4. (16 marks total) fan 12 mo bypass air ma LP turbine 4 HP turbine compressor combustor - The sketch shows a fan jet aircraft engine. A large flow of air enters the fan at T =0C, P = 100 kPa, and is compressed in the fan to P, 170 kPa. A portion of this air m is then split off and is discharged through a nozzle at the back of the engine (the "bypass" air). The remaining air flow c (the "core" flow) then passes through the rest of the engine, comprising the compressor, the high pressure (HP) turbine which drives the compressor, and the low pressure (LP) turbine which drives the fan. The pressure P, -4200 kPa, and the temperature T-1400C. Assume that the isentropic efficiencies of the fan, the compressor and both turbines are all ne nr=0.90. (a) (2 marks) Sketch a T-s diagram for this cycle. (b) (4 marks) If the exit temperature from the fan T, = 322.7K, determine the compressor work in kJ/kg. (c) (3 marks) Noting that the high pressure turbine drives only the compressor, determine the temperature T, at the HP turbine outlet. (d) (4 marks) Calculate the pressure P, at the outlet of the HP turbine. (e) (3 marks) If the core mass flow 140 kg/s, determine the bypass flow .. The low pressure turbine specific work is WTLP-480 kJ/kg and the fan specific work is w;= -50.2 kJ/kg. Use constant specific heat, assuming that for air C, -1.01 kJ/kg K, k = 1.4. Saturated Steam - Temperature Table T (C) P (kPa) v, (m/kg) h(kJ/kg) h, (kJ/kg) S, (kJ/kgK) s, (kJ/kg K) 0.01 0.6113 0.001 0.01 2501.4 0.0000 9.1562 5 0.8721 0.001 20.98 2510.6 0.0761 9.0257 10 1.2276 0.001 42.01 2519.8 0.1510 8.9008 15 1.7051 0.001001 62.99 2528.9 0.2245 8.7814 20 2.339 0.001002 83.96 2538.1 0.2966 8.6672 25 3.169 0.001003 104.89 2547.2 0.3674 8.5580 30 4.246 0.001004 125.79 2556.3 0.4369 8.4533 35 5.628 0.001006 146.68 2565.3 0.5053 8.3531 40 7.384 0.001008 167.57 2574.3 0.5725 8.2570 45 9.593 0.001010 188.45 2583.2 0.6387 8.1648 50 12.349 0.001012 209.33 2592.1 0.7038 8.0763 Saturated Steam - Pressure Table P (kPa) T (C) 5 32.88 v, (m/kg) h(kJ/kg) h, (kJ/kg) S, (kJ/kgK) s, (kJ/kg K) 0.001005 137.82 2561.5 0.4764 8.3951 10 45.81 0.001010 191.83 2584.7 0.6493 8.1502 20 60.06 0.001017 251.4 2609.7 0.8320 7.9085 30 69.10 0.001022 289.23 2625.3 0.9439 7.7686 50 81.33 0.001030 340.49 2645.9 1.0910 7.5939 75 91.78 0.001037 384.39 2663.0 1.2130 7.4564 100 99.63 0.001043 417.46 2675.5 1.3026 7.3594 200 120.23 0.001061 504.70 2706.7 1.5301 7.1271 300 133.55 0.001073 561.47 2725.3 1.6718 6.9919 400 143.63 0.001084 604.74 2738.6 1.7766 6.8959 500 151.86 0.001093 640.23 2748.7 1.8607 6.8213 Superheated Water Vapour P-5.0 MPa P=0.3 MPa T (C) h (kJ/kg) s (kJ/kg K) T (C) h (kJ/kg) s (kJ/kg K) Sat 2794.3 5.9734 Sat 2725.3 6.9919 300 2924.5 6.2084 150 2761.0 7.0778 350 3068.4 6.4493 200 2865.6 7.3115 400 3195.7 6.6459 250 2967.6 7.5166 450 3316.2 6.8186 300 3069.3 7.7022 500 3433.8 6.9759 400 3275.0 8.0330 Equations and Other Data Isentropic relation for a perfect gas with constant specific heat: (A) T25 - T (k-1)/k Reversible work done on an incompressible liquid in steady flow: 2 W-- -vdP = v (P - P)