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

GAS TURBINE DRIVEN GENERATORS 27From here onwards the following substitutions will be used in order to keep the presentationof the equations in a simpler format.β = γ − 1 ,β c = γ c − 1, β t = γ t − 1γγ c γ tδ = 1 − γγ,δ c = 1 − γ c,δ t = 1 − γ tγ c γ tWhere subscript ‘c’ refers to the compressor and ‘t’ to the turbine, the absence of a subscriptmeans a general case.Divide (2.2) by (2.13) to obtain an expression for the compressor,Similarly for the turbine,(P2P 1) δ= T 1T 2(2.14)(P3P 4) δ= T 4T 3(2.15)It is of interest to determine the work done on the generator in terms of the ambient temperatureT 1 and the combustion temperature T 3 .From (2.14),And from (2.15),Therefore (2.11) becomes,T 2 = T 1 r pβT 4 = T 3 r pδU out = C p (T 3 − T 3 r p δ − T 1 r p β + T 1 )= C p T 3 (1 − r p δ ) − C p T 1 (r p β − 1) (2.16)The ideal cycle efficiency η i can also be expressed in terms of T 1 and T 3 .η i = 1 −(T3 r δ )p − T 1T 3 − T 1 rβ p(2.17)The specific heat C p is assumed to be constant and equal for both compression and expansion.In practice these assumptions are not valid because the specific heat C p is a function of temperature.The average temperature in the turbine is about twice that in the compressor. Also the productsof combustion i.e. water vapour and carbon dioxide, slightly increase the specific heat of air–gasmixture in the turbine. Figures 2.8 and 2.9 show the spread of values for the pressure ratio andexhaust temperature for a range of gas turbines from 1 MW to approximately 75 MW.