Thermodynamics

868 | ThermodynamicsQ .EXAMPLE 17–15Rayleigh Flow in a Tubular CombustorP 1 480 kPaT 1 550 KV 1 80 m/sCombustortubeP 2 , T 2 , V 2FIGURE 17–58Schematic of the combustor tubeanalyzed in Example 17–15.A combustion chamber consists of tubular combustors of 15-cm diameter.Compressed air enters the tubes at 550 K, 480 kPa, and 80 m/s (Fig.17–58). Fuel with a heating value of 42,000 kJ/kg is injected into the airand is burned with an air–fuel mass ratio of 40. Approximating combustionas a heat transfer process to air, determine the temperature, pressure, velocity,and Mach number at the exit of the combustion chamber.Solution Fuel is burned in a tubular combustion chamber with compressedair. The exit temperature, pressure, velocity, and Mach number are to bedetermined.Assumptions 1 The assumptions associated with Rayleigh flow (i.e., steadyone-dimensional flow of an ideal gas with constant properties through a constantcross-sectional-area duct with negligible frictional effects) are valid.2 Combustion is complete, and it is treated as a heat transfer process, withno change in the chemical composition of the flow. 3 The increase in massflow rate due to fuel injection is disregarded.Properties We take the properties of air to be k 1.4, c p 1.005 kJ/kg · K,and R 0.287 kJ/kg · K (Table A–2a).Analysis The inlet density and mass flow rate of air arer 1 P 1RT 1480 kPa10.287 kJ>kg # K21550 K2 3.041 kg>m 3m # air r 1 A 1 V 1 13.041 kg>m 3 23p 10.15 m2 2 >44 180 m>s2 4.299 kg>sThe mass flow rate of fuel and the rate of heat transfer arem # fuel m# air 4.299 kg>s 0.1075 kg>sAF 40Q # m # fuel HV 10.1075 kg>s2142,000 kJ>kg2 4515 kWq Q#m # airThe stagnation temperature and Mach number at the inlet areT 01 T 1 V 12 180 m>s2 2 550 K 2c p 2 11.005 kJ>kg #a 1 kJ>kgK2 1000 m 2 >s b 553.2 K21000 mc 1 2kRT 1 11.4210.287 kJ>kg # 2 >s 2K21550 K2 a b 470.1 m>sB 1 kJ>kgMa 1 V 1 80 m/sc 1 470.1 m/s 0.17024515 kJ>s 1050 kJ>kg4.299 kg>sThe exit stagnation temperature is, from the energy equation q c p (T 02 T 01 ),T 02 T 01 q c p 553.2 K 1050 kJ/ kg 1598 K1.005 kJ/ kg # K