def calc_lhv(self):
r"""
Calculate the lower heating value of the combustion chambers fuel.
Returns
-------
val : float
Lower heating value of the combustion chambers fuel.
.. math::
LHV = \sum_{fuels} \left(-\frac{\sum_i {\Delta H_f^0}_i -
\sum_j {\Delta H_f^0}_j }
{M_{fuel}} \cdot x_{fuel} \right)\\
\forall i \in \text{reation products},\\
\forall j \in \text{reation educts},\\
\forall fuel \in \text{fuels},\\
\Delta H_f^0: \text{molar formation enthalpy},\\
x_{fuel}: \text{mass fraction of fuel in fuel mixture}
"""
hf = {}
hf['hydrogen'] = 0
hf['methane'] = -74.85
hf['ethane'] = -84.68
hf['propane'] = -103.8
hf['butane'] = -124.51
hf['O2'] = 0
hf['CO2'] = -393.5
# water (gaseous)
hf['H2O'] = -241.8
lhv = 0
for f, x in self.fuel.val.items():
molar_masses[f] = CP.PropsSI('M', f)
fl = set(list(hf.keys())).intersection(
set([a.replace(' ', '') for a in CP.get_aliases(f)]))
if len(fl) == 0:
continue
if list(fl)[0] in self.fuels():
structure = fluid_structure(f)
n = {}
for el in ['C', 'H', 'O']:
if el in structure.keys():
n[el] = structure[el]
else:
n[el] = 0
lhv += (-(n['H'] / 2 * hf['H2O'] + n['C'] * hf['CO2'] -
((n['C'] + n['H'] / 4) * hf['O2'] +
hf[list(fl)[0]])) / molar_masses[f] * 1000) * x
return lhv
def fluid_header(Fluid):
aliases = CP.get_aliases(str(Fluid))
aliases = ', '.join(['``' + a.strip() + '``' for a in aliases])
BTC = BibTeXerClass()
EOSkey = CP.get_BibTeXKey(Fluid, "EOS")
CP0key = CP.get_BibTeXKey(Fluid, "CP0")
SURFACE_TENSIONkey = CP.get_BibTeXKey(Fluid, "SURFACE_TENSION")
VISCOSITYkey = CP.get_BibTeXKey(Fluid, "VISCOSITY")
CONDUCTIVITYkey = CP.get_BibTeXKey(Fluid, "CONDUCTIVITY")
ECS_LENNARD_JONESkey = CP.get_BibTeXKey(Fluid, "ECS_LENNARD_JONES")
ECS_FITSkey = CP.get_BibTeXKey(Fluid, "ECS_FITS")
BibInfo = ''
if EOSkey:
BibInfo += '**Equation of State**: ' + BTC.entry2rst(EOSkey) + '\n\n'
if CP0key:
BibInfo += '**Ideal-Gas Specific Heat**: ' + BTC.entry2rst(
CP0key) + '\n\n'
if SURFACE_TENSIONkey:
BibInfo += '**Surface Tension**: ' + BTC.entry2rst(
SURFACE_TENSIONkey) + '\n\n'
if VISCOSITYkey:
BibInfo += '**Viscosity**: ' + BTC.entry2rst(VISCOSITYkey) + '\n\n'
if CONDUCTIVITYkey:
BibInfo += '**Conductivity**: ' + BTC.entry2rst(
CONDUCTIVITYkey) + '\n\n'
if ECS_LENNARD_JONESkey:
BibInfo += '**Lennard-Jones Parameters for ECS**: ' + BTC.entry2rst(
ECS_LENNARD_JONESkey) + '\n\n'
if ECS_FITSkey:
BibInfo += '**ECS Correction Fit**: ' + BTC.entry2rst(
ECS_FITSkey) + '\n\n'
return textwrap.dedent("""
********************
{Fluid:s}
********************
Aliases
================================================================================
{Aliases:s}
Bibliographic Information
=========================
{Reference:s}
""".format(
Fluid=Fluid,
Aliases=aliases,
Reference=BibInfo,
))
def fluid_header(Fluid):
aliases = CP.get_aliases(str(Fluid))
aliases = ', '.join(['``'+a.strip()+'``' for a in aliases])
BTC = BibTeXerClass()
EOSkey = CP.get_BibTeXKey(Fluid, "EOS")
CP0key = CP.get_BibTeXKey(Fluid, "CP0")
SURFACE_TENSIONkey = CP.get_BibTeXKey(Fluid, "SURFACE_TENSION")
VISCOSITYkey = CP.get_BibTeXKey(Fluid, "VISCOSITY")
CONDUCTIVITYkey = CP.get_BibTeXKey(Fluid, "CONDUCTIVITY")
ECS_LENNARD_JONESkey = CP.get_BibTeXKey(Fluid, "ECS_LENNARD_JONES")
ECS_FITSkey = CP.get_BibTeXKey(Fluid, "ECS_FITS")
BibInfo = ''
if EOSkey:
BibInfo += '**Equation of State**: ' + BTC.entry2rst(EOSkey) + '\n\n'
if CP0key:
BibInfo += '**Ideal-Gas Specific Heat**: ' + BTC.entry2rst(CP0key) + '\n\n'
if SURFACE_TENSIONkey:
BibInfo += '**Surface Tension**: ' + BTC.entry2rst(SURFACE_TENSIONkey) + '\n\n'
if VISCOSITYkey:
BibInfo += '**Viscosity**: ' + BTC.entry2rst(VISCOSITYkey) + '\n\n'
if CONDUCTIVITYkey:
BibInfo += '**Conductivity**: ' + BTC.entry2rst(CONDUCTIVITYkey) + '\n\n'
if ECS_LENNARD_JONESkey:
BibInfo += '**Lennard-Jones Parameters for ECS**: ' + BTC.entry2rst(ECS_LENNARD_JONESkey) + '\n\n'
if ECS_FITSkey:
BibInfo += '**ECS Correction Fit**: ' + BTC.entry2rst(ECS_FITSkey) + '\n\n'
return textwrap.dedent(
"""
********************
{Fluid:s}
********************
Aliases
================================================================================
{Aliases:s}
Bibliographic Information
=========================
{Reference:s}
""".format(Fluid=Fluid,
Aliases = aliases,
Reference = BibInfo,
)
)
def calc_lhv(self, f):
r"""
Calculate the lower heating value of the combustion chamber's fuel.
- Source for fluids O2, H2O and CO2: :cite:`CODATA1989`
- Source for all other fluids: :cite:`CRCHandbook2021`
Parameters
----------
f : str
Alias of the fuel.
Returns
-------
val : float
Lower heating value of the combustion chambers fuel.
.. math::
LHV = -\frac{\sum_i {\Delta H_f^0}_i -
\sum_j {\Delta H_f^0}_j }
{M_{fuel}}\\
\forall i \in \text{reation products},\\
\forall j \in \text{reation educts},\\
\Delta H_f^0: \text{molar formation enthalpy}
"""
hf = {}
hf['hydrogen'] = 0
hf['methane'] = -74.6
hf['ethane'] = -84.0
hf['propane'] = -103.8
hf['butane'] = -125.7
hf['nDodecane'] = -289.4
hf[self.o2] = 0
hf[self.co2] = -393.51
# water (gaseous)
hf[self.h2o] = -241.826
key = set(list(hf.keys())).intersection(
set([a.replace(' ', '') for a in CP.get_aliases(f)]))
val = (-(self.fuels[f]['H'] / 2 * hf[self.h2o] +
self.fuels[f]['C'] * hf[self.co2] -
((self.fuels[f]['C'] + self.fuels[f]['H'] / 4) * hf[self.o2] +
hf[list(key)[0]])) / molar_masses[f] * 1000)
return val
def comp_init(self, nw):
if not self.P.is_set:
self.set_attr(P='var')
msg = ('The power output of cogeneration units must be set! '
'We are adding the power output of component ' +
self.label + ' as custom variable of the system.')
logging.info(msg)
component.comp_init(self, nw)
o2 = [x for x in nw.fluids if x in [
a.replace(' ', '') for a in CP.get_aliases('O2')]]
if len(o2) == 0:
msg = ('Missing oxygen in network fluids, component ' +
self.label + ' of type ' + self.component() +
' requires oxygen in network fluids.')
logging.error(msg)
raise ValueError(msg)
else:
self.o2 = o2[0]
h2o = [x for x in nw.fluids if x in [
a.replace(' ', '') for a in CP.get_aliases('H2O')]]
if len(h2o) == 0:
msg = ('Missing water in network fluids, component ' +
self.label + ' of type ' + self.component() +
' requires water in network fluids.')
logging.error(msg)
raise ValueError(msg)
else:
self.h2o = h2o[0]
h2 = [x for x in nw.fluids if x in [
a.replace(' ', '') for a in CP.get_aliases('H2')]]
if len(h2) == 0:
msg = ('Missing hydrogen in network fluids, component ' +
self.label + ' of type ' + self.component() +
' requires hydrogen in network fluids.')
logging.error(msg)
raise ValueError(msg)
else:
self.h2 = h2[0]
self.e0 = self.calc_e0()
# number of mandatroy equations for
# cooling loop fluids: num_fl
# fluid composition at reactor inlets/outlets: 3 * num_fl
# mass flow balances: 3
# pressure: 2
# energy balance: 1
# reactor outlet temperatures: 1
self.num_eq = self.num_nw_fluids * 4 + 7
for var in [self.e, self.eta, self.eta_char, self.Q, self.pr_c,
self.zeta]:
if var.is_set is True:
self.num_eq += 1
self.mat_deriv = np.zeros((
self.num_eq,
self.num_i + self.num_o + self.num_vars,
self.num_nw_vars))
self.vec_res = np.zeros(self.num_eq)
pos = self.num_nw_fluids * 4
self.mat_deriv[0:pos] = self.fluid_deriv()
self.mat_deriv[pos:pos + 3] = self.mass_flow_deriv()
self.mat_deriv[pos + 3:pos + 5] = self.pressure_deriv()
def stoich_flue_gas(self, nw):
r"""
Calculate the fluid composition of the stoichiometric flue gas.
- uses one mole of fuel as reference quantity and :math:`\lambda=1`
for stoichiometric flue gas calculation (no oxygen in flue gas)
- calculate molar quantities of (reactive) fuel components to determine
water and carbondioxide mass fraction in flue gas
- calculate required molar quantity for oxygen and required fresh
air mass
- calculate residual mass fractions for non reactive components of
fresh air in the flue gas
- calculate flue gas fluid composition
- generate custom fluid porperties
Reactive components in fuel
.. math::
m_{fuel} = \frac{1}{M_{fuel}}\\
m_{CO_2} = \sum_{i} \frac{x_{i} \cdot m_{fuel} \cdot num_{C,i}
\cdot M_{CO_{2}}}{M_{i}}\\
m_{H_{2}O} = \sum_{i} \frac{x_{i} \cdot m_{fuel} \cdot
num_{H,i} \cdot M_{H_{2}O}}{2 \cdot M_{i}}\\
\forall i \in \text{fuels in fuel vector},\\
num = \text{number of atoms in molecule}
Other components of fuel vector
.. math::
m_{fg,j} = x_{j} \cdot m_{fuel}\\
\forall j \in \text{non fuels in fuel vecotr, e.g. } CO_2,\\
m_{fg,j} = \text{mass of fluid component j in flue gas}
Non-reactive components in air
.. math::
n_{O_2} = \left( \frac{m_{CO_2}}{M_{CO_2}} +
\frac{m_{H_{2}O}}
{0,5 \cdot M_{H_{2}O}} \right) \cdot \lambda,\\
n_{O_2} = \text{mol of oxygen required}\\
m_{air} = \frac{n_{O_2} \cdot M_{O_2}}{x_{O_{2}, air}},\\
m_{air} = \text{required total air mass}\\
m_{fg,j} = x_{j, air} \cdot m_{air}\\
m_{fg, O_2} = 0,\\
m_{fg,j} = \text{mass of fluid component j in flue gas}
Flue gas composition
.. math::
x_{fg,j} = \frac{m_{fg, j}}{m_{air} + m_{fuel}}
Parameters
----------
nw : tespy.networks.network.Network
TESPy network to generate stoichiometric flue gas for.
"""
lamb = 1
n_fuel = 1
m_fuel = 1 / molar_mass_flow(self.fuel.val) * n_fuel
m_fuel_fg = m_fuel
m_co2 = 0
m_h2o = 0
molar_masses[self.h2o] = CP.PropsSI('M', self.h2o)
molar_masses[self.co2] = CP.PropsSI('M', self.co2)
molar_masses[self.o2] = CP.PropsSI('M', self.o2)
self.fg = {}
self.fg[self.co2] = 0
self.fg[self.h2o] = 0
for f, x in self.fuel.val.items():
fl = set(list(self.fuels())).intersection(
set([a.replace(' ', '') for a in CP.get_aliases(f)]))
if len(fl) == 0:
if f in self.fg.keys():
self.fg[f] += x * m_fuel
else:
self.fg[f] = x * m_fuel
else:
n_fluid = x * m_fuel / molar_masses[f]
m_fuel_fg -= n_fluid * molar_masses[f]
structure = fluid_structure(f)
n = {}
for el in ['C', 'H', 'O']:
if el in structure.keys():
n[el] = structure[el]
else:
n[el] = 0
m_co2 += n_fluid * n['C'] * molar_masses[self.co2]
m_h2o += n_fluid * n['H'] / 2 * molar_masses[self.h2o]
self.fg[self.co2] += m_co2
self.fg[self.h2o] += m_h2o
n_o2 = (m_co2 / molar_masses[self.co2] +
0.5 * m_h2o / molar_masses[self.h2o]) * lamb
m_air = n_o2 * molar_masses[self.o2] / self.air.val[self.o2]
self.air_min = m_air / m_fuel
for f, x in self.air.val.items():
if f != self.o2:
if f in self.fg.keys():
self.fg[f] += m_air * x
else:
self.fg[f] = m_air * x
m_fg = m_fuel + m_air
for f in self.fg.keys():
self.fg[f] /= m_fg
if not self.path.is_set:
self.path.val = None
TESPyFluid(
self.fuel_alias.val, self.fuel.val, [1000, nw.p_range_SI[1]],
path=self.path.val)
TESPyFluid(
self.fuel_alias.val + '_fg', self.fg, [1000, nw.p_range_SI[1]],
path=self.path.val)
msg = (
'Generated lookup table for ' + self.fuel_alias.val + ' and for '
'stoichiometric flue gas at component ' + self.label + '.')
logging.debug(msg)
if self.air_alias.val not in ['Air', 'air']:
TESPyFluid(
self.air_alias.val, self.air.val, [1000, nw.p_range_SI[1]],
path=self.path.val)
msg = ('Generated lookup table for ' + self.air_alias.val +
' at stoichiometric combustion chamber ' + self.label + '.')
else:
msg = ('Using CoolProp air at stoichiometric combustion chamber ' +
self.label + '.')
logging.debug(msg)
def comp_init(self, nw):
if not self.fuel.is_set or not isinstance(self.fuel.val, dict):
msg = ('You must specify the fuel composition for stoichimetric '
'combustion chamber ' + self.label + '.')
logging.error(msg)
raise TESPyComponentError(msg)
if not self.fuel_alias.is_set:
msg = ('You must specify a fuel alias for stoichimetric '
'combustion chamber ' + self.label + '.')
logging.error(msg)
raise TESPyComponentError(msg)
if not self.air.is_set or not isinstance(self.air.val, dict):
msg = ('You must specify the air composition for stoichimetric '
'combustion chamber ' + self.label + '.')
logging.error(msg)
raise TESPyComponentError(msg)
if not self.air_alias.is_set:
msg = ('You must specify an air alias for stoichimetric '
'combustion chamber ' + self.label + '.')
logging.error(msg)
raise TESPyComponentError(msg)
Component.comp_init(self, nw)
# adjust the names for required fluids according to naming in the
# network air
for f in list(self.air.val.keys()):
alias = [x for x in self.nw_fluids if x in [
a.replace(' ', '') for a in CP.get_aliases(f)]]
if len(alias) > 0:
self.air.val[alias[0]] = self.air.val.pop(f)
# fuel
for f in list(self.fuel.val.keys()):
alias = [x for x in self.air.val.keys() if x in [
a.replace(' ', '') for a in CP.get_aliases(f)]]
if len(alias) > 0:
self.fuel.val[alias[0]] = self.fuel.val.pop(f)
# list of all fluids of air and fuel
fluids = list(self.air.val.keys()) + list(self.fuel.val.keys())
# oxygen
alias = [x for x in fluids if x in [
a.replace(' ', '') for a in CP.get_aliases('O2')]]
if len(alias) == 0:
msg = 'Oxygen missing in input fluids.'
logging.error(msg)
raise TESPyComponentError(msg)
else:
self.o2 = alias[0]
# carbondioxide
self.co2 = [x for x in self.nw_fluids if x in [
a.replace(' ', '') for a in CP.get_aliases('CO2')]]
if len(self.co2) == 0:
self.co2 = 'CO2'
else:
self.co2 = self.co2[0]
# water
self.h2o = [x for x in self.nw_fluids if x in [
a.replace(' ', '') for a in CP.get_aliases('H2O')]]
if len(self.h2o) == 0:
self.h2o = 'H2O'
else:
self.h2o = self.h2o[0]
# calculate lower heating value of specified fuel
self.lhv = self.calc_lhv()
msg = ('Combustion chamber fuel (' + self.fuel_alias.val +
') LHV is ' + str(self.lhv) + ' for component ' +
self.label + '.')
logging.debug(msg)
# generate fluid properties for stoichiometric flue gas
self.stoich_flue_gas(nw)
