Turbine (Outlet Stage)#

This is a steam power generation turbine model for the outlet stage. The turbine outlet 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.

Example#

from pyomo.environ import ConcreteModel, SolverFactory
from idaes.core import FlowsheetBlock
from idaes.models_extra.power_generation.unit_models.helm import HelmTurbineOutletStage
from idaes.models.properties import iapws95

m = ConcreteModel()
m.fs = FlowsheetBlock(dynamic=False)
m.fs.properties = iapws95.Iapws95ParameterBlock()
m.fs.turb = HelmTurbineOutletStage(property_package=m.fs.properties)
# set inlet
m.fs.turb.inlet[:].enth_mol.fix(47115)
m.fs.turb.inlet[:].flow_mol.fix(15000)
m.fs.turb.inlet[:].pressure.fix(8e4)

m.fs.turb.initialize()

Degrees of Freedom#

Usually the inlet stream, or the inlet stream minus flow rate plus discharge pressure are fixed. There are also a few variables which are turbine parameters and are usually fixed. See the variables section for more information.

Model Structure#

The turbine outlet stage model contains one ControlVolume0DBlock block called control_volume and inherits the HelmIsentropicTurbine <reference_guides/model_libraries/power_generation/unit_models/turbine_inlet:Turbine (Isentropic)>.

Variables#

The variables below are defined int the TurbineInletStage model. Additional variables are in inherited from the :HelmIsentropicTurbine <reference_guides/model_libraries/power_generation/unit_models/turbine_inlet:Turbine (Isentropic)> model.

Variable	Symbol	Index Sets	Doc
`eff_dry`	\(\eta_{dry}\)	None	Turbine efficiency when no liquid is present.
`efficiency_mech`	\(\eta_{mech}\)	None	Mechanical Efficiency (accounts for losses in bearings…)
`flow_coeff`	\(C_{flow}\)	None	Turbine stage flow coefficient [kg*C^0.5/Pa/s]
`design_exhaust_flow_vol`	\(V_{des,exhaust}\)	None	Design volumetric flow out of stage [m^3/s]

The table below shows important variables inherited from the pressure changer model.

Variable	Symbol	Index Sets	Doc
`efficiency_isentropic`	\(\eta_{isen}\)	time	Isentropic efficiency
`deltaP`	\(\Delta P\)	time	Pressure change (\(P_{out} - P_{in}\)) [Pa]
`ratioP`	\(P_{ratio}\)	time	Ratio of discharge pressure to inlet pressure \(\left(\frac{P_{out}}{P_{in}}\right)\)

Expressions#

Variable	Symbol	Index Sets	Doc
`power_thermo`	\(\dot{w}_{thermo}\)	time	Turbine stage power output not including mechanical loss [W]
`power_shaft`	\(\dot{w}_{shaft}\)	time	Turbine stage power output including mechanical loss (bearings…) [W]
`tel`	\(\text{TEL}\)	time	Total exhaust loss [J/mol]

The expression defined below provides a total exhaust loss.

\[\text{TEL} = 1\times 10^6*\left(-0.0035f^5 + 0.022f^4 - 0.0542f^3 + 0.0638f^2 - 0.0328f + 0.0064\right)\]

Where \(f\) is the total volumetric flow of the exhaust divided by the design flow.

Constraints#

In addition to the constraints inherited from the PressureChanger model with the isentropic options, this model contains two more constraints, one to estimate efficiency and one pressure-flow relation. From the isentropic pressure changer model, these constraints eliminate the need to specify efficiency and either inlet flow or outlet pressure.

The isentropic efficiency is given by:

\[\eta_{isen} = \eta_{dry}x\left(1 - 0.65(1 - x)\right)*\left(1 + \frac{\text{TEL}}{\Delta h_{isen}}\right)\]

Where \(x\) is the steam quality (vapor fraction).

The pressure-flow relation is given by the Stodola Equation:

\[\dot{m}\sqrt{Tin - 273.15} = C_{flow}P_{in}\sqrt{1 - Pr^2}\]

Initialization#

The initialization method for this model will save the current state of the model before commencing initialization and reloads it afterwards. The state of the model will be the same after initialization, only the initial guesses for unfixed variables will be changed except for optional calculation of the flow coefficient. To initialize this model, provide a starting value for the inlet port variables. Then provide a guess for one of: discharge pressure, deltaP, or ratioP. Since a good flow coefficient can be difficult to determine, the calculate_cf option will calculate and set a flow coefficient based on the specified inlet flow and deltaP.

The model should initialize readily, but it is possible to provide a flow coefficient that is incompatible with the given flow rate resulting in an infeasible problem.