Aerodynamics - Part 2 PDF

Aerodynamics – Part 2 1 Airfoil Characteristics Inviscid flow airfoil theory 1. This chapter deals primarily with airfoil theory for an inviscid, incompressible flow. 2. This theory can predict the followings. - Lift slope ( ) - Zero-lift angle of attack ( ) 3. T...

Aerodynamics – Part 2 1 Airfoil Characteristics Inviscid flow airfoil theory 1. This chapter deals primarily with airfoil theory for an inviscid, incompressible flow. 2. This theory can predict the followings. - Lift slope ( ) - Zero-lift angle of attack ( ) 3. This theory is incapable of predicting the followings - Maximum lift coefficient ( ) - Airfoil drag Inviscid flow airfoil theory Viscous flow airfoil theory NACA 2412 airfoil Y-coordinate for Y-coordinate for NACA 2412 airfoil The lift slope is not is dependent upon Re influenced by Re Experimental data are given for various Re Experimental Results is governed by viscous effect is dependent upon Re NACA 2412 airfoil Experimental data are given for various Re The is insensitive to Re except at large Y-coordinate for about C/4 point NACA 2412 airfoil The Resultant Aerodynamic Force The integration of pressure distribution and shear stress distribution over the airfoil. R The resultant aerodynamic force The integration of p and τ c Chord The linear distance from LE to TE Freestream velocity The flow velocity far ahead of the body Normal Force & Axial Force N Normal Force The component of R perpendicular to chord line A Axial Force The component of R parallel to chord line Angle of attack The angle between C & Angle of attack α The angle between L & N The angle between D & A Lift & Drag L Lift The component of R perpendicular to freestream ( ) D Drag The component of R parallel to freestream ( ) Lift & Drag Lift Drag Lift & Drag Lift Drag Lift & Drag Lift Drag  Lift & Drag Determine the magnitude of Lift (L), Drag (D), of an airfoil that is at 10o AOA and has a Normal force of 100 N, Axial force of 50 N?  Lift & Drag Determine the magnitude of Lift (L), Drag (D), of an airfoil that is at 10o AOA and has a Normal force of 100 N, Axial force of 50 N? Reynolds number (Re) Chord (c) 𝜌∞ 𝑉∞ 𝑐 Wing area (S) 𝑅𝑒 = Diameter (d) 𝜇∞ Length (l) 𝜌∞ 𝑉∞ 𝑐 𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑅𝑒 = = 𝜇∞ 𝑉𝑖𝑠𝑐𝑜𝑢𝑠 𝑓𝑜𝑟𝑐𝑒 Chord (c) Dimensional Analysis Dimensional Analysis The actual magnitude of Lift (L), Drag (D), and Moment (M) depends on following parameters. Parameter Symbol Physical parameter Free-stream velocity Free-stream air density Altitude Size of the aerodynamic surface , , , Wing area, chord, diameter, length Angle of attack Shape of the airfoil Airfoil type Viscosity coefficient Reynolds number (Re) Mach number Compressibility of the airflow For a given shape airfoil at a given angle of attack (α). Dimensional Analysis 2. Dimension of physical variables (low speed aerodynamics) Unit Variable Dimension SI British Length L l Mass M m Kg Slug Time T T s s Area L2 l2 ft2 Velocity L/T lT-1 m/s ft/s Density M/L3 ml-3 kg/m3 Slug/ft3 Force M(L/T2) mlT-2 N Viscosity M/(LT) ml-1T-1 Kg/(m·s) Slug/(ft·s) 1 N=1 kg × 1m/s2 1 lb= 1 slug × 1 ft/s2 Dimensional Analysis Lift VIMP Drag Moment Example 1 A model wing of constant chord length is placed in a low-speed subsonic wind tunnel, spanning the test section. The wing has an NACA 2412 airfoil and a chord length of 1.3 m. The flow in the test section is at a velocity of 50 m/s at standard sea-level conditions. If the wing is at a 4° angle of attack, calculate (a) , , and (b)The lift, drag, and moments about the quarter chord (c/4), per unit span Given condition Chord length 1.3 m Velocity 50 m/s Angle of attack 4° Altitude Standard sea level Solution 1 NACA 2412 airfoil data (lift curve) 1.2250 × 50 × 1.3 = 1.7894 × 10−5 Given Solution 1 NACA 2412 airfoil data (drag polar) Solution 1 (b) Per unit span Unit span 1 m c=1.3 m Wing area (S) Example 2 The same wing in the same flow as in Example 5.1 is pitched to an angle of attack such that the lift per unit span (L’) is 700 N (157 lb). (a) What is the angle of attack? (b) To what angle of attack must the wing be pitched to obtain zero lift? Per unit span Solution 2 (a) From Example 5.1 Therefore 1m c=1.3m Wing area Solution 2 Lift curve (b) From the lift curve Lift curve Example 5.3 The shape of the NASA LS(1)-0417 airfoil is shown in Figure below; this airfoil is the subject of Example 4.29. In that example, a constant-chord wing model with tips are flush with the vertical side walls of the tunnel. Based on our discussion in the present section, the measured data are therefore for an infinite wing. At a zero angle of attack, the drag on the wing model is given in Example 4.48 to be 34.7 N when the flow in the test section is at a velocity of 97 m/s at standard sea-level conditions. The chord length is 0.6 m and the wingspan across the test section is 1 m. Hence the measured drag of 34.7 N is the drag per unit span as discussed in the present section. Calculate the drag coefficient. Example 3 Wing tip Wing tip Example 3 Wall Infinite Wing Wall Flush with the vertical side walls of the tunnel Example 3 Solution 3 1 1 𝑞∞ = 𝜌∞ 𝑉∞ = 1.23 972 = 5786.5 𝑁Τ𝑚2 2 2 2 1 c=0.6 Wing area Wash in and Wash out 8.2 - Aerodyanamics 34 Icing Effects 8.2 - Aerodyanamics 35 Ice Protection System 8.2 - Aerodyanamics 36 787 Advanced Ice Protection System 8.2 - Aerodyanamics 37 Mixed Ice, Snow, frost Contaminations 8.2 - Aerodyanamics 38 Aircraft Speeds 8.2 - Aerodyanamics 39 Aircraft Speeds 8.2 - Aerodyanamics 40 Indicated Air Speed 8.2 - Aerodyanamics 41 Indicated Air Speed 8.2 - Aerodyanamics 42 True Air Speed 8.2 - Aerodyanamics 43 Ground Speed 8.2 - Aerodyanamics 44 Airspeed VS Indicated Airspeed 8.2 - Aerodyanamics 45 Ground Speed VS Air Speed 8.2 - Aerodyanamics 46 8.2 - Aerodyanamics 47