Turbine (Inlet Stage)

pair: idaes.power_generation.unit_models.helm.turbine_inlet;HelmTurbineInletStage

idaes.power_generation.unit_models.helm.turbine_inlet

This is a steam power generation turbine model for the inlet stage. It inherits HelmIsentropicTurbine <technical_specs/model_libraries/power_generation/unit_models/turbine_inlet:Turbine (Isentropic)>.

The turbine inlet 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, TransformationFactory, units from idaes.core import FlowsheetBlock from idaes.power_generation.unit_models.helm import HelmTurbineInletStage from idaes.generic_models.properties import iapws95

m = ConcreteModel() m.fs = FlowsheetBlock(default={"dynamic": False}) m.fs.properties = iapws95.Iapws95ParameterBlock() m.fs.turb = HelmTurbineInletStage(default={"property_package": m.fs.properties}) hin = iapws95.htpx(T=880*units.K, P=2.4233e7*units.Pa) # set inlet m.fs.turb.inlet[:].enth_mol.fix(hin) m.fs.turb.inlet[:].flow_mol.fix(26000/4.0) m.fs.turb.inlet[:].pressure.fix(2.4233e7) m.fs.turb.eff_nozzle.fix(0.95) m.fs.turb.blade_reaction.fix(0.9) m.fs.turb.flow_coeff.fix(1.053/3600.0) m.fs.turb.blade_velocity.fix(110.0) m.fs.turb.efficiency_mech.fix(0.98)

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, like flow coefficients. See the variables section for more information.

Model Structure

The turbine inlet stage model contains one ControlVolume0DBlock block <technical_specs/core/control_volume_0d:0D Control Volume Class> called control_volume and inherits HelmIsentropicTurbine <technical_specs/model_libraries/power_generation/unit_models/turbine_inlet:Turbine (Isentropic)>.

Variables

The variables below are defined in the HelmIsentropicTurbine model.

Variable	Symbol	Index Sets	Doc
`blade_reaction`	R	None	Blade reaction
`eff_nozzle`	η_nozzle	None	Nozzle efficiency
`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]
`blade_velocity`	V_rbl	None	Turbine blade velocity (should be constant while running) [m/s]
`delta_enth_isentropic`	Δh_isen	time	Isentropic enthalpy change through stage [J/mol]

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]
`steam_entering_velocity`	V₀	time	Steam velocity entering stage [m/s]

The expression defined below provides a calculation for steam velocity entering the stage, which is used in the efficiency calculation.

$$V_0 = 1.414\sqrt{\frac{-(1 - R)\Delta h_{isen}}{WT_{in}\eta_{nozzel}}}$$

Constraints

In addition to the constraints inherited from the HelmTurbineStage <technical_specs/model_libraries/power_generation/unit_models/turbine_inlet:Turbine (Stage)>, 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:

$$\eta_{isen} = 2 \frac{V_{rbl}}{V_0}\left[\left(\sqrt{1 - R} - \frac{V_{rbl}}{V_0}\right) + \sqrt{\left(\sqrt{1 - R} - \frac{V_{rbl}}{V_0}\right)^2 + R}\right]$$

The pressure-flow relation is given by:

$$\dot{m} = C_{flow}\frac{P_{in}}{\sqrt{T_{in}-273.15}}\sqrt{\frac{\gamma}{\gamma-1} \left[ \left(\frac{P_{out}}{P_{in}}\right)^{\frac{2}{\gamma}} - \left(\frac{P_{out}}{P_{in}}\right)^{\frac{\gamma+1}{\gamma}} \right]}$$

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 and optionally a flow coefficient value can be calculated. 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 it can be hard to determine a proper flow coefficient, the calculate_cf argument of the initialize() method can be set to True, and the deltaP guess will be used to calculate and set a corresponding flow coefficient.

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.