Turbine (2P)

Two-phase turbine in a thermodynamic cycle

Since R2022b

• 

Libraries:
Simscape / Fluids / Two-Phase Fluid / Fluid Machines

Description

The Turbine (2P) block models a turbine in a two-phase fluid network. You can parameterize the block as a tabulated turbine map that is either a 1-D function of pressure ratio or 2-D function of pressure ratio and corrected mass flow rate. Fluid flowing from port A to port B generates torque. Port R reports shaft torque and angular velocity relative to port C, which represents the turbine casing.

When enabled, port VN represents the nozzle opening fraction. This value linearly scales the corrected mass flow rate but does not influence the turbine efficiency. A value of 1 corresponds to the data in the turbine map.

The Turbine (2P) block assumes that superheated fluid enters the inlet. You can use the Report when fluid is not fully vapor parameter to choose what the block does when the fluid does not meet superheated conditions.

Turbine Map

To visualize the block map, right-click the block and select Fluids > Plot Turbine Map.

Each time you modify the block settings, click Reload Data on the figure window.

The turbine map relates turbine performance, as a function of pressure ratio, to the corrected mass flow rate and isentropic efficiency. The pressure ratio is the ratio between the turbine inlet pressure and outlet pressure.

The turbine map plots two separate graphs: corrected mass flow rate versus pressure ratio and isentropic efficiency versus pressure ratio. When you set the Turbine map parameterization to Tabulated data - flow rate and efficiency vs. corrected speed and pressure ratio, the plots also depend on the corrected rotor speed, N. The indexing variable β does not need to be the same between the mass flow rate and efficiency tables.

Corrected Mass Flow Rate

Due to the large changes in pressure and temperature inside a turbine, the turbine map plots performance in terms of the corrected mass flow rate. The block adjusts the corrected mass flow rate from the inlet mass flow rate by using a corrected pressure and temperature

$${\dot{m}}_A\sqrt{\frac{T_A}{T_{corr}}}={\dot{m}}_{corr}\frac{p_A}{p_{corr}},$$

where:

• $$\dot{m}$$_A is the mass flow rate at port A.

• T_A is the temperature at port A.

• T_corr is the Reference temperature for corrected flow parameter. Refer to the data sheet for your turbine for this value.

• $$\dot{m}$$_corr is the corrected mass flow rate.

  When Turbine map parameterization is Analytical - nominal pressure ratio and corrected mass flow rate, this is the value of the Nominal corrected mass flow rate parameter.

  When Turbine map parameterization is Tabulated data - Flow rate and efficiency vs. pressure ratio, this is the value of the Corrected mass flow rate vector, mdot(pr) parameter.

  When Turbine map parameterization is Tabulated data - Flow rate and efficiency vs. corrected speed and pressure ratio, this is the value of the Corrected mass flow rate table, mdot(N,beta) parameter.

• p_A is the pressure at port A.

• p_corr is the Reference pressure for corrected flow parameter. Refer to the data sheet for your turbine for this value.

Corrected Speed

The block also adjusts the shaft speed, ω, according to the reference temperature, such that the corrected shaft speed is

$${\omega }_{corr}=\frac{\omega }{\sqrt{\frac{T_A}{T_{ref}}}}.$$

Shaft Torque

The block calculates the shaft torque, τ, as

$$\tau =\frac{{\eta }_m{\dot{m}}_A\Delta h_{total}}{\omega },$$

where:

• Δh_total is the total change in the fluid specific enthalpy.

• η_m is the value of the Mechanical efficiency parameter.

• ω is the relative shaft angular velocity, ω_R - ω_C.

Reversed flow, from port B to port A, is outside of the typical turbine operation mode and may not return accurate results. A threshold region when flow approaches zero ensures the block generates no torque when the flow rate is near zero or reversed.

Analytical Parametrization

Use the analytical parametrization to create a turbine based on the expected nominal operating conditions. When Turbine map parameterization is Analytical – nominal pressure ratio and corrected mass flow rate, the turbine isentropic efficiency is constant and the mass flow rate is a function of the pressure ratio.

This image shows the default turbine map when you use the analytical parameterization.

Parameterization by Pressure Ratio

When Turbine map parameterization is Tabulated data - Flow rate and efficiency vs. pressure ratio, the turbine isentropic efficiency and mass flow rate are a function of the pressure ratio and do not account for any changes in the turbine rotational speed.

The last element of the Corrected mass flow rate vector, mdot(pr) and the Pressure ratio vector, pr parameters represents the corrected mass flow rate and pressure ratio at choked flow conditions.

This image shows the default turbine map when you use the 1-D parameterization.

Parameterization by Pressure Ratio and Corrected Mass Flow Rate

When Turbine map parameterization is set to Tabulated data - Flow rate and efficiency vs. corrected speed and pressure ratio, the turbine isentropic efficiency, pressure ratio, and corrected mass flow rate are a function of the corrected speed, N, and the map index, β. The block uses linear interpolation between data points for the efficiency, pressure ratio, and corrected mass flow rate parameters.

The last column of the Corrected mass flow rate table, mdot(N,beta) and the Pressure ratio table, pr(N,beta) represent the corrected mass flow rate and pressure ratio at choked flow conditions.

This image shows the default turbine map when you use the 2-D parameterization.

Continuity Equations

Mass is preserved over the block:

$${\dot{m}}_A+{\dot{m}}_B=0,$$

where $$\dot{m}$$_B is the mass flow rate at port B.

The block calculates the energy balance as

$${\Phi }_A+{\Phi }_B-P_{fluid}=0,$$

where:

• Φ_A is the energy flow rate at port A.

• Φ_B is the energy flow rate at port B.

• P_fluid is the work done by the fluid, which the block determines from the change in total fluid specific enthalpy, $$P_{fluid}={\dot{m}}_A\Delta h_{total}.$$

Assumptions and Limitations

• The shaft does not rotate under reversed flow conditions. Results during reversed flows may not be accurate.

Examples

Liquid Air Energy Storage System

Models a grid-scale energy storage system based on cryogenic liquid air. When there is excess power, the system liquefies ambient air based on a variation of the Claude cycle. The cold liquid air is stored in a low-pressure insulated tank until needed. When there is high power demand, the system expands the stored liquid air to produce power based on the Rankine cycle.

• Open Model

Ports

Input

VN — Nozzle opening fraction, unitless

physical signal

Variable nozzle opening fraction, specified as a unitless physical signal. The corrected mass flow rate scales linearly with the value of VN. A fraction of 1 corresponds to the tabulated data. The nozzle opening fraction does not influence the isentropic efficiency.

Dependencies

To enable this port, select the Enable variable nozzle input port parameter.

Conserving

A — Two-phase fluid inlet

two-phase fluid

Two-phase fluid conserving port associated with the fluid entry port.

B — Two-phase fluid outlet

two-phase fluid

Two-phase fluid conserving port associated with the fluid exit port.

C — Turbine case

mechanical translational

Port associated with the turbine casing.

R — Turbine shaft

mechanical translational

Port associated with the turbine shaft torque and angular velocity.

Parameters

Parameterization

Turbine map parameterization — Performance parameterization

Analytical - Nominal pressure ratio and corrected mass flow rate (default) | Tabulated data - Flow rate and efficiency vs. pressure ratio | Tabulated data - Flow rate and efficiency vs. corrected speed and pressure ratio

Performance parameterization specification:

• Analytical - Nominal pressure ratio and corrected mass flow rate: Parameterize turbine isentropic efficiency and corrected mass flow rate analytically.

• Tabulated data - Flow rate and efficiency vs. pressure ratio: Parameterize turbine isentropic efficiency and corrected mass flow rate by pressure ratio.

• Tabulated data - Flow rate and efficiency vs. corrected speed and pressure ratio: Parameterize turbine isentropic efficiency and corrected mass flow rate by corrected speed and pressure ratio.

Enable variable nozzle input port — Whether to enable the variable nozzle input port

Off (default) | On

Whether to enable the variable nozzle input port VN. When you do not enable the VN port, the nozzle remains constant at 1.

Minimum nozzle opening fraction — Minimum opening fraction

1e-3 (default) | positive scalar in the range (0,1]

Minimum nozzle opening fraction. This value is the lower boundary to the signal at VN. The block multiplies the value of this parameter by the mass flow rate to obtain the minimum corrected mass flow rate through the turbine.

Dependencies

To enable this parameter, select Enable variable nozzle input port.

Maximum nozzle opening fraction — Maximum opening fraction

1 (default) | positive scalar in the range (0,1]

Maximum nozzle opening fraction. This value is the upper boundary to the signal at VN. The block multiplies the value of this parameter by the mass flow rate to obtain the maximum corrected mass flow rate through the turbine.

Dependencies

To enable this parameter, select Enable variable nozzle input port.

Report when fluid is not fully vapor — Fluid not fully vapor notification

None (default) | Warning | Error

Whether the block does nothing, generates a warning, or generates an error when the block detects fluid that is not fully vapor.

Corrected speed index vector, N — Tabulated data shaft speed indices

250 .* [50, 60, 70, 80, 90, 100, 110] rpm (default) | vector of positive scalars

Vector of constant shaft speeds for tabular parameterization of corrected mass flow rate and isentropic efficiency.

Dependencies

To enable this parameter, set Turbine map parameterization to Tabulated data - Flow rate and efficiency vs. corrected speed and pressure ratio.

Flow Rate Data

Nominal pressure ratio — Pressure ratio value

2 (default) | positive scalar

Pressure ratio value under nominal operating conditions for the analytical parameterization.

Dependencies

To enable this parameter, set Turbine map parameterization to Analytical - Nominal pressure ratio and corrected mass flow rate.

Nominal corrected mass flow rate — Corrected mass flow rate value

0.48 kg/s (default) | positive scalar

Corrected mass flow rate value under nominal operating conditions for the analytical parameterization.

Dependencies

To enable this parameter, set Turbine map parameterization to Analytical - Nominal pressure ratio and corrected mass flow rate.

Pressure ratio vector, pr — Vector of pressure ratios

[1.251, 1.345, 1.442, 1.521, 1.596, 1.692, 1.849, 1.972, 2.1, 2.173, 2.259, 2.3424] (default) | vector of positive scalars

Vector of pressure ratio values for the tabulated parameterization of corrected mass flow rate. This vector must have the same number of elements as the Corrected mass flow rate vector, mdot(pr) parameter and all elements must be greater than 1. The last element must be the pressure ratio at choked conditions.

Dependencies

To enable this parameter, set Turbine map parameterization to Tabulated data - Flow rate and efficiency vs. pressure ratio.

Corrected mass flow rate vector, mdot(pr) — Vector of corrected mass flow rate values

0.01.*[39.439, 43.01, 45.556, 46.801, 47.792, 48.388, 48.634, 48.67, 48.689, 48.747, 48.825, 48.912] kg/s (default) | vector of positive scalars

Vector of corrected mass flow rate values for the tabulated parameterization of corrected mass flow rate. This vector must have the same number of elements as the Pressure ratio vector, pr parameter and all elements must be greater than 0. The last element must be the corrected mass flow rate at choked conditions.

Dependencies

To enable this parameter, set Turbine map parameterization to Tabulated data - Flow rate and efficiency vs. pressure ratio.

Pressure ratio table, pr(N,beta) — Turbine map pressure ratio data

M-by-N matrix (default)

M-by-N matrix of turbine outlet-to-inlet pressure ratios at the specified corrected shaft speed and β value. The block employs linear interpolation between the table elements. M and N are the sizes of the corresponding vectors:

• M is the number of vector elements in the Corrected speed index vector, N parameter.

• N is the number of β indices in the table.

The default table values are:

[1.217, 1.285, 1.323, 1.363, 1.402, 1.427, 1.495, 1.545, 1.6, 1.687, 1.747, 1.8074; 1.231, 1.302, 1.356, 1.404, 1.443, 1.473, 1.525, 1.577, 1.635, 1.709, 1.782, 1.845; 1.242, 1.328, 1.388, 1.437, 1.528, 1.617, 1.704, 1.811, 1.915, 1.979, 2.053, 2.1226; 1.244, 1.339, 1.417, 1.465, 1.528, 1.584, 1.692, 1.787, 1.899, 2, 2.075, 2.1492; 1.245, 1.34, 1.425, 1.492, 1.546, 1.684, 1.748, 1.882, 1.987, 2.084, 2.167, 2.2458; 1.251, 1.345, 1.442, 1.521, 1.596, 1.692, 1.849, 1.972, 2.1, 2.173, 2.259, 2.3424; 1.248, 1.348, 1.447, 1.516, 1.581, 1.651, 1.749, 1.839, 1.93, 2.024, 2.154, 2.242]

Dependencies

To enable this parameter, set Turbine map parameterization to Tabulated data - Flow rate and efficiency vs. corrected speed and pressure ratio.

Corrected mass flow rate table, mdot(N,beta) — Turbine map corrected mass flow rate data

M-by-N matrix (default)

M-by-N matrix of corrected mass flow rates at the specified corrected shaft speed and β value. The block employs linear interpolation between the table elements. M and N are the sizes of the corresponding vectors:

• M is the number of vector elements in the Constant speed index vector, N parameter.

• N is the number of β indices in the table.

The default table values are:

0.01.*[40.403, 44.417, 46.653, 47.966, 48.97, 49.544, 50.001, 50.081, 50.086, 50.095, 50.09, 50.0922; 40.044, 43.754, 46.125, 47.626, 48.513, 49.105, 49.481, 49.58, 49.597, 49.624, 49.638, 49.633; 39.941, 43.795, 46.017, 47.335, 48.795, 49.199, 49.279, 49.27, 49.248, 49.23, 49.255, 49.2428; 39.896, 43.512, 45.914, 47.061, 48.011, 48.558, 48.943, 49.042, 49.069, 49.01, 49.046, 49.0266; 39.524, 42.934, 45.686, 46.743, 47.715, 48.67, 48.777, 48.836, 48.876, 48.836, 48.845, 48.8184; 39.439, 43.01, 45.556, 46.801, 47.792, 48.388, 48.634, 48.67, 48.639, 48.647, 48.625, 48.5912; 39.502, 42.849, 45.336, 46.385, 47.312, 47.877, 48.222, 48.397, 48.459, 48.482, 48.455, 48.414] kg/s

Dependencies

To enable this parameter, set Turbine map parameterization to Tabulated data - Flow rate and efficiency vs. corrected speed and pressure ratio.

Efficiency Data

Constant isentropic efficiency — Isentropic efficiency value

0.8 (default) | positive scalar

Isentropic efficiency under nominal operating conditions for the analytical parametrization.

Dependencies

To enable this parameter, set Turbine map parameterization to Analytical - Nominal pressure ratio and corrected mass flow rate.

Pressure ratio vector, pr — Vector of pressure ratios

[1.252, 1.328, 1.425, 1.544, 1.642, 1.757, 1.873, 2.005, 2.1, 2.204, 2.248, 2.28] (default) | vector of positive scalars

Vector of pressure ratio values for the tabulated parameterization of isentropic efficiency. This vector must have the same number of elements as the Isentropic efficiency vector, eta(pr)) parameter and all elements must be greater than 1.

Dependencies

To enable this parameter, set Turbine map parameterization to Tabulated data - Flow rate and efficiency vs. pressure ratio.

Isentropic efficiency vector, eta(pr) — Vector of isentropic efficiencies

[.559, .61, .673, .741, .788, .835, .869, .895, .908, .899, .854, .751] (default) | vector of elements in the range (0,1]

Vector of isentropic efficiency values for the tabulated parameterization of isentropic efficiency. This vector must have the same number of elements as the Pressure ratio vector, pr parameter and all elements must be greater than 0 and less than or equal to 1.

Dependencies

To enable this parameter, set Turbine map parameterization to Tabulated data - Flow rate and efficiency vs. pressure ratio.

Pressure ratio table, pr(N,beta) — Turbine map pressure ratio data

M-by-N matrix (default)

M-by-N matrix of turbine outlet-to-inlet pressure ratios at the specified corrected shaft speed and β value. The block employs linear interpolation between the table elements. M and N are the sizes of the corresponding vectors:

• M is the number of vector elements in the Constant speed index vector, N parameter.

• N is the number of β indices in the table.

The default table values are:

[1.224, 1.246, 1.292, 1.387, 1.457, 1.534, 1.61, 1.686, 1.743, 1.79, 1.871, 1.914; 1.237, 1.25, 1.28, 1.369, 1.459, 1.553, 1.629, 1.716, 1.799, 1.846, 1.927, 1.97; 1.241, 1.255, 1.283, 1.326, 1.401, 1.509, 1.591, 1.704, 1.806, 1.913, 1.994, 2.037; 1.25, 1.265, 1.308, 1.364, 1.456, 1.532, 1.637, 1.739, 1.851, 1.934, 2.042, 2.085; 1.281, 1.314, 1.371, 1.425, 1.498, 1.574, 1.647, 1.749, 1.878, 1.979, 2.091, 2.18; 1.252, 1.328, 1.425, 1.544, 1.642, 1.757, 1.873, 2.005, 2.1, 2.204, 2.248, 2.28; 1.382, 1.43, 1.495, 1.586, 1.688, 1.791, 1.887, 1.99, 2.079, 2.158, 2.249, 2.217]

Dependencies

To enable this parameter, set Turbine map parameterization to Tabulated data - Flow rate and efficiency vs. corrected speed and pressure ratio.

Isentropic efficiency table, eta(N,beta) — Turbine map isentropic efficiency data

M-by-N matrix (default)

M-by-N matrix of turbine isentropic efficiencies at the specified constant shaft speed and β value. The block employs linear interpolation between the table elements. M and N are the sizes of the corresponding vectors:

• M is the number of vector elements in the Constant speed index vector, N parameter.

• N is the number of β indices in the table.

The default table values are:

[.72, .754, .759, .739, .714, .679, .643, .603, .554, .524, .494, .48; .716, .757, .794, .819, .812, .788, .761, .728, .692, .662, .632, .618; .629, .691, .775, .831, .858, .869, .859, .842, .816, .782, .752, .738; .594, .668, .757, .804, .857, .883, .892, .893, .884, .865, .835, .821; .664, .72, .779, .823, .858, .883, .897, .905, .904, .896, .883, .868; .559, .61, .673, .741, .788, .835, .869, .895, .908, .899, .854, .751; .718, .785, .824, .855, .882, .9, .908, .906, .884, .857, .804, .701]

Dependencies

To enable this parameter, set Turbine map parameterization to Tabulated data - Flow rate and efficiency vs. corrected speed and pressure ratio.

Reference Data

Reference pressure for corrected flow — Correcting pressure

0.101325 MPa (default) | positive scalar

Pressure at which the turbine data consolidates to a corrected trend line.

Reference temperature for corrected flow — Correcting temperature

373.15 K (default) | positive scalar

Temperature at which the turbine data consolidates to a corrected trend line.

Mechanical efficiency — Efficiency of conversion to torque

0.9 (default) | positive scalar in the range [0,1]

Efficiency of the conversion from reduction in specific enthalpy to shaft torque.

Inlet area at port A — Turbine inlet area

0.01 m^2 (default) | positive scalar

Turbine inlet cross-sectional area.

Outlet area at port B — Turbine outlet area

0.01 m^2 (default) | positive scalar

Turbine outlet cross-sectional area.

References

[1] Kurzke, Joachim. "How to Get Component Maps for Aircraft Gas Turbine Performance Calculations." Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; General, American Society of Mechanical Engineers, 1996, p. V005T16A001.

[2] Plencner, Robert M. “Plotting component maps in the Navy/NASA Engine Program (NNEP): A method and its usage.” NASA Technical Memorandum, 1989.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2022b

R2023a: Control visibility of port VN

Use the Enable variable nozzle input port parameter to enable the variable nozzle control port VN.