Function

An approximate calculation of the working cycle for a specific cylinder of your choice can be carried out with the program given here. The original version of this program was compiled by Mr. Matthias Kornfeld, TU Vienna on the occasion of the 5^th EFRC- workshop in 2008.

When using this program, you can choose quality criteria for clearance volume, the compressor valves and the wear condition of the cylinder 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. For the first consideration, we assume the compressor working without any losses. The clearance volume as is necessary by the design is V₀. By cooling the cylinder, the compression will become polytropic, which is between the isothermal and isentropic compression. The working cycle can be shown in a p,V-diagram (indicator diagram), which shows both the change in the conditions of state and the changes of masses, see Figure 5.1.

The polytropic compression starts in bottom dead center BDC (1) at suction conditions and ends when the discharge pressure is reached (2). Then the discharge valve opens, and gas is pushed out at constant pressure until top dead center TDC (3) is reached. There the sign of the volume change alters, and the discharge valve closes. The re-expansion of the remaining gas from the clearance volume back to suction pressure follows until suction pressure is reached (4). The suction valve now opens and fresh gas is sucked in at suction conditions up to bottom dead center BDC (1).

The suction and discharge process are ideally pure changes in mass.

In the case of an ideal process, the changes of state of compression and re-expansion have the same polytropic exponent. The clearance volume then only causes a diminished flow of gas.

In real compressors, there are irreversible processes in terms of gas velocity, temperature and pressure which only happen in one direction of time and which are unavoidable. These can be superimposed onto the idealised compression cycle. The work as supplied by the piston (internal work) can therefore not be entirely used for the compression of the gas.

Through these superimposed compensation processes the p,V-diagram changes, see Figure 5.2.

The enclosed 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. The losses due to gas flow in and out the working chamber are highlighted with dashes in the 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 discharge 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 internal losses.

The losses due to heat storage in the cylinder walls can be seen in the T,s-diagram in Figure 5.3. Due to their higher heat capacity, various components of the cylinder have a nearly constant temperature, which lies between the suction and the discharge temperature of the gas.

Due to heat transfer on intake of the gas compression starts at T₁ > T_S. The compression line 1-2 deviates due to the heat transfer (which changes with time) between wall and gas from the polytropic line (dashed) which goes through the start and end point. At the beginning of the compression heat will be transferred to the gas (the specific entropy s increases). When the gas temperature has reached the wall temperature, the direction of heat transfer reverses (specific entropy s decreases).

After the heat transfer of the remaining gas during the pushing out of the gas the re-expansion 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 the cylinder wall at compression and re-expansion the area of the p,V-diagram and thereby the internal work is 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.

There are also losses due to leakages of the working chamber, because the working chamber is not perfectly sealed against suction and discharge side, even at fully closed valves, see Figure 5.4.

Table 5.1 shows the signs of Figure 5.4 with the description.

There can also occur some leakage through 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).