Compressor Theory
Volumetric Efficiency (VE): This
is the ratio of the actual delivered gas volume to the swept volume of
the cylinder. Referring to the P-V diagram, the suction volumetric efficiency,
and the discharge volumetric efficiency, . This
represents the length of time available for gas to move through the compressor
valves, into or out of the cylinder. The
discharge event is this discharge
volumetric efficiency expressed in milliseconds of time rather than percent
of stroke.
Figure
1 - Ideal P-V Diagram
Given these laws governing and
definitions describing gas behavior, let us look at how they are applied
to a typical reciprocating compressor cycle. One of the preferred tools
for analyzing compressor performance is the Pressure-Volume (P-V) diagram.
The P-V diagram which is to be discussed here depicts the relationship
of the pressure and volume of the gas within one end of a cylinder of
a reciprocating compressor to the displacement of the piston. To start
with we will look at an ideal P-V diagram in which there are no valve
losses and the compression is adiabatic.
- Suction
valve opens and gas is drawn into the cylinder (1 - 2).
- Suction
valve closes and gas compression begins (2 - 3).
- Discharge
valve opens and the compressed gas is discharged from the cylinder (3
- 4).
- Discharge
valve closes. Note that a gap is shown in this diagram between zero volume
and the volume at position 4. This represents the clearance volume in
the cylinder. As the piston begins its return stroke, the gas which remains
in this space re-expands ( 4 - 1).
Effect
of Clearance Volume on Capacity
Gas is trapped in the clearance
volume after each stroke. This volume of gas must be re-expanded before
gas at suction conditions is admitted into the cylinder to be compressed.
Effect of Clearance Volume
Figure
2 - Effect of Clearance Volume
The re-expansion of the gas trapped
at the end of the discharge cycle does not influence the horsepower losses
but has a direct effect on the volumetric efficiency of the cylinder.
Figure 2 shows two P-V curves with different clearance volumes superimposed.
The opening positions of the valves change dramatically. With the higher
clearance volume the volumetric efficiency is considerably lower but so
is the horsepower consumption.
Pd = discharge pressure [psia]
Ps = suction pressure [psia]
CL% = clearance volume in %
k = effective cylinder isentropic
exponent
Figure
3 - Clearance Volume - Low Ratio
In applications where the compression
ratio is relatively small, the extra clearance volume has a lesser effect
on the volumetric efficiency. The reason for this is demonstrated in figures
2 and 3. In figure 3 an application with a 2.7:1 compression ratio is
shown with clearance volumes of 10% and 50%. With more clearance volume,
the piston must travel farther in its compression stroke before the cylinder
pressure exceeds the discharge line pressure enough to open the discharge
valve. The discharge volumetric efficiency (VEd) decreases and can be
reduced to a point (especially in high speed machines) where the compressed
gas cannot be discharged quickly enough and the valve is forced to close
late. A similar reduction in volumetric efficiency, and therefore in capacity,
can be expected on the suction valve when the clearance volume is increased.
Adjusted equivalent
valve area
Adjusted equivalent valve area
is a measure of the effective orifice area of the complete valve assembly.
The equivalent area is a static measure and does not assure good dynamic
behavior of the valve. This is a useful term to compare valve designs,
as a valve with a higher adjusted equivalent area will generally have
a lower pressure drop and better efficiency.
Equivalent area is a function
of valve lift and port area. Increasing lift or port area increases equivalent
area. However, higher lift valves generally have a shorter life than lower
lift valves--thus the trade-off between efficiency and durability
Below is a comparison of lift
vs. equivalent area for several valves.
Ariel
Corporation Application Manual
7-Sept-2001