Aircraft Propulsion Introductions to Concepts March 30, 2014 Outline Introduction Thermal efficiency Propulsive efficiency Specific impulse and range Ramjets Brayton cycle Turbojets Turbofans References [1] Jack L Kerrebrock, Aircraft engines and gas turbine, The MIT press, 1992 [2] Yunus AC, Michael A.B., Thermodynamics an engineering approach, McGrawHill, 20132 Biomimetics and Intelligent Microsystem Laboratory Introduction Describe in simple physical terms the fundamental characteristics of gas turbines and related flight vehicle propulsion systems • Thermodynamic • Fluid-dynamic • Mechanical Control and limit their design and applications Thermal energy Useful work Thermal efficiency Propulsive efficiency Overall efficiency • Compromise between “high overall efficiency” and other factors (example T/W) in various flight regimes Types of engines: Turbojets, turbofans, turboprops, … Biomimetics and Intelligent Microsystem Laboratory Introduction Some aspects should be considered: • Weight and size • Takeoff noise (noise per unit of thrust) • Emission of smoke and gaseous pollutants Thermal efficiency • The laws of thermodynamics Upper limit on the thermal efficiency • Carnot cycle (Yunus AC, Michael A.B., Thermodynamics an engineering approach, McGrawHill, 2013) Biomimetics and Intelligent Microsystem Laboratory • 1-2: T=const., reversible isothermal expansion • 2-3: s=const., reversible adiabatic expansion • 3-4: T=const., reversible isothermal compression • 4-1: s=const., reversible adiabatic compression Thermal efficiency Thermal efficiency • Maximum thermal efficiency can be attained by a Carnot cycle c T0 , where Tm T0: Heat sink (heat-rejection temperature) Tm: Maximum heat addition temperature • T0 (TL): ~ atmosphere temperature • Tm (TH): ~ principle limited only by the characteristics of the combustion process • Example: • T0 = 217oK (11km~30km altitude) Tm = 1500oK c ~ 0.85 Automotive and stationary gas turbine T0 = 300oK Tm ≤ 1300oK Biomimetics and Intelligent Microsystem Laboratory c ~ 0.77 Propulsive efficiency Propulsive efficiency p • Thrust power delivered to vehicle Net mechanical power delivered to engine mass flow Linear momentum P dP F dt udV , system • Using Reynolds transport theorem F udV t CV Time change of the linear momentum within the CV u (u.dA) CS net rate of the linear momentum flux in &out through the CS F m (ue u0 ) • Ignore the amount of the fuel flow (2%-4% of the air flow for most aircraft engines) Biomimetics and Intelligent Microsystem Laboratory Propulsive efficiency Propulsive efficiency m (ue u0 )u0 2u0 p ue2 u02 ue2 u02 ue u0 m m Fu0 u0: flight velocity ue: exhaust velocity Kinetic energy per unit of mass ue2 u02 m Total power input in the fuel 2 Power rejected in the form of heat Biomimetics and Intelligent Microsystem Laboratory Propulsive efficiency Propulsive efficiency • Propulsive efficiency vs F /(m u0 ) F m (ue u0 ) p u 1 e u0 F u e 1 m u0 u0 p F 2 m u0 Given m and u0 ue/u0 increases ηp decreases ue/u0 increases F /(m u0 ) increases Increases mass flow Increases weight and size Drag Biomimetics and Intelligent Microsystem Laboratory Propulsive efficiency Propulsive efficiency • Propulsive efficiency vs F /(m u0 ) Biomimetics and Intelligent Microsystem Laboratory Specific Impulse and Range Specific impulse Number of unit thrus t Unit of fuel weight flow rate F I dW / dt I • W: weight of the aircraft Steady flight: D = F, W = L, F = W/(L/D) dW F W dt I I L/D dW dt I ( L / D ) W • • If I = const., L/D =const t I ( L / D ) ln Wg Wg W f Wg = gross (initial) weight, Wf = fuel weight Biomimetics and Intelligent Microsystem Laboratory 10 Example: The simple ideal Brayton cycle[2] Example 1: • Total heat input, qin = h3 – h2 = 1395.97 – 544.35 = 851.62 kJ/kg • Thermal efficiency: th wnet 362.4kJ/kg 0.426 qin 851.62kJ/kg qout th qin qout h4 h1 • Note: %% Cold-air-standard condition (constant specific heat specific values) % T2/T1=(P2/P1)^[(k-1)/k]=(P3/P4)^[(k-1)/k]=T3/T4 T2=T1*rp^((k-1)/k); % T at the exit of the compressor T4=T3/(rp^((k-1)/k)); % T at the exit of the turbine nu=1-1/(rp^((k-1)/k)); disp(['T2 = ',num2str(T2),'K; T4 = ',num2str(T4),'K; nu = ',num2str(nu)]); T2 = 543.4342K; T4 = 717.6582K; Biomimetics and Intelligent Microsystem Laboratory nu = 0.44796 21 Ideal jet-propulsion cycles Ideal jet-propulsion cycles • Example: A turbojet aircraft flies with a velocity of 260m/s at an altitude where the air is 35kPa and -40̊C The compressor has a pressure ratio of 10, and the temperature of the gases at the turbine inlet 1100̊C Air enters the compressor at the rate of 45kg/s Utilizing the cold-air-standard assumptions, determine (a) the temperature and pressure of the gases at the turbine exit, (b) velocity of the gases at the nozzle exit, and (c) the propulsive efficiency (Assumptions: Steady condition; cold-air-standard, cp =1.005KJ/kg.̊C, k=1.4; kinetic at the nozzle exit only; turbine work output = compressor work input and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 22 Ideal jet-propulsion cycles Ideal jet-propulsion cycles V = 260 m/s T1 = 233K, P1 = 35kPa rp = P3/P2 = 10 T4=1373K Air enters the compressor at the rate of 45kg/s (Assumptions: Steady condition; cold-air-standard, cp =1.005KJ/kg.̊C, k=1.4; kinetic at the nozzle exit only; turbine work output = compressor work input and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 23 Ideal jet-propulsion cycles Ideal jet-propulsion cycles • Process 1-2: isentropic compression of an ideal gas in a diffuser V1 260 m/s V2 m/s V22 V12 h2 h1 2 V12 c p (T2 T1 ) V12 T2 T1 267 K 2c p T P2 P1 T1 k /( k 1) 56.4kPa and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 24 Ideal jet-propulsion cycles Ideal jet-propulsion cycles • Process 2-3: isentropic compression of an ideal gas in a compressor P3 rp P2 564kPa ( P4 ) P T3 T2 P2 ( k 1) / k 515K • Process 4-5: isentropic expansion of an ideal gas in a turbine wcomp ,in wturb,out h3 h2 h4 h5 c p (T3 T2 ) c p (T4 T5 ) T5 1125K T5 P5 P4 T4 k /( k 1) 281kPa and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 25 Ideal jet-propulsion cycles Ideal jet-propulsion cycles (b) Velocity at the nozzle exit Nozzle exit temperature: P T6 T5 P5 ( k 1) / k 620K Steady-flow energy equation: V62 V52 h6 h5 h5 2 V6 1007m / s (c) Propulsive efficiency W p m (Vexit Vinlet )VAircraft 8740kW Q in m c p (T4 T3 ) 38,803kW W p p 22.5% Qin and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 26 Ideal jet-propulsion cycles Ideal jet-propulsion cycles Discussion: 100% - 22.5% = 77.5%, where does the 77.5% energy go? Kinetic energy & increase in enthalpy of the gases KE out m Q out Vg2 ? m (h6 h1 ) ? and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 27 Problems and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 28 Problems 9-88 Air is used as the working fluid in a simple ideal Brayton cycle that has pressure ratio of 12, a compressor inlet temperature of 300K, and the turbine inlet temperature of 1000K Determine the required mass flow rate of air for a net power output of 70MW Assume constant specific heats at room temperature 9-91 An aircraft engine operates on a simple ideal Brayton cycle with a pressure ratio of 10 Heat is added to the cycle at a rate of 500kW; air passes through the engine at the rate of 1kg/s; and the air at the beginning of the compression is at 70kPa and 0̊C Determine the power produced by this engine and its thermal efficiency Use constant specific heats at room temperature 9-127C What is propulsive power? How is it related to thrust? 9-128C What is propulsive efficiency? How is it determined? and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 29 Problems 9-130 A turboprop-aircraft propulsion engine operates where the air is at 55kPa and – 23 ̊C, on an aircraft flying at a speed of 180 m/s The Brayton cycle pressure ratio is 10 and the air temperature at the turbine inlet is 505 ̊C The propeller diameter is m and the mass flow rate through the propeller is 20 times that through the compressor Determine the thrust force generated by this propulsion system Assume ideal operation for all components and constant specific heat at room temperature 9-131 How much change would result in the thrust of Prob 9-30 if the ropeller diameter were reduced to 2.4 m while maintaining the same mass flow rate through the compressor Note: The mass flow rate ratio will no longer be 20 9-132 A turbofan engine operating on an aircraft flying at 200 m/s at an altitude where the air is at 50 kPa and -20 ̊C is to produce 50,000N of thrust The inlet diameter of the engine is 2.5 m; the compressor pressure ratio is 12; and the mass flow rate ratio is Determine the air temperature at the fan outlet needed to produce this thrust Assume ideal operation for all components and constant specific heats at room temperature and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 30 Problems 9-133 A pure jet engine propels an aircraft at 240 m/s through air at 45 kPa and 13 ̊C The inlet diameter of this engine is 1.6 m, the compressure ratio is 13, and the temperature at the turbine inlet is 557 ̊C Determine the velocity at the exit of this engine’s nozzle and the thrust produced Assume ideal operation for all components and constant specific heats at room temperature 9-134 A turbojet aircraft is flying with velocity of 320 m/s at an altitude of 9150 m, where the ambient conditions are 32 kPa and -32 ̊C The pressure ratio across the compressor is 12, and the temperature at the turbine inlet is 1400K Air enters the compressor at a rate of 60 kg/s, and the jet fuel has a heating value of 42,700kJ/kg Assuming ideal operation for all components and constant specific heats for air at room temperature, determine (a) the velocity of the exhaust gases, (b) the propulsive power developed, and © the rate of fuel consumption and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 31 Problems 9-135 Repeat Prob 9-34 using a compressor efficiency of 80% and a turbine of 85% 9-136 Consider an aircraft powered by a turbojet engine that has a pressure ratio of The aircraft is stationary on the ground, held in position by it brakes The ambient air is at ̊C and 95 kPa and enters the engine at a rate of 20 kg/s The jet fuel has a heating value of 42,700kJ/kg and it is burned completely at a rate of 0.5 kg/s Neglecting the effect of diffuser and disregarding the slight increase in the mass at the engine exit as well as the inefficiencies of the engine components, determine the force that must be appliied on the brakes to hold the plane stationary and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 32 and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 33 and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 34 and A.B., Intelligent Microsystem Laboratory YunusBiomimetics AC, Michael Thermodynamics an engineering approach, McGrawHill, 2013 35