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# Compressor (G)

Gas compressor in a thermodynamic cycle

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• Simscape / Fluids / Gas / Turbomachinery

## Description

The Compressor (G) block models a dynamic compressor, such as a centrifugal or axial compressor, in a gas network. You can parameterize the block analytically or by a tabulated compressor map. Fluid flowing from port A to port B generates torque. Port R reports shaft torque and angular velocity relative to port C, which is associated with the compressor casing.

In the tabulated data parameterization, the surge margin, the ratio between the surge pressure ratio at a given mass flow rate and the operating point pressure ratio minus `1`, is output at port SM.

The compressor design point is the intended operational pressure ratio over 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

A compressor map depicts compressor performance as a function of pressure ratio, the compressor outlet pressure to the inlet pressure, and corrected mass flow rate. The map plots the isentropic efficiency of the compressor between the two extremes of choked flow and surge flow. Compressor maps use β lines to assess performance at an interval across shaft speeds. Choked flow corresponds to β = 0 and surge flow corresponds to β = 1. β lines are perpendicular to the compressor shaft constant speed lines, N, which are also corrected for pressure and temperature changes in the compressor.

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 corrected pressure and corrected temperature:

`${\stackrel{˙}{m}}_{A}\sqrt{\frac{{T}_{A}}{{T}_{corr}}}={\stackrel{˙}{m}}_{corr}\frac{{p}_{A}}{{p}_{corr}},$`

where:

• $\stackrel{˙}{m}$A is the mass flow rate at port A.

• TA is the temperature at port A.

• Tcorr is the Reference temperature for corrected flow. When using a tabulated compressor map, the data supplier specifies this value. When using the analytical parameterization, this is the temperature at which the pressure ratio–mass flow rate relationship over a range of temperatures converges to a single trend line.

• $\stackrel{˙}{m}$corr is the corrected mass flow rate.

When Parameterization is set to `Analytical`, this is the Corrected mass flow rate at design point.

When Parameterization is set to `Tabulated`, this is derived from the Corrected mass flow rate table, mdot(N,beta).

• pA is the pressure at port A.

• pcorr is the Reference pressure for corrected flow. When using a tabulated compressor map, the data supplier specifies this value. When using the analytical parameterization, this is the pressure at which the pressure ratio–mass flow rate relationship over a range of pressures converges to a single trend line.

### Shaft Torque

The shaft torque, τ, is calculated as:

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

where:

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

• ηm is the compressor Mechanical efficiency.

• ω is the relative shaft angular velocity, ωR - ωC.

Reversed flow, from B to A, is outside of the typical compressor operation mode and accurate results should not be expected. A threshold region when flow approaches zero ensures that no torque is generated when the flow rate is near zero or reversed.

### Analytical Parameterization

If you do not have tabulated compressor data available, you can model the compressor pressure ratio, corrected mass flow rate, and isentropic efficiency analytically. The analytical method does not use β lines and the block does not report a surge margin.

Pressure Ratio

The pressure ratio at a given shaft speed and mass flow rate is calculated as:

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

where:

• πD is the Pressure ratio at design point.

• $\stackrel{˜}{N}$ is the normalized corrected shaft speed,

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

where ND is the Corrected speed at design point.

• $\stackrel{˜}{m}$ is the normalized corrected mass flow rate,

`$\frac{{\stackrel{˙}{m}}_{corr}}{{\stackrel{˙}{m}}_{D}},$`

where $\stackrel{˙}{m}$D is the Corrected mass flow rate at design point.

• a is the Spine shape, a.

• b is the Speed line spread, b.

• k is the Speed line roundness, k.

The map spine refers to the analytical line denoting the nominal compressor performance. The map speed lines are the shaft constant-speed lines that intersect the spine perpendicularly. The spine and speed line variables are tunable parameters that can be adjusted for different performance characteristics.

Analytical Parameterization Default Compressor Map

Isentropic Efficiency Parameterization

When Efficiency specification is set to `Analytical`, the block models variable compressor efficiency as:

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

where:

• η0 is the Maximum isentropic efficiency.

• C is the Efficiency contour gradient orthogonal to spine, C.

• D is the Efficiency contour gradient along spine, D.

• c is the Efficiency peak flatness orthogonal to spine, c.

• d is the Efficiency peak flatness along spine, d.

• $\stackrel{˜}{p}$ is the normalized corrected pressure ratio,

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

where πD is the Corrected pressure ratio at design point.

• $\stackrel{˜}{m}$0 is the normalized corrected mass flow rate at which the compressor reaches its Maximum isentropic efficiency.

The efficiency variables are tunable parameters that you can adjust for different performance characteristics. a measures the relationship between the operating point and the point of maximum efficiency. When Δa = 0, the compressor operates at the point of maximum efficiency.

Alternatively, you can model constant efficiency by assigning a Constant efficiency value.

### Tabulated Data Parameterization

When Parameterization is set to `Tabulated`, the compressor 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.

If the simulation conditions exceed β = 1, surge flow is modeled: the pressure ratio remains at its value at β = 1, while the mass flow rate continues to change. If the simulation conditions fall below β = 0, choked flow is modeled: 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 static 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 Characteristics.

Each time you modify the block settings, click at the bottom of the dialog box, then click on the figure window.

Tabulated Parameterization Default Compressor Map

### Continuity Equations

Mass is preserved over the block:

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0,$`

where $\stackrel{˙}{m}$B is the mass flow rate at port B.

The energy balance in the block is calculated as:

`${\Phi }_{A}+{\Phi }_{B}+{P}_{fluid}=0,$`

where:

• ΦA is the energy flow rate at port A.

• ΦB is the energy flow rate at port B.

• Pfluid is the hydraulic power delivered to the fluid, which is determined from the change in total fluid specific enthalpy: ${P}_{fluid}={\stackrel{˙}{m}}_{A}\Delta {h}_{total}.$

### Assumptions and Limitations

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

• The block only models dynamic compressors.

• Successful simulation initialization requires a moderately accurate pressure input.

## Ports

### Conserving

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Fluid entry port.

Fluid exit port.

Port associated with the compressor casing.

Port associated with the compressor shaft torque and angular velocity.

### Output

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Outputs the compressor surge margin, the ratio between the operating point pressure ratio and the surge pressure ratio, at a given mass flow rate:

`$SM\left({\stackrel{˙}{m}}_{corr}\right)=\frac{{p}_{r,surge}\left({\stackrel{˙}{m}}_{corr}\right)}{{p}_{r}\left({\stackrel{˙}{m}}_{corr}\right)}-1.$`

#### Dependencies

To enable this port, set Parameterization to `Tabulated`.

## Parameters

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### Compressor Map

Compressor performance model. You can choose either:

• `Analytical`: A pressure ratio–corrected mass flow rate curve defines peak compressor performance. You can choose to model isentropic efficiency as a constant or analytically.

• `Tabulated`: A user-supplied compressor map defines the compressor performance. The compressor operating points are determined by linear interpolation between the corrected mass flow rate, pressure ratio, and isentropic efficiency tables at given points in the user-provided corrected shaft speed and β vectors. The default map comes from data reported in [3].

Shaft speed at the intended compressor pressure ratio and corrected mass flow rate, corrected for pressure and temperature.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical`.

Outlet-to-inlet pressure ratio at the intended compressor corrected mass flow rate.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical`.

Mass flow rate at the intended compressor pressure ratio, corrected for temperature and pressure.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical`.

Isentropic efficiency model type. Choose a constant or variable (analytical) model.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical`.

Maximum compressor isentropic efficiency. Isentropic efficiency is the ratio of the change in total specific enthalpy to the change in total specific isentropic enthalpy.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical` and Efficiency specification to `Analytical`.

Mass flow rate at maximum efficiency, corrected for temperature and pressure. The point of maximum efficiency does not necessarily coincide with the compressor design point in your simulation.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical` and Efficiency specification to `Analytical`.

Pressure ratio at maximum efficiency. The point of maximum efficiency does not necessarily coincide with the compressor design point in your simulation.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical` and Efficiency specification to `Analytical`.

Value of constant isentropic efficiency in the analytical parameterization.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical` and Efficiency specification to `Constant`.

Vector of corrected shaft speeds.

#### Dependencies

To enable this parameter, set Parameterization to `Tabulated`.

Vector of intervals between 0 and 1 at which to assess compressor performance. Choked flow is defined as β = 0 and surge flow is defined at β = 1. β lines are perpendicular to the compressor shaft constant speed lines, N.

#### Dependencies

To enable this parameter, set Parameterization to `Tabulated`.

M-by-N matrix of compressor outlet-to-inlet pressure ratios at the specified corrected shaft speed and β value. Linear interpolation is employed between 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 vector elements in the parameter.

#### Dependencies

To enable this parameter, set Parameterization to `Tabulated`.

M-by-N matrix of corrected mass flow rates at the specified corrected shaft speed and β value. Linear interpolation is employed between 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 vector elements in the parameter.

#### Dependencies

To enable this parameter, set Parameterization to `Tabulated`.

M-by-N matrix of compressor isentropic efficiencies at the specified corrected shaft speed and β value. Linear interpolation is employed between 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 vector elements in the parameter.

#### Dependencies

To enable this parameter, set Parameterization to `Tabulated`.

Whether to notify if the compressor operating point pressure ratio exceeds the surge pressure ratio at the given corrected mass flow rate.

#### Dependencies

To enable this parameter, set Parameterization to `Tabulated`.

### Map Coefficients

To enable this tab, set Parameterization to `Analytical`.

Exponent in the analytical parameterization of the pressure ratio that characterizes the spine shape.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical`.

Exponent in the analytical parameterization of the pressure ratio that characterizes the constant speed line spacing.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical`.

Coefficient in the analytical parameterization of the pressure ratio that characterizes the constant speed line shape.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical`.

Exponent in the analytical efficiency model that characterizes the efficiency curve shape.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical` and Efficiency specification to `Analytical`.

Exponent in the analytical efficiency model.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical` and Efficiency specification to `Analytical`.

Coefficient in the analytical efficiency model.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical` and Efficiency specification to `Analytical`.

Coefficient in the analytical efficiency model.

#### Dependencies

To enable this parameter, set Parameterization to `Analytical` and Efficiency specification to `Analytical`.

### Reference Data

Pressure at which compressor data consolidates to a corrected trend line. When Parameterization is set to `Tabulated`, the data supplier specifies this value. When Parameterization is set to `Analytical`, this is the pressure at which the pressure ratio–mass flow rate relationship over a range of pressures converges to a single trend line.

Temperature at which compressor data becomes consolidated to a corrected trend line. When Parameterization is set to `Tabulated`, the data supplier specifies this value. When Parameterization is set to `Analytical`, this is the temperature at which the pressure ratio–mass flow rate relationship over a range of temperatures converges to a single trend line.

Efficiency of conversion from gain in specific enthalpy to shaft torque.

Compressor inlet cross-sectional area.

Compressor outlet cross-sectional area.

## 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.

## See Also

Introduced in R2021a

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