FLUID MECHANICS: DERIVATION OF THRUST EQUATION

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Presentation transcript:

FLUID MECHANICS: DERIVATION OF THRUST EQUATION Chemical Energy Thermal Energy Kinetic Energy Flow through engine is conventionally called THRUST Composed of net change in momentum of inlet and exit air Fluid that passes around engine is conventionally called DRAG

THERMODYANMICS: BRAYTON CYCLE MODEL 1-2: Inlet, Compressor and/or Fan: Adiabatic compression with spinning blade rows 2-3: Combustor: Constant pressure heat addition 3-4: Turbine and Nozzle: Adiabatic expansion Take work out of flow to drive compressor Remaining work to accelerate fluid for jet propulsion Thermal efficiency of Brayton Cycle, hth=1-T1/T2 Function of temperature or pressure ratio across inlet and compressor

EFFICIENCY SUMMARY Overall Efficiency What you get / What you pay for Propulsive Power / Fuel Power Propulsive Power = TUo Fuel Power = (fuel mass flow rate) x (fuel energy per unit mass) Thermal Efficiency Rate of production of propulsive kinetic energy / fuel power This is cycle efficiency Propulsive Efficiency Propulsive Power / Rate of production of propulsive kinetic energy, or Power to airplane / Power in Jet

PROPULSIVE EFFICIENCY AND SPECIFIC THRUST AS A FUNCTION OF EXHAUST VELOCITY Conflict

COMMERCIAL AND MILITARY ENGINES (APPROX. SAME THRUST, APPROX COMMERCIAL AND MILITARY ENGINES (APPROX. SAME THRUST, APPROX. CORRECT RELATIVE SIZES) GE CFM56 for Boeing 737 T~30,000 lbf, a ~ 5 Demand higher efficiency Fly at lower speed (subsonic, M∞ ~ 0.85) Engine has large inlet area Engine has lower specific thrust Ue/Uo → 1 and hprop ↑ Demand high T/W Fly at high speed Engine has small inlet area (low drag, low radar cross-section) Engine has high specific thrust Ue/Uo ↑ and hprop ↓ P&W 119 for F- 22, T~35,000 lbf, a ~ 0.3

EXAMPLE: SPECIFIC IMPULSE PW4000 Turbofan SSME Space Shuttle Main Engine T ~ 2,100,000 N (vacuum) LH2 flow rate ~ 70 kg/s LOX flow rate ~ 425 kg/s Isp ~ 430 seconds Airbus A310-300, A300-600, Boeing 747-400, 767-200/300, MD-11 T ~ 250,000 N TSFC ~ 17 g/kN s ~ 1.7x10-5 kg/Ns Fuel mass flow ~ 4.25 kg/s Isp ~ 6,000 seconds