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Appl. Sci. 2020, 10, 9060 5 of 25 kinetic energy and total heat input Q ̇ b. The propulsion efficiency ηprop relates the thrust power τ ̇ = τua required by the turbofan to the propulsive kinetic energy. The overall efficiency ηoverall is the ratio of the thrust power to the total heat input ηoverall = ηthηprop. Table 2. Thermodynamic states of the turbofan engine. State Mass Flow Rate am ̇a Temperature Pressure Ta Pa Tta γa−1 2 Ta=1+ 2 M − 1) − 1) m ̇cg T Pt4=1−∆P 0a 01 02 03 04 05 06 7 8 4. Exergy Analysis 4.1. Exergy Forms m ̇ a m ̇ a m ̇ a m ̇a Pa=(1+ 2 M) Pt1 γa−1 2 γa1 Tt1=Tta T 1 γa1 Pa=(1+ηD 2 M) P t2 = 1 + (π γa Ta ηF F t2 = πF Pt1 T1γa1 t3 = 1 + (π γa P t3 = πC 1+β Tt2 ηC C t4 Pt3b m ̇cg Tt5=Tt4− Tt3−Tt2 1 + (1 + β) f ar γcg γa Pta γa−1 2 γa1 Pt2 Pt5=[1− 1 (1−Tt5)]γcg1 Pt4 ηHPT Tt4 Pt6=[1− 1 (1−Tt6)]γcg1 γa m ̇cg Tt6=Tt4−(1+β)(Tt2−Tt1) 1 + (1 + β) f ar γcg β m ̇ a 1 + β ⎡ γa⎤ T 8 ⎢ Pa γa1 ⎥ ⎥ Tt2 = 1 − ηFN ⎢1 − ( Pt2) ⎥ ⎣⎦ ⎡ γcg⎤ T7 ⎢ Pa γcg1⎥ Pt5 ηLPT Tt5 P7 = Pa P8 = Pa m ̇cg Tt6=1−ηN ⎢ ⎢ ⎢1−(Pt6) ⎥ ⎥ ⎥ ⎣⎦ Exergy is defined as the maximum useful work that can be produced by a system interacting with a specified reference environment (known as the dead state and denoted by a zero subscript). In the absence of influences such as nuclear effects, magnetism, electricity, and surface tension, the exergy of a stream of a substance comprises its kinetic (E ̇K), potential (E ̇P), physical (E ̇PH), and chemical (E ̇CH) exergies. E ̇t = E ̇K +E ̇P +E ̇PH +E ̇CH (6) The kinetic exergy is equal to the kinetic energy when the velocity is considered relative to the surface of the Earth, and the potential exergy is equal to the potential energy when considered with respect to the average surface level of the Earth in the environment of the process under consideration [23]. m ̇ u 2 E ̇K=2 andE ̇P=m ̇gz (7) where u and z are respectively the velocity and elevation relative to coordinates of the environment and g is the gravity.PDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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