Page 182 - Wind Energy Handbook

156 AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

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Edward Arnold, London, UK.
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Reinhold Co., New York, USA.
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Appendix: Lift and Drag of Aerofoils

The forces acting on a body immersed in a fluid moving fluid can be resolved into
stream-wise (drag) and normal (lift) components. Neglecting buoyancy, the fluid
mechanics which give rise to lift and drag are associated with the boundary layer of
slow-moving fluid close to the body’s surface. The fluid force on the surface of the
body can be either parallel to the surface (viscous or skin friction force) or normal to
the surface (pressure force).
For a thorough understanding of the phenomena of lift and drag an aerody-
namics text should be consulted but for the purposes of wind-turbine aerodynamics
the basic results are given below.

A3.1 Definition of Drag

The drag on a body immersed in an oncoming flow is defined as the force on the
body in a direction parallel to the flow direction. In a very slow-moving fluid the
drag on a body may be directly attributable to the viscous, frictional shear stresses
set up in the fluid due to the fact that, at the body wall, there is no relative motion.
This type of flow is known as Stokes’ flow after Sir George Stokes.
Two centuries before Stokes, Isaac Newton showed that that the shear stress t at a
boundary wall, or between two layers of fluid moving relative to one another, is
proportional to the transverse velocity gradient at the boundary, or between the
two layers:

du
ô ¼ ì (A3:1)
dy

where the constant of proportionality is ì the fluid viscosity.
Using Newton’s theory, Stokes determined the drag force on a sphere in creeping
flow (Figure A3.1).
Drag ¼ 3ðìUd (A3:2)

where d is the sphere diameter and U is the general flow velocity.