Turbine (Outlet Stage)

.. index::
  pair: idaes.power_generation.unit_models.turbine_outlet;TurbineOutletStage

.. module:: idaes.power_generation.unit_models.turbine_outlet

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

.. testcode::

    from pyomo.environ import ConcreteModel, SolverFactory
    from idaes.core import FlowsheetBlock
    from idaes.power_generation.unit_models import TurbineOutletStage
    from idaes.generic_models.properties 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 :ref:`ControlVolume0DBlock block <technical_specs/core/control_volume_0d:0D Control Volume Class>` called control_volume and inherits the :ref:`PressureChanger model <technical_specs/model_libraries/generic/unit_models/pressure_changer:Pressure Changer>` using the isentropic option.

Variables

The variables below are defined int the TurbineInletStage model. Additional variables are in inherited from the :ref:`PressureChanger model <technical_specs/model_libraries/generic/unit_models/pressure_changer:Pressure Changer>` 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 :ref:`PressureChanger model <technical_specs/model_libraries/generic/unit_models/pressure_changer:Pressure Changer>` 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. 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.