Page 187 - Wind Energy Handbook

LAMINAR AND TURBULENT BOUNDARY LAYERS 161

begins to reverse under the action of the adverse pressure. At this point, where the
pressure is still low, the boundary layer separates from the body surface forming a
wake of stagnant, low-pressure fluid (Figure A3.7), the resulting pressure distribu-
tion is thereby dramatically altered as shown in Figure A3.5. The high pressure
acting at and around the forward stagnation point is no longer balanced by the high
pressure at the rear and so a drag-wise pressure force is exerted.

A3.5 Laminar and Turbulent Boundary Layers

A boundary layer grows in thickness from the forward stagnation point, or leading
edge. Initially, the flow in the layer is ordered and smooth (laminar) but, at a critical
distance l from the stagnation point, characterized by Re crit ¼ rUl=ì, the flow
begins to become turbulent (Figure A3.8). This turbulence causes mixing of the
boundary layer with the faster moving fluid outside resulting in re-energization
and delaying of the point of separation. The result is to reduce the pressure drag,
because the low-pressure stagnant rear area is reduced, to increase the viscous
(frictional) drag, because the velocity gradient at the surface is increased, and
increase the boundary-layer thickness.
The coefficient of drag, therefore, varies with Re in a complex fashion (Figure
A3.9). For small bodies at low speeds the critical Re is never reached and so
separation takes place early. For large bodies, or high speeds, turbulence develops
quickly and separation is delayed.
Turbulence can be artificially triggered by roughening the body surface or simply
by using a ‘trip wire’. General flow turbulence tends to produce turbulent boundary
layers at Reynolds numbers ostensibly below the critical value and this certainly
seems to happen in the case of wind-turbine blades. A sharp edge on a body will
always cause separation. For a flat plate broad side on to the flow (Figure A3.10) the
boundary layer separates at the sharp edges and C d is almost independent of Re,
but is dependent upon the plate’s aspect ratio.
So-called streamlined bodies such as an aerfoil taper gently in the aft region so
that the adverse pressure gradient is small and separation is delayed until very
close to the trailing edge. This produces a very much narrower wake and a very
low drag because it is largely caused by skin friction rather than pressure (Figure
A3.11).

l

Figure A3.8 Laminar and Turbulent Boundary Layers