lyte, self.phi_m, T,
self.ndD_s["elyteModelType"])
# Define average filling fraction in particle
eq = self.CreateEquation("cbar")
eq.Residual = self.cbar()
for k in range(N):
eq.Residual -= self.c(k) * volfrac_vec[k]
# Define average rate of filling of particle
eq = self.CreateEquation("dcbardt")
eq.Residual = self.dcbardt()
for k in range(N):
eq.Residual -= self.c.dt(k) * volfrac_vec[k]
c = np.empty(N, dtype=object)
c[:] = [self.c(k) for k in range(N)]
if ndD["type"] in ["ACR", "diffn", "CHR"]:
# Equations for 1D particles of 1 field varible
self.sld_dynamics_1D1var(c, mu_O, act_lyte, self.ISfuncs,
self.noise)
elif ndD["type"] in ["homog", "homog_sdn"]:
# Equations for 0D particles of 1 field variables
self.sld_dynamics_0D1var(c, mu_O, act_lyte, self.ISfuncs,
self.noise)
for eq in self.Equations:
eq.CheckUnitsConsistency = False
def __init__(self,
Name,
Parent=None,
Description="",
ndD=None,
ndD_s=None):
dae.daeModel.__init__(self, Name, Parent, Description)
if (ndD is None) or (ndD_s is None):
raise Exception("Need input parameter dictionary")
self.ndD = ndD
self.ndD_s = ndD_s
# Domain
self.Dmn = dae.daeDomain("discretizationDomain", self, dae.unit(),
"discretization domain")
# Define some variable types
mole_frac_t = dae.daeVariableType(name="mole_frac_t",
units=dae.unit(),
lowerBound=0,
upperBound=1,
initialGuess=0.25,
absTolerance=ndD_s["absTol"])
# Variables
self.c = dae.daeVariable("c", mole_frac_t, self,
"Concentration in active particle",
[self.Dmn])
self.cbar = dae.daeVariable(
"cbar", mole_frac_t, self,
"Average concentration in active particle")
self.dcbardt = dae.daeVariable("dcbardt", dae.no_t, self,
"Rate of particle filling")
if ndD["type"] not in ["ACR"]:
self.Rxn = dae.daeVariable("Rxn", dae.no_t, self,
"Rate of reaction")
else:
self.Rxn = dae.daeVariable("Rxn", dae.no_t, self,
"Rate of reaction", [self.Dmn])
# Ports
self.portInLyte = ports.portFromElyte("portInLyte", dae.eInletPort,
self,
"Inlet port from electrolyte")
self.portInBulk = ports.portFromBulk(
"portInBulk", dae.eInletPort, self,
"Inlet port from e- conducting phase")
self.phi_lyte = self.portInLyte.phi_lyte()
self.c_lyte = self.portInLyte.c_lyte()
self.phi_m = self.portInBulk.phi_m()
def __init__(self,
Name,
Parent=None,
Description="",
ndD=None,
ndD_s=None):
dae.daeModel.__init__(self, Name, Parent, Description)
if (ndD is None) or (ndD_s is None):
raise Exception("Need input parameter dictionary")
self.ndD = ndD
self.ndD_s = ndD_s
# Domain
self.Dmn = dae.daeDomain("discretizationDomain", self, dae.unit(),
"discretization domain")
# Variables
self.c1 = dae.daeVariable(
"c1", mole_frac_t, self,
"Concentration in 'layer' 1 of active particle", [self.Dmn])
self.c2 = dae.daeVariable(
"c2", mole_frac_t, self,
"Concentration in 'layer' 2 of active particle", [self.Dmn])
self.cbar = dae.daeVariable(
"cbar", mole_frac_t, self,
"Average concentration in active particle")
self.c1bar = dae.daeVariable(
"c1bar", mole_frac_t, self,
"Average concentration in 'layer' 1 of active particle")
self.c2bar = dae.daeVariable(
"c2bar", mole_frac_t, self,
"Average concentration in 'layer' 2 of active particle")
self.dcbardt = dae.daeVariable("dcbardt", dae.no_t, self,
"Rate of particle filling")
if ndD["type"] not in ["ACR2"]:
self.Rxn1 = dae.daeVariable("Rxn1", dae.no_t, self,
"Rate of reaction 1")
self.Rxn2 = dae.daeVariable("Rxn2", dae.no_t, self,
"Rate of reaction 2")
else:
self.Rxn1 = dae.daeVariable("Rxn1", dae.no_t, self,
"Rate of reaction 1", [self.Dmn])
self.Rxn2 = dae.daeVariable("Rxn2", dae.no_t, self,
"Rate of reaction 2", [self.Dmn])
#Get reaction rate function from dictionary name
self.calc_rxn_rate = getattr(reactions, ndD["rxnType"])
# Ports
self.portInLyte = ports.portFromElyte("portInLyte", dae.eInletPort,
self,
"Inlet port from electrolyte")
self.portInBulk = ports.portFromBulk(
"portInBulk", dae.eInletPort, self,
"Inlet port from e- conducting phase")
self.phi_lyte = self.portInLyte.phi_lyte
self.c_lyte = self.portInLyte.c_lyte
self.phi_m = self.portInBulk.phi_m
def DeclareEquations(self):
dae.daeModel.DeclareEquations(self)
ndD = self.ndD
N = ndD["N"] # number of grid points in particle
T = self.ndD_s["T"] # nondimensional temperature
r_vec, volfrac_vec = geo.get_unit_solid_discr(ndD['shape'], N)
# Prepare the Ideal Solution log ratio terms
self.ISfuncs1 = self.ISfuncs2 = None
if ndD["logPad"]:
self.ISfuncs1 = np.array([
extern_funcs.LogRatio("LR1", self, dae.unit(), self.c1(k))
for k in range(N)
])
self.ISfuncs2 = np.array([
extern_funcs.LogRatio("LR2", self, dae.unit(), self.c2(k))
for k in range(N)
])
ISfuncs = (self.ISfuncs1, self.ISfuncs2)
# Prepare noise
self.noise1 = self.noise2 = None
if ndD["noise"]:
numnoise = ndD["numnoise"]
noise_prefac = ndD["noise_prefac"]
tvec = np.linspace(0., 1.05 * self.ndD_s["tend"], numnoise)
noise_data1 = noise_prefac * np.random.randn(numnoise, N)
noise_data2 = noise_prefac * np.random.randn(numnoise, N)
# Previous_output is common for all external functions
previous_output1 = []
previous_output2 = []
self.noise1 = [
extern_funcs.InterpTimeVector("noise1", self, dae.unit(),
dae.Time(), tvec, noise_data1,
previous_output1, _position_)
for _position_ in range(N)
]
self.noise2 = [
extern_funcs.InterpTimeVector("noise2", self, dae.unit(),
dae.Time(), tvec, noise_data2,
previous_output2, _position_)
for _position_ in range(N)
]
noises = (self.noise1, self.noise2)
# Figure out mu_O, mu of the oxidized state
mu_O, act_lyte = calc_mu_O(self.c_lyte(), self.phi_lyte(),
self.phi_m(), T,
self.ndD_s["elyteModelType"])
# Define average filling fractions in particle
eq1 = self.CreateEquation("c1bar")
eq2 = self.CreateEquation("c2bar")
eq1.Residual = self.c1bar()
eq2.Residual = self.c2bar()
for k in range(N):
eq1.Residual -= self.c1(k) * volfrac_vec[k]
eq2.Residual -= self.c2(k) * volfrac_vec[k]
eq = self.CreateEquation("cbar")
eq.Residual = self.cbar() - utils.mean_linear(self.c1bar(),
self.c2bar())
# Define average rate of filling of particle
eq = self.CreateEquation("dcbardt")
eq.Residual = self.dcbardt()
for k in range(N):
eq.Residual -= utils.mean_linear(self.c1.dt(k),
self.c2.dt(k)) * volfrac_vec[k]
c1 = np.empty(N, dtype=object)
c2 = np.empty(N, dtype=object)
c1[:] = [self.c1(k) for k in range(N)]
c2[:] = [self.c2(k) for k in range(N)]
if ndD["type"] in ["diffn2", "CHR2"]:
# Equations for 1D particles of 1 field varible
self.sld_dynamics_1D2var(c1, c2, mu_O, act_lyte, ISfuncs, noises)
elif ndD["type"] in ["homog2", "homog2_sdn"]:
# Equations for 0D particles of 1 field variables
self.sld_dynamics_0D2var(c1, c2, mu_O, act_lyte, ISfuncs, noises)
for eq in self.Equations:
eq.CheckUnitsConsistency = False
def __init__(self,
Name,
Parent=None,
Description="",
ndD_s=None,
ndD_e=None):
dae.daeModel.__init__(self, Name, Parent, Description)
if (ndD_s is None) or (ndD_e is None):
raise Exception("Need input parameter dictionaries")
self.ndD = ndD_s
self.profileType = ndD_s['profileType']
Nvol = ndD_s["Nvol"]
Npart = ndD_s["Npart"]
self.trodes = trodes = ndD_s["trodes"]
# Domains where variables are distributed
self.DmnCell = {} # domains over full cell dimensions
self.DmnPart = {} # domains over particles in each cell volume
if Nvol["s"] >= 1: # If we have a separator
self.DmnCell["s"] = dae.daeDomain(
"DmnCell_s", self, dae.unit(),
"Simulated volumes in the separator")
for trode in trodes:
self.DmnCell[trode] = dae.daeDomain(
"DmnCell_{trode}".format(trode=trode), self, dae.unit(),
"Simulated volumes in electrode {trode}".format(trode=trode))
self.DmnPart[trode] = dae.daeDomain(
"Npart_{trode}".format(trode=trode), self, dae.unit(),
"Particles sampled in each control " +
"volume in electrode {trode}".format(trode=trode))
# Variables
self.c_lyte = {}
self.phi_lyte = {}
self.phi_bulk = {}
self.phi_part = {}
self.R_Vp = {}
self.ffrac = {}
for trode in trodes:
# Concentration/potential in electrode regions of elyte
self.c_lyte[trode] = dae.daeVariable(
"c_lyte_{trode}".format(trode=trode), conc_t, self,
"Concentration in the elyte in electrode {trode}".format(
trode=trode), [self.DmnCell[trode]])
self.phi_lyte[trode] = dae.daeVariable(
"phi_lyte_{trode}".format(trode=trode), elec_pot_t, self,
"Electric potential in elyte in electrode {trode}".format(
trode=trode), [self.DmnCell[trode]])
self.phi_bulk[trode] = dae.daeVariable(
"phi_bulk_{trode}".format(trode=trode), elec_pot_t, self,
"Electrostatic potential in the bulk solid",
[self.DmnCell[trode]])
self.phi_part[trode] = dae.daeVariable(
"phi_part_{trode}".format(trode=trode), elec_pot_t, self,
"Electrostatic potential at each particle",
[self.DmnCell[trode], self.DmnPart[trode]])
self.R_Vp[trode] = dae.daeVariable(
"R_Vp_{trode}".format(trode=trode), dae.no_t, self,
"Rate of reaction of positives per electrode volume",
[self.DmnCell[trode]])
self.ffrac[trode] = dae.daeVariable(
"ffrac_{trode}".format(trode=trode), mole_frac_t, self,
"Overall filling fraction of solids in electrodes")
if Nvol["s"] >= 1: # If we have a separator
self.c_lyte["s"] = dae.daeVariable(
"c_lyte_s", conc_t, self,
"Concentration in the electrolyte in the separator",
[self.DmnCell["s"]])
self.phi_lyte["s"] = dae.daeVariable(
"phi_lyte_s", elec_pot_t, self,
"Electrostatic potential in electrolyte in separator",
[self.DmnCell["s"]])
# Note if we're doing a single electrode volume simulation
# It will be in a perfect bath of electrolyte at the applied
# potential.
if Nvol["a"] == 0 and Nvol["s"] == 0 and Nvol["c"] == 1:
self.SVsim = True
else:
self.SVsim = False
if not self.SVsim:
# Ghost points (GP) to aid in boundary condition (BC) implemenation
self.c_lyteGP_L = dae.daeVariable("c_lyteGP_L", conc_t, self,
"c_lyte left BC GP")
self.phi_lyteGP_L = dae.daeVariable("phi_lyteGP_L", elec_pot_t,
self, "phi_lyte left BC GP")
self.phi_applied = dae.daeVariable(
"phi_applied", elec_pot_t, self,
"Overall battery voltage (at anode current collector)")
self.phi_cell = dae.daeVariable(
"phi_cell", elec_pot_t, self,
"Voltage between electrodes (phi_applied less series resistance)")
self.current = dae.daeVariable("current", dae.no_t, self,
"Total current of the cell")
self.endCondition = dae.daeVariable(
"endCondition", dae.no_t, self,
"A nonzero value halts the simulation")
# Create models for representative particles within electrode
# volumes and ports with which to talk to them.
self.portsOutLyte = {}
self.portsOutBulk = {}
self.particles = {}
for trode in trodes:
Nv = Nvol[trode]
Np = Npart[trode]
self.portsOutLyte[trode] = np.empty(Nv, dtype=object)
self.portsOutBulk[trode] = np.empty((Nv, Np), dtype=object)
self.particles[trode] = np.empty((Nv, Np), dtype=object)
for vInd in range(Nv):
self.portsOutLyte[trode][vInd] = ports.portFromElyte(
"portTrode{trode}vol{vInd}".format(trode=trode, vInd=vInd),
dae.eOutletPort, self, "Electrolyte port to particles")
for pInd in range(Np):
self.portsOutBulk[trode][vInd, pInd] = ports.portFromBulk(
"portTrode{trode}vol{vInd}part{pInd}".format(
trode=trode, vInd=vInd, pInd=pInd),
dae.eOutletPort, self,
"Bulk electrode port to particles")
solidType = ndD_e[trode]["indvPart"][vInd, pInd]['type']
if solidType in ndD_s["2varTypes"]:
pMod = mod_electrodes.Mod2var
elif solidType in ndD_s["1varTypes"]:
pMod = mod_electrodes.Mod1var
else:
raise NotImplementedError("unknown solid type")
self.particles[trode][vInd, pInd] = pMod(
"partTrode{trode}vol{vInd}part{pInd}".format(
trode=trode, vInd=vInd, pInd=pInd),
self,
ndD=ndD_e[trode]["indvPart"][vInd, pInd],
ndD_s=ndD_s)
self.ConnectPorts(
self.portsOutLyte[trode][vInd],
self.particles[trode][vInd, pInd].portInLyte)
self.ConnectPorts(
self.portsOutBulk[trode][vInd, pInd],
self.particles[trode][vInd, pInd].portInBulk)
def DeclareEquations(self):
dae.daeModel.DeclareEquations(self)
# Some values of domain lengths
trodes = self.trodes
ndD = self.ndD
Nvol = ndD["Nvol"]
Npart = ndD["Npart"]
Nlyte = np.sum(list(Nvol.values()))
# Define the overall filling fraction in the electrodes
for trode in trodes:
eq = self.CreateEquation("ffrac_{trode}".format(trode=trode))
eq.Residual = self.ffrac[trode]()
dx = 1. / Nvol[trode]
# Make a float of Vtot, total particle volume in electrode
# Note: for some reason, even when "factored out", it's a bit
# slower to use Sum(self.psd_vol_ac[l].array([], [])
tmp = 0
for vInd in range(Nvol[trode]):
for pInd in range(Npart[trode]):
Vj = ndD["psd_vol_FracVol"][trode][vInd, pInd]
tmp += self.particles[trode][vInd, pInd].cbar() * Vj * dx
eq.Residual -= tmp
# Define dimensionless R_Vp for each electrode volume
for trode in trodes:
for vInd in range(Nvol[trode]):
eq = self.CreateEquation("R_Vp_trode{trode}vol{vInd}".format(
vInd=vInd, trode=trode))
# Start with no reaction, then add reactions for each
# particle in the volume.
RHS = 0
# sum over particle volumes in given electrode volume
for pInd in range(Npart[trode]):
# The volume of this particular particle
Vj = ndD["psd_vol_FracVol"][trode][vInd, pInd]
RHS += -(ndD["beta"][trode] *
(1 - ndD["poros"][trode]) * ndD["P_L"][trode] *
Vj * self.particles[trode][vInd, pInd].dcbardt())
eq.Residual = self.R_Vp[trode](vInd) - RHS
# Define output port variables
for trode in trodes:
for vInd in range(Nvol[trode]):
eq = self.CreateEquation(
"portout_c_trode{trode}vol{vInd}".format(vInd=vInd,
trode=trode))
eq.Residual = (self.c_lyte[trode](vInd) -
self.portsOutLyte[trode][vInd].c_lyte())
eq = self.CreateEquation(
"portout_p_trode{trode}vol{vInd}".format(vInd=vInd,
trode=trode))
phi_lyte = self.phi_lyte[trode](vInd)
eq.Residual = (phi_lyte -
self.portsOutLyte[trode][vInd].phi_lyte())
for pInd in range(Npart[trode]):
eq = self.CreateEquation(
"portout_pm_trode{trode}v{vInd}p{pInd}".format(
vInd=vInd, pInd=pInd, trode=trode))
eq.Residual = (
self.phi_part[trode](vInd, pInd) -
self.portsOutBulk[trode][vInd, pInd].phi_m())
# Simulate the potential drop along the bulk electrode
# solid phase
simBulkCond = ndD['simBulkCond'][trode]
if simBulkCond:
# Calculate the RHS for electrode conductivity
phi_tmp = utils.add_gp_to_vec(
utils.get_var_vec(self.phi_bulk[trode], Nvol[trode]))
porosvec = utils.pad_vec(
utils.get_const_vec(
(1 -
self.ndD["poros"][trode])**(1 -
ndD["BruggExp"][trode]),
Nvol[trode]))
poros_walls = utils.mean_harmonic(porosvec)
if trode == "a": # anode
# Potential at the current collector is from
# simulation
phi_tmp[0] = self.phi_cell()
# No current passes into the electrolyte
phi_tmp[-1] = phi_tmp[-2]
else: # cathode
phi_tmp[0] = phi_tmp[1]
# Potential at current at current collector is
# reference (set)
phi_tmp[-1] = ndD["phi_cathode"]
dx = ndD["L"][trode] / Nvol[trode]
dvg_curr_dens = np.diff(-poros_walls * ndD["sigma_s"][trode] *
np.diff(phi_tmp) / dx) / dx
# Actually set up the equations for bulk solid phi
for vInd in range(Nvol[trode]):
eq = self.CreateEquation("phi_ac_trode{trode}vol{vInd}".format(
vInd=vInd, trode=trode))
if simBulkCond:
eq.Residual = -dvg_curr_dens[vInd] - self.R_Vp[trode](vInd)
else:
if trode == "a": # anode
eq.Residual = self.phi_bulk[trode](
vInd) - self.phi_cell()
else: # cathode
eq.Residual = self.phi_bulk[trode](
vInd) - ndD["phi_cathode"]
# Simulate the potential drop along the connected
# particles
simPartCond = ndD['simPartCond'][trode]
for vInd in range(Nvol[trode]):
phi_bulk = self.phi_bulk[trode](vInd)
for pInd in range(Npart[trode]):
G_l = ndD["G"][trode][vInd, pInd]
phi_n = self.phi_part[trode](vInd, pInd)
if pInd == 0: # reference bulk phi
phi_l = phi_bulk
else:
phi_l = self.phi_part[trode](vInd, pInd - 1)
if pInd == (Npart[trode] -
1): # No particle at end of "chain"
G_r = 0
phi_r = phi_n
else:
G_r = ndD["G"][trode][vInd, pInd + 1]
phi_r = self.phi_part[trode](vInd, pInd + 1)
# charge conservation equation around this particle
eq = self.CreateEquation(
"phi_ac_trode{trode}vol{vInd}part{pInd}".format(
vInd=vInd, trode=trode, pInd=pInd))
if simPartCond:
# -dcsbar/dt = I_l - I_r
eq.Residual = (
self.particles[trode][vInd, pInd].dcbardt() +
((-G_l * (phi_n - phi_l)) - (-G_r *
(phi_r - phi_n))))
else:
eq.Residual = self.phi_part[trode](vInd,
pInd) - phi_bulk
# If we have a single electrode volume (in a perfect bath),
# electrolyte equations are simple
if self.SVsim:
eq = self.CreateEquation("c_lyte")
eq.Residual = self.c_lyte["c"].dt(0) - 0
eq = self.CreateEquation("phi_lyte")
eq.Residual = self.phi_lyte["c"](0) - self.phi_cell()
else:
disc = geom.get_elyte_disc(Nvol, ndD["L"], ndD["poros"],
ndD["BruggExp"])
cvec = utils.get_asc_vec(self.c_lyte, Nvol)
dcdtvec = utils.get_asc_vec(self.c_lyte, Nvol, dt=True)
phivec = utils.get_asc_vec(self.phi_lyte, Nvol)
Rvvec = utils.get_asc_vec(self.R_Vp, Nvol)
# Apply concentration and potential boundary conditions
# Ghost points on the left and no-gradients on the right
ctmp = np.hstack((self.c_lyteGP_L(), cvec, cvec[-1]))
phitmp = np.hstack((self.phi_lyteGP_L(), phivec, phivec[-1]))
# If we don't have a porous anode:
# 1) the total current flowing into the electrolyte is set
# 2) assume we have a Li foil with BV kinetics and the specified rate constant
eqC = self.CreateEquation("GhostPointC_L")
eqP = self.CreateEquation("GhostPointP_L")
if Nvol["a"] == 0:
# Concentration BC from mass flux
Nm_foil = get_lyte_internal_fluxes(ctmp[0:2], phitmp[0:2],
disc["dxd1"][0],
disc["eps_o_tau_edges"][0],
ndD)[0]
eqC.Residual = Nm_foil[0]
# Phi BC from BV at the foil
# We assume BV kinetics with alpha = 0.5,
# exchange current density, ecd = k0_foil * c_lyte**(0.5)
cWall = utils.mean_harmonic(ctmp[0], ctmp[1])
ecd = ndD["k0_foil"] * cWall**0.5
# -current = ecd*(exp(-eta/2) - exp(eta/2))
# note negative current because positive current is
# oxidation here
# -current = ecd*(-2*sinh(eta/2))
# eta = 2*arcsinh(-current/(-2*ecd))
BVfunc = -self.current() / ecd
eta_eff = 2 * np.arcsinh(-BVfunc / 2.)
eta = eta_eff + self.current() * ndD["Rfilm_foil"]
# # Infinitely fast anode kinetics
# eta = 0.
# eta = mu_R - mu_O = -mu_O (evaluated at interface)
# mu_O = [T*ln(c) +] phiWall - phi_cell = -eta
# phiWall = -eta + phi_cell [- T*ln(c)]
phiWall = -eta + self.phi_cell()
if ndD["elyteModelType"] == "dilute":
phiWall -= ndD["T"] * np.log(cWall)
# phiWall = 0.5 * (phitmp[0] + phitmp[1])
eqP.Residual = phiWall - utils.mean_linear(
phitmp[0], phitmp[1])
# We have a porous anode -- no flux of charge or anions through current collector
else:
eqC.Residual = ctmp[0] - ctmp[1]
eqP.Residual = phitmp[0] - phitmp[1]
Nm_edges, i_edges = get_lyte_internal_fluxes(
ctmp, phitmp, disc["dxd1"], disc["eps_o_tau_edges"], ndD)
dvgNm = np.diff(Nm_edges) / disc["dxd2"]
dvgi = np.diff(i_edges) / disc["dxd2"]
for vInd in range(Nlyte):
# Mass Conservation (done with the anion, although "c" is neutral salt conc)
eq = self.CreateEquation(
"lyte_mass_cons_vol{vInd}".format(vInd=vInd))
eq.Residual = disc["porosvec"][vInd] * dcdtvec[vInd] + (
1. / ndD["num"]) * dvgNm[vInd]
# Charge Conservation
eq = self.CreateEquation(
"lyte_charge_cons_vol{vInd}".format(vInd=vInd))
eq.Residual = -dvgi[vInd] + ndD["zp"] * Rvvec[vInd]
# Define the total current. This must be done at the capacity
# limiting electrode because currents are specified in
# C-rates.
eq = self.CreateEquation("Total_Current")
eq.Residual = self.current()
limtrode = ("c" if ndD["z"] < 1 else "a")
dx = 1. / Nvol[limtrode]
rxn_scl = ndD["beta"][limtrode] * (
1 - ndD["poros"][limtrode]) * ndD["P_L"][limtrode]
for vInd in range(Nvol[limtrode]):
if limtrode == "a":
eq.Residual -= dx * self.R_Vp[limtrode](vInd) / rxn_scl
else:
eq.Residual += dx * self.R_Vp[limtrode](vInd) / rxn_scl
# Define the measured voltage, offset by the "applied" voltage
# by any series resistance.
# phi_cell = phi_applied - I*R
eq = self.CreateEquation("Measured_Voltage")
eq.Residual = self.phi_cell() - (self.phi_applied() -
ndD["Rser"] * self.current())
if self.profileType == "CC":
# Total Current Constraint Equation
eq = self.CreateEquation("Total_Current_Constraint")
if ndD["tramp"] > 0:
eq.Residual = self.current() - (
ndD["currPrev"] + (ndD["currset"] - ndD["currPrev"]) *
(1 - np.exp(-dae.Time() / (ndD["tend"] * ndD["tramp"]))))
else:
eq.Residual = self.current() - ndD["currset"]
elif self.profileType == "CV":
# Keep applied potential constant
eq = self.CreateEquation("applied_potential")
if ndD["tramp"] > 0:
eq.Residual = self.phi_applied() - (
ndD["phiPrev"] + (ndD["Vset"] - ndD["phiPrev"]) *
(1 - np.exp(-dae.Time() / (ndD["tend"] * ndD["tramp"]))))
else:
eq.Residual = self.phi_applied() - ndD["Vset"]
elif self.profileType == "CCsegments":
if ndD["tramp"] > 0:
ndD["segments_setvec"][0] = ndD["currPrev"]
self.segSet = extern_funcs.InterpTimeScalar(
"segSet", self, dae.unit(), dae.Time(),
ndD["segments_tvec"], ndD["segments_setvec"])
eq = self.CreateEquation("Total_Current_Constraint")
eq.Residual = self.current() - self.segSet()
#CCsegments implemented as discontinuous equations
else:
#First segment
time = ndD["segments"][0][1]
self.IF(dae.Time() < dae.Constant(time * s), 1.e-3)
eq = self.CreateEquation("Total_Current_Constraint")
eq.Residual = self.current() - ndD["segments"][0][0]
#Middle segments
for i in range(1, len(ndD["segments"]) - 1):
time = time + ndD["segments"][i][1]
self.ELSE_IF(dae.Time() < dae.Constant(time * s), 1.e-3)
eq = self.CreateEquation("Total_Current_Constraint")
eq.Residual = self.current() - ndD["segments"][i][0]
#Last segment
self.ELSE()
eq = self.CreateEquation("Total_Current_Constraint")
eq.Residual = self.current() - ndD["segments"][-1][0]
self.END_IF()
elif self.profileType == "CVsegments":
if ndD["tramp"] > 0:
ndD["segments_setvec"][0] = ndD["phiPrev"]
self.segSet = extern_funcs.InterpTimeScalar(
"segSet", self, dae.unit(), dae.Time(),
ndD["segments_tvec"], ndD["segments_setvec"])
eq = self.CreateEquation("applied_potential")
eq.Residual = self.phi_applied() - self.segSet()
#CVsegments implemented as discontinuous equations
else:
#First segment
time = ndD["segments"][0][1]
self.IF(dae.Time() < dae.Constant(time * s), 1.e-3)
eq = self.CreateEquation("applied_potential")
eq.Residual = self.phi_applied() - ndD["segments"][0][0]
#Middle segments
for i in range(1, len(ndD["segments"]) - 1):
time = time + ndD["segments"][i][1]
self.ELSE_IF(dae.Time() < dae.Constant(time * s), 1.e-3)
eq = self.CreateEquation("applied_potential")
eq.Residual = self.phi_applied() - ndD["segments"][i][0]
#Last segment
self.ELSE()
eq = self.CreateEquation("applied_potential")
eq.Residual = self.phi_applied() - ndD["segments"][-1][0]
self.END_IF()
for eq in self.Equations:
eq.CheckUnitsConsistency = False
#Ending conditions for the simulation
if self.profileType in ["CC", "CCsegments"]:
#Vmax reached
self.ON_CONDITION((self.phi_applied() <= ndD["phimin"])
& (self.endCondition() < 1),
setVariableValues=[(self.endCondition, 1)])
#Vmin reached
self.ON_CONDITION((self.phi_applied() >= ndD["phimax"])
& (self.endCondition() < 1),
setVariableValues=[(self.endCondition, 2)])
def __init__(self, Name, ninemlComponent, Parent = None, Description = ""):
"""
Iterates over *Parameters*, *State variables*, *Aliases*, *Analogue ports*, *Event ports*,
*Sub-nodes* and *Port connections* and creates corresponding daetools objects.
:param Name: string
:param ninemlComponent: AL component object
:param Parent: daeModel-derived object
:param Description: string
:raises: RuntimeError
"""
#start = time()
daet.daeModel.__init__(self, Name, Parent, Description)
#print(' daeModel.__init__({0}) = {1}'.format(Name, time() - start))
start = time()
self.ninemlComponent = ninemlComponent
self.nineml_parameters = []
self.nineml_state_variables = []
self.nineml_aliases = []
self.nineml_analog_ports = []
self.nineml_reduce_ports = []
self.nineml_event_ports = []
self.ninemlSubComponents = []
# AL component may be None (useful in certain cases); therefore do not raise an exception
if not self.ninemlComponent:
return
# 1) Create parameters
for param in self.ninemlComponent.parameters:
self.nineml_parameters.append( daet.daeParameter(param.name, daet.unit(), self, "") )
# 2) Create state-variables (diff. variables)
for var in self.ninemlComponent.state_variables:
self.nineml_state_variables.append( daet.daeVariable(var.name, dae_nineml_t, self, "") )
# 3) Create alias variables (algebraic)
for alias in self.ninemlComponent.aliases:
self.nineml_aliases.append( daet.daeVariable(alias.lhs, dae_nineml_t, self, "") )
# 4) Create analog-ports and reduce-ports
for analog_port in self.ninemlComponent.analog_ports:
if analog_port.mode == 'send':
self.nineml_analog_ports.append( ninemlAnalogPort(analog_port.name, daet.eOutletPort, self, "") )
elif analog_port.mode == 'recv':
self.nineml_analog_ports.append( ninemlAnalogPort(analog_port.name, daet.eInletPort, self, "") )
elif analog_port.mode == 'reduce':
self.nineml_reduce_ports.append( ninemlReduceAnalogPort(analog_port.name, self) )
else:
raise RuntimeError("")
# 5) Create event-ports
for event_port in self.ninemlComponent.event_ports:
if event_port.mode == 'send':
self.nineml_event_ports.append( daet.daeEventPort(event_port.name, daet.eOutletPort, self, "") )
elif event_port.mode == 'recv':
self.nineml_event_ports.append( daet.daeEventPort(event_port.name, daet.eInletPort, self, "") )
else:
raise RuntimeError("")
# 6) Create sub-nodes
for name, subcomponent in list(self.ninemlComponent.subnodes.items()):
self.ninemlSubComponents.append( nineml_daetools_bridge(name, subcomponent, self, '') )
# 7) Create port connections
for port_connection in self.ninemlComponent.portconnections:
#print 'try to connect {0} to {1}'.format(port_connection[0].getstr('.'), port_connection[1].getstr('.'))
portFrom = getObjectFromNamespaceAddress(self, port_connection[0], look_for_ports = True, look_for_reduceports = True)
portTo = getObjectFromNamespaceAddress(self, port_connection[1], look_for_ports = True, look_for_reduceports = True)
#print ' {0} -> {1}\n'.format(type(portFrom), type(portTo))
connectPorts(portFrom, portTo, self)
# Search for the 'name' in the 'root' model (in the types of objects given in **kwargs)
return findObjectInModel(root, objectName, **kwargs)
def fixObjectName(name):
"""
Replaces spaces in the 'name' string with underscores and returns the modified string.
:param name: string
:rtype: string
:raises:
"""
new_name = name.replace(' ', '_')
return new_name
dae_nineml_t = daet.daeVariableType("dae_nineml_t", daet.unit(), -1.0e+20, 1.0e+20, 0.0, 1e-12)
class ninemlAnalogPort(daet.daePort):
"""
Represents NineML analogue ports with a single variable (referred to with the 'value' daet.daeVariable).
"""
def __init__(self, Name, PortType, Model, Description = ''):
"""
:param Name: string
:param PortType: daetools port type (eInlet, eOutlet, eInletOutlet)
:param Model: daeModel-derived object
:param Description: string
:raises: RuntimeError
"""
daet.daePort.__init__(self, Name, PortType, Model, Description)
def __init__(self, Name, ninemlComponent, Parent=None, Description=""):
"""
Iterates over *Parameters*, *State variables*, *Aliases*, *Analogue ports*, *Event ports*,
*Sub-nodes* and *Port connections* and creates corresponding daetools objects.
:param Name: string
:param ninemlComponent: AL component object
:param Parent: daeModel-derived object
:param Description: string
:raises: RuntimeError
"""
#start = time()
daet.daeModel.__init__(self, Name, Parent, Description)
#print(' daeModel.__init__({0}) = {1}'.format(Name, time() - start))
start = time()
self.ninemlComponent = ninemlComponent
self.nineml_parameters = []
self.nineml_state_variables = []
self.nineml_aliases = []
self.nineml_analog_ports = []
self.nineml_reduce_ports = []
self.nineml_event_ports = []
self.ninemlSubComponents = []
# AL component may be None (useful in certain cases); therefore do not raise an exception
if not self.ninemlComponent:
return
# 1) Create parameters
for param in self.ninemlComponent.parameters:
self.nineml_parameters.append(
daet.daeParameter(param.name, daet.unit(), self, ""))
# 2) Create state-variables (diff. variables)
for var in self.ninemlComponent.state_variables:
self.nineml_state_variables.append(
daet.daeVariable(var.name, dae_nineml_t, self, ""))
# 3) Create alias variables (algebraic)
for alias in self.ninemlComponent.aliases:
self.nineml_aliases.append(
daet.daeVariable(alias.lhs, dae_nineml_t, self, ""))
# 4) Create analog-ports and reduce-ports
for analog_port in self.ninemlComponent.analog_ports:
if analog_port.mode == 'send':
self.nineml_analog_ports.append(
ninemlAnalogPort(analog_port.name, daet.eOutletPort, self,
""))
elif analog_port.mode == 'recv':
self.nineml_analog_ports.append(
ninemlAnalogPort(analog_port.name, daet.eInletPort, self,
""))
elif analog_port.mode == 'reduce':
self.nineml_reduce_ports.append(
ninemlReduceAnalogPort(analog_port.name, self))
else:
raise RuntimeError("")
# 5) Create event-ports
for event_port in self.ninemlComponent.event_ports:
if event_port.mode == 'send':
self.nineml_event_ports.append(
daet.daeEventPort(event_port.name, daet.eOutletPort, self,
""))
elif event_port.mode == 'recv':
self.nineml_event_ports.append(
daet.daeEventPort(event_port.name, daet.eInletPort, self,
""))
else:
raise RuntimeError("")
# 6) Create sub-nodes
for name, subcomponent in list(self.ninemlComponent.subnodes.items()):
self.ninemlSubComponents.append(
nineml_daetools_bridge(name, subcomponent, self, ''))
# 7) Create port connections
for port_connection in self.ninemlComponent.portconnections:
#print 'try to connect {0} to {1}'.format(port_connection[0].getstr('.'), port_connection[1].getstr('.'))
portFrom = getObjectFromNamespaceAddress(self,
port_connection[0],
look_for_ports=True,
look_for_reduceports=True)
portTo = getObjectFromNamespaceAddress(self,
port_connection[1],
look_for_ports=True,
look_for_reduceports=True)
#print ' {0} -> {1}\n'.format(type(portFrom), type(portTo))
connectPorts(portFrom, portTo, self)
def fixObjectName(name):
"""
Replaces spaces in the 'name' string with underscores and returns the modified string.
:param name: string
:rtype: string
:raises:
"""
new_name = name.replace(' ', '_')
return new_name
dae_nineml_t = daet.daeVariableType("dae_nineml_t", daet.unit(), -1.0e+20,
1.0e+20, 0.0, 1e-12)
class ninemlAnalogPort(daet.daePort):
"""
Represents NineML analogue ports with a single variable (referred to with the 'value' daet.daeVariable).
"""
def __init__(self, Name, PortType, Model, Description=''):
"""
:param Name: string
:param PortType: daetools port type (eInlet, eOutlet, eInletOutlet)
:param Model: daeModel-derived object
:param Description: string
:raises: RuntimeError
"""This defines the ports by which mod_cell interacts with mod_electrodes."""
import daetools.pyDAE as dae
mole_frac_t = dae.daeVariableType(
name="mole_frac_t", units=dae.unit(), lowerBound=0,
upperBound=1, initialGuess=0.25, absTolerance=1e-6)
elec_pot_t = dae.daeVariableType(
name="elec_pot_t", units=dae.unit(), lowerBound=-1e20,
upperBound=1e20, initialGuess=0, absTolerance=1e-5)
class portFromElyte(dae.daePort):
def __init__(self, Name, PortType, Model, Description=""):
dae.daePort.__init__(self, Name, PortType, Model, Description)
self.c_lyte = dae.daeVariable(
"c_lyte", mole_frac_t, self,
"Concentration in the electrolyte")
self.phi_lyte = dae.daeVariable(
"phi_lyte", elec_pot_t, self,
"Electric potential in the electrolyte")
class portFromBulk(dae.daePort):
def __init__(self, Name, PortType, Model, Description=""):
dae.daePort.__init__(self, Name, PortType, Model, Description)
self.phi_m = dae.daeVariable(
"phi_m", elec_pot_t, self,
"Electric potential in the e- conducting phase")