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_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_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_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 calculate_ext(Tvap, Pvap, To, fNtub_tube, L, Do):
# Calculating properties
T = 0.5 * (Tvap + To)
g = 9.80665
film_density = density(T, Pvap, simplified=True)
film_heat_capacity = heat_capacity(T, Pvap, simplified=True)
film_conductivity = conductivity(T, Pvap, simplified=True)
film_viscosity = viscosity(T, Pvap, simplified=True)
film_prandtl = film_heat_capacity * film_viscosity / film_conductivity
exhaust_steam_density = vapour_density(Pvap, simplified=True)
exhaust_vaporization_heat = vaporization_enthalpy(Pvap, simplified=True)
num = (g * film_density * (film_density - exhaust_steam_density) *
film_conductivity**3. * exhaust_vaporization_heat)
den = film_viscosity * (Tvap - To) * Do
hext_row1 = 0.729 * (num / den)**0.25
Resext_row1 = 1 / (pi * Do * hext_row1 * L)
hext = hext_row1 * fNtub_tube
Resext = Resext_row1 / fNtub_tube
return hext, Resext, exhaust_vaporization_heat
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_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_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 calculate_int(Tin, Tout, Pin, Pout, m_tube, ep, Df, L, Di):
g = 9.81
T = 0.5 * (Tin + Tout)
P = 0.5 * (Pin + Pout)
# Calculating properties
int_film_density = density(T, P, simplified=True)
int_film_heat_capacity = heat_capacity(T, P, simplified=True)
int_film_conductivity = conductivity(T, P, simplified=True)
int_film_viscosity = viscosity(T, P, simplified=True)
int_film_prandtl = int_film_heat_capacity * int_film_viscosity / int_film_conductivity
v = (m_tube / int_film_density) / (0.25 * pi * Df**2) # m/s
v_abs = abs(v)
Re_tube = Df * int_film_density * v_abs / int_film_viscosity
ff = calculate_fanning(ep, Df, Re_tube)
fD_tube = 4 * ff
# Calculating Darcy
int_film_Re = Df * int_film_density * v_abs / int_film_viscosity
int_film_fD = calculate_darcy(fD_tube, ep, Df, int_film_Re)
# Calculates the Nussel dimensionless number using Petukhov correlation modified by Gnielinski. See Incropera 4th Edition [8.63]
nusselt = (int_film_fD / 8.) * (int_film_Re - 1000.) * int_film_prandtl / (
1. + 12.7 * (int_film_fD / 8.)**0.5 * (int_film_prandtl**(2 / 3) - 1.))
hint = nusselt * int_film_conductivity / Di # W/m2K
Resint = 1 / (pi * Df * hint * L) # W/K
tau = (1 / 8) * fD_tube * int_film_density * v**2
hL = 0.5 * fD_tube * v**2 / (Di * g)
DeltaP = g * int_film_density * hL
pressure_loss_in_tube = DeltaP * L
Pout_ = Pin - pressure_loss_in_tube
return hint, Resint, int_film_heat_capacity, Pout_, fD_tube, pressure_loss_in_tube, v, Re_tube, int_film_density, int_film_viscosity