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4-1 Aircraft propulsion systems 67 where W ̇ PR,CR and W ̇ PR,FN correspond to the contributions of the core and the fan respec- tively. In order to estimate the propulsive and thermal efficiency, it is necessary to obtain these contributions. Consider Figure 4-1, which shows a scheme of a turbofan engine with the correspondent station numbering. The uninstalled thrust of the core side can be calculated Figure 4-1: Turbofan schematic diagram. as the momentum balance in this component without the drag effects due to the inlet and nozzle surfaces, FCR = f9v9 − fCRv0 + (P9 − P0)A9. (4-6) The air mass flow entering the core is fCR, while f9 corresponds to the mass flow leaving the core with a velocity v9 and pressure P9. It is desirable to expand the exhaust gas to the ambient pressure [9]. In this case, P9 = P0 and expression (4-6) reduces to FCR = f9v9 − fCRv0. (4-7) The propulsion power generated by the engine is a function of the mass flow rates and their correspondent velocities, W ̇ PR,CR = 21 f9v92 − fCRv02 . (4-8) Equations (4-7) and (4-8) can be used for the fan analysis as well. The air mass flow through the core side is calculated with the bypass ratio and the fan mass flow, fCR = fFN , (4-9) B+1 which gives a core mass flow of 93.08 kg/s. The fuel mass flow is calculated using the thrust specific fuel consumption and the thrust from Table 4-1, which gives a value of fFL = 0.94 kg/s. The cruise velocity is calculated with the correspondent speed of sound at cruise altitude (10670 m), v0 = M0a0. (4-10) Considering that core produces about 20% of the total thrust in this engines [73], the core nozzle velocity can be calculated with expression (4-7). Finally, the core propulsive power in equation (4-8) can be calculated replacing the core exhaust mass flow (f9) with the sum of the air mass flow (fCR) and the fuel mass flow (fFL). A similar procedure is followed for the fan analysis. The results of both procedures and the engine efficiencies are presented in Table 4-2. Master of Science Thesis J.S. Bahamonde NoriegaPDF Image | Design method for s-CO2 gas turbine power plants
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