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Appl. Sci. 2020, 10, 9060 4 of 25 Table 1. Energy balance and adiabatic efficiency of the turbofan components. Component D F C CC HPT LPT FN N Turbofan The fuel-to-air ratio (far) is obtained from the energy balance for the CC (Table 1) and is expressed as: far=m ̇f=⎛1⎞ ht4−ht3 (2) m ̇ a ⎝ β + 1 ⎠ η b L H V − h t 4 where ht4 and ht3 are the stagnation enthalpies of air and combustion gases in States 3 and 4, respectively, and ηb is the adiabatic efficiency of the CC. Table 2 lists the temperatures and pressures of each state, as derived from the energy balance. Tt and Pt are the stagnation temperature and pressure, respectively. If the nozzles are not choked, then the pressure at the exit of each nozzle is equal to the specified back pressure (P7 = Pa = P8), as shown in Table 2. The resulting velocities are expressed as follows. ⎡ γcg⎤ ⎡ γa⎤ (3) In this study, the thrust is the net force acting on the x-surface of the control volume in the x-direction. If the densit√y is constant at the entrance and exit surfaces, the exhaust plane pressure is atmospheric and ua = M γaRaTa. The thrust per unit airflow is then given as: τ = [1+(1+β) far]u7 −ua +β(u8 −ua) (4) m ̇ a 1 + β The energy balance of the turbofan presented in Table 1 can be expressed as: Q ̇b = [1+(1+β)far]u27−u2a+β(u28−u2a)m ̇a+ [1+(1+β)far]h7−ha+β(h7−ha)m ̇a (5) 1+β 1+β Propulsive kinetic energy (useful energy) Thermal energy (unuseful energy) The energy performance indicators are the thermal efficiency, propulsion efficiency, and overall efficiency. According to Equation (5), the thermal efficiency ηth is the relation between the propulsive Energy Balance H ̇ t 1 − H ̇ a = 1 m ̇ a u 2a 2 W ̇ F = H ̇ t 2 − H ̇ t 1 W ̇ C = H ̇ t 3 − H ̇ t 2 Q ̇b=H ̇t4−H ̇t3 W ̇HPT =H ̇t4−H ̇t5 =W ̇C W ̇LPT =H ̇t5−H ̇t6 =W ̇F βH ̇t2−(1+β)H ̇8= βm ̇a u28 Adiabatic Efficiency η D = h t 1 s − h a ht1 − ha η F = h t 2 s − h t 1 ht2 − ht1 η C = h t 3 s − h t 2 ht3 − ht2 ηb= qb LHV ηHPT = ht4−ht5 ht4 − ht5s ηLPT = ht5−ht6 ht5 − ht6s 1+β 2(1+β) H ̇t6−H ̇7=1m ̇cgu27 ηFN= ht2−h8 ht2 −ht8s 2 H ̇ta +Q ̇b = H ̇t7 +H ̇t8 ηN= ht6−h7 ht6 − ht7s 2γcg ⎢ ⎛Pa⎞γcg1⎥ 2γa ⎢ ⎛Pa⎞γa1⎥ u7 = γ −1RcgTt6ηN ⎢1−⎝P ⎠ ⎥ and u8 = γ −1RaTt2ηFN ⎢1−⎝P ⎠ ⎥ cg ⎢⎣ t6 ⎥⎦ a ⎣ t2 ⎦PDF Image | Residue Cost Formation of a High Bypass Turbofan Engine
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