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AE 429 - Aircraft Perform Ance and Flight Mechanics

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AE 429 - Aircraft Perform Ance and Flight Mechanics AE 429 - Aircraft Perform ance and Flight Mechanics Propulsion Characteristics Types of Aircraft Propulsion Mechanics Important Characteristics: Reciprocating engine/propeller •Thrust (or power) Turbojet •Fuel consumption Turbofan Turboprop 1 Engine Design - Goals Thrust and Efficiency tradeoff Propeller/reciprocating engine œ (low trust, great efficiency) Turbojet (higher trust, less efficiency) Rocket (very high trust, poor efficiency) Tradeoff: more power means less efficiency Thrust (Power)- Propulsive force (—move as much air as fast as you can“) Fuel consumption- Efficiency in producing force 2 Thrust of all flight propulsion systems comes from the same principle reaction-as expressed by Newton's second law of motion force = rate of change of momentum or force = mass flow rate times the change in fluid velocity Propulsion principle is the same for propeller. turbojet. ramjet, and rocket. F = thrust (assumed same for all in comparison): m = mass flow of working fluid (air or exhaust gas) ; VJ = exhaust gas velocity; VO= flight velocity. (NACA, 1953) Aircraft thrust requirements increase with speed. (NACA, 1953.) 3 Turbine Engine Propulsion Systems Thrust Fundamentals Newton‘s 3rd Law- For every action, and equal and opposite reaction; Device exerts equal and opposite force T on air Newton‘s 2nd Law- Force is equal to time rate of change of momentum Momentum = Mass*Velocity (kg*m/s) T = m# Vj -m# VÑ = m# (Vj -VÑ ) Thrust Eq. For Generic Propulsion Device Thrust exerted on device via pressure and shear forces by air on exposed surfaces 7 Efficiency Fundamentals Air stationary, device moving by… … V=0 Power = ForceìVelocity PA = TVÑ 1 2 PTotal = TVÑ + m# (Vj -VÑ ) 2 /asted kinetic energy causes the sub-optimal efficiency 1 2 m# (V j -VÑ ) 2 useful power avaliable PA h p = = total power genrated PTotal Plug in thrust equation, total and available power m# (V j -VÑ )VÑ h = p 1 2 m# V j -VÑ VÑ + m# V j -VÑ ( ) 2 ( ) 1 1 h = = 2 p 1 1 h p = 1+ V -V /V 1+V /V 1+Vj /VÑ 2 ( j Ñ ) Ñ 2 ( j Ñ ) Observations: • Max efficiency for , but Thrust = 0 ! VÑ = V j • Propeller: Thrust through large m # , small V j -VÑ so h p is high • Caveat: Thrust via Propellers is limited by tip speed, due to shock formation and resultant power loss; thus, propellers become ineffective at high speeds • Jet engine: thrust through smaller m # and higher V j - VÑ higher thrust but lower h p (wasted kinetic energy) 5 Reciprocating Engine + Propeller Use energy of combustion to expand products, move piston, turn crankshaft Power Production 7Engine Size- Displacement (d) • Volume swept out by piston; total displacement is this volume multiplied by # of cylinders • Speed- Revolutions per Minute (rpm) • Number of power strokes per minute • Pressure- Mean effective pressure (pe) • Higher the pressure on piston head, larger the power output Pî (d )( pe )(rpm) Efficiency- Specific Fuel Consum ption weight of fuel consumed per unit time c = (power)(time) W ant lots of power for little fuel . So minimize c !! lb 1 [c] = = units ( ft∂lb/ s) s ft Same idea, different units lb [SFC] = hp ∂ h 8 Propeller The propeller (as a collection of twisted wings) is subject to P = h P, h < 1 same drag sources as main wing, which results in losses A pr pr Propeller efficiency is a function of the advance ratio, J N = # propeller revolutions per second VÑ J = D = propeller diameter ND b = pitch angle (between chord line and plane of rotation VÑ is small, a is positive, —lift“ is in thrust direction….good VÑ is large, a is negative, —lift“ is opposite thrust ….bad r = radial distance of airfoil section to hub w = angular velocity of propeller rw = D / 2 2p N = p ND ( )tip ( )( ) V V Ñ = Ñ rw r(2pN ) ≈ V ’ V V J ∆ Ñ ÷ = Ñ = Ñ = « rw ◊tip (D / 2)(2pN ) pND p Advance ratioJ captures the critical efficiency metric of the propeller, the ratio of free- stream velocity to rotational translation 7 Increasing V Ñ produces an —alpha sweep“ from high + to high -; there is an a that corresponds to (L/D)max for the section and thus h pr is maximized Note: Pitched-fixed, N fixed J Max efficiency occurs at specific , and thus specific VÑ This is the design point, but what happens at different velocities drastic decrease in efficiency ! Solution: Adjustb to select proper J to traverse locus of maximum efficiency . … the variable-pitch propeller However, variable pitch propeller created more aerodynamic torque, tending to retard rotation of propeller P So h pr was increasing, but was decreasing somewhat some loss in available power PA Solution: Adjust b to select maximize h pr P , the power available PA . … the constant-speed propeller (constant rpm) 8 Turbojet Concentrates more on ( V j - V Ñ ) to generate high T Net thrust is resultant of pressure and shear forces on engine surfaces Compression & expansion combustion adds energy T = Fnet> 0 3 Thrust of Turbojet Recall, T = m# Vj -m# VÑ = m# (Vj -VÑ ) T = (m# air + m# fuel )Vj -m# airVÑ +( pe - pÑ ) Ae pe = Eas pressure at nozzle exit pÑ = ambient pressure Ae = nozzle exit area Pressure term usually small Thrust specific fuel consum ption weight of fuel consumed per unit time c = t (thrust)(time) lb 1 »c ÿ= = t ⁄ (lb) s s Conventionally used thrust specific fuel consumption (TSFC) is slightly different, lb 1 [TSFC] = = (lb)h h 10 Sensitivity of T and TSFC with Velocity and Altitude Thrust- Subsonic Mach numbers Similar to Drag, Thrust and engine efficiency depends on —flight condition“, i.e. velocity and altitude m# air = rÑ A1VÑ T = (m# air + m# fuel )V j - m# airVÑ + ( pe - pÑ ) Ae Increase in m # a i r tends to cancel decrease in (V j -VÑ ) T is approximately constant with V T r = Thrust proportional to density as T0 r0 altitude changes sub0 Ω sea-level value Sensitivity of T and TSFC with Velocity and Altitude TSFC can be optimized via —cycle“ parameters (items such as pressure ratios, temperatures, etc.). This is achieved through proper design of the components (compressor, combustor, turbine, etc.) TSFC is approximately constant with altitude TSFC . kM = 1 0 + Ñ k is a function of altitude and throttle (rpm) 11 Supersonic conditions (g .(g -4)) ptotal ≈ g -1 2 ’ = ∆1+ M ÷ pstatic « 2 ◊ Tî M Ñ supersonic conditions T/TM =1 =1.0 +1.18(M Ñ -1) Large total pressure recovered at diffuser inlet; thus, as speed increases, more pressure recovered and delivered to compressor, thus increasing Vj and thrust d = p / p0 Ratio of pressures at altitude and sea level TSFC is approximately constant with speed Turbofan • 2 airflows, one through core (turbojet) and one —by-passed“ • Thrust obtained from by-passed flow approaches efficiency of propeller • COMBINATION of improved efficiency and high thrust has made the Turbofan the choice for modern transport airplanes mass bypassed air By-Pass ratio = mass core air By-Pass ratio means TSFC 12 Turbofan Performance Variations (high BPR) Thrust variations depend on flight condition V In general, T decreases with but to a lesser extent at high altitude Turbofan Performance Variations (High BPR) Turbofan thrust specific fuel consumption variations: c V • T increases with increasing c B kM Only valid for M T = (1+ Ñ ) 0.7 < Ñ < 0.85 c M Recall T ~ constant above Ñ for turbojet • cT about constant with altitude T T AM -n A and n / V =0 = Ñ are function of the altitude At 3 Km: T T M -0.305 / V =0 = 0.369 Ñ m T ≈ r ’ = m about 1 T ∆ ÷ 0 «r0 ◊ sub 0 Ω sea-level value 13 -ow BPR Designs Primarily used on military fighters: • Need thrust at high Mach, not efficiency ! • More like a turbojet ! • BPR between 0 and 1 Turboprops • Propeller driven by gas turbine engine • Its —niche“- • More thrust than reciprocating engine, but less than turbojet/fan • Better specific fuel consumption than turbojet/fan, but less than reciprocating Turboprop Power available: PA = (Tp + T j )VÑ Shaft Power is most important (95%): PA = h pr Ps + TjVÑ Equivalent Shaft Power is often used: PA = h pr Pes T V Equivalent Shaft Power defined: j Ñ Pes = Ps + h pr 14 Turboprops ct = w# fuel T Thrust fuel consumption c = w P cA = w# fuel PA cS = w# fuel PS es # fuel es n ≈ r ’ P . P = PA = TAVÑ is constant with speed A A0 ∆ ÷ variation with altitude «r0 ◊ n = 0.7 Reciprocating Engine/Propeller Com bination 15 Turbofan Engine Turbojet Engine 16 Turboprop Engine The basic com ponents of an air-breathing (jet) engine are the inlet, a com pressor or fan, the combustor (burner), a turbine, and an exit nozzle. Different engines will use these com ponents in various combinations. Som e engine designs even leave out one or m ore of these components. But these are the basic building blocks of an engine. The figure below shows a typical jet engine design and its components. Inlet: The design of the inlet, or air intake, helps determine the amount of air flow into an engine. After deciding the cruise speed of the aircraft, engineers design the inlet to suck in as much of the air coming toward it as needed. Subsonic, supersonic and hypersonic cruise speeds each require a different inlet design. Inside the engine the next component, the compressor, works much, much better when the air enters fairly slowly, (usually much slower than cruise velocity), so the inner walls of the inlet are designed to slow the velocity of the air stream as it comes to the compressor.
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