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 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_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_energy_balance(self):
"""
This method writes the mass balance to the correspondent node instance
:return:
"""
# Starting with the external mass flow rate
cp_ext = heat_capacity(self.Text()/Constant(1*K), self.data['parameters']['Pext'], simplified=True)
residual_aux = self.w() * self.Text() * cp_ext * Constant(1 * (J ** (1)) * (K ** (-1)) * (kg ** (-1)))
for edge_name in self.get_inlet():
residual_aux += self.Parent.submodels[edge_name].Hub()
# Mass to the node outlet
for edge_name in self.get_outlet():
residual_aux -= self.Parent.submodels[edge_name].Hlb()
eq = self.CreateEquation("NEB_source_energy_balance_2")
eq.Residual = residual_aux
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
