# 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.

## TurbineOutletStage Class¶

class idaes.models_extra.power_generation.unit_models.helm.turbine_outlet.HelmTurbineOutletStage(*args, **kwds)

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 (class) – Pyomo ctype of the block. Default - pyomo.environ.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: { useDefault - get flag from parent (default = False), True - construct holdup terms, False - do not construct holdup terms}

material_balance_type

Indicates what type of mass balance should be constructed, default - MaterialBalanceType.useDefault. Valid values: { MaterialBalanceType.useDefault - refer to property package for default balance type **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.useDefault. Valid values: { EnergyBalanceType.useDefault - refer to property package for default balance type **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.}

has_pressure_change

Indicates whether terms for pressure change should be constructed, default - False. Valid values: { True - include pressure change terms, False - exclude pressure change terms.}

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.}

has_work_transfer

True if model a has work transfer term.

has_heat_transfer

True if model has a heat transfer term.

• 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

(HelmTurbineOutletStage) New instance

## TurbineOutletStageData Class¶

class idaes.models_extra.power_generation.unit_models.helm.turbine_outlet.HelmTurbineOutletStageData(component)[source]
build()[source]

Add model equations to the unit model. This is called by a default block construnction rule when the unit model is created.

initialize_build(outlvl=0, solver=None, optarg=None, calculate_cf=True)[source]

Initialize the outlet turbine stage model. This deactivates the specialized constraints, then does the isentropic turbine initialization, then reactivates the constraints and solves.

Parameters
• outlvl – sets output level of initialization routine

• solver (str) – Solver to use for initialization

• optarg (dict) – Solver arguments dictionary