modelSteamTurbine
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
| Type | Name | Default | Description |
|---|---|---|---|
| SI.Pressure | p_crit (from SteamTurbineBase) | Medium.fluidConstants[1].criticalPressure | Medium critical pressure |
| Real | partialArc_nominal | 1 | Nominal partial arc |
| SI.MassFlowRate | m_flow_nominal | m_flow_start | Nominal mass flowrate |
| SI.Pressure | p_inlet_nominal | p_a_start | Nominal inlet pressure |
| SI.Area | Kt | Flow area coefficient | |
| Assumptions | |||
| Boolean | allowFlowReversal (from SteamTurbineBase) | system.allowFlowReversal | = true to allow flow reversal, false restricts to design direction |
| Advanced | |||
| Integer | nUnits (from SteamTurbineBase) | 1 | Number of turbine units, e.g., high pressure and low pressure |
| Dynamics | energyDynamics (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 | |||
| Real | eta_mech (from SteamTurbineBase) | 1.0 | Mechanical efficiency |
| Initialization › Start Value: Absolute Pressure | |||
| Medium.AbsolutePressure | p_a_start (from SteamTurbineBase) | system.p_start | Pressure at port a |
| Medium.AbsolutePressure | p_b_start (from SteamTurbineBase) | p_a_start | Pressure at port b |
| Initialization › Start Value: Temperature | |||
| Boolean | use_T_start (from SteamTurbineBase) | true | Use T_start if true, otherwise h_start |
| Medium.Temperature | T_a_start (from SteamTurbineBase) | system.T_start | Temperature at port a |
| Medium.Temperature | T_b_start (from SteamTurbineBase) | T_a_start | Temperature at port b |
| Initialization › Start Value: Specific Enthalpy | |||
| Medium.SpecificEnthalpy | h_a_start (from SteamTurbineBase) | Medium.specificEnthalpy_pTX(p_a_start, T_a_start, X_start) | Specific enthalpy at port a |
| Medium.SpecificEnthalpy | h_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_default | Mass 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.MassFlowRate | m_flow_start (from SteamTurbineBase) | system.m_flow_start | Mass flow rate |
| Stodola's Law Coefficient | |||
| Boolean | use_Stodola | true | =true to use Stodola's law, i.e., infinite stages per unit |
| SI.Area | Kt_constant | 0.01 | Constant coefficient of Stodola's law |
| Boolean | use_NominalInlet | true | =true then Kt is calculated from nominal inlet conditions |
| SI.Pressure | p_outlet_nominal | p_b_start | Nominal outlet pressure |
| Boolean | use_T_nominal | true | =true then use temperature for Kt else density |
| SI.Temperature | T_nominal | T_a_start | Nominal inlet temperature |
| SI.Density | d_nominal | Medium.density(Medium.setState_pTX(p_inlet_nominal, T_nominal, Medium.reference_X)) | Nominal inlet density |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| TRANSFORM.Fluid.Interfaces.FluidPort_Flow | portHP (from SteamTurbineBase) | high pressure port | |
| TRANSFORM.Fluid.Interfaces.FluidPort_Flow | portLP (from SteamTurbineBase) | low pressure port | |
| Modelica.Mechanics.Rotational.Interfaces.Flange_a | shaft_a (from SteamTurbineBase) | ||
| Modelica.Mechanics.Rotational.Interfaces.Flange_b | shaft_b (from SteamTurbineBase) | ||
| Modelica.Blocks.Interfaces.RealInput | partialArc (from SteamTurbineBase) |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Fluid.System | system (from SteamTurbineBase) | System properties | |
| Eta_wetSteam | eta_wetSteam (from SteamTurbineBase) | ||
| Medium.ThermodynamicState | state_a (from SteamTurbineBase) | ||
| Medium.ThermodynamicState | state_b (from SteamTurbineBase) | ||
| Real | p_ratio (from SteamTurbineBase) | p_out/p_in pressure ratio | |
| SI.Angle | phi (from SteamTurbineBase) | Shaft rotation angle | |
| SI.Torque | tau (from SteamTurbineBase) | Net torque acting on the turbine | |
| SI.AngularVelocity | omega (from SteamTurbineBase) | Shaft angular velocity | |
| SI.MassFlowRate | m_flow (from SteamTurbineBase) | Mass flow rate | |
| Medium.SpecificEnthalpy | h_in (from SteamTurbineBase) | Inlet enthalpy | |
| Medium.SpecificEnthalpy | h_out (from SteamTurbineBase) | Outlet enthalpy | |
| Medium.SpecificEnthalpy | h_is (from SteamTurbineBase) | Isentropic outlet enthalpy | |
| Medium.AbsolutePressure | p_in (from SteamTurbineBase) | Inlet pressure | |
| Medium.AbsolutePressure | p_out (from SteamTurbineBase) | Outlet pressure | |
| SI.Power | Q_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.Efficiency | eta_is (from SteamTurbineBase) | Isentropic efficiency | |
| Medium.SaturationProperties | sat_in (from SteamTurbineBase) | Medium.setSat_p(p_in) | Properties of saturated fluid at inlet |
| Medium.SaturationProperties | sat_out (from SteamTurbineBase) | Medium.setSat_p(p_out) | Properties of saturated fluid at outlet |
| Medium.ThermodynamicState | bubble_in (from SteamTurbineBase) | Medium.setBubbleState(sat_in, 1) | Bubble point state at inlet |
| Medium.ThermodynamicState | dew_in (from SteamTurbineBase) | Medium.setDewState(sat_in, 1) | Dew point state at inlet |
| Medium.ThermodynamicState | bubble_out (from SteamTurbineBase) | Medium.setBubbleState(sat_out, 1) | Bubble point state at outlet |
| Medium.ThermodynamicState | dew_out (from SteamTurbineBase) | Medium.setDewState(sat_out, 1) | Dew point state at outlet |
| SI.SpecificEnthalpy | h_fsat_in (from SteamTurbineBase) | bubble_in.h | Saturated liquid specific enthalpy at inlet |
| SI.SpecificEnthalpy | h_gsat_in (from SteamTurbineBase) | dew_in.h | Saturated vapor specific enthalpy at inlet |
| SI.SpecificEnthalpy | h_fsat_out (from SteamTurbineBase) | bubble_out.h | Saturated liquid specific enthalpy at outlet |
| SI.SpecificEnthalpy | h_gsat_out (from SteamTurbineBase) | dew_out.h | Saturated vapor specific enthalpy at outlet |
| Units.NonDim | x_th_in (from SteamTurbineBase) | Inlet thermodynamic quality | |
| Units.NonDim | x_abs_in (from SteamTurbineBase) | Inlet absolute mass quality | |
| Units.NonDim | x_th_out (from SteamTurbineBase) | Outlet thermodynamic quality | |
| Units.NonDim | x_abs_out (from SteamTurbineBase) | Outlet absolute mass quality |