Handbook of Electrical Engineering For Practitioners in the Oil, Gas ...

2.2.1 Effect of an Inefficient Compressor and TurbineGAS TURBINE DRIVEN GENERATORS 29Frictional losses in the compressor raise the output temperature. Similarly the losses in the turbineraise the exhaust temperature. These losses are quantified by modifying the temperatures T 2 and T 4to account for their increases.The compression ratio (P 2 /P 1 ) of the compressor is usually given by the manufacturer andtherefore the temperature of the air leaving the compressor is easily found from (2.13). If the efficiencyof compression η c is known e.g. 90% and that of the turbine η t is known e.g. 85% then a betterestimate of the output energy can be calculated. In this situation T 2 becomes T 2e and T 4 becomesT 4e , as follows:-T 2e = T 2+(1 − 1 )T 1 and T 4e = T 4 η t + (1 − η t )T 3 (2.18)η c η cThese would be the temperatures measurable in practice. In (2.14) and (2.15) the pressureratios are theoretically equal, and in practice nearly equal, hence:T 2T 1= T 3T 4= r pβ(2.19)Where r p is the pressure ratio P 2P 1or P 3P 4In practice the temperatures T 1 and T 3 are known from the manufacturer or from measuringinstruments installed on the machine. The pressure ratio r p is also known. The ratio of specific heatsis also known or can be taken as 1.4 for air. If the compressor and turbine efficiencies are taken intoaccount then the practical cycle efficiency η p of the gas turbine can be expressed as:η p = T 3(1 − r p δ )η c η t − T 1 (r p β − 1)T 3 η c − T 1 (r p − 1 + η c )(2.20)which has a similar form to (2.17) for comparison.2.2.1.1 Worked exampleA light industrial gas turbine operates at an ambient temperature T 1 of 25 ◦ C and the combustiontemperature T 3 is 950 ◦ C. The pressure ratio r p is 10.If the overall efficiency is 32% find the efficiency of the compressor assuming the turbineefficiency to be 86%.From (2.20),T 1 = 273 + 25 = 298 ◦ KT 3 = 273 + 950 = 1223 ◦ Kr δ p = 10 −0.2857 = 0.51796 and r β p = 10 +0.2857 = 1.93063