ME 425: Aerodynamics

Transcription

1 ME 45: Aerodynamics r. A.B.M. oufique Hasan Professor epartment of Mechanical Engineering Bangladesh University of Engineering & echnology (BUE), haka Lecture-4 //9 Airplane pa Performance toufiquehasan.buet.ac.bd hrust Available, A hrust required, R of an airplane is dictated by the aerodynamics and weight of the airplane itself; it is an airframe - associated phenomena. In contrast, the thrust available, A is strictly associated with the engine of the airplane. In reciprocating engines with propellers (urbo-prop) prop), thrust at zero velocity (static thrust) is a imum and decreases with forward velocity (Fig. (a)). Examples are light, general aviation aircraft, regional liner etc (ASH 8, MRJ etc.). In jet engines (urbo-jet), thrust is relatively constant with velocity (Fig. (b)). Examples are large commercial transports, military aircraft etc. (GE, P, SNECM Rolls- Royce etc.) A constant However, a discontinuity exists near the sonic speed due to compressibility effects.

2 Power Available, P A Power required, P R is a characteristic of the aerodynamic design and weight of the airplane itself. In contrast, the power available, P A is a characteristic of the power plant of the airplane. In reciprocating engines with propellers (urbo-prop), Power available, P A varies with as shown in Fig. (a) due to variation of A with he jet engines (urbo-jet) derives its thrust by combustion heating and incoming stream of air and then exhausting this hot air at high velocities through a nozzle. Since, A is reasonably constant with velocity, the power available, P A curve varies essentially linearly with. 3 Power Available, P A he imum flight velocity, is determined by the high-speed intersection of the imum P A and the P R curves. P A P R excess power 4

3 Maximum velocity, is frequently a part of the set of specifications for a new airplane design. hat are the parameter govern this velocity?? Consider a steady, level flight at a particular itude: q S C q S C, C L q S q S C, q S C, q S q q S C, S drag coefficient, C C C, C lift coefficient,, i, q S q L CL q S q S q S C, q S Quadratic equation in terms of q 5 he solution of the quadratic equation is: q S C, q S 4 S C, S q S C, Recalling q ; replacing with and A with expression, gives the expression of imum velocity, as : and taking ve A in the quadratic A A S S C,, hree important airplane design parameter: () hrust-to-weight ratio ( A /) () ing loading (/S) (3) C, Maximum velocity achievable at a given itude 6 3

4 A A S S C,, hus, depends on 3 factors and these are A S C, : : : Maximumthrust to weightratio ingloading Zero- lift drag coefficient Airbus A 38 Boeing 777 Engine 4x (Rolls Royce rent 9) Maximum speed, Engine x (GE/P) Maximum speed, 4x 3 kn M.96 ( km/hr) x 377 kn M.89 (945 km/hr) 7 A jet-powered executive aircraft, Cessna Citation 3 has the following characteristics: ing span = 6.5 m ing area = 9.54 m gross weight = N Fuel capacity = 9 gal Power plant = x turbofan engine 64.5 N at seal level Parasite drag coefficient, C, =. Oswald efficiency factor, e =.8 θ Calculate the imum velocity of Cessna Citation jet (a) At sea level where ρ =.5 kg/m 3 (b) At a itude m where ρ =.6kg/m 3 Both graphically and analytically. 8 4

5 AR = b /S = 8.94 (m/s) C L =/(q S) C = C, +C L /πear C L /C R, = /(C L /C ) (kn) P R, = R, (k) P = (k) Sea-level condition () PR, P P P R (k) 8 6 P 4 P R, (m/s) 5

6 Analytically: (at sea-level condition ()) A S S C A, , (.5)(.) (.) (.8)(8.94) 99 m/s sea level hrust available for a jet engine, is almost proportional to the air density: m m ( A ) ( A ) x turbofan engine 64.5 N at seal-level (total of N), engine power plant will generate:.6 (64.5) N at itude of m from sea - level 6

7 (m/s) C L = /(q S) C = R, = C,+C L /πear CL/C /(C L/C ) (KN) P R, = R,* (K) P = * (k) = *(ρ /ρ ).5 (m/s) P R, = P R,*(ρ /ρ ).5 (k) P = * (k) Sea-level condition () At itude m Analytically: (at m itude) A A S S C C,, (.6)(.) (.) (.8)(8.94) 95m/s < 99 m/s at sea-level condition () sea level 4 7