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Appl. Sci. 2020, 10, 9060 3 of 25 air is moved to the bypass nozzle (FN), and the remainder moves to the core engine (m ̇ a = m ̇ ca + m ̇ ha). The relation between air flowing through the FN (m ̇ ca) and gas turbine (m ̇ ha) is called the bypass ratio: β = m ̇ ca/m ̇ ha. The fraction of the air mass flow rate m ̇ ca = βm ̇ a/(1 + β) is accelerated in the FN and exhausted to the environment, whereas the remaining fraction (m ̇ ha = m ̇ a/(1 + β)) enters the compressor (C) of the two-shaft gas turbine. In the combustion chamber (CC), the compressed air is heated (Q ̇ b) by mixing and combustion with the atomized aviation fuel Jet-A1 (kerosene). The combustion reaction between this fuel and air, which is assumed to have a molar composition of 79% N2 and 21% O2, is given by: CnHm +⎛n+ m⎞(1+λ)(O2 +3.76N2) → [n(1−k4)−k1]CO2 ⎝4⎠⎡⎤ +m(1−k4)H2O+⎢3.76⎛n+ m⎞(1+λ) −k2 +k3⎥N2 (1) 2 ⎢⎣⎝4⎠ 2⎥⎦ ⎡⎢ ⎢ ⎛ m ⎞ k 1 − k 2 ⎤⎥ ⎥ +⎢⎝n+ 4⎠(1+λ)+ 2 −k3⎥O2 +k1CO+k2NO+k3NO2 +k4CnHm ⎣⎦ where n and m are the numbers of C and H atoms present in the fuel, λ is the excess of air, and k1 to k4 are the stoichiometric coefficients for CO, NO, NO2, and CnHm, respectively. This reaction determines the chemical composition of the combustion gases. The mass flow rate m ̇ cg = m ̇ ha + m ̇ f and m ̇ f is the fuel mass flow rate. The combustion gases leave the CC at a substantially high pressure and temperature and are expanded in the high pressure turbine (HPT) and low pressure turbine (LPT) to generate useful work for driving the C and F, respectively. The exhaust gases exiting the LPT are accelerated and expelled through the exhaust nozzle (N) at considerably high speeds. FN mf mc ma 2.2. Assumptions a t1t2 D F C 8 t3 t4t5 t6 7 CC HPTLPT N Figure 1. Schematic diagram of a turbofan engine. In this study, the following assumptions were made. • The engine operates in a steady state with a steady flow. • Air and combustion gases behave as mixtures of ideal gases and one-dimensional and adiabatic steady flows. • The chemical formula of JET-A1 is C12H23, and its lower heating value (LHV) is 42,800 kJ/kg [21]. • The changes in potential energy within the engine are negligible. • The cooling air mass flow is not considered for analysis [22]. • The heat exchangers (air–fuel, fuel–oil) are not considered. • The temperature and pressure in the dead state are 288.15 K and 101.33 kPa, respectively. 3. Energy Analysis The energy balances of the turbofan components are presented in Table 1. H ̇ t is the stagnation enthalpy flow, which is the sum of the flow rates for the static enthalpy (H ̇ ) and kinetic energy (m ̇ u2/2).PDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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