# Compressor (G)

Gas compressor in a thermodynamic cycle

**Library:**Simscape / Fluids / Gas / Turbomachinery

## Description

The Compressor (G) block represents a dynamic compressor,
such as a centrifugal or axial compressor, in a gas network. You can parameterize the
block analytically based on the design point or by using a tabulated compressor map by
setting **Parameterization** to `Analytical`

or `Tabulated`

, respectively. A positive rotation of port
**R** relative to port **C** causes fluid to flow
from port **A** to port **B**. Port
**R** and port **C** are mechanical rotational
conserving ports associated with the compressor shaft and casing, in that order.

The *surge margin* is the ratio between the surge pressure ratio at a
given mass flow rate and the operating point pressure ratio minus `1`

.
When you set **Parameterization** to
`Tabulated`

, the block outputs the surge margin at port
**SM**.

The *design point* of the compressor is the design operational
pressure ratio across and mass flow rate through the compressor during simulation. The
compressor operating point and the point of maximum efficiency do not need to
coincide.

### Compressor Map

The map plots the isentropic efficiency of the compressor between the two extremes
of choked flow and surge flow. The map plots the lines of constant corrected shaft
speed between the two extremes of choked flow and surge flow. Each corrected speed
line tells you how pressure ratio varies with corrected mass flow rate when the
shaft spins at the corresponding corrected speed. The variable *β*
indicates the relative position along the corrected speed lines between the two
extremes. Choked flow corresponds to *β* = 0, and surge flow corresponds to *β* = 1. The map also plots contours of isentropic efficiency as a
function of pressure ratio and corrected mass flow rate. This provides a relative
indication of how much power the compressor needs to operate at various combinations
of pressure ratio and corrected mass flow rate.

**Corrected Mass Flow Rate**

Due to the large changes in pressure and temperature inside a compressor, the compressor map plots performance in terms of a corrected mass flow rate. The corrected mass flow rate is adjusted from the inlet mass flow rate with a reference pressure and reference temperature:

$${\dot{m}}_{corr}={\dot{m}}_{A}\left(\frac{{p}_{A}}{{p}_{ref}}/\sqrt{\frac{{T}_{A}}{{T}_{ref}}}\right),$$

where:

*ṁ*is the mass flow rate at port_{A}**A**.*T*is the temperature at port_{A}**A**.*T*is the_{ref}**Reference temperature for corrected flow**. When you set**Parameterization**to`Analytical`

, this is the inlet temperature at the design operating condition.$$\dot{m}$$

is the corrected mass flow rate._{corr}When you set

**Parameterization**to`Analytical`

, the block uses the**Corrected mass flow rate at design point**parameter.When you set

**Parameterization**to`Tabulated`

, the block uses the**Corrected mass flow rate table, mdot(N,beta)**parameter.*p*is the pressure at port_{A}**A**.*p*is the_{ref}**Reference pressure for corrected flow**parameter. When using the analytical parameterization, this is the inlet pressure at the design operating condition.

The block derives *T _{A}*
from the specific internal energy,

*u*, and specific pressure,

_{A}*p*.

_{A}**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:

$$\tau =\frac{{\dot{m}}_{A}\Delta {h}_{total}}{{\eta}_{m}\omega},$$

where:

*Δh*is the change in specific total enthalpy._{total}*η*is the compressor_{m}**Mechanical efficiency**.*ω*is the relative shaft angular velocity,*ω*._{R}- ω_{C}

The block relates the efficiency in the compressor map as

$$\Delta {h}_{total}=\frac{\Delta {h}_{isen}}{{\eta}_{isen}},$$

where

*Δh*is the isentropic change is specific total enthalpy._{isen}*η*is the isentropic efficiency._{isen}

A threshold region when flow approaches zero ensures that no torque is generated when the flow rate is near zero or reversed.

### Analytical Parameterization

You can generate the compressor map analytically by setting
**Parameterization** to `Analytical`

.
The block fits a model of the compressor map based on Greitzer et al, 2010 to the
specified values for the **Corrected speed at design
point**,** Pressure ratio at design point**, and
**Corrected mass flow rate at design point** parameters. This
method does not use *β* lines and the block does not report a surge
margin.

**Pressure Ratio**

The block finds the pressure ratio at a given shaft speed and mass flow rate as:

$$\pi =1+\left({\pi}_{D}-1\right)\left[{\tilde{N}}^{ab}+2\tilde{N}k\mathrm{ln}\left(1-\frac{\tilde{m}-{\tilde{N}}^{b}}{k}\right)\right],$$

where:

*π*is the_{D}**Pressure ratio at design point**parameter.$$\tilde{N}$$ is the normalized corrected shaft speed,

$$\frac{N}{{N}_{D}},$$

where

*N*is the_{D}**Corrected speed at design point**parameter.$$\tilde{m}$$ is the normalized corrected mass flow rate,

$$\frac{{\dot{m}}_{corr}}{{\dot{m}}_{D}},$$

where $$\dot{m}$$

is the_{D}**Corrected mass flow rate at design point**.*a*is the**Spine shape, a**parameter.*b*is the**Speed line spread, b**parameter.*k*is the**Speed line roundness, k**parameter.

The *spine* refers to the black line where the
isentropic efficiency contours start to bend. The map *speed
lines* are the shaft constant-speed lines that intersect the spine
perpendicularly.

**Analytical Parameterization Default Compressor Map**

**Isentropic Efficiency Parameterization**

When you set **Efficiency specification** to
`Analytical`

, the block models variable compressor
efficiency as:

$$\eta ={\eta}_{0}\left(1-C{\left|\frac{\tilde{p}}{{\tilde{m}}^{a+\Delta a-1}}-\tilde{m}\right|}^{c}-D{\left|\frac{\tilde{m}}{{\tilde{m}}_{0}}-1\right|}^{d}\right),$$

where:

*η*is the_{0}**Maximum isentropic efficiency**parameter.*C*is the**Efficiency contour gradient orthogonal to spine, C**parameter.*D*is the**Efficiency contour gradient along spine, D**parameter.*c*is the**Efficiency peak flatness orthogonal to spine, c**parameter.*d*is the**Efficiency peak flatness along spine, d**parameter.$$\tilde{p}$$ is the normalized corrected pressure ratio,

$$\frac{\pi -1}{{\pi}_{D}-1},$$

where

*π*is the_{D}**Corrected pressure ratio at design point**parameter.$$\tilde{m}$$

is the normalized corrected mass flow rate at which the compressor reaches its_{0}**Maximum isentropic efficiency**parameter.

You can adjust the efficiency variables for different performance characteristics.

Alternatively, you can choose a constant efficiency value by using the
**Constant isentropic efficiency** parameter.

### Tabulated Data Parameterization

When you set **Parameterization** to
`Tabulated`

, the isentropic efficiency, pressure ratio,
and corrected mass flow rate of the compressor are functions 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.

If *β* exceeds 1, compressor surge occurs, and the block assumes
the pressure ratio remains at *β* = 1, while the mass flow rate continues to change. If the simulation
conditions fall below *β* = 0, the block includes the effects of choked flow: the mass flow rate
remains at its value at *β* = 0, while the pressure ratio continues to change. To constrain the
compressor performance within the map boundaries, the block extrapolates isentropic
efficiency to the nearest point.

You can choose to be notified when the operating point pressure ratio exceeds the surge
pressure ratio. Set **Report when surge margin is negative** to
`Warning`

to receive a warning or to
`Error`

to stop the simulation when this occurs.

### Visualizing the Block Compressor Map

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

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

**Tabulated Parameterization Default Compressor Map**

### Continuity Equations

The block conserves mass such that

$${\dot{m}}_{A}+{\dot{m}}_{B}=0,$$

where $$\dot{m}$$* _{B}* is the mass flow rate
at port

**B**.

The block computes the energy balance equation 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 hydraulic power delivered to the fluid, which is determined from the change in specific : $${P}_{fluid}={\dot{m}}_{A}\Delta {h}_{total}.$$_{fluid}

### Assumptions and Limitations

The block assumes that superheated fluid enters at

**A**.The block only defines compressor map flow from port

**A**to port**B**. Reverse flow results may not be accurate.The block only represents dynamic compressors.

## Ports

### Conserving

### Output

## Parameters

## Model Examples

## References

[1] Greitzer, E. M. et al. “N+3
Aircraft Concept Designs and Trade Studies. Volume 2: Appendices – Design Methodologies
for Aerodynamics, Structures, Weight, and Thermodynamic Cycles.” *NASA
Technical Report*, 2010.

[2] 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.

[3] 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**