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Positive-Displacement Compressor (MA)

Positive displacement compressor in a moist air network

Since R2024a

Libraries:
Simscape / Fluids / Moist Air / Turbomachinery

Description

The Positive-Displacement Compressor (MA) block represents a positive-displacement compressor, such as a reciprocating piston, rotary screw, rotary vane, or scroll, in a moist air network. Port R and port C are mechanical rotational conserving ports associated with the compressor shaft and casing, respectively. When there is positive rotation at port R with respect to port C, moist air flows from port A to port B. The block may not be accurate for reversed flow.

The figure shows the steps of a piston compressor on a P-V diagram, which has these states:

  • a — The compressor cylinder is full at inlet pressure.

  • b — The pressure inside the compressor exceeds that of the outlet, which results in fluid discharge.

  • c — The compressor reaches the top of the piston stroke, and only the clearance volume remains in the cylinder.

  • d — The pressure inside the cylinder drops below the inlet pressure, which results in fluid intake.

Figure showing piston compressor process where point A is at low pressure, high volume, point B is at high pressure, high volume, port C is at high pressure, low volume, and point d is at low pressure, low volume.

Mass Flow Rate

The block calculates the mass flow rate as

m˙=ηVωVdispvs,

where:

  • is the mass flow rate.

  • ω is the angular velocity of port R relative to port C.

  • vs is the specific volume at the inlet. The block calculates this value from the nominal inlet conditions.

  • Vdisp is the displacement volume that the block uses.

Displacement Volume

When you set Displacement specification to Volumetric displacement, the block uses the Displacement volume parameter as the value for Vdisp.

When you set Displacement specification to Nominal mass flow rate and shaft speed, the block calculates the displacement volume as

Vdisp=m˙nominalvs,nominalωnominalηVnominal,

where:

  • nominal is the value of the Nominal mass flow rate parameter.

  • ωnominal is the value of the Nominal shaft speed parameter.

  • ηVnominal is the value of the Nominal volumetric efficiency parameter when the Efficiency specification parameter is Analytical. When the Volumetric efficiency parameter is Tabulated, the block uses the tablelookup function to interpolate ηVnominal as a function of the shaft speed and the pressure ratio.

Volumetric Efficiency

You can parameterize the volumetric efficiency by using analytical values or a lookup table.

Analytical Volumetric Efficiency

When you set Efficiency specification to Analytical, the block calculates the volumetric efficiency by using analytical values. When the Thermodynamic model parameter is Polytropic, the volumetric efficiency is

ηV=1+CC(poutpin)1n,

where pin and pout are the inlet and outlet pressures, respectively, and n is the value of the Polytropic exponent parameter. The block calculates the clearance volume fraction, C, as

C=1ηVnominalpratio1/n1,

where ηVnominal is the value of the Nominal volumetric efficiency parameter and pratio is the value of the Nominal pressure ratio parameter.

When the Thermodynamic model parameter is Isentropic, the volumetric efficiency is

ηV=1+CC(vinvout),

where vin and vout are the inlet and outlet specific volumes, respectively. The block calculates the clearance volume fraction, C, as

C=1-ηVnominalvrnominal-1

where vrnominal=vinnominal/voutnominal is the nominal specific volume ratio. The block calculates this value from the nominal inlet conditions and the isentropic efficiency.

Tabulated Volumetric Efficiency

When you set Efficiency specification to Tabulated, the block calculates the volumetric efficiency by interpolating the values of the Volumetric efficiency table, eta_vol(pr,w) parameter as a function of the shaft speed and the pressure ratio.

Continuity Equations

The block conserves mass such that

m˙A+m˙B=0m˙wA+m˙wB=0m˙gA+m˙gB=0m˙dA+m˙dB=0

where:

  • m˙B is the mixture mass flow rate at port B.

  • m˙wA and m˙wB are the water vapor mass flow rates at ports A and B, respectively.

  • m˙gA and m˙gB are the trace gas mass flow rates at ports A and B, respectively.

  • m˙dA and m˙dB are the water droplets mass flow rates at ports A and B, respectively.

The block conserves energy such that

ϕA+ϕB+m˙AΔht=0,

where Δht is the change in specific total enthalpy and AΔht is the fluid power, which is equal to the mechanical power, torque*ω.

When the Thermodynamic model parameter is Polytropic, the fluid power is

W˙c=ωnn1ηVpinVdisp[(pinpout)n1n1],

where the block uses the polytropic relationship pvn=constant to relate pin, pout, vin, and vout.

When the Thermodynamic model parameter is Isentropic, the fluid power is

W˙C=m˙AΔht.

The block calculates Δht from the isentropic efficiency, ηisen. When the Efficiency specification parameter is Analytical, ηisen is equal to the value of the Isentropic efficiency parameter. When the Efficiency specification parameter is Tabulated, the block calculates ηisen by interpolating the values of the Isentropic efficiency table, eta_isen(pr,w) parameter as a function of the pressure ratio and the shaft speed.

Visualizing the Volumetric Efficiency

To visualize the block volumetric efficiency, right-click the block and select Fluids > Plot Volumetric Efficiency.

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

When you set Efficiency specification to Analytical and Thermodynamic model to Polytropic, the block plots the compressor volumetric efficiency against the pressure ratio.

Volumetric Efficiency

When you set Efficiency specification to Analytical and Thermodynamic model to Isentropic, the block plots the compressor volumetric efficiency against the pressure ratio at Tout nom, the nominal outlet temperature.

Volumetric Efficiency

When you set Efficiency specification to Tabulated, the block plots the compressor volumetric efficiency against the pressure ratio for each element in the Shaft speed vector, w parameter.

Volumetric Efficiency

Assumptions and Limitations

  • The block may not be accurate for flow from port B to port A.

  • The block assumes that the flow is quasi-steady. The compressor does not accumulate mass.

Examples

Ports

Conserving

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Moist air conserving port associated with the compressor inlet.

Moist air 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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Displacement

Whether to specify the fluid displacement according to volume per cycle or nominal condition values.

Fluid volume displaced per cycle. The block defines a cycle as one compression stroke and one expansion stroke, which occur during a single crank shaft revolution. This volume is the difference between the maximum cylinder volume and the clearance volume, (VaVc). In general, the displacement volume is the volume swept out by the compressor over one shaft revolution.

Dependencies

To enable this parameter, set Displacement specification to Volumetric displacement.

Nominal mass flow rate that the block uses to find the displacement volume.

Dependencies

To enable this parameter, set Displacement specification to Nominal mass flow rate and shaft speed.

Nominal shaft speed that the block uses to find the displacement volume.

Dependencies

To enable this parameter, set Displacement specification to Nominal mass flow rate and shaft speed.

Efficiency

The table shows how the options for the Thermodynamic model and Efficiency specification parameters affect the availability of dependent efficiency parameters.

Thermodynamic model
PolytropicIsentropic
Efficiency specificationEfficiency specification
AnalyticalTabulatedAnalyticalTabulated
Polytropic exponent Polytropic exponent Isentropic efficiency Isentropic efficiency table, eta_isen(pr,w)
Nominal volumetric efficiencyPressure ratio vector, prNominal volumetric efficiencyPressure ratio vector, pr
Shaft speed vector, wShaft speed vector, w
Volumetric efficiency table, eta_vol(pr,w)Volumetric efficiency table, eta_vol(pr,w)

Whether to parameterize the displacement volumetric efficiency by using analytical equations or tabulated data.

Whether to use a polytropic or isentropic thermodynamic model.

Exponent that the block uses when implementing the polytropic pressure-volume relationship.

Dependencies

To enable this parameter, set Thermodynamic model to Polytropic.

Constant efficiency the block uses when implementing the analytical isentropic pressure-volume relationship.

Dependencies

To enable this parameter, set Thermodynamic model to Isentropic and Efficiency specification to Analytical.

Efficiencies the block uses when implementing the tabulated isentropic pressure-volume relationship.

Dependencies

To enable this parameter, set Thermodynamic model to Isentropic and Efficiency specification to Tabulated.

Nominal volumetric efficiency to compute the clearance volume fraction. The nominal volumetric efficiency is the volumetric efficiency when the compressor operates at nominal conditions.

Dependencies

To enable this parameter, set Efficiency specification to Analytical.

Vector of pressure ratios that correspond to the compressor volumetric efficiency. Each element corresponds to a row of the Volumetric efficiency table, eta_vol(pr,w) parameter. This parameter must be a vector of size N, where N is the length of the Volumetric efficiency table, eta_vol(pr,w) parameter.

Dependencies

To enable this parameter, set Efficiency specification to Tabulated.

Vector of shaft speeds that correspond to the compressor volumetric efficiency. Each element corresponds to a column of the Volumetric efficiency table, eta_vol(pr,w) parameter. This parameter must be a vector of size M, where M is the width of the Volumetric efficiency table, eta_vol(pr,w) parameter.

Dependencies

To enable this parameter, set Efficiency specification to Tabulated.

Volumetric efficiency for a given shaft speed and pressure ratio. This parameter must be a matrix of size N by M, where N is the length of the Pressure ratio vector, pr parameter and M is the length of the Shaft speed vector, w parameter.

Dependencies

To enable this parameter, set Efficiency specification to Tabulated.

Nominal Conditions

The table shows how the options for the Displacement specification, Thermodynamic model, and Efficiency specification parameters affect the availability of dependent nominal condition parameters.

This table shows the dependent parameters when you set the Displacement specification parameter to Volumetric displacement:

When the Displacement specification parameter is Volumetric displacement
Efficiency specification
AnalyticalTabulated
Thermodynamic modelThermodynamic model
PolytropicIsentropicPolytropicIsentropic
Nominal pressure ratioNominal pressure ratio Nominal pressure ratio
Nominal inlet pressureNominal inlet pressure
Nominal inlet temperatureNominal inlet temperature
Nominal inlet humidity, water droplet, and trace gas parameters Nominal inlet humidity, water droplet, and trace gas parameters

When you set Displacement specification to Nominal mass flow rate and shaft speed, the parameters in Nominal Conditions do not depend on the Efficiency specification or Thermodynamic model parameters.

Nominal pressure ratio that the block uses to compute the clearance volume fraction.

Dependencies

To enable this parameter, select any parametrization except when Displacement specification is Volumetric displacement, Thermodynamic model is Polytropic, and Efficiency specification is Tabulated.

Nominal inlet pressure that the block uses to find the displacement volume.

Dependencies

To enable this parameter, either set Displacement specification to Nominal mass flow rate and shaft speed or set Displacement specification to Volumetric displacement and set Thermodynamic model to Isentropic.

Nominal inlet temperature that the block uses to find the displacement volume.

Dependencies

To enable this parameter, either set Displacement specification to Nominal mass flow rate and shaft speed or set Displacement specification to Volumetric displacement and set Thermodynamic model to Isentropic.

Whether to describe the inlet moist air humidity level using the relative humidity, specific humidity, water vapor mole fraction, or humidity ratio.

Dependencies

To enable this parameter, either set Displacement specification to Nominal mass flow rate and shaft speed or set Displacement specification to Volumetric displacement and set Thermodynamic model to Isentropic.

Moist air relative humidity at the inlet under nominal operating conditions.

Dependencies

To enable this parameter, either set:

  • Displacement specification to Nominal mass flow rate and shaft speed and Inlet humidity specification to Relative humidity.

  • Displacement specification to Volumetric displacement, Thermodynamic model to Isentropic, and Inlet humidity specification to Relative humidity.

Moist air specific humidity, defined as the mass fraction of water vapor in a moist air mixture, at the inlet under nominal operating conditions.

Dependencies

To enable this parameter, either set:

  • Displacement specification to Nominal mass flow rate and shaft speed and Inlet humidity specification to Specific humidity.

  • Displacement specification to Volumetric displacement, Thermodynamic model to Isentropic, and Inlet humidity specification to Specific humidity.

Mole fraction of the water vapor in a moist air mixture at the inlet under nominal operating conditions.

Dependencies

To enable this parameter, either set:

  • Displacement specification to Nominal mass flow rate and shaft speed and Inlet humidity specification to Mole fraction.

  • Displacement specification to Volumetric displacement, Thermodynamic model to Isentropic, and Inlet humidity specification to Mole fraction.

Moist air humidity ratio, defined as the mass ratio of water vapor to dry air and trace gas, at the inlet under nominal operating conditions.

Dependencies

To enable this parameter, either set:

  • Displacement specification to Nominal mass flow rate and shaft speed and Inlet humidity specification to Humidity ratio.

  • Displacement specification to Volumetric displacement, Thermodynamic model to Isentropic, and Inlet humidity specification to Humidity ratio.

Wet-bulb temperature of the moist air mixture at the inlet under nominal operating conditions.

Dependencies

To enable this parameter, either set:

  • Displacement specification to Nominal mass flow rate and shaft speed and Inlet humidity specification to Wet-bulb temperature.

  • Displacement specification to Volumetric displacement, Thermodynamic model to Isentropic, and Inlet humidity specification to Wet-bulb temperature.

Whether to use the mass fraction or mole fraction to describe the trace gas level at the inlet.

Dependencies

To enable this parameter, either set Displacement specification to Nominal mass flow rate and shaft speed or set Displacement specification to Volumetric displacement and set Thermodynamic model to Isentropic.

Mass fraction of the trace gas in a moist air mixture at the inlet under nominal operating conditions.

Dependencies

To enable this parameter, either set:

  • Displacement specification to Nominal mass flow rate and shaft speed and Inlet trace gas specification to Mass fraction.

  • Displacement specification to Volumetric displacement, Thermodynamic model to Isentropic, and Inlet trace gas specification to Mass fraction.

Mole fraction of the trace gas in a moist air mixture at the inlet under nominal operating conditions.

Dependencies

To enable this parameter, either set:

  • Displacement specification to Nominal mass flow rate and shaft speed and Inlet trace gas specification to Mole fraction.

  • Displacement specification to Volumetric displacement, Thermodynamic model to Isentropic, and Inlet trace gas specification to Mole fraction.

Mass ratio of water droplets to moist air at the inlet under nominal operating conditions.

Dependencies

To enable this parameter, either set Displacement specification to Nominal mass flow rate and shaft speed or set Displacement specification to Volumetric displacement and set Thermodynamic model to Isentropic.

Relative humidity above which condensation occurs in the condenser.

Dependencies

To enable this parameter, either set Displacement specification to Nominal mass flow rate and shaft speed or set Displacement specification to Volumetric displacement and set Thermodynamic model to Isentropic.

Parameters

Ratio of the fluid power to the mechanical shaft power.

Inlet area associated with port A.

Outlet area associated with port B.

References

[1] Mitchell, John W., and James E. Braun. Principles of Heating, Ventilation, and Air Conditioning in Buildings. Hoboken, NJ: Wiley, 2013.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2024a

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