WORK DONE IN A SINGLE STAGE RECIPROCATING COMPRESSOR WITH CLEARANCE VOLUME:
Considering clearance volume: With clearance volume the cycle is represented on Figure. The work done for compression of air polytropically can be given by the are a enclosed in cycle 1-2-
3-4. Clearance volume in compressors varies from 1.5% to 35% depending upon type of compressor.
In the cylinder of reciprocating compressor (V1-V4) shall be the actual volume of air delivered per cycle. Vd = V1 – V4. This (V1 – V4) is actually the volume of air in hated in the cycle and delivered subsequently.
If air is considered to behave as perfect gas then pressure, temperature, volume and mass can be inter related using perfect gas equation. The mass at state 1 may be given as m1 mass at state 2 shall be m1, but at state 3 after delivery mass reduces to m2 and at state 4 it shall be m2.
Ideally there shall be no change in temperature during suction and delivery i.e., T4 = T1 and T2 = T3 from earlier equation
Thus (m1-m2) denotes the mass of air sucked or delivered. For unit mass of air delivered the work done per kg of air can be given as,
Thus from above expressions it is obvious that the clearance volume reduces the effective swept volume i.e., the mass of air handled but the work done per kg of air delivered remains unaffected. From the cycle work estimated as above the theoretical power required for running compressor shall be,
For single acting compressor running with N rpm, power input required, assuming clearance volume.