Thermodynamics

522 | ThermodynamicsT3P = const.q in 56q out412345621P = const.sDiffuser Compressor Burner section Turbine NozzleFIGURE 9–48Basic components of a turbojet engine and the T-s diagram for the ideal turbojet cycle.Source: The Aircraft Gas Turbine Engine and Its Operation. © United Aircraft Corporation (now United Technologies Corp.), 1951, 1974.FV, m/s·W P = F VFIGURE 9–49Propulsive power is the thrust actingon the aircraft through a distance perunit time.Fdetermined from Newton’s second law. The pressures at the inlet and theexit of a turbojet engine are identical (the ambient pressure); thus, the netthrust developed by the engine isF 1m # V2 exit 1m # V2 inlet m # 1V exit V inlet 21N2(9–27)where V exit is the exit velocity of the exhaust gases and V inlet is the inlet velocityof the air, both relative to the aircraft. Thus, for an aircraft cruising in stillair, V inlet is the aircraft velocity. In reality, the mass flow rates of the gases atthe engine exit and the inlet are different, the difference being equal to thecombustion rate of the fuel. However, the air–fuel mass ratio used in jetpropulsionengines is usually very high, making this difference very small.Thus, ṁ in Eq. 9–27 is taken as the mass flow rate of air through the engine.For an aircraft cruising at a constant speed, the thrust is used to overcome airdrag, and the net force acting on the body of the aircraft is zero. Commercialairplanes save fuel by flying at higher altitudes during long trips since air athigher altitudes is thinner and exerts a smaller drag force on aircraft.The power developed from the thrust of the engine is called the propulsivepower W . P , which is the propulsive force (thrust) times the distance this forceacts on the aircraft per unit time, that is, the thrust times the aircraft velocity(Fig. 9–49):W # P FV aircraft m # 1V exit V inlet 2V aircraft 1kW2(9–28)The net work developed by a turbojet engine is zero. Thus, we cannotdefine the efficiency of a turbojet engine in the same way as stationary gasturbineengines. Instead, we should use the general definition of efficiency,which is the ratio of the desired output to the required input. The desiredoutput in a turbojet engine is the power produced to propel the aircraft W . P ,and the required input is the heating value of the fuel Q . in . The ratio of thesetwo quantities is called the propulsive efficiency and is given byh P Propulsive powerEnergy input rate W# PQ # in(9–29)Propulsive efficiency is a measure of how efficiently the thermal energyreleased during the combustion process is converted to propulsive energy. The