Reciprocating Air Compressors Tutorial sheet 1. A single-stage double acting air compressor has a stroke volume of 0.056 m 3 and a clearance volume of 0.0028 m3. Find the volumetric efficiency and the mass of air delivered per hour when the speed is 200 rev/min, the suction pressure and temperature 0.9 bar and 50 ºC, respectively, and the delivery pressure 6 bar. Determine also the indicated power to drive the compressor. Assume the law of compression and re-expansion is pV 1.35 = constant. (Answer: 0.846, 1104 kg/h, 69.7 kW) 2. The following observations were made during a test on a single-stage double-acting, singlecylinder air compressor, with piston diameter 23 cm and piston stroke 23 cm; speed 170 rev/min; mean indicator card area and length, 15 cm2 and 8 cm; spring no. 110 kN/m2/cm; air delivered 3 kg/min; air temperature at compressor inlet 15 ºC and at outlet 164 ºC; delivery pressure 9 bar gauge; barometric pressure 75 cm Hg; jacket water flow 2 kg/min with temperature at inlet 13 ºC and at outlet 37 ºC. Calculate (a) the indicated power of the compressor, (b) the volumetric efficiency of the compressor based on atmospheric conditions, and (c) the isothermal efficiency. Also draw up an energy balance for the test (kJ/s). (Answer: 11.17 kW, 0.76; 0.85, 11.17 kJ/s, 7.49 kJ/s, 3.35 kJ/s, radiation 0.32 kJ/s) 3. Derive an expression for the theoretical volumetric efficiency ηv of a single stage reciprocating air compressor in terms of the fractional clearance volume, k, the pressure ratio, rp, and the indices of compression and re-expansion assuming these to be of equal value n. Hence show that 1k the ratio of air mass in the cylinder during compression to the mass delivered is given by . A reciprocating air compressor has a cylinder diameter of 0.15 m, stroke 0.2 m, and clearance volume of 1.8×10-3 m3. Air is induced at pressure 0.95 bar, temperature 21 ºC, and delivered at pressure 5.5 bar, compression and re-expansion taking place according to the law pV 1.2 = constant. Determine for one cycle (a) the net work transfer, (b) the heat transfer from the air to the jacket cooling water during the compression process, (c) the work done per kg of air delivered. v
(Answer: 0.57 kJ/cycle, 0.30 kJ/cycle, 172.2 kJ/kg) 4. A tank of 2.8 m3 capacity stores compressed air at a pressure of 55 bar and a temperature of 15 ºC. It is charged by a two-stage single-acting reciprocating air compressor, having one high pressure cylinder and one low pressure cylinder. The compressor delivers at a steady pressure and the air subsequently passes through a reducing valve. Neglecting the quantity of air initially in the tank, calculate, from the following data, the compressor power and the cylinder diameters: time taken to charge the tank 10 minutes; suction conditions 1.013 bar and 15 ºC; compressor delivery pressure 82 bar; index of compression and re-expansion in both stages n = 1.3; clearance in both stages 6 % of stroke volume; speed 200 rev/min; common stroke of HP and LP stages 45 cm; stage pressures in geometric progression; air temperature at inlet to HP cylinder 15 ºC. If an aftercooler is fitted before the reducing valve to extract 60 kJ/s, calculate the pressure in the tank at the end of the 10 minute charging period. Neglect radiation losses from a tank. (Answer: 146 kW, 54 cm, 18 cm, 76.1 bar) 5. A two-stage air compressor is designed to supply 8.4 m 3 of free air per minute (referred to 1.012 bar nad 15 ºC) with a delivery pressure 28 bar. The suction conditions in the compressor are 0.96 bar and 21 ºC, the interstage pressure is the geometric mean of the inlet and outlet pressures, there is perfect intercooling and the index of compression and re-expansion in both cylinders is n = 1.3. Find the power required and the effective swept volumes of the LP and HP cylinders. If
the water supply to the intercooler is shut off so that no intercooling takes place, determine the interstage pressure which will result and the new power input required. The suction pressure, final delivery pressure and speed are unaltered but the volumetric efficiencies alter as follows: (a) the LP decreases by 6 %, (b) th HP increases by 10 % on their initial values. (Answer: 59.7 kW, 9.05 m3/min, 1.68 m3/min, 7.0 bar, 69.45 kW) 6. A 3-stage air compressor is used to compress 8.4 m3/min of free air (measured at pressure 1.013 bar and temperature 21 ºC) from suction conditions of pressure 0.965 bar and temperature 38 ºC to a final pressure 83 bar. The law pV 1.35 = constant applies to both compression and reexpansion in each cylinder and the stage pressures are in geometric progression. The intercooling is perfect and the fractional clearance volumes of the 3 stages are: HP 0.09, IP 0.09, LP 0.095. Estimate the indicated power to drive the compressor, the swept volumes of the three cylinders in m3/min and isothermal efficiency of the compressor. (Answer: 81.54 kW, 11.53 m3/min, 2.58 m3/min, 0.584 m3/min, 82 %)
