JNTU
JNTU B.Tech III AEROSPACE PROPULSION I Previous Question Paper (October - 2020 - R13)
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Main
Define thrust of an engine and derive the thrust equation for a general propulsion system.
Answer
Thrust is the reaction force generated by an engine that propels an aerospace vehicle forward, resulting from the change in momentum of the working fluid and the pressure difference across the engine exit. For a general propulsion system, consider a control volume surrounding the engine with inlet area A_i and exit area A_e.
Applying the momentum theorem to the control volume:
Where m_e and m_i are the mass flow rates at exit and inlet, v_e and v_i are the velocities, p_e is the exit pressure, and p_a is the ambient pressure. Assuming fuel mass flow m_f is added to the air mass flow m_a, the total exit mass flow is m_e = m_a + m_f. Neglecting the small contribution of fuel mass flow to momentum change, the thrust equation simplifies to:
where f = m_f / m_a is the fuel-to-air ratio.
A turbojet engine flying at sea level and at a Mach number equal to 0.7 ingests air at a rate of 75 kg/s. The compressor total pressure ratio is 15. The calorific value of fuel is 41 MJ/kg and the burner exit total temperature is 1400 K. assuming the specific heat ratio of 1.4. Determine the thrust developed and the thrust specific fuel consumption (TSFC).
Answer
Given: M = 0.7, m_a = 75 kg/s, r_p = 15, Q_R = 41 MJ/kg, T_t4 = 1400 K, gamma = 1.4, R = 287 J/kgK, c_p = 1005 J/kgK. At sea level, T_a = 288 K, p_a = 101.3 kPa.
1. Inlet conditions: T_t1 = T_a(1 + 0.2 M^2) = 288(1 + 0.2(0.7)^2) = 316.2 K. v_i = M * sqrt(gamma * R * T_a) = 0.7 * sqrt(1.4 * 287 * 288) = 238.7 m/s.
2. Burner: f = (c_p(T_t4 - T_t3)) / (Q_R * eta_b - c_p T_t4). Assuming isentropic compression, T_t3 = T_t1 * (r_p)^((gamma-1)/gamma) = 316.2 * (15)^0.2857 = 675.6 K. Assuming eta_b = 1, f = (1005(1400 - 675.6)) / (41e6 - 1005 * 1400) = 0.0186.
3. Exit velocity: Assuming ideal expansion (p_e = p_a), v_e = sqrt(2 * c_p * T_t4 * (1 - (p_a/p_t4)^((gamma-1)/gamma))). With p_t4 = p_t3 = p_a(1 + 0.2 M^2)^(gamma/(gamma-1)) * 15 = 101.3 * 1.628 * 15 = 2474 kPa. v_e = sqrt(2 * 1005 * 1400 * (1 - (101.3/2474)^0.2857)) = 1386 m/s.
4. Thrust: T = m_a((1 + f)v_e - v_i) = 75 * ((1.0186 * 1386) - 238.7) = 88,040 N = 88.04 kN.
5. TSFC: TSFC = f / ((1 + f)v_e - v_i) = 0.0186 / (1386 * 1.0186 - 238.7) = 0.0158 kg/Ns = 15.8 g/kN/s.
Explain the criteria for selection of engine for aircraft. How the altitude, flight speed, Mach number will affect the performance of aircraft? Use sketches and plots.
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What are the advantages of closed cycle gas turbine cycle?
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Draw the T-s diagram of gas turbine engine and the two important parameter of the cycle identity
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A turbojet engine is traveling at 270 m/s at an altitude of 5000 m. The compressor pressure ratio is 8:1 and maximum cycle temperature is 1200 K. By assuming the following data, calculate the specific thrust and TSFC. Ram efficiency 93%, Isentropic efficiency of the compressor 87%, Pressure loss in the combustion chamber delivery 4% of compressor. Calorific value of the fuel 43,100 kJ/kg, Isentropic efficiency of the turbine 99%, Isentropic efficiency of propelling nozzle 90%, Ambient condition at 5000 m are 0.505 bar and 255.7 K.
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Explain the working principle of a turbofan engine with a neat sketch.
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In a twin spool turbofan engine, with the fan driven by the LP turbine and the compressor by the HP turbine, separate cold and hot nozzles are used. Overall pressure ratio 19, Fan pressure ratio 1.65, By-pass ratio 3.0, Turbine inlet temperature 1300 K Fan, compressor and turbine polytropic efficiency 0.90 Isentropic efficiency of each propelling nozzle 0.95, Mechanical efficiency of each spool 0.99, Combustion pressure loss 1.25 bar, Total mass flow rate of air 115 kg/s. Calculate thrust under sea level static conditions where the ambient pressure and temperature are 1 bar and 288 K.
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Explain successive steps in the acceleration and over speeding of a one dimensional supersonic inlet with sketches.
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Derive the relation between area ratio Amax/Ai and external deceleration ration ui/ua.
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Discuss in detail the various methods of flame stabilization.
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Air flows isentropically through a convergent-divergent nozzle of inlet area 12 cm2 at a rate of 0.7 kg/s. The conditions at the inlet and exit of the nozzle are 8 kg/m2 and 300K respectively. Find the cross-sectional area, the pressure and Mach number at the exit of the nozzle.
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Define loss coefficient for nozzle and rotor blade of an axial turbine stage and derive a relationship for stage isentropic efficiency relating nozzle and rotor loss coefficient.
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How does the magnitude of turbine inlet temperature influence the resulting component match?
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Write the general procedure steps for component matching analysis for a single spool turbojet with simplifying assumptions.
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