Compressor (G)

A gas compressor in a thermodynamic cycle.

blockType: EngeeFluids.Gas.Turbomachinery.Compressor

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/Physical Modeling/Fluids/Gas/Turbomachinery/Compressor (G)

Description

Block Compressor (G) It is a dynamic compressor, for example, centrifugal or axial, in a gas network. Parameter Parameterization It can be used for analytical parameterization of the unit based on the calculated mode or using tabular characteristic data of the compressor. The positive rotation of port R relative to port C causes fluid to move from port A to port B. Ports R and C are non—directional ports connected to the compressor shaft and housing, respectively.

The surge margin is the ratio between the hydrodynamic pressure drop at a given mass flow rate and the pressure drop at the design point. 1. If for the parameter Parameterization the value is set Tabulated, the unit outputs the surge reserve in the SM port.

The design mode is the calculated ratio of the differential pressure in the compressor and the mass flow through the compressor during the simulation. The design point of the compressor and the maximum efficiency point do not necessarily have to coincide.

Compressor Characteristics

The characteristic data of the compressor displays the isentropic efficiency of the compressor and the lines of constant reduced shaft speed between two extreme values: critical mode and surge mode.

conducted mass flow rate

Due to the large pressure and temperature differences inside the compressor, the performance characteristics of the compressor are calculated depending on the specified mass flow rate. The specified mass flow rate is calculated based on the mass flow rate at the inlet, as well as using characteristic data: reference pressure and reference temperature

where

— mass flow rate at the input port A.
— temperature at the input port A.
— parameter value Reference temperature for corrected flow. If for the parameter Parameterization the value is set Analytical, then this is the inlet temperature under the design operating conditions.
— the specified mass flow rate.

If for the parameter Parameterization the value is set Analytical, the block uses the parameter Corrected mass flow rate at design point.

If for the parameter Parameterization the value is set Tabulated, the block uses the parameter Corrected mass flow rate table, mdot(N,beta).
— pressure at the input port A.
— parameter Reference pressure for corrected flow. If for the parameter Parameterization the value is set Analytical, then this value corresponds to the inlet pressure under the design operating conditions.

In the block calculated from the specific internal energy and pressure .

The specified rotation speed

Angular rotation speed of the shaft is brought to the reference temperature, so that the reduced angular velocity of the shaft is

Shaft torque

Shaft torque defined as

where

— change in specific total enthalpy;
— mechanical efficiency of the compressor;
— relative angular velocity of the shaft, .

The block relates the efficiency of the compressor characteristic data as follows:

where

— isentropic change in specific total enthalpy;
— isentropic efficiency.

The threshold range at which the flow rate approaches zero, or negative, ensures that zero shaft torque is generated in the compressor.

Analytical parameterization

You can set the compressor characteristics analytically by setting the parameter Parameterization meaning Analytical. The block defines the compressor characteristic data model based on [1] to the set parameter values Corrected speed at design point, Pressure ratio at design point and Corrected mass flow rate at design point.

pressure difference

The unit finds the pressure drop at a given shaft speed and mass flow rate as

where

— parameter Pressure ratio at design point;
— normalized reduced shaft speed

where — parameter Corrected speed at design point;

— normalized reduced mass flow rate

where — parameter Corrected mass flow rate at design point;

— parameter Spine shape, a;
— parameter Speed line spread, b;
— parameter Speed line roundness, k.

parametrization of isentropic efficiency

If for the parameter Efficiency specification the value is set Analytical, the block models the variable efficiency of the compressor as

where

— parameter value Maximum isentropic efficiency;
— parameter value Efficiency contour gradient orthogonal to spine, C;
— parameter value Efficiency peak flatness along spine, d;
— parameter value Efficiency contour gradient orthogonal to spine, C;
— parameter value Efficiency peak flatness along spine, d;
— normalized reduced pressure drop

where — parameter Pressure ratio at design point;

— the normalized reduced mass flow rate at which the compressor reaches the value of the parameter Maximum isentropic efficiency.

You can adjust the efficiency variables for different performance characteristics. Alternatively, you can select a constant efficiency value using the parameter Constant isentropic efficiency.

Parameterization of the compressor using tabular characteristic data

If for the parameter Parameterization the value is set Tabulated, The isentropic efficiency, pressure drop, and reduced mass flow rate of the compressor are functions of the reduced velocity. and the index of characteristic data . The unit uses linear interpolation between data points for efficiency, differential pressure, and reduced mass flow.

If exceeds 1, the compressor is surging, and the unit assumes that the pressure drop remains at the level of while the mass flow rate continues to change. If the simulation conditions fall below , the block simulates the effect of a critical flow in which the mass flow remains at the level of , and the pressure drop continues to change. To limit the compressor’s performance within the limits of the characteristic data, the unit extrapolates the isentropic efficiency to the nearest point.

You can receive notifications when the pressure drop at the design point exceeds the surge pressure drop. Set for the parameter Report when surge margin is negative meaning Error to stop the simulation in this case.

Equations of continuity

The mass in the block is stored according to the following expression:

where — mass flow rate at the output port B.

The block calculates the energy balance equation as

where

— energy flow through port A.
— energy flow through port B.
— the hydraulic power transferred to the liquid is determined by the change in specific enthalpy .

Assumptions and limitations

The unit assumes that the superheated liquid enters port A.
The unit only determines the flow of the compressor from port A to port B. The results for reverse flows may be inaccurate.
The block contains only dynamic compressors.

Ports

Conserving

# A — gas inlet port
gas

Details

A non-directional port connected to the compressor input.

Program usage name

inlet

# C — compressor housing
translational mechanics

Details

A non-directional port connected to the compressor housing.

Program usage name

case_flange

# B — gas outlet port
gas

Details

A non-directional port connected to the compressor outlet.

Program usage name

outlet

# R — compressor shaft
translational mechanics

Details

A non-directional port related to the torque on the compressor shaft and the angular velocity.

Program usage name

rod_flange

Parameters

Compressor Map

# Parameterization — parameterization of compressor performance
Analytical | Tabulated

Details

Parameterization of compressor performance. Select analytical or tabular parameterization:

Analytical — the curve of the dependence of the reduced pressure drop on the mass flow determines the peak performance of the compressor. You can choose to model the isentropic efficiency as a constant value or analytically determined.
Tabulated — User-defined compressor characteristics determine compressor performance. The unit determines the operating points of the compressor using linear interpolation in tabular data between the values of the reduced mass flow rate, pressure drop and isentropic efficiency at specified points in the reduced shaft speed vectors provided by the user and . The default characteristic data is based on the data provided in [3].

Values	`Analytical` \| `Tabulated`
Default value	`Analytical`
Program usage name	`parameterization`
Evaluatable	No

Details

The speed of the shaft at a given pressure drop in the compressor and a given mass flow rate adjusted for temperature.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical.

Units	`rad/s` \| `deg/s` \| `rad/min` \| `deg/min` \| `rpm` \| `rps`
Default value	`10000.0 rpm`
Program usage name	`w_nominal`
Evaluatable	Yes

# Pressure ratio at design point — new pressure drop from outlet to inlet

Details

Pressure drop from outlet to inlet at the calculated reduced mass flow rate of the compressor.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical.

Default value	`7.5`
Program usage name	`p_ratio_nominal`
Evaluatable	Yes

Details

The mass flow rate at a given pressure drop in the compressor, adjusted for temperature and pressure.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical.

Units	`kg/s` \| `kg/hr` \| `kg/min` \| `g/hr` \| `g/min` \| `g/s` \| `t/hr` \| `lbm/hr` \| `lbm/min` \| `lbm/s`
Default value	`33.0 kg/s`
Program usage name	`mdot_nominal`
Evaluatable	Yes

# Efficiency specification — isentropic efficiency model
Constant | Analytical

Details

A type of isentropic efficiency model. Choose a continuous efficiency model or an analytical model. Use the value Analytical to specify the values of variables.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical.

Values	`Constant` \| `Analytical`
Default value	`Analytical`
Program usage name	`efficiency_type`
Evaluatable	No

# Maximum isentropic efficiency — maximum compressor efficiency

Details

The maximum isentropic efficiency of the compressor. Isentropic efficiency is the ratio of the operation of a liquid in the isentropic approximation to the actual operation of the liquid.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical, and for the parameter Efficiency specification meaning Analytical.

Default value	`0.887`
Program usage name	`max_efficiency`
Evaluatable	Yes

# Minimum isentropic efficiency — minimum compressor efficiency

Details

The minimum isentropic efficiency of the compressor. Isentropic efficiency is the ratio of the operation of a liquid in the isentropic approximation to the actual operation of the liquid.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical, and for the parameter Efficiency specification meaning Analytical.

Default value	`0.5`
Program usage name	`min_efficiency`
Evaluatable	Yes

Details

Mass flow at maximum efficiency, adjusted for temperature and pressure. The maximum efficiency point does not necessarily coincide with the design point of the compressor.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical, and for the parameter Efficiency specification meaning Analytical.

Units	`kg/s` \| `kg/hr` \| `kg/min` \| `g/hr` \| `g/min` \| `g/s` \| `t/hr` \| `lbm/hr` \| `lbm/min` \| `lbm/s`
Default value	`30.0 kg/s`
Program usage name	`mdot_at_max_efficiency`
Evaluatable	Yes

# Pressure ratio at maximum efficiency point — pressure drop at maximum compressor efficiency

Details

Pressure drop at maximum efficiency. The maximum efficiency point does not necessarily coincide with the design point of the compressor.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical, and for the parameter Efficiency specification meaning Analytical.

Default value	`7.0`
Program usage name	`p_ratio_at_max_efficiency`
Evaluatable	Yes

Map Coefficients

# Spine shape, a — an indicator of the degree of shape of isolines of isentropic efficiency

Details

An indicator of the degree of analytical parameterization of the characteristic data of the compressor, characterizing the isolines of isentropic efficiency depending on the pressure drop and the reduced flow rate.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical.

Default value	`1.5`
Program usage name	`coefficient_a`
Evaluatable	Yes

# Speed line spread, b — exponent for angular velocity isolines

Details

An indicator of the degree in the analytical parameterization of the characteristic data of the compressor, characterizing the constant pitch of the angular velocity isolines.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical.

Default value	`5.0`
Program usage name	`coefficient_b`
Evaluatable	Yes

# Speed line roundness, k — angular velocity contour line shape coefficient

Details

The coefficient in the analytical parameterization of the characteristic data of the compressor, characterizing the shape of the angular velocity isolines.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical.

Default value	`0.03`
Program usage name	`coefficient_k`
Evaluatable	Yes

# Efficiency peak flatness orthogonal to spine, c — an indicator of the degree characterizing the form of analytical isentropic efficiency

Details

An exponent related to the smoothness of the peak of the characteristic data of the isentropic efficiency surface orthogonal to its isolines.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical, and for the parameter Efficiency specification meaning Analytical.

Default value	`3.0`
Program usage name	`coefficient_c`
Evaluatable	Yes

# Efficiency peak flatness along spine, d — an indicator of the degree characterizing the form of analytical isentropic efficiency

Details

The exponent associated with the smoothness of the peak of the characteristic data of the isentropic efficiency surface along its isolines.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical, and for the parameter Efficiency specification meaning Analytical.

Default value	`4.0`
Program usage name	`coefficient_d`
Evaluatable	Yes

# Efficiency contour gradient orthogonal to spine, C — the coefficient characterizing the form of analytical isentropic efficiency

Details

A coefficient related to the gradient of the isentropic efficiency surface orthogonal to its isolines.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical, and for the parameter Efficiency specification meaning Analytical.

Default value	`15.0`
Program usage name	`coefficient_C`
Evaluatable	Yes

# Efficiency contour gradient along spine, D — the coefficient characterizing the form of analytical isentropic efficiency

Details

The coefficient related to the gradient of the isentropic efficiency surface along its isolines.

Dependencies

To use this parameter, set for the parameter Parameterization meaning Analytical, and for the parameter Efficiency specification meaning Analytical.

Default value	`1.0`
Program usage name	`coefficient_D`
Evaluatable	Yes

Reference Data

# Reference pressure for corrected flow — corrective pressure
Pa | uPa | hPa | kPa | MPa | GPa | kgf/m^2 | kgf/cm^2 | kgf/mm^2 | mbar | bar | kbar | atm | ksi | psi | mmHg | inHg

Details

The reference inlet pressure for the compressor characteristics. If for the parameter Parameterization the value is set Tabulated, the data provider specifies this value according to the tabular data of the compressor. If for the parameter Parameterization the value is set Analytical, this value corresponds to the inlet pressure under the design operating conditions.

Units	`Pa` \| `uPa` \| `hPa` \| `kPa` \| `MPa` \| `GPa` \| `kgf/m^2` \| `kgf/cm^2` \| `kgf/mm^2` \| `mbar` \| `bar` \| `kbar` \| `atm` \| `ksi` \| `psi` \| `mmHg` \| `inHg`
Default value	`0.101325 MPa`
Program usage name	`p_ref`
Evaluatable	Yes

Details

Reference inlet temperature for compressor characteristics. If for the parameter Parameterization the value is set Tabulated, the data provider specifies this value relative to the tabular compressor data. If for the parameter Parameterization the value is set Analytical, this value represents the inlet temperature under the calculated operating conditions.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`288.15 K`
Program usage name	`T_ref`
Evaluatable	Yes

# Mechanical efficiency — torque conversion efficiency

Details

The ratio of the power transmitted to the fluid flow to the mechanical power driving the shaft.

Default value	`0.9`
Program usage name	`mechanical_efficiency`
Evaluatable	Yes

# Inlet area at port A — compressor inlet cross-section area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area at the compressor inlet.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`1.0 m^2`
Program usage name	`inlet_area`
Evaluatable	Yes

# Outlet area at port B — compressor output cross-section area
m^2 | um^2 | mm^2 | cm^2 | km^2 | in^2 | ft^2 | yd^2 | mi^2 | ha | ac

Details

The cross-sectional area at the outlet to the compressor.

Units	`m^2` \| `um^2` \| `mm^2` \| `cm^2` \| `km^2` \| `in^2` \| `ft^2` \| `yd^2` \| `mi^2` \| `ha` \| `ac`
Default value	`1.0 m^2`
Program usage name	`outlet_area`
Evaluatable	Yes

List of literature

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.
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.
Plencner, Robert M. «Plotting component maps in the Navy/NASA Engine Program (NNEP): A method and its usage.» NASA Technical Memorandum, 1989.