# Turbine (G)

**Libraries:**

Simscape /
Fluids /
Gas /
Turbomachinery

## Description

The Turbine (G) block models a turbine in a gas 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.

### 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:

$$\dot{m}$$

is the mass flow rate at port_{A}**A**.*T*is the temperature at port_{A}**A**.*T*is the_{corr}**Reference temperature for corrected flow**parameter. Refer to the data sheet for your turbine for this value.$$\dot{m}$$

is the corrected mass flow rate._{corr}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*is the pressure at port_{A}**A**.*p*is the_{corr}**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*is the total change in the fluid specific enthalpy._{total}*η*is the value of the_{m}**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 ```
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)** 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 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*is the energy flow rate at port_{A}**A**.*Φ*is the energy flow rate at port_{B}**B**.*P*is the work done by the fluid, which the block determines from the change in total fluid specific enthalpy, $${P}_{fluid}={\dot{m}}_{A}\Delta {h}_{total}.$$_{fluid}

### Assumptions and Limitations

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

## Examples

## Ports

### Input

### Conserving

## Parameters

## 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

## Version History

**Introduced in R2021a**