Broadening of Fundamentals in Aerospace Science and Technology 2- Aerodynamics / Flight principles II 23/09/2014 BFAE Sep-14 Slide 1 2- Aerodynamics / Flight principles II Airfoil • airfoil: cross-sectional shape obtained by the intersection of the wing with the perpendicular plane • airfoil nomenclature: BFAE Sep-14 Slide 2 2- Aerodynamics / Flight principles II Lift, drag and moments How is lift produced? Symmetric airfoil BFAE Sep-14 Slide 3 2- Aerodynamics / Flight principles II Lift, drag and moments How is lift produced? • mass continuity (continuity equation): flow velocity increases over the top surface of airfoil more than it does over the bottom surface • Bernoulli effect: pressure over the top surface of the airfoil is less than pressure over the bottom surface • due to the lower pressure over top surface and higher pressure over bottom surface, the airfoil feels a lift force in the upward direction BFAE Sep-14 Slide 4 2- Aerodynamics / Flight principles II Lift, drag and moments • V∞: relative wind • α: angle of attack of the airfoil • R: aerodynamic force created by the pressure and shear stress • D: drag: component of the aerodynamic force parallel to the relative wind • L: lift: component of the aerodynamic force perpendicular to the relative wind BFAE Sep-14 Slide 5 2- Aerodynamics / Flight principles II Lift, drag and moments • M: moment created by the surface pressure and shear stress distribution that tends to rotate the wing • Mc/4: moment taken at the quarter-chord point • drag, lift, moments vary with the angle of attack α • at the aerodynamic center, moments do not vary with α, Mac=const (for low-speed subsonic airfoils, close to Mc/4) BFAE Sep-14 Slide 6 2- Aerodynamics / Flight principles II Lift, drag and moments L, D and M depend on • free-stream velocity V∞ • free-stream density ρ∞ (altitude) • size of the aerodynamic surface (wing area S) • angle of attack α • shape of the airfoil • viscosity coefficient μ∞ (from skin friction distributions) • compressibility of the airflow (governed by the value of Mach number M∞=V∞/a∞) For a given shape airfoil at a given angle of attack: L = f ( V∞ , ρ∞ , S, µ ∞ , a ∞ ) BFAE Sep-14 Slide 7 2- Aerodynamics / Flight principles II Lift, drag and moments Lift, Drag and Moment coefficients L = q ∞ × S × cl D = q ∞ × S × cd M = q∞ × S × cm × c L cl ≡ q ∞S D cd ≡ q ∞S M cm ≡ q ∞Sc cl = f1 ( α, M ∞ , Re) cd = f 2 ( α, M ∞ , Re) c m = f 3 ( α, M ∞ , Re) BFAE Sep-14 Slide 8 2- Aerodynamics / Flight principles II Lift, drag and moments • a large bulk of experimental airfoil data was compiled over the years by the National Advisory Committee for Aeronautics (NACA: later absorbed in the creation of National Aeronautics and Space Administration-NASA) • lift, drag and moment coefficient were systematically measured for many airfoil shapes in low-speed subsonic wind tunnels • obtained data for coefficients variation with α, for different Re, for numerous airfoils BFAE Sep-14 Slide 9 2- Aerodynamics / Flight principles II Lift, drag and moments NACA airfoil NACA four-digit wing sections define the profile by One digit describing maximum camber as percentage of the chord. One digit describing the distance of maximum camber from the airfoil leading edge in tens of percents of the chord. Two digits describing maximum thickness of airfoil as % of chord. NACA 2412 airfoil has a maximum camber of 2% located 40% (0.4 chords) from the leading edge with a maximum thickness of 12% of the chord BFAE Sep-14 Slide 10 2- Aerodynamics / Flight principles II Lift, drag and moments • cl varies linearly with α over a large range of angle of attack • lift curve for a symmetric airfoil goes trough the origin • for large values of α, the linearity of the lift curve breaks down • airfoil stall: caused by flow separation on the upper surface of the airfoil BFAE Sep-14 Slide 11 2- Aerodynamics / Flight principles II Lift, drag and moments Infinite wing versus finite wing Aspect ratio b2 AR ≡ S b: wingspan For a finite wing: use capital letters CL, CD, CM, (compared to cl, cd, cm) BFAE Sep-14 Slide 12 2- Aerodynamics / Flight principles II Lift, drag and moments Aspect ratio: High value: gliders Low value: fighters Eurofighter Typhoon Viking glider BFAE Sep-14 Slide 13 2- Aerodynamics / Flight principles II Lift, drag and moments Pressure coefficient CP ≡ p − p∞ p − p∞ ≡ 1 ρ V2 q∞ 2 ∞ ∞ important quantity: leads to value of cl NACA 0016 Pressure Coefficient Distribution, Angle of Attack = 2° BFAE Sep-14 Slide 14 2- Aerodynamics / Flight principles II Lift, drag and moments Lift coefficient from CP: for small angles of attack (<5º) 1 c cl ≈ ∫ (C p,l − C p,u ) dx c 0 pressure coefficient on upper surface pressure coefficient on lower surface NACA 0016 Pressure Coefficient Distribution, Angle of Attack = 2° BFAE Sep-14 Slide 15 2- Aerodynamics / Flight principles II Lift, drag and moments Compressibility corrections: modify (correct) the low-speed pressure coef, to take into account the effects of compressibility • Cp is essentially constant with velocity at low speeds: low speed (incompressible) value of Cp is Cp,0 . • for 0.3<M∞<0.7 Prandtl-Glauert rule Cp = Cp, 0 1 − M ∞2 cl = BFAE Sep-14 Slide 16 2- Aerodynamics / Flight principles II cl , 0 1 − M 2∞ Influence of Mach number Critical Mach number and critical pressure coefficient • critical Mach number: free-stream Mach number at which sonic flow is first obtained somewhere on the airfoil surface • Mcr is an important quantity because at some free-stream Mach number above Mcr the airfoil will experience a dramatic increase in drag • Mcr is higher for thin airfoils than for thick airfoil (flow expansion is stronger for thick airfoil, velocity increases to larger values, sonic conditions obtained sooner) → airfoils on modern, high-speed airplanes are relatively thin BFAE Sep-14 Slide 17 2- Aerodynamics / Flight principles II Influence of Mach number Drag divergence Mach number BFAE Sep-14 Slide 18 2- Aerodynamics / Flight principles II Influence of Mach number Shock waves: characterized by an abrupt, nearly discontinuous, change in the characteristics of the medium. Across a shock there is always an extremely rapid rise in pressure, temperature and density of the flow BFAE Sep-14 Slide 19 2- Aerodynamics / Flight principles II Influence of Mach number Mach wave 1. beeper moving at less than speed of sound 2. origin of Mach waves and shock waves: beeper moving faster than speed of sound BFAE Sep-14 Slide 21 2- Aerodynamics / Flight principles II Mach wave https://engineering.purdue.edu/~wassgren/applet/ BFAE Sep-14 Slide 22 2- Aerodynamics / Flight principles II Influence of Mach number Prandtl-Meyer expansion fan: centered expansion process, which turns a supersonic flow around a convex corner. • fan consists of infinite number of expansion waves, diverging from a sharp corner. • each wave in the expansion fan turns the flow gradually (in small steps). • across the expansion fan, the flow accelerates (velocity increases) and the Mach number increases, while the static pressure, temperature and density decrease. • isentropic process BFAE Sep-14 Slide 23 2- Aerodynamics / Flight principles II Airfoil drag Total drag of an airfoil D=Df+Dp+Dw D: total drag on airfoil Df: skin friction drag Dp: pressure drag due to flow separation profile drag Dw: wave drag (only at transonic and supersonic speeds) see variation of cd with M for incompressible to supersonic speeds BFAE Sep-14 Slide 24 2- Aerodynamics / Flight principles II Finite wing drag Finite wings: wing tip vortices BFAE Sep-14 Slide 25 2- Aerodynamics / Flight principles II Finite wing drag Finite wings: wing tip vortices BFAE Sep-14 Slide 26 2- Aerodynamics / Flight principles II Finite wing drag Finite wings: wing tip vortices • angle of attack of the airfoil sections of the wing is effectively reduced in comparison to the angle of attack of the wing referenced to V∞ (slope of the lift curve for a finite wing is less than for an infinite wing) • increase in the drag: induced drag due to alteration of the flow field about the wing by wing tip vortices → CL<cl → CD>cd BFAE Sep-14 Slide 27 2- Aerodynamics / Flight principles II Finite wing drag Calculation of total drag • profile drag (form drag) is drag caused by moving a solid object through a fluid (skin friction and pressure drag due to separation are components of profile drag) • lift-induced drag, induced drag: drag force which occurs whenever a lifting body or a wing of finite span generates lift • total drag coef for a finite wing at subsonic speed C2L C D = cd + πeAR e: span efficiency factor: for elliptical platform=1, for typical subsonic aircraft 0.85<e<0.95 AR: aspect ratio=b2/S BFAE Sep-14 Slide 28 2- Aerodynamics / Flight principles II Finite wing drag Polar of an airfoil Cd = f(Cl) Can be approximated as a parabola: Cd = cd0 + j Cl + k Cl2 Symmetric airfoil symmetric polar BFAE Sep-14 Slide 29 2- Aerodynamics / Flight principles II Finite wing drag Calculation of total drag BFAE Sep-14 Slide 30 2- Aerodynamics / Flight principles II Finite wing drag Winglets Detailed view of an Airbus A319 'wingtip fence' Interior of WestJet Boeing 737-700 winglet BFAE Sep-14 Slide 31 2- Aerodynamics / Flight principles II Finite wing drag Raked wingtip higher degree of sweep than the rest of the wing, increasing the effective aspect ratio of the wing Boeing 767 raked wingtips BFAE Sep-14 Slide 32 2- Aerodynamics / Flight principles II Finite wing drag Raked + blended wingtip 747-8, 787, A350: new kind of wings, no separate winglet, but raked, and blended wingtips integrated, without sharp angle between wing and winglet BFAE Sep-14 Slide 33 2- Aerodynamics / Flight principles II Swept wings • by sweeping the wings of subsonic aircraft, drag divergence is delayed to higher Mach numbers • sweep angle Ω Mcr for airfoil<actual Mcr for swept wing< Mcr for airfoil/cos(Ω) • for subsonic flight, increasing the wing sweep reduces the lift • for supersonic flight advantage is to obtain a decrease in the wave drag and if the wing is swept inside the Mach cone, a considerable decrease can be obtained BFAE Sep-14 Slide 34 2- Aerodynamics / Flight principles II Swept wings F-14 Tomcat A380 BFAE Sep-14 Slide 35 2- Aerodynamics / Flight principles II Swept wings Grumman X-29 BFAE Sep-14 Slide 36 2- Aerodynamics / Flight principles II Flaps • airplane encounters its lowest flight velocities at takeoff or landing • stalling speed: slowest speed at which an airplane can fly in straight and level flight Vstall = 2W ρ∞SCL, max • to decrease Vstall, CL, max must be increased: use artificial high-lift devices: flap at the end of the trailing edge of the wing BFAE Sep-14 Slide 37 2- Aerodynamics / Flight principles II Flaps When the flap is deflected downward, lift is increased for 2 reasons • camber of the airfoil is increased (higher lift coef) • virtual chord line → virtual increase in angle of attack BFAE Sep-14 Slide 38 2- Aerodynamics / Flight principles II Flaps • slot: fixed (non-moving) opening behind the wing’s leading edge • at low angles of attack the airflow just passes over and under the slot. • at higher angles of attack air starts to move through the slot from the higher pressure air below the wing to the lower pressure air on top of the wing. The mixture of the air coming over the leading edge and through the slot has greater momentum and thus sticks to the upper surface of the wing to a higher angle of attack than if the slot were not there. BFAE Sep-14 Slide 39 2- Aerodynamics / Flight principles II Flaps BFAE Sep-14 Slide 40 a. original airfoil b. plain flap c. split flap d. flap zap e. single slotted flap f. double slotted flap 2- Aerodynamics / Flight principles II Flaps g. flap Fowler single slotted flap h. flap Fowler double slotted flap i. flap Krueger j. slot k. leading-edge slat (retractable slot) l. leading-edge slat (opened) m. single-slotted flap w/ leading-edge slat n. double-slotted flap w/ leading-edge slat BFAE Sep-14 Slide 41 2- Aerodynamics / Flight principles II Flaps • increase in CL,max due to flaps can be very high • if flap designed not only to rotate downward but also to translate rearward to increase the effective wing area, CL,max can be increased by approximately a factor of 2 • if additional high-lift devices are used (slats, slots) can be increased by a factor 3 or more. BFAE Sep-14 Slide 42 2- Aerodynamics / Flight principles II References • Introduction to Flight, J. Anderson, Jr., Mc Graw-Hill International Edition, Fifth Edition, 2005. • Introducción a la Ingeniería Aeroespacial, S. Franchini, O López García, 2ª Edición, Garceta, 2012 BFAE Sep-14 Slide 43 2- Aerodynamics / Flight principles II Exercise Some aerodynamic measurements are run in a wind tunnel on a wing with symmetric airfoil, with a chord c = 170cm, and a wing area S = 2.55m2. During the measurements, the Mach number in the test section is M = 0.2, and the environment conditions correspond to standard atmosphere at z = 600m. When the angle of attack α = 0º, L = 0N and D = 33.6N. When the angle of attack α = 8º, L = 5380N and D = 60.6N. The lineal part of the lift curve is within the range ±12º. 1. Given that at 600m, μ = 1.7 10-5N s/m2, calculate the Reynolds number. 2. Calculate the equation of the lift coefficient curve in its lineal part. 3. Calculate the equation of the polar of the airfoil. BFAE Sep-14 Slide 44 2- Aerodynamics / Flight principles II
