Positive-Displacement Compressor (2P)
Two-phase fluid positive-displacement compressor in a thermodynamic cycle
Since R2022a
Libraries:
Simscape /
Fluids /
Two-Phase Fluid /
Fluid Machines
Description
The Positive-Displacement Compressor (2P) block represents a
positive-displacement compressor, such as reciprocating piston, rotary screw, rotary
vane, and scroll, in a two-phase fluid network. You can control how the block
parameterizes a positive displacement compressor by setting
Parameterization to Analytical
or
Tabulated
. 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, two-phase fluid
flows from port A to port B. The block may not
be accurate for reversed flow.
The block treats the positive displacement process as polytropic such that pvn is constant, where p is pressure, v is specific volume, and n is the Polytropic exponent parameter. You can use the block to model isentropic processes by setting n equal to the isentropic exponent, k. The figure shows the steps of a positive-displacement 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.
Efficiency
When you set Volumetric efficiency parameterization to
Analytical
, the block calculates the volumetric
efficiency as
where the block implements the polytropic pressure-volume relationship. The block calculates the clearance volume fraction, C, as
where ηVnominal is the Nominal volumetric efficiency parameter, and pratio is the ratio of saturation pressures that correspond to Nominal condensing temperature and Nominal evaporating temperature.
When you set Volumetric efficiency parameterization to
Tabulated
, the block interpolates the values of the
Volumetric efficiency table, eta(pr,w) parameter as a
function of the shaft speed and the pressure ratio.
Continuity Equations
The block calculates the mass flow rate as
where
ṁ 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.
Vdisp is the displacement volume that the block uses.
When you set Displacement specification to
Volumetric displacement
, the block uses the
Displacement volume parameter. When you set
Displacement specification to Nominal mass
flow rate and shaft speed
, the block calculates the displacement
volume as
where
ṁnominal is the Nominal mass flow rate parameter.
ωnominal is the Nominal shaft speed parameter.
ηVnominal is the Nominal volumetric efficiency parameter.
The block calculates the nominal inlet specific volume,
vs, based upon the
Nominal conditions specification parameter. When you select
Nominal pressure ratio
, the block uses the
Nominal inlet pressure and Nominal inlet
temperature parameters. When you select Nominal
evaporating and condensing temperatures
, the block uses the
Nominal evaporating temperature and Nominal
evaporator superheat parameters.
The block conserves mass such that
where ṁA and ṁB are the mass flow rates of ports A and B, respectively. The block conserves energy such that
where Δht is the change in specific total enthalpy, and ṁAΔht is the fluid power.
The block equates the fluid power to the polytropic power such that
where ηM is the Mechanical efficiency parameter, and τ is the shaft torque.
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 on the figure window.
When you set Volumetric efficiency parameterization to
Analytical
, the block plots compressor volumetric
efficiency vs. pressure ratio.
Analytical Parameterization Default Volumetric Efficiency
When you set Volumetric efficiency parameterization to
Tabulated
, the block plots compressor volumetric
efficiency vs. pressure ratio for each entry in the Shaft speed vector,
w.
Tabulated Parameterization Default 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.
The block is designed to operate in superheated vapor. The block may not be accurate in two-phase mixture or subcooled liquid.
Ports
Conserving
Parameters
References
[1] Mitchell and Braun, Principles of Heating, Ventilation, and Air Conditioning in Buildings, chap. SM6, 2012.
Extended Capabilities
Version History
Introduced in R2022a