BENG2 APPLIED THERMODYNAMICS
(THER 205)
TUTORIAL EXAMPLES in RECIPROCATING COMPRESSORS
(SSL
conditions: 15ºC ; 101.325 kPa)
1. A reciprocating air compressor induces
5.65 x 10-3 m³ of air per cycle at SSL conditions. If the
delivery pressure is 620 kPa, calculate the work transfer per cycle if the
compression and expansion processes are:-
(a) reversible
polytropic, n = 1.2.
(b) reversible
adiabatic. [1.210,
1.359 kJ]
2. Air is to be compressed through a
pressure ratio of 10:1 from SSL conditions.
Find the
power required for a free air delivery (FAD) of 0.05 m³ /s.
Also find
the rotational speed if the swept volume is 14.5 x 10-3 m³ .
The clearance
volume is 6 per cent of the swept volume, and n = 1.3 for compression and
expansion. [15.2 kW, 293 RPM]
3. Air is compressed in a reciprocating
compressor from SSL conditions to a pressure of 0.9 MPa in one stage. The
polytropic index of compression and expansion is 1.3, and the clearance
volume is 4 per cent of the swept volume.
Calculate the work transfer per kg of air delivered and the heat
transfer during compression and expansion per kg of air delivered. [ 234.7 kJ/kg, -58.7 kJ/kg del., 12.1 kJ/kg del.]
4. A single acting reciprocating
compressor running at 240 RPM delivers 0.1 m³/s FAD. Inlet
conditions are SSL and the delivery
pressure is 482 kPa. The clearance
volume is 5 per cent of the swept volume and the compression and re-expansion
processes are considered reversible and governed by the law pV1.2 =
const. Calculate:
(a) the
swept volume;
(b) the
power required to drive the compressor if its mechanical efficiency is 85%;
(c) the
maximum pressure against which the compressor could theoretically operate. [0.0288 m³ , 21.2 kW, 3.912 MPa]
5. A single stage reciprocating air
compressor is required to deliver 7 m³ /min FAD. The induction conditions
are 95 kPa and 32 ºC.
Delivery is at 0.7 MPa and the law for the compression and expansion
processes is: pV1.3 =
constant.
If the
clearance volume is 5% of the swept volume, calculate the indicated power and
the volumetric efficiency based on SSL
conditions. [31.8
kW; 72.4 %]
6. A three stage reciprocating air
compressor has a free air delivery of 2.83 m³/min based on SSL
conditions. The induction pressure and
temperature are 98 kPa and 32 ºC
respectively. Calculate the ideal
minimum indicated power (stating the assumptions required) for a delivery
pressure of 7 MPa and an index of compression
n = 1.3. What are the interstage pressures? [25.6 kW, 407 & 1687 kPa]
7. A four stage reciprocating compressor
takes in air at 1 bar & 32 ºC and delivers it at 112 bar. The index of compression for each stage is
1.28 and inter-cooling is used so that the inlet temperature is the same for
each stage. The pressure ratios are
chosen to give equal work per stage.
Determine
the volume of air delivered (at SSL conditions)
per kWh work input, and the air delivery temperature. [6.23 m³/kWh,
122 ºC]