Unformatted text preview: Mechanical Engineering Module
Spring 2010
Lecture 3
Airfoils Engineering
Engineering 10:
Engineering Design & Analysis WebWebbased 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 (roottotip)
(roottoNumber
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 NonNonsymmetric 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/Joukowskilarge.jpg) 12
ρu + p = C
2 FarField 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.mhaerotools.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.
 Spring '10
 SETHIAN
 Mechanical Engineering

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