E10+ME+Lecture+3A+Airfoils

E10+ME+Lecture+3A+Airfoils - Mechanical Engineering Module...

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Unformatted text preview: Mechanical Engineering Module Spring 2010 Lecture 3 Airfoils Engineering Engineering 10: Engineering Design & Analysis WebWeb-based airfoil calculations Lift Lift and drag Basics Basics of airfoils Characteristics Characteristics of turbine blades Today’s Today’s Lecture Discuss Discuss in small groups the basic characteristics of (most) wind turbine blades. What What are the relevant design parameters that you will will need to complete your blade specification? Characteristics Characteristics of Wind Turbine Blades Basic Characteristics Length Area of blade Wind speed, etc. Taper (root-to-tip) (root-toNumber Twist Weight Basic Characteristics Mass distribution Material Airfoil shape Slant (different than twist?) Max rotation speed Surface finish Wind Wind Turbine Blades Thickness (specified as % of chord length and location [12% at 0.3c]) Chord Line (straight line between leading and trailing edges) Camber (specified as % of chord length and location [5% at 0.4c]) Mean Camber Line (curve midway between upper and lower surfaces) (NACA 5412) Airfoil Airfoil Geometry wind and chord line) Angle of Attack (measured between Wind Vector wind direction) Lift (force perpendicular to the direction) Drag (force parallel to the wind Lift Lift and Drag NonNon-symmetric airfoil (camber = 5% of chord): NACA 5414 Symmetric Symmetric airfoil (camber = 0, thickness = 14% of chord): NACA 0014 At the “stagnation point” Where Where will the pressure be highest? 12 ρu + p = C 2 http://www.diam.unige.it/~irro/lecture_e.html Streamlines around a Joukowski Airfoil Consequences Consequences of Bernoulli’s Eqn: In this image, the thickness of the grey lines represents pressure – high on the lower surface, low along the top surface (http://www.bugman123.com/FluidMotion/Joukowski-large.jpg) 12 ρu + p = C 2 Far-Field Wind α Streamlines around a Joukowski Airfoil Consequences Consequences of Bernoulli’s Eqn: NACA NACA 5412 Attack Angle =8º 1 2 FL = C L ρAu 2 1 2 FD = C D ρAu 2 Lift Lift and drag are given for a particular body (a wing with total area A, for example) in terms of coefficients that multiply this force 1 2 F = ρAu 2 Recall Recall from Bernoulli’s equation that the force on a surface of area A that stops the wind is Lift Lift and Drag 1 2 FD = C D ρAu 2 Increase Increase coefficients (design & environment) Increase Increase wind speed (environment) Increase Increase area (design) Increase Increase density (hmmm … how, exactly?) How How can we increase the lift (usually good) and/or drag (usually bad) forces? 1 2 FL = C L ρAu 2 Lift Lift and Drag 1 2 FD = C D ρAu 2 In In this case we would have A=cL, where L is the length of the blade. The The equations for lift and drag given so far are useful if the blade has the same cross section (airfoil with the same chord, camber, attack angle, etc.) along its entire length. 1 2 FL = C L ρAu 2 Lift Lift and Drag c dx 1 2 dFL = Cl ρ (cdx)u 2 1 2 dFD = Cd ρ (cdx)u 2 Blades Blades rarely have uniform cross section, but vary along the length (often getting “smaller” near the tip) It It is common, then, to introduce the “section parameters” parameters” Cl and Cd Lift Lift and Drag Total Total lift force: dx L 0 FL = ∫ dFL = ∫ c ( 1 2 2 ) Cl ρ cu dx Lift Lift and Drag ρuc Re = µ Lift Lift and drag coefficients are generally determined at different velocities and angles of attack for a particular airfoil. The The velocity is usually given in terms of a dimensionless parameter known as “Reynolds Number” (Re): Lift Lift and Drag Reynolds Reynolds number for an object in a flow gives the ratio between between the “inertial” force on the object to the “friction” “friction” force “Low” “Low” Reynolds number generally corresponds to “smooth” or laminar flow “High” “High” Reynolds number generally corresponds to turbulent flow ρuc Re = µ Lift Lift and Drag http://www.mhhttp://www.mh-aerotools.de/airfoils/javafoil.htm Javafoil: Javafoil: A way to compute lift and way drag coefficients ...
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This note was uploaded on 01/24/2012 for the course ENGINEERIN 10 taught by Professor Sethian during the Spring '10 term at Berkeley.

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