Idealised working cycle
An approximate calculation of the working cycle for a specific cylinder of your choice can be carried out with the program below. The original version of this program was compiled by Mr. Matthias Kornfeld, TU Vienna on the occasion of the 5th EFRC- workshop in 2008.
When using this program you can chose quality criteria for clearance volume, the compressor valves and the wear condition of the cylinder in question as ´´ very good ´´ or ´´ less good ´´. According to your choice the program then defines the clearance volume ratio, the temperature and mass factor of the performance ratio, the polytropic exponent and the effective valve area in relation to the piston area. Thereby it is possible to assess the influence of these quality criteria on compressor throughput and power consumption .
The overall proceedings in the working chamber are called the working cycle. To start let us assume the compressor working without any losses . The clearance volume as is necessary by the design is Vo . By cooling the cylinder the compression will be polytropic, which is between the isothermal and isentropic compression.
The working cycle can be shown with a p,V diagram ( indicator diagram ), which shows both the change in the conditions of state and the changes of masses.
The polytropic compression starts in bottom dead center UT (1) at suction conditions and ends when the delivery pressure has been reached (2). Then the delivery valve opens and gas is pushed out at constant pressure up to top dead center OT (3). There the sign of the volume change alters and the delivery valve closes. The reexpansion of the remaining gas from the clearance volume back to suction pressure follows (4). The suction valve now opens and fresh gas is sucked in at suction conditions up to bottom dead center UT (1).
The suction and discharge process are ideally pure changes in mass and are called (similar to the combustion engines ) load changes.
In the case of ideal process the changes of state of compression and reexpansion have the same polytropic exponent. The clearance volume then only causes a diminished flow of gas.
In real compressors there are compensation processes of gas velocity , temperature and pressure which only happen in one direction and which are unavoidable ( irreversabilities ). These are superimposed onto the idealised compression cycle. The work as supplied by the piston ( internal work ) can therefore not be used in its entirety for the compression of the gas.
Through these super imposed compensation processes the p,V diagram changes. The area of the diagram corresponds to the real internal work per compression cycle. As the mass flow has also changed, the mass specific internal work has to be taken for the evaluation of the losses.
Losses due to gas flow in and out of the working chamber (see p,V-diagram )
Due to friction losses during the gas flow in and out of the working chamber, the pressure in the cylinder between (4) and (1) is lower than in the suction chamber and higher between (2) and (3) than in the delivery chamber. The pressure loss is at any point proportional to the square of the piston speed. The increase in the area of the p,V ?diagram gives the additional work done due to the throttling losses.
Losses due to heat storage in the cylinder walls (see T,s-diagram).
Due to their high heat capacity various components of the cylinder have a nearly constant temperature, which lies between the suction and the delivery temperature of the gas.
Due to heat transfer on intake of the gas compression starts at T1 > Ts. The compression line 1-2 deviates due to the heat transfer (which changes with time ) between wall and gas from the ploytropic line which goes through the start and end point. At the beginning of the compression heat will be transferred to the gas ( s increases ). When the gas temperature has reached the wall temperature, the direction of heat transfer is reversed (s decreases ).
After the heat transfer of the remaining gas during the pushing out of the gas the reexpansion starts at T3 < T2. The condition of state 3 ? 4 deviates for the same reasons from the corresponding polytropic expansion. Due to the heat exchange between cylinder wall at compression and reexpansion the area of the p,V- diagram and thereby the internal work is slightly increased.
The main losses, however, occur through heating up of the gas during the intake of gas , which reduces the mass flow whilst the internal work remains the same. Whilst bad heat transfer conditions before the cylinder are beneficial , good heat transfer conditions within the cylinder are beneficial as the polytropic exponent is thereby reduced and the ratio between the polytropic and isothermal compression work is reduced .
Losses due to leakages of the working chamber
The working chamber is not completely sealed against suction and delivery side, even at fully closed valves. There can also occur some leakage past the piston rings and pressure packings either to an adjacent working chamber or to the outside. Leakages of the working chambers do not lead necessarily to an increase of the internal work, but they always cause a reduction in mass flow and thereby to an increase of the specific work (leakage losses).