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4-1 Aircraft propulsion systems 71 inlet and outlet of the fan are known from the calculations in Section 4-1-1. This information is enough to reveal the thermodynamics of the fan. The first equation used to do so is related to the fan pressure ratio, ΠFN = P019 . (4-23) P02 The isentropic efficiency of the fan is a function of the polytropic efficiency and the pressure ratio, (4-24) γ−1 Πγ−1 η = FN . FN γ−1 eFN Πγ −1 FN The total enthalpy leaving the fan is a function of the pressure ratio, the entering enthalpy and the isentropic efficiency, h019 =h(ΠFN,h02,ηFN). (4-25) The entropy leaving the fan, s019, is obtained with its correspondent total pressure and enthalpy and it is used to obtain the enthalpy at point (19), h19 =h(P19,s019), (4-26) where P19 equals the environmental pressure. The velocity of the air leaving the fan is a function of the stagnation enthalpy at (019) and the enthalpy at (19), v19 = 2(h019 − h19). (4-27) The cruise velocity v19 is known from previous calculations. Thus, it is necessary to iterate on the value of the total pressure P019 until the required cruise velocity is matched. The fan propulsive power is the difference between the kinetic energy entering and leaving this system, v2 v2 W ̇PR,FN =fFN 19 − 0 =fFN[(h013 −h19)−(h02 −h0)]. (4-28) 22 The shaft power used to drive the fan is function of the leaving and entering total enthalpies, W ̇ 2−13 = fFN (h013 − h02) . (4-29) The T-s diagram for the fan and the related information is presented in Figure 4-3. Core side analysis A general T-s diagram of the process in the core is shown in Figure 4-5. The assumptions considered for the fan are valid for the core side as well. The total enthalpy at the inlet of the engine (00) equals the one entering the compressor (02), and the total enthalpy leaving the turbine (05) equals the one leaving the nozzle (09). The pressure at the outlet of the core side (9) equals the environmental pressure (0) since it is assumed that the expansion is done until environmental conditions. The thermodynamic states can be found with the available information from the cycle and using a similar procedure to the one used for the fan. The enthalpy leaving the high pressure compressor is a function of the entering enthalpy and the pressure ratio, Master of Science Thesis h03 =h(ηCM,h02). (4-30) J.S. Bahamonde NoriegaPDF Image | Design method for s-CO2 gas turbine power plants
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