modelSteamTurbine

Steam turbine: Includes options for Stodola's ellipse law, multiple units, etc.

Extends from TRANSFORM.Fluid.Machines.BaseClasses.SteamTurbineBase (Steam turbine).

Information

This model extends SteamTurbineBase by adding the actual performance characteristics:

  • Stodola's law with an optional correction due to degradation using Baumann's formula
  • Constant isentropic efficiency

The inlet flowrate is also proportional to the partialArc signal if the corresponding connector is wired. In this case, it is assumed that the flow rate is reduced by partial arc admission, not by throttling (i.e., no loss of thermodynamic efficiency occurs). To simulate throttling, insert a valve model before the turbine inlet.

Parameter use_NominalInlet decides if the flow area coefficient is given as a parameter Kt or calculated from nominal values at an operating point. The flow area coefficient Kt, defined at design conditions by Kt = m_flow*sqrt(R*T)/sqrt(p1^2 - p2^2), can be interpreted as effective turbine flow area.

Isentropic efficiency

By default is the isentropic efficiency a parmeter equal to eta_is_nom. But if use_Baumann is true the efficiency is degraded if the fluid enters the two-phase region according to Baumans formula: eta_is = eta_is_nom*(1 - a_Baumann*(1 - x)), where a_Baumann is a parameter and x is the inlet steam quality.

Assumptions

Stodola's law (infinite number of stages)

Constant isentropic efficiency with an optional efficiency degradation using Baumann's formula

No energy or mass storage

No shaft inertia. If needed, connect a Modelica.Mechanics.Rotational.Components.Inertia model to one of the shaft connectors.

References

Cooke, D. H., 'On Prediction of Off-Design Multistage Turbine Pressures by Stodola's Ellipse,'

J. Eng. Gas Turbines Power, Volume 107, Issue 3, pp. 596, 1985.

Parameters

TypeNameDefaultDescription
SI.Pressurep_crit (from SteamTurbineBase)Medium.fluidConstants[1].criticalPressureMedium critical pressure
RealpartialArc_nominal1Nominal partial arc
SI.MassFlowRatem_flow_nominalm_flow_startNominal mass flowrate
SI.Pressurep_inlet_nominalp_a_startNominal inlet pressure
SI.AreaKtFlow area coefficient
Assumptions
BooleanallowFlowReversal (from SteamTurbineBase)system.allowFlowReversal= true to allow flow reversal, false restricts to design direction
Advanced
IntegernUnits (from SteamTurbineBase)1Number of turbine units, e.g., high pressure and low pressure
DynamicsenergyDynamics (from SteamTurbineBase)Dynamics.SteadyState=true to use turbine dynamics
SI.Time[nUnits]taus (from SteamTurbineBase)fill(1, nUnits)Characteristic time constant of each unit
SIadd.NonDim[nUnits]Q_fracs (from SteamTurbineBase)fill(1/nUnits, nUnits)Fraction of power provided per unit
Initialization
SI.Power[nUnits]Q_units_start (from SteamTurbineBase)fill(m_flow_start*(h_a_start - h_b_start)/nUnits, nUnits)Initial power output per unit
Efficiency
Realeta_mech (from SteamTurbineBase)1.0Mechanical efficiency
Initialization › Start Value: Absolute Pressure
Medium.AbsolutePressurep_a_start (from SteamTurbineBase)system.p_startPressure at port a
Medium.AbsolutePressurep_b_start (from SteamTurbineBase)p_a_startPressure at port b
Initialization › Start Value: Temperature
Booleanuse_T_start (from SteamTurbineBase)trueUse T_start if true, otherwise h_start
Medium.TemperatureT_a_start (from SteamTurbineBase)system.T_startTemperature at port a
Medium.TemperatureT_b_start (from SteamTurbineBase)T_a_startTemperature at port b
Initialization › Start Value: Specific Enthalpy
Medium.SpecificEnthalpyh_a_start (from SteamTurbineBase)Medium.specificEnthalpy_pTX(p_a_start, T_a_start, X_start)Specific enthalpy at port a
Medium.SpecificEnthalpyh_b_start (from SteamTurbineBase)Medium.isentropicEnthalpy(p_b_start, Medium.setState_phX(p_a_start, h_a_start, X_start))Specific enthalpy at port b
Initialization › Start Value: Mass Fractions
Medium.MassFraction[Medium.nX]X_start (from SteamTurbineBase)Medium.X_defaultMass fractions m_i/m
Initialization › Start Value: Trace Substances
Medium.ExtraProperty[Medium.nC]C_start (from SteamTurbineBase)fill(0, Medium.nC)Trace substances
Initialization › Start Value: Mass Flow Rate
Medium.MassFlowRatem_flow_start (from SteamTurbineBase)system.m_flow_startMass flow rate
Stodola's Law Coefficient
Booleanuse_Stodolatrue=true to use Stodola's law, i.e., infinite stages per unit
SI.AreaKt_constant0.01Constant coefficient of Stodola's law
Booleanuse_NominalInlettrue=true then Kt is calculated from nominal inlet conditions
SI.Pressurep_outlet_nominalp_b_startNominal outlet pressure
Booleanuse_T_nominaltrue=true then use temperature for Kt else density
SI.TemperatureT_nominalT_a_startNominal inlet temperature
SI.Densityd_nominalMedium.density(Medium.setState_pTX(p_inlet_nominal, T_nominal, Medium.reference_X))Nominal inlet density

Connectors

TypeNameDefaultDescription
TRANSFORM.Fluid.Interfaces.FluidPort_FlowportHP (from SteamTurbineBase)high pressure port
TRANSFORM.Fluid.Interfaces.FluidPort_FlowportLP (from SteamTurbineBase)low pressure port
Modelica.Mechanics.Rotational.Interfaces.Flange_ashaft_a (from SteamTurbineBase)
Modelica.Mechanics.Rotational.Interfaces.Flange_bshaft_b (from SteamTurbineBase)
Modelica.Blocks.Interfaces.RealInputpartialArc (from SteamTurbineBase)

Components

TypeNameDefaultDescription
Modelica.Fluid.Systemsystem (from SteamTurbineBase)System properties
Eta_wetSteameta_wetSteam (from SteamTurbineBase)
Medium.ThermodynamicStatestate_a (from SteamTurbineBase)
Medium.ThermodynamicStatestate_b (from SteamTurbineBase)
Realp_ratio (from SteamTurbineBase)p_out/p_in pressure ratio
SI.Anglephi (from SteamTurbineBase)Shaft rotation angle
SI.Torquetau (from SteamTurbineBase)Net torque acting on the turbine
SI.AngularVelocityomega (from SteamTurbineBase)Shaft angular velocity
SI.MassFlowRatem_flow (from SteamTurbineBase)Mass flow rate
Medium.SpecificEnthalpyh_in (from SteamTurbineBase)Inlet enthalpy
Medium.SpecificEnthalpyh_out (from SteamTurbineBase)Outlet enthalpy
Medium.SpecificEnthalpyh_is (from SteamTurbineBase)Isentropic outlet enthalpy
Medium.AbsolutePressurep_in (from SteamTurbineBase)Inlet pressure
Medium.AbsolutePressurep_out (from SteamTurbineBase)Outlet pressure
SI.PowerQ_mech (from SteamTurbineBase)Total mechanical power
SI.Power[nUnits]Q_units (from SteamTurbineBase)Mechanical power per unit
SI.Power[nUnits]Qbs (from SteamTurbineBase)Power balance
SI.Efficiencyeta_is (from SteamTurbineBase)Isentropic efficiency
Medium.SaturationPropertiessat_in (from SteamTurbineBase)Medium.setSat_p(p_in)Properties of saturated fluid at inlet
Medium.SaturationPropertiessat_out (from SteamTurbineBase)Medium.setSat_p(p_out)Properties of saturated fluid at outlet
Medium.ThermodynamicStatebubble_in (from SteamTurbineBase)Medium.setBubbleState(sat_in, 1)Bubble point state at inlet
Medium.ThermodynamicStatedew_in (from SteamTurbineBase)Medium.setDewState(sat_in, 1)Dew point state at inlet
Medium.ThermodynamicStatebubble_out (from SteamTurbineBase)Medium.setBubbleState(sat_out, 1)Bubble point state at outlet
Medium.ThermodynamicStatedew_out (from SteamTurbineBase)Medium.setDewState(sat_out, 1)Dew point state at outlet
SI.SpecificEnthalpyh_fsat_in (from SteamTurbineBase)bubble_in.hSaturated liquid specific enthalpy at inlet
SI.SpecificEnthalpyh_gsat_in (from SteamTurbineBase)dew_in.hSaturated vapor specific enthalpy at inlet
SI.SpecificEnthalpyh_fsat_out (from SteamTurbineBase)bubble_out.hSaturated liquid specific enthalpy at outlet
SI.SpecificEnthalpyh_gsat_out (from SteamTurbineBase)dew_out.hSaturated vapor specific enthalpy at outlet
Units.NonDimx_th_in (from SteamTurbineBase)Inlet thermodynamic quality
Units.NonDimx_abs_in (from SteamTurbineBase)Inlet absolute mass quality
Units.NonDimx_th_out (from SteamTurbineBase)Outlet thermodynamic quality
Units.NonDimx_abs_out (from SteamTurbineBase)Outlet absolute mass quality

Revisions