Question

A mechanically coupled supercharger is run by a four-stroke four –cylinder square diesel engine with a bore of 100 mm. Air enters the compressor at 27 °C and the compressor pressure ratio is 1.6. From the compressor the air is passed on to a cooler where 1200 kJ/min of heat is rejected. The air leaves the cooler at 67 oC. Some air from the compressor is bled after the cooler to supercharge the engine. The volumetric efficiency is 85 % based on intake manifold pressure and temperature. The other details about the engine are ?m is 85 %. Determine (i) Indicated mean effective pressure (imep) of the engine, in bar (ii) Air consumption rate of the engine, in kg/min (iii) The air handling capacity of the compressor, in kg/min. Take isentropic efficiency of the compressor to be 85%, N = 3000rpm; Pb = 30 kW

Answer 1

According to, 4-stroke, 4-cylinder square diesel engine d = 120 mm T_1 = 25 degreescelsius = 298 k H_p = 1.7 T_3 = 67 degreescelsius = 340 k eta_v = 0.85 B.P = 55 KW N = 2500 rpm eta_much = 85% eta_ibe(comp) = 85% phi_R = 1250 KJ/min For process 1-2 T_2/T_1 = (mu_p)^r - 1/r = 298(1.7)^1.4 - 1/1.4 rightarrow T_2 = 346.78 k \r\n But eta_ise = 0.85 = T_2 - T_1/T_2a - T_1 = 346.78 - 298/T_2a - 298 rightdoublearrow T_2a = 355.39 k Now, for process 2-3 phi_R = m_ac_p(Delta T) = mc_p(T_2 - T_3) m_a = 1250/60 times 1.005 times (355.39 - 340) rightdoublearrow m_a = 1.347 kg/s Now, Indicated , I.P = B.P/eta_much = 55/0.85 = 64.7 KN i) imep = I.P/V_s = 64.7/0.158 = 409.53 Kpa = 4.0953 bar ii) Now, eta_v = V_a/V_s rightdoublearrow V_a = eta_v times V_s = 0.85 times 0.158 = 0.1343 m^3/s rightdoublerarrow eta_v = 8.058 m^3/min