Turbine (Outlet Stage)

pair: idaes.power_generation.unit_models.helm.turbine_outlet;HelmTurbineOutletStage

idaes.power_generation.unit_models.helm.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

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

m = ConcreteModel() m.fs = FlowsheetBlock(default={"dynamic": False}) m.fs.properties = iapws95.Iapws95ParameterBlock() m.fs.turb = HelmTurbineOutletStage(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 <technical_specs/core/control_volume_0d:0D Control Volume Class> called control_volume and inherits the HelmIsentropicTurbine <technical_specs/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 <technical_specs/model_libraries/power_generation/unit_models/turbine_inlet:Turbine (Isentropic)> model.

Variable	Symbol	Index Sets	Doc
`eff_dry`	η_dry	None	Turbine efficiency when no liquid is present.
`efficiency_mech`	η_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`	η_isen	time	Isentropic efficiency
`deltaP`	ΔP	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`	ẇ_thermo	time	Turbine stage power output not including mechanical loss [W]
`power_shaft`	ẇ_shaft	time	Turbine stage power output including mechanical loss (bearings...) [W]
`tel`	TEL	time	Total exhaust loss [J/mol]

The expression defined below provides a total exhaust loss.

TEL = 1 × 10⁶ * (−0.0035f⁵+0.022f⁴−0.0542f³+0.0638f²−0.0328f+0.0064)

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 <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 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.