Weekend Flyer
Lastly, I am intrigued by the laminar flow argument. It makes sense that lifting the vortex away from the wing tip to the tip of the winglet would keep the vortex flow away from the wing upper surface near the tip, which would, as you say, permit laminar flow to persist over a slightly larger area of the wing. Are you saying that the entire drag reduction from the winglet is due to this effect?
Like you I was intrigued by the laminar flow argument so I decided to put some numbers into the equations, using the B737 geometry as an example. Basically, to get the cruise gains Boeing quote one would have to have completely laminar flow over a large chunk of the wing - upper and lower surfaces, from LE to TE extending from the notional 'wingtip' (at the supposed wing/winglet boundary inboard to about 80% span.
I have great difficulty envisaging any flow mechanism whereby a highly turbulent vortex flow springing from the trailing edge of the winglet tip could encourage laminar flow at the LE, let alone the undersurface LE. At 737 cruise conditions the Reynolds Number is about one million per foot, so one would normally expect transition from laminar to turbulent flow about three or four inches back from the LE. Beyond that it is very doubtful that laminar flow would persist aft of any small discontinuity such as the retracted slat/wing interface and I have never, ever, come across a turbulent flow reverting to laminar so that any laminarisation effect has to start from the LE . All of which leads me to believe that this laminar flow argument is a nonstarter.
I reckoned that Boeing ought to know how their wing works so I went to their website where I found : (my bolding)
Winglets affect the part of drag called induced drag. As air is deflected by the lift of the wing, the total lift vector tilts back. The aft component of this lift vector is the induced drag (
fig. 1).
The magnitude of the induced drag is determined by the spanwise distribution of vortices shed downstream of the wing trailing edge (TE), which is related in turn to the spanwise lift distribution. Induced drag can be reduced by increasing the horizontal span or the vertical height of the lifting system (i.e., increasing the length of the TE that sheds the vortices). The winglets increase the spread of the vortices along the TE, creating more lift at the wingtips (
figs. 2 and
3). The result is a reduction in induced drag (
fig. 4).
The maximum benefit of the induced drag reduction depends on the spanwise lift distribution on the wing. Theoretically, for a planar wing, induced drag is optimized with an elliptical lift distribution that minimizes the change in vorticity along the span. For the same amount of structural material, nonplanar wingtip devices can achieve a similar induced drag benefit as a planar span increase; however, new Boeing airplane designs focus on minimizing induced drag with wingspan influenced by additional design benefits.
Notice that there is no mention of reduced vortex strength, which is as it should be, because winglets do not change the total vortex strength as FPOBN says.
[Vortex strength is another name for what aerodynamicists call circulation, which in turn is related to lift by the expression:
Lift/unit span equals circulation times airspeed.
If you integrate lift/unit span from winglet tip to winglet tip you will get total lift (equals weight) and total circulation (total vortex strength). With a little manipulation this gives you:
Vortex strength equals aircraft weight divided by airspeed
Span doesn't appear in this expression so adding winglets doesn't change the total vortex strength behind the aircraft]
So the commonly held view that winglets reduce drag by reducing the vortex strength is wrong - they work by changing the vortex distribution to give the same vortex strength.
I now think of it in terms of the old-fashioned expression for induced drag coefficient - Cdi = k*CL^2/(Pi*A). Keeping the vortex strength constant is roughly similar to holding constant CL I reckon, which leaves the winglets working on k/A. They certainly increase span and hence aspect ratio and with careful design one can optimise k (or in the USA optimise Oswald's efficiency factor e)