# Compressor (2P)

Two-phase fluid compressor in a thermodynamic cycle

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• Simscape / Fluids / Two-Phase Fluid / Fluid Machines

## Description

The Compressor (2P) block represents a dynamic compressor, such as a centrifugal or axial compressor, in a two-phase fluid 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.

The Compressor (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.

### 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:

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

where:

• A is the mass flow rate at port A.

• TA is the temperature at port A.

• Tref is the Reference temperature for corrected flow. When you set Parameterization to Analytical, this is the inlet temperature at the design operating condition.

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

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.

• pA is the pressure at port A.

• pref is the Reference pressure for corrected flow parameter. When using the analytical parameterization, this is the inlet pressure at the design operating condition.

The block derives TA from the specific internal energy, uA, and specific pressure, pA.

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:

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

where:

• Δhtotal is the change in specific total enthalpy.

• ηm is the compressor Mechanical efficiency.

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

The block relates the efficiency in the compressor map as

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

where

• Δhisen is the isentropic change is specific total enthalpy.

• ηisen is the isentropic efficiency.

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:

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

where:

• πD is the Pressure ratio at design point parameter.

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

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

where ND is the Corrected speed at design point parameter.

• $\stackrel{˜}{m}$ 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 parameter.

• 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:

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

where:

• η0 is the Maximum isentropic efficiency 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.

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

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

where πD is the Corrected pressure ratio at design point parameter.

• $\stackrel{˜}{m}$0 is the normalized corrected mass flow rate at which the compressor reaches its 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 on the figure window.

Tabulated Parameterization Default Compressor Map

### Continuity Equations

The block conserves mass such that

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

where $\stackrel{˙}{m}$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:

• 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 specific : ${P}_{fluid}={\stackrel{˙}{m}}_{A}\Delta {h}_{total}.$

### 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

### Output

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Physical signal output port associated with the surge margin at a given mass flow rate. The block calculates the surge margin as

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

#### Dependencies

To enable this port, set Parameterization to Tabulated.

### Conserving

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Two-phase fluid conserving port associated with the compressor inlet.

Two-phase fluid conserving port associated with the compressor outlet.

Mechanical rotational conserving port associated with the compressor case.

Mechanical rotational conserving port associated with the compressor shaft.

## Parameters

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### Compressor Map

Compressor performance parameterization.

• Analytical: A pressure ratio corrected mass flow rate curve defines peak compressor performance. You can choose to include 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.

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

Option to parameterize efficiency using a constant value or analytically. 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 isentropic change to actual change.

#### Dependencies

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

Minimum compressor isentropic efficiency. Isentropic efficiency is the ratio of isentropic change to actual change.

#### 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.

#### 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.

#### Dependencies

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

Value of constant isentropic efficiency.

#### 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 relative positions along the corrected speed lines. 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. The block uses linear interpolation 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. The block uses linear interpolation 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 the block does nothing, generates a warning, or generates an error when it detects a negative surge margin.

#### Dependencies

To enable this parameter, set Parameterization to Tabulated.

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

### Map Coefficients

To enable the Map Coefficients parameters, set Parameterization to Analytical.

Exponent in the analytical parameterization of the compressor map that characterizes the spine shape.

Exponent in the analytical parameterization of the compressor map that characterizes the constant speed line spacing.

Coefficient in the analytical parameterization of the compressor map that characterizes the constant speed line shape.

Exponent associated with the compressor map peak flatness orthogonal to the spine.

Exponent associated with the efficiency map peak flatness along the spine.

Coefficient associated with the efficiency contour gradient orthogonal to the spine.

Coefficient associated with the efficiency contour gradient along the spine.

### Reference data

Reference inlet pressure for compressor map. When Parameterization is set to Tabulated, the data supplier specifies this value When you set Parameterization to Analytical, this is the inlet pressure at the design operating condition.

Reference inlet temperature for compressor map. When you set Parameterization to Tabulated, the data supplier specifies this value. When you set Parameterization to Analytical, this is the inlet temperature at the design operating condition.

Ratio of the power delivered to the fluid flow to the power driving the mechanical shaft.

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.

## Version History

Introduced in R2022a