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.unit_models.power_generation import TurbineOutletStage
from idaes.property_models import iapws95
m = ConcreteModel()
m.fs = FlowsheetBlock(default={"dynamic": False})
m.fs.properties = iapws95.Iapws95ParameterBlock()
m.fs.turb = TurbineOutletStage(default={"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 PressureChanger model using the isentropic option.
Variables¶
The variables below are defined int the TurbineInletStage model. Additional variables are in inherited from the PressureChanger model 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.
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:
Where \(x\) is the steam quality (vapor fraction).
The pressure-flow relation is given by the Stodola Equation:
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. 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.
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.
TurbineOutletStage Class¶
-
class
idaes.unit_models.power_generation.turbine_outlet.TurbineOutletStage(*args, **kwargs)¶ Outlet stage steam turbine model
Parameters: - rule (function) – A rule function or None. Default rule calls build().
- concrete (bool) – If True, make this a toplevel model. Default - False.
- ctype (str) – Pyomo ctype of the block. Default - “Block”
- default (dict) –
Default ProcessBlockData config
- Keys
- dynamic
- Indicates whether this model will be dynamic or not, default = useDefault. Valid values: { useDefault - get flag from parent (default = False), True - set as a dynamic model, False - set as a steady-state model.}
- has_holdup
- Indicates whether holdup terms should be constructed or not. Must be True if dynamic = True, default - False. Valid values: { True - construct holdup terms, False - do not construct holdup terms}
- material_balance_type
- Indicates what type of mass balance should be constructed, default - MaterialBalanceType.componentPhase. Valid values: { MaterialBalanceType.none - exclude material balances, MaterialBalanceType.componentPhase - use phase component balances, MaterialBalanceType.componentTotal - use total component balances, MaterialBalanceType.elementTotal - use total element balances, MaterialBalanceType.total - use total material balance.}
- energy_balance_type
- Indicates what type of energy balance should be constructed, default - EnergyBalanceType.enthalpyTotal. Valid values: { EnergyBalanceType.none - exclude energy balances, EnergyBalanceType.enthalpyTotal - single enthalpy balance for material, EnergyBalanceType.enthalpyPhase - enthalpy balances for each phase, EnergyBalanceType.energyTotal - single energy balance for material, EnergyBalanceType.energyPhase - energy balances for each phase.}
- momentum_balance_type
- Indicates what type of momentum balance should be constructed, default - MomentumBalanceType.pressureTotal. Valid values: { MomentumBalanceType.none - exclude momentum balances, MomentumBalanceType.pressureTotal - single pressure balance for material, MomentumBalanceType.pressurePhase - pressure balances for each phase, MomentumBalanceType.momentumTotal - single momentum balance for material, MomentumBalanceType.momentumPhase - momentum balances for each phase.}
- has_phase_equilibrium
- Indicates whether terms for phase equilibrium should be constructed, default = False. Valid values: { True - include phase equilibrium terms False - exclude phase equilibrium terms.}
- compressor
- Indicates whether this unit should be considered a compressor (True (default), pressure increase) or an expander (False, pressure decrease).
- thermodynamic_assumption
- Flag to set the thermodynamic assumption to use for the unit. - ThermodynamicAssumption.isothermal (default) - ThermodynamicAssumption.isentropic - ThermodynamicAssumption.pump - ThermodynamicAssumption.adiabatic
- property_package
- Property parameter object used to define property calculations, default - useDefault. Valid values: { useDefault - use default package from parent model or flowsheet, PropertyParameterObject - a PropertyParameterBlock object.}
- property_package_args
- A ConfigBlock with arguments to be passed to a property block(s) and used when constructing these, default - None. Valid values: { see property package for documentation.}
- initialize (dict) – ProcessBlockData config for individual elements. Keys are BlockData indexes and values are dictionaries described under the “default” argument above.
- idx_map (function) – Function to take the index of a BlockData element and return the index in the initialize dict from which to read arguments. This can be provided to overide the default behavior of matching the BlockData index exactly to the index in initialize.
Returns: (TurbineOutletStage) New instance
TurbineOutletStageData Class¶
-
class
idaes.unit_models.power_generation.turbine_outlet.TurbineOutletStageData(component)[source]¶