### Wind Engineering Module 4.1 Blade Element Theory

```Wind Engineering
Module 4.1
Lakshmi N Sankar
[email protected]
Recap
• In Module 1, we looked at an overview of the
course objectives, syllabus, and deliverables. We
also reviewed history of wind technology,
nomenclature, and case studies.
• In Module 2, we looked at the wind turbine as an
actuator disk, and established the theoretical
maximum for power that may be captured.
• In module 3, we reviewed airfoil aerodynamics,
and discussed how to compute lift and drag
coefficients. We also reviewed airfoil design
issues.
OVERVIEW
• In this module 4.1, we will review the basics of
• In module 4.2, we will talk about public
domain solvers, and show how to use these.
• When module 4.2 is done, you are ready to
validate one of these solvers using available
wind turbine data.
– This will be the second deliverable for this course.
• We look at a reference blade from a multi-blade system (typically 2 or 3).
to be known or chosen.
• On each strip/element
– We find the local section angle of attack.
– We look up the corresponding lift and drag coefficients from a table of airfoil
characteristics.
– We correct these for tip losses, root losses, stall delay, swirl losses as needed.
– We find lift and drag forces.
– We find the propulsive force (in the plane of rotation)
– We find the torque contribution of that strip.
• Sum up the toque contribution over all strips to find torque for one blade.
• Multiply by the number of blades, B.
• Vary the wind speed and compute the entire performance map.
Calculation of Angle of Attack
• The figure on the right is from
AeroDyne Theory manual, found
in the resource section.
– b is pitch angle (known from
– U∞ is wind speed
– a is the axial induction factor
(axial induced velocity v divided
by wind speed), discussed later.
– a’ is a tangential induction
factor (tangential induced
velocity divided by wr),
discussed later.
– lr is the local speed ratio Wr/
U∞
Lift and Drag are functions of Angle of
Attack, a
• Once a is known, we can
look up lift and drag
coefficients: Cl and Cd .
• Unfortunately, these
quantities influence the axial
induction factor a and the
tangential induction factor a’.
• An iteration is needed as
discussed later.
• If Cl and Cd are known, we
can find sectional forces and
torques as shown on the
right side.
Thrust generated by the Strip of
width dr and chord c, for all