def eq_calculate_hext(self):
eq = self.CreateEquation("Hext", "Heat balance - Hext")
xdomains = distribute_on_domains(self.XDomains, eq, eClosedClosed)
ydomains = distribute_on_domains(self.YDomains, eq, eClosedClosed)
domains = xdomains + ydomains
g = self.g
Text = self.Text()
Do = self.Do()
To = daeVariable_wrapper(self.To, domains)
hext = daeVariable_wrapper(self.hext, domains)
fNtub = daeVariable_wrapper(self.fNtub, ydomains)
Tast = 0.5 * (Text + To) / Constant(1 * K)
Past = self.Pext() / Constant(1 * Pa)
hvap = vaporization_enthalpy(Past, simplified = True) * Constant(1 * J * (kg**-1) )
rhov = vapour_density( Past, simplified = True) * Constant(1 * (kg ** (1))*(m ** (-3)))
rho_o = density( Tast, Past, simplified = True) * Constant(1 * (kg ** (1))*(m ** (-3)))
mu_o = viscosity( Tast, Past, simplified = True) * Constant(1 * (Pa ** (1))*(s ** (1)))
kappa_o = conductivity( Tast, Past, simplified = True) * Constant(1 * (K ** (-1))*(W ** (1))*(m ** (-1)))
num = (g * rho_o * (rho_o - rhov) * kappa_o ** 3 * hvap)
den = mu_o * Abs(Text - To) * Do
hd1 = (0.729 * (num / den) ** 0.25)
eq.Residual = hext - fNtub * hd1
def eq_fD(self):
eq = self.CreateEquation("fDturb", "Turbulent darcy factor")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
fD = daeVariable_wrapper(self.fD, domains)
v = daeVariable_wrapper(self.v, domains)
D = daeVariable_wrapper(self.D, domains)
T = daeVariable_wrapper(self.T, domains)
P = daeVariable_wrapper(self.P, domains)
Tast = T / Constant(1 * K)
Past = P / Constant(1 * Pa)
mu = viscosity(Tast, Past, simplified=True) * Constant(1 * (Pa**(1)) *
(s**(1)))
rho = density(Tast, Past, simplified=True) * Constant(1 * (kg**(1)) *
(m**(-3)))
Re = D * Abs(v) * rho / mu
A = (2.457 * Log(((7 / Re)**0.9 + 0.27 * self.epw() / D)**-1))**16
B = (37530 / Re)**16
ff = 2 * ((8 / Re)**12 + (A + B)**-1.5)**(1 / 12)
eq.Residual = fD - 4 * ff
def eq_heat_balance(self):
eq = self.CreateEquation("HeatBal", "Heat balance - T")
ydomains = distribute_on_domains(self.YDomains, eq, eClosedClosed)
xdomains = distribute_on_domains(self.XDomains, eq, eOpenClosed)
domains = xdomains + ydomains
L = self.L()
D = daeVariable_wrapper(self.D, domains)
k = daeVariable_wrapper(self.k, domains)
Qout = daeVariable_wrapper(self.Qout, domains)
T = daeVariable_wrapper(self.T, domains)
P = daeVariable_wrapper(self.P, domains)
Tast = T / Constant(1 * K)
Past = P / Constant(1 * Pa)
cp = heat_capacity(Tast, Past, simplified=True) * Constant(1 *
(J**(1)) *
(K**(-1)) *
(kg**(-1)))
rho = density(Tast, Past, simplified=True) * Constant(1 * (kg**(1)) *
(m**(-3)))
A = 0.25 * 3.14 * D**2
eq.Residual = self.dt(rho * cp * A * T) + \
d(k * cp * T, self.x, eCFDM) / L - \
Qout
def eq_calculate_Ti(self):
eq = self.CreateEquation("WallHeat", "Heat balance - wall")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
Qout = daeVariable_wrapper(self.Qout, domains)
To = daeVariable_wrapper(self.To, domains)
Ti = daeVariable_wrapper(self.Ti, domains)
Reswall = Log(self.Do() / self.Di()) / (2 * self.pi * self.kwall())
eq.Residual = Qout - (To - Ti ) / Reswall
def eq_Rf(self):
eq = self.CreateEquation("Rf", "Rf")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
D = daeVariable_wrapper(self.D, domains)
Rf = daeVariable_wrapper(self.Rf, domains)
kf = self.kf
Di = self.Di()
eq.Residual = Rf - Di * Log(Di / D) / (2 * kf)
def eq_internal_diameter(self):
eq = self.CreateEquation("D", "D_internal_flow_diameter")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
D = daeVariable_wrapper(self.D, domains)
mf = daeVariable_wrapper(self.mf, domains)
rhof = self.rhof
Di = self.Di()
eq.Residual = D - Sqrt(Di**2 - 4 * mf * Di / rhof)
def eq_calculate_To(self):
eq = self.CreateEquation("WallHeat1", "Heat balance - wall")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
Do = self.Do()
Text = self.Text()
pi = self.pi
To = daeVariable_wrapper(self.To, domains)
hext = daeVariable_wrapper(self.hext, domains)
Qout = daeVariable_wrapper(self.Qout, domains)
eq.Residual = Qout - (Text - To) * (pi * Do * hext)
def eq_calculate_Ti(self):
eq = self.CreateEquation("WallHeat2", "Heat balance - wall")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
kwall = self.kwall()
Do = self.Do()
Di = self.Di()
pi = self.pi
Ti = daeVariable_wrapper(self.Ti, domains)
To = daeVariable_wrapper(self.To, domains)
Qout = daeVariable_wrapper(self.Qout, domains)
eq.Residual = Qout * Log(Do / Di) - (To - Ti) * (2 * pi * kwall)
def eq_phid(self):
eq = self.CreateEquation("phid", "phid")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
k2 = self.k2
ksp = self.ksp
conc_H = 10**(-self.pH())
conc_Ca = self.Ca() / 1000 / 40.078
conc_CO3 = k2 * self.Alc() / 1000 / (100.0869 * (conc_H + 2 * k2))
phid = daeVariable_wrapper(self.phid, domains)
D = daeVariable_wrapper(self.D, domains)
v = daeVariable_wrapper(self.v, domains)
T = daeVariable_wrapper(self.T, domains)
P = daeVariable_wrapper(self.P, domains)
#Tast = 35+273.15
Tast = T / Constant(1 * K)
Past = P / Constant(1 * Pa)
vast = v / Constant(1 * m / s)
rho = density(Tast, Past, simplified=True) * Constant(1 * (kg**(1)) *
(m**(-3)))
kappa = conductivity(Tast, Past, simplified=True) * Constant(
1 * (K**(-1)) * (W**(1)) * (m**(-1)))
muast = viscosity(Tast, Past, simplified=True)
mu = muast * Constant(1 * (Pa**(1)) * (s**(1)))
Re = D * v * rho / mu
kr = Exp(38.74 - Constant(20700.0 * 4.184 * J / mol) / (self.Rg * T))
Dab = Constant(3.07e-15 * m**2 / s) * (Tast / muast)
Sc = mu / (rho * Dab)
kd = 0.023 * vast * Re**-0.17 * Sc**-0.67
# eq.Residual = phid - 24 * 3600 * Constant(1 * kg * m ** -2 * s ** -1) * kd * \
# conc_CO3 * (1 - ksp / (conc_Ca * conc_CO3)) / \
# (1 + kd / (kr * conc_CO3) + conc_CO3 / conc_Ca)
eq.Residual = phid - Constant(1 * kg * m ** -2 * s ** -1) * kd * \
conc_CO3 * (1 - ksp / (conc_Ca * conc_CO3)) / \
(1 + kd / (kr * conc_CO3) + conc_CO3 / conc_Ca)
def eq_entalphy(self):
eq = self.CreateEquation("Entalphy", "Fluid Entalphy")
xdomains = distribute_on_domains(self.XDomains, eq, eClosedClosed)
ydomains = distribute_on_domains(self.YDomains, eq, eClosedClosed)
domains = xdomains + ydomains
k = daeVariable_wrapper(self.k, domains)
H = daeVariable_wrapper(self.H, domains)
T = daeVariable_wrapper(self.T, domains)
P = daeVariable_wrapper(self.P, domains)
Tast = T / Constant(1 * K)
Past = P / Constant(1 * Pa)
cp = heat_capacity( Tast, Past, simplified = True) * Constant(1 * (J ** (1))*(K ** (-1))*(kg ** (-1)))
eq.Residual = k * cp * T - H
def eq_total_he(self):
eq = self.CreateEquation("TotalHeat", "Heat balance - Qout")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
T = daeVariable_wrapper(self.T, domains)
To = daeVariable_wrapper(self.To, domains)
Qout = daeVariable_wrapper(self.Qout, domains)
hint = daeVariable_wrapper(self.hint, domains)
D = daeVariable_wrapper(self.D, domains)
Resint = 1 / (self.pi * D * hint) # mK/W
Reswall = Log(self.Do() / self.Di()) / (2 * self.pi * self.kwall()) # mK/W
# TODO - Lembrar de colocar o Refilme no caso com Biofilme
#Resfilm = Log(self.Di() / self.D()) / (2 * self.pi * self.kappa())
Resistance = (Resint + Reswall + self.ResF() * self.pi * D) # mK/W
eq.Residual = Qout * Resistance - ( To - T)
def eq_upperbound_pressureloss(self):
eq = self.CreateEquation("UpperBoundPressureLoss", "Upper Bound Pressure Loss")
xdomains = distribute_on_domains(self.XDomains, eq, eUpperBound)
ydomains = distribute_on_domains(self.YDomains, eq, eClosedClosed)
domains = xdomains + ydomains
dPub = daeVariable_wrapper(self.dPub, ydomains)
T = daeVariable_wrapper(self.T, domains)
P = daeVariable_wrapper(self.P, domains)
v = daeVariable_wrapper(self.v, domains)
Kub = self.Kub()
Tast = T / Constant(1 * K)
Past = P / Constant(1 * Pa)
rho = density(Tast, Past, simplified=True) * Constant(1 * (kg ** (1)) * (m ** (-3)))
eq.Residual = dPub - 0.5 * Kub * rho * v ** 2
def eq_ep(self):
eq = self.CreateEquation("Roughness", "Roughness")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
ep = daeVariable_wrapper(self.ep, domains)
epw = self.epw()
eq.Residual = ep - epw
def eq_internal_diameter(self):
eq = self.CreateEquation("D", "D_internal_flow_diameter")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
Di = self.Di()
D = daeVariable_wrapper(self.D, domains)
eq.Residual = D - Di
def eq_total_he(self):
eq = self.CreateEquation("TotalHeat", "Heat balance - Qout")
Text = self.Text()
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
T = daeVariable_wrapper(self.T, domains)
Qout = daeVariable_wrapper(self.Qout, domains)
hint = daeVariable_wrapper(self.hint, domains)
hext = daeVariable_wrapper(self.hext, domains)
D = daeVariable_wrapper(self.D, domains)
Resint = 1 / (self.pi * D * hint) # mK/W
Reswall = Log(self.Do() / self.Di()) / (2 * self.pi * self.kwall()) # mK/W
#Resfilm = Log(self.Di() / D) / (2 * self.pi * self.kappa())
Resext = 1 / (self.pi * self.Do() * hext)
#Resistance = (Resext + Resint + Reswall + Resfilm + self.ResF() * self.L()) # mK/W
Resistance = (Resext + Resint + Reswall + self.ResF() * self.L()) # mK/W
eq.Residual = Qout * Resistance - ( Text - T )
def eq_velocity(self):
eq = self.CreateEquation("v", "v_fluid_velocity")
xdomains = distribute_on_domains(self.XDomains, eq, eClosedClosed)
ydomains = distribute_on_domains(self.YDomains, eq, eClosedClosed)
domains = xdomains + ydomains
k = daeVariable_wrapper(self.k, domains)
D = daeVariable_wrapper(self.D, domains)
v = daeVariable_wrapper(self.v, domains)
T = daeVariable_wrapper(self.T, domains)
P = daeVariable_wrapper(self.P, domains)
Tast = T / Constant(1 * K)
Past = P / Constant(1 * Pa)
rho = density( Tast, Past, simplified = True) * Constant(1 * (kg ** (1))*(m ** (-3)))
A = 0.25 * 3.14 * D ** 2
eq.Residual = v - k / ( rho * A )
def eq_mass_balance(self):
eq = self.CreateEquation("MassBal", "Mass balance")
ydomains = distribute_on_domains(self.YDomains, eq, eClosedClosed)
xdomains = distribute_on_domains(self.XDomains, eq, eOpenClosed)
domains = xdomains + ydomains
L = self.L()
k = daeVariable_wrapper(self.k, domains)
D = daeVariable_wrapper(self.D, domains)
T = daeVariable_wrapper(self.T, domains)
P = daeVariable_wrapper(self.P, domains)
Tast = T / Constant(1 * K)
Past = P / Constant(1 * Pa)
rho = density( Tast, Past, simplified = True) * Constant(1 * (kg ** (1))*(m ** (-3)))
Area = 0.25 * 3.14 * D ** 2
eq.Residual = self.dt(rho * Area ) + 24 * 3600 * d(k, self.x, eCFDM) / L
def eq_mommentum_balance(self):
eq = self.CreateEquation("MomBal", "Momentum balance")
ydomains = distribute_on_domains(self.YDomains, eq, eClosedClosed)
xdomains = distribute_on_domains(self.XDomains, eq, eOpenClosed)
domains = xdomains + ydomains
g = self.g
L = self.L()
tetha = self.tetha()
k = daeVariable_wrapper(self.k, domains)
fD = daeVariable_wrapper(self.fD, domains)
v = daeVariable_wrapper(self.v, domains)
D = daeVariable_wrapper(self.D, domains)
T = daeVariable_wrapper(self.T, domains)
P = daeVariable_wrapper(self.P, domains)
Tast = T / Constant(1 * K)
Past = P / Constant(1 * Pa)
rho = density( Tast, Past, simplified = True) * Constant(1 * (kg ** (1))*(m ** (-3)))
hL = 0.5 * fD * (v ** 2) / ( D * g )
DeltaP = g * rho * hL
A = 0.25 * 3.14 * D ** 2
eq.Residual = A * d(P, self.x,eCFDM) / L + \
A * DeltaP + A * rho * g * Sin(tetha)
def eq_calculate_hint(self):
eq = self.CreateEquation("InternalConvection", "Internal convection - hint")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
T = daeVariable_wrapper(self.T, domains)
P = daeVariable_wrapper(self.P, domains)
fD = daeVariable_wrapper(self.fD, domains)
hint = daeVariable_wrapper(self.hint, domains)
D = daeVariable_wrapper(self.D, domains)
v = daeVariable_wrapper(self.v, domains)
# Calculates the Nussel dimensionless number using Petukhov correlation modified by Gnielinski. See Incropera 4th Edition [8.63]
mu = viscosity( T / Constant(1 * K) , P / Constant(1 * Pa), simplified = True)
kappa = conductivity( T / Constant(1 * K), P / Constant(1 * Pa), simplified = True)
cp = heat_capacity( T / Constant(1 * K), P / Constant(1 * Pa), simplified = True)
rho = density( T / Constant(1 * K), P / Constant(1 * Pa), simplified = True)
Dast = D / Constant(1 * m )
vast = v / Constant(1 * m * s ** -1)
Re = Dast * Abs(vast) * rho / mu
prandtl = cp * mu / kappa
nusselt = (fD / 8.) * (Re - 1000.) * prandtl / (
1. + 12.7 * Sqrt(fD / 8.) * (prandtl ** (2 / 3)) - 1.)
eq.Residual = hint - nusselt * kappa / Dast * Constant(1 * W/(K * m**2))
def eq_film(self):
self.stnFouling = self.STN("stnFouling")
self.STATE("Static")
eq = self.CreateEquation("FilmOFF", "Film - OFF")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
mf = daeVariable_wrapper(self.mf, domains)
eq.Residual = mf - self.mfi()
self.STATE("Dynamic")
self.IF(Time() < 0.1 * Constant(1 * s), eventTolerance=1E-1)
eq = self.CreateEquation("FilmOFF", "Film - OFF")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
mf = daeVariable_wrapper(self.mf, domains)
eq.Residual = mf - self.mfi()
self.ELSE()
eq = self.CreateEquation("FilmON", "Film - ON")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
mf = daeVariable_wrapper(self.mf, domains)
phid = daeVariable_wrapper(self.phid, domains)
phir = daeVariable_wrapper(self.phir, domains)
#sigmoidal = 1/(1+np.exp( 3 * ( 30 - Time() / Constant(1 * s)) )) - 1/(1+np.exp( 3 * (30 - 0.1 ) ))
#sigmoidal = 1 #FORCED
eq.Residual = self.dt(mf) - (phid - phir)
# eq.Residual = self.dt(mf) - sigmoidal * (phid - phir)
self.END_IF()
self.END_STN()
def eq_phir(self):
eq = self.CreateEquation("phir", "phir")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
phir = daeVariable_wrapper(self.phir, domains)
phid = daeVariable_wrapper(self.phid, domains)
D = daeVariable_wrapper(self.D, domains)
v = daeVariable_wrapper(self.v, domains)
kf = self.kf
rhof = self.rhof
psi = self.psi
Di = self.Di()
espes = (Di - D) / 2
vast = v / Constant(1 * m / s)
kfast = kf / Constant(1 * (W**(1)) * (m**(-1)) * (K**(-1)))
espesast = espes / Constant(1 * m)
rhofast = rhof / Constant(1 * kg / m**3)
eq.Residual = phir - phid * 0.00212 * vast**2 / (Sqrt(kfast) * psi)
def eq_total_he(self):
eq = self.CreateEquation("TotalHeat", "Heat balance - Qout")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
Text = self.Text()
T = daeVariable_wrapper(self.T, domains)
Qout = daeVariable_wrapper(self.Qout, domains)
hext = daeVariable_wrapper(self.hext, domains)
hint = daeVariable_wrapper(self.hint, domains)
D = daeVariable_wrapper(self.D, domains)
Rf = daeVariable_wrapper(self.Rf, domains)
kwall = self.kwall()
Do = self.Do()
Di = self.Di()
pi = self.pi
Resext = 1 / (pi * Do * hext)
Resint = 1 / (pi * D * hint)
Reswall = Log(Do / Di) / (2 * pi * kwall)
eq.Residual = Qout * (Resint + Reswall + Resext + Rf /
(Di * pi)) - (Text - T)
def eq_total_he(self):
eq = self.CreateEquation("TotalHeat", "Heat balance - Qout")
domains = distribute_on_domains(self.Domains, eq, eClosedClosed)
Qout = daeVariable_wrapper(self.Qout, domains)
eq.Residual = Qout
