#################################################################################
# The Institute for the Design of Advanced Energy Systems Integrated Platform
# Framework (IDAES IP) was produced under the DOE Institute for the
# Design of Advanced Energy Systems (IDAES).
#
# Copyright (c) 2018-2024 by the software owners: The Regents of the
# University of California, through Lawrence Berkeley National Laboratory,
# National Technology & Engineering Solutions of Sandia, LLC, Carnegie Mellon
# University, West Virginia University Research Corporation, et al.
# All rights reserved. Please see the files COPYRIGHT.md and LICENSE.md
# for full copyright and license information.
#################################################################################
"""
Steam turbine outlet stage model. This model is based on:
Liese, (2014). "Modeling of a Steam Turbine Including Partial Arc Admission
for Use in a Process Simulation Software Environment." Journal of Engineering
for Gas Turbines and Power. v136.
"""
# TODO: Missing docstrings
# pylint: disable=missing-class-docstring
__Author__ = "John Eslick"
from pyomo.environ import Var, sqrt, value, units as pyunits
from idaes.models_extra.power_generation.unit_models.helm.turbine import (
HelmIsentropicTurbineData,
)
from idaes.core import declare_process_block_class
from idaes.core.util import from_json, to_json, StoreSpec
from idaes.core.solvers import get_solver
import idaes.core.util.scaling as iscale
import idaes.logger as idaeslog
_log = idaeslog.getLogger(__name__)
[docs]
@declare_process_block_class(
"HelmTurbineOutletStage",
doc="Outlet stage steam turbine model",
)
class HelmTurbineOutletStageData(HelmIsentropicTurbineData):
# Same settings as the default pressure changer, but force to expander with
# isentropic efficiency
CONFIG = HelmIsentropicTurbineData.CONFIG()
[docs]
def build(self):
super().build()
self.flow_coeff = Var(
initialize=0.0333,
doc="Turbine flow coefficient [kg*C^0.5/s/Pa]",
units=pyunits.kg * pyunits.K**0.5 / pyunits.s / pyunits.Pa,
)
self.eff_dry = Var(initialize=0.87, doc="Turbine dry isentropic efficiency")
self.design_exhaust_flow_vol = Var(
initialize=6000.0,
doc="Design exit volumetirc flowrate [m^3/s]",
units=pyunits.m**3 / pyunits.s,
)
self.efficiency_mech = Var(initialize=1.0, doc="Turbine mechanical efficiency")
self.efficiency_isentropic.unfix()
self.eff_dry.fix()
self.design_exhaust_flow_vol.fix()
self.flow_coeff.fix()
self.efficiency_mech.fix()
self.tel_c0 = Var(
initialize=0.0064 * 1e6,
units=pyunits.J / pyunits.mol,
doc="c0 in tel = c0 + c1*fr + c2*fr**2 + ... + c5*fr**5 (fr is ratio"
" of exhaust volumetric flow to design exhaust volumetric flow)",
)
self.tel_c1 = Var(
initialize=-0.0328 * 1e6,
units=pyunits.J / pyunits.mol,
doc="c1 in tel = c0 + c1*fr + c2*fr**2 + ... + c5*fr**5 (fr is ratio"
" of exhaust volumetric flow to design exhaust volumetric flow)",
)
self.tel_c2 = Var(
initialize=0.0638 * 1e6,
units=pyunits.J / pyunits.mol,
doc="c2 in tel = c0 + c1*fr + c2*fr**2 + ... + c5*fr**5 (fr is ratio"
" of exhaust volumetric flow to design exhaust volumetric flow)",
)
self.tel_c3 = Var(
initialize=-0.0542 * 1e6,
units=pyunits.J / pyunits.mol,
doc="c3 in tel = c0 + c1*fr + c2*fr**2 + ... + c5*fr**5 (fr is ratio"
" of exhaust volumetric flow to design exhaust volumetric flow)",
)
self.tel_c4 = Var(
initialize=0.022 * 1e6,
units=pyunits.J / pyunits.mol,
doc="c4 in tel = c0 + c1*fr + c2*fr**2 + ... + c5*fr**5 (fr is ratio"
" of exhaust volumetric flow to design exhaust volumetric flow)",
)
self.tel_c5 = Var(
initialize=-0.0035 * 1e6,
units=pyunits.J / pyunits.mol,
doc="c5 in tel = c0 + c1*fr + c2*fr**2 + ... + c5*fr**5 (fr is ratio"
" of exhaust volumetric flow to design exhaust volumetric flow)",
)
self.tel_c0.fix()
self.tel_c1.fix()
self.tel_c2.fix()
self.tel_c3.fix()
self.tel_c4.fix()
self.tel_c5.fix()
@self.Expression(self.flowsheet().time, doc="Total exhaust loss curve")
def tel(b, t):
f = b.control_volume.properties_out[t].flow_vol / b.design_exhaust_flow_vol
return (
+self.tel_c5 * f**5
+ self.tel_c4 * f**4
+ self.tel_c3 * f**3
+ self.tel_c2 * f**2
+ self.tel_c1 * f
+ self.tel_c0
)
@self.Constraint(self.flowsheet().time, doc="Stodola eq. choked flow")
def stodola_equation(b, t):
flow = b.control_volume.properties_in[t].flow_mol
mw = b.control_volume.properties_in[t].mw
Tin = b.control_volume.properties_in[t].temperature
Pin = b.control_volume.properties_in[t].pressure
Pr = b.ratioP[t]
cf = b.flow_coeff
return flow**2 * mw**2 * (Tin) == (cf**2 * Pin**2 * (1 - Pr**2))
@self.Constraint(self.flowsheet().time, doc="Efficiency correlation")
def efficiency_correlation(b, t):
x = b.control_volume.properties_out[t].vapor_frac
eff = b.efficiency_isentropic[t]
dh_isen = b.delta_enth_isentropic[t]
tel = b.tel[t]
return eff == b.eff_dry * x * (1 - 0.65 * (1 - x)) * (1 + tel / dh_isen)
@self.Expression(self.flowsheet().time, doc="Thermodynamic power [J/s]")
def power_thermo(b, t):
return b.control_volume.work[t]
@self.Expression(self.flowsheet().time, doc="Shaft power [J/s]")
def power_shaft(b, t):
return b.power_thermo[t] * b.efficiency_mech
[docs]
def initialize_build(
self,
outlvl=idaeslog.NOTSET,
solver=None,
optarg=None,
calculate_cf=True,
):
"""
Initialize the outlet turbine stage model. This deactivates the
specialized constraints, then does the isentropic turbine initialization,
then reactivates the constraints and solves.
Args:
outlvl : sets output level of initialization routine
solver (str): Solver to use for initialization
optarg (dict): Solver arguments dictionary
"""
init_log = idaeslog.getInitLogger(self.name, outlvl, tag="unit")
solve_log = idaeslog.getSolveLogger(self.name, outlvl, tag="unit")
sp = StoreSpec.value_isfixed_isactive(only_fixed=True)
istate = to_json(self, return_dict=True, wts=sp)
# sp is what to save to make sure state after init is same as the start
# saves value, fixed, and active state, doesn't load originally free
# values, this makes sure original problem spec is same but initializes
# the values of free vars
for t in self.flowsheet().time:
if self.outlet.pressure[t].fixed:
self.ratioP[t] = value(self.outlet.pressure[t] / self.inlet.pressure[t])
self.deltaP[t] = value(self.outlet.pressure[t] - self.inlet.pressure[t])
# Deactivate special constraints
self.stodola_equation.deactivate()
self.efficiency_correlation.deactivate()
self.efficiency_isentropic.fix()
self.deltaP.unfix()
self.ratioP.unfix()
self.inlet.fix()
self.outlet.unfix()
super().initialize_build(outlvl=outlvl, solver=solver, optarg=optarg)
for t in self.flowsheet().time:
mw = self.control_volume.properties_in[t].mw
Tin = self.control_volume.properties_in[t].temperature
Pin = self.control_volume.properties_in[t].pressure
Pr = self.ratioP[t]
if not calculate_cf:
cf = self.flow_coeff
self.inlet.flow_mol[t].fix(
value(cf * Pin * sqrt(1 - Pr**2) / mw / sqrt(Tin))
)
super().initialize_build(outlvl=outlvl, solver=solver, optarg=optarg)
self.control_volume.properties_out[:].pressure.fix()
# Free eff_isen and activate special constraints
self.efficiency_isentropic.unfix()
self.outlet.pressure.fix()
if calculate_cf:
self.flow_coeff.unfix()
self.inlet.flow_mol.unfix()
self.inlet.flow_mol[0].fix()
flow = self.control_volume.properties_in[0].flow_mol
mw = self.control_volume.properties_in[0].mw
Tin = self.control_volume.properties_in[0].temperature
Pin = self.control_volume.properties_in[0].pressure
Pr = self.ratioP[0]
self.flow_coeff.value = value(flow * mw * sqrt(Tin / (1 - Pr**2)) / Pin)
else:
self.inlet.flow_mol.unfix()
self.stodola_equation.activate()
self.efficiency_correlation.activate()
# Create solver
slvr = get_solver(solver, optarg)
with idaeslog.solver_log(solve_log, idaeslog.DEBUG) as slc:
res = slvr.solve(self, tee=slc.tee)
init_log.info(
"Initialization Complete (Outlet Stage): {}".format(idaeslog.condition(res))
)
# reload original spec
if calculate_cf:
cf = value(self.flow_coeff)
from_json(self, sd=istate, wts=sp)
if calculate_cf:
# cf was probably fixed, so will have to set the value again here
# if you ask for it to be calculated.
self.flow_coeff = cf
def calculate_scaling_factors(self):
super().calculate_scaling_factors()
for t, c in self.stodola_equation.items():
s = (
iscale.get_scaling_factor(
self.control_volume.properties_in[t].flow_mol,
default=1,
warning=True,
)
** 2
)
iscale.constraint_scaling_transform(c, s, overwrite=False)
