Page 50 - Handbook of Electrical Engineering
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GAS TURBINE DRIVEN GENERATORS      29

           2.2.1 Effect of an Inefficient Compressor and Turbine


           Frictional losses in the compressor raise the output temperature. Similarly the losses in the turbine
           raise the exhaust temperature. These losses are quantified by modifying the temperatures T 2 and T 4
           to account for their increases.
                 The compression ratio (P 2 /P 1 ) of the compressor is usually given by the manufacturer and
           therefore the temperature of the air leaving the compressor is easily found from (2.13). If the efficiency
           of compression η c is known e.g. 90% and that of the turbine η t is known e.g. 85% then a better
           estimate of the output energy can be calculated. In this situation T 2 becomes T 2e and T 4 becomes
           T 4e , as follows:-

                                   T 2       1
                             T 2e =  + 1 −      T 1  and T 4e = T 4 η t + (1 − η t )T 3   (2.18)
                                   η c      η c
                 These would be the temperatures measurable in practice. In (2.14) and (2.15) the pressure
           ratios are theoretically equal, and in practice nearly equal, hence:

                                               T 2  T 3    β
                                                 =     = r p                              (2.19)
                                               T 1  T 4

                                     P 2   P 3
           Where r p is the pressure ratio  or
                                     P 1   P 4
                 In practice the temperatures T 1 and T 3 are known from the manufacturer or from measuring
           instruments installed on the machine. The pressure ratio r p is also known. The ratio of specific heats
           is also known or can be taken as 1.4 for air. If the compressor and turbine efficiencies are taken into
           account then the practical cycle efficiency η p of the gas turbine can be expressed as:

                                                               β
                                                   δ
                                           T 3 (1 − r p )η c η t − T 1 (r p − 1)
                                      η p =                                               (2.20)
                                              T 3 η c − T 1 (r p − 1 + η c )
           which has a similar form to (2.17) for comparison.


           2.2.1.1 Worked example

                                                                           ◦
           A light industrial gas turbine operates at an ambient temperature T 1 of 25 C and the combustion
                             ◦
           temperature 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 turbine
           efficiency to be 86%.
                 From (2.20),

                                              ◦
                            T 1 = 273 + 25 = 298 K
                                                ◦
                            T 3 = 273 + 950 = 1223 K
                             δ
                                                          β
                           r p = 10 −0.2857  = 0.51796  and r p = 10 +0.2857  = 1.93063
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