Spanwise flow and swept wings

[John235]

I have read that when an aircraft wing flies with positive angle of attack to produce lift, it results in downwash and some spanwise air flow near the tips of the wing. My understanding is that for a rectangular wing platform such as case 1 in the attachment, the downwash will result in an outward spanwise flow on the bottom side of the wing, and inward spanwise flow on the top side.

My question is how the spanwise flow is affected by sweepback. For moderate sweepback of around 20 degrees used on a model aircraft, how much will the spanwise flow be affected? Is it likely that outward spanwise flow will occur on both top and bottom surfaces of the wing?

Although the angles on my diagram are probably exaggerated, please let me know your opinion of whether the spanwise flow directions shown on my diagram are correct or not.

[John235]

Please refer to the attachment that is taken from Andy Lennon's book 'R/C model airplane design'. Can anyone give an explanation of why the examples 'B' and 'F' in the diagram show completely different stalling patterns for swept and unswept wings?

[Majortomski]

John, you first have to make the distinction between the localized distortion in the flow due to the effects of the wing tip, and true spanwise flow caused by the airflow turning away from the fuselage and distorting the airflow over the entire wing.

Your first drawing is correct but lacking the true spanwise flow component.

In Lennons drawings B and F differ due to wing loading and spanwise flow. The tip in B stalls last due to the weight distribution over the span of the wing. The wingtip is doing less work to begin with. Untwisted swept wings stall tip first because of the distorted spanwise flow.

At least that's what I remember from 30 years ago.

[ciurpita]

i don't have a specific answer. but part of the explanation for stall patterns lie with the effective Cl. for example, in case B, the rectangular wing, the lift distribution, and hence the Cl distribution, is roughly elliptical meaning that the tip is producing less lift than the root even though the wing chords are the same. since the Cl near the tip is less than near the root, it stalls after the root. part of the reason for the reduced lift/Cl near the tip is the vortex around the tip.

in the tapered wing cases, the lift/cl distributions are still roughly elliptical, but the chord decreases quickly resulting in the Cl distribution increasing toward tip (while dropping to zero at the tip), even though the lift is decreasing. since the Cl is higher near the tip, the stall starts nearer the tip.

in the swept wing case, the tip vortex is less. this means the lift/Cl distributions doesn't decrease as quickly toward the tip as it does for the unswept case. hence, the wing would stall more toward the tip than it does for the unswept case (the diagram may exaggerate this).

[nmasters]

http://www.rcgroups.com/forums/showthread.php?t=806512

[John235]

Thanks for well thought out replies. I am still reading through the NASA Technical report in the thread that is linked above. It makes sense that the stalling patterns are due to the variations in lift distribution for each planform, so that seems to be a large part of the answer to the second question. I think the lift distribution is very interesting because it has a major effect on the wing's efficiency.

The other part of the question in my mind is the relationship between the spanwise flow and the lift distribution of the wing. I have read about the "infinite swept wing theory" where the spanwise flow is constant along the span for a wing, and the lift co-efficient is the same as the unswept case. Does anyone know if there is some relationship between the spanwise flow and the lift distribution of a wing? Is the lift distribution of the wing somehow related to the spanwise position-derivative of the spanwise flow component?

[nmasters]

It's about induced upwash. Here are some links:
http://www.google.com/search?client=googlet&q=induced%20upwash%20al%20bowers
http://www.rcgroups.com/forums/showthread.php?p=772144&highlight=upwash#post772144
http://www.rc-soar.com/tech/winganalysis.htm
http://www.rcgroups.com/forums/showthread.php?p=8975862#post8975862
http://www.rcgroups.com/forums/showthread.php?p=8260889&highlight=Henk+Tennekes#post8260889

Sorry it's mostly swept flying wing stuff, but it's a major issue for them so that's where the info is.

--Norm

[CaterhamTone]

That second diagram originated in "Aerodynamics for Naval Aviators", arguably the 'bible' of Principles of Flight.

Stalling is caused by airflow separation and the amount of separation depends upon the relationship between the "Adverse Pressure Gradient" (Pressure increasing in the direction of flow) and the Kinetic Energy in the boundary layer. The increase in adverse pressure gradient (usually caused by increasing the angle of attack because that reduces the pressure on the top surface of the wing) for a given boundary layer kinetic energy increases separation.

A rectangular planform has strong tip vortices anchored at the tips which decreases the effective angle of attack at the tips. As the angle of attack of the whole wing is increased the root reaches the stall angle first. A rectangular planform will give 'ideal' stall characteristics - strong nose down pitching moment, moderate wing drop, and will retain aileron effectiveness to a higher angle of attack.

A tapered planform has its tip vortices anchored slightly in from the tips so the angle of attack is not reduced so much at the tip and the critical angle of attack tends to occur more towards the tips - more violent wing drop, less strong nose down pitching moment and loss of aileron effectiveness.

A swept back wing (also usually tapered and therefore suffering from the increased tendency for tip stall as above) has another characteristic that further increases the tendency to stall at the tip first. The points of minimum pressure on the wing are angled backwards :eek: and the tendency of the very lowest layers of the boundary layer is to follow these isobars towards the tips instead of towards the trailing edge. This causes increased skin friction because of the longer path and therefore a greater loss of boundary layer Kinetic Energy and hence greater tendency for boundary layer separation - tip stall at a lower angle of attack. But because the tips are aft of the CG, a tendency to pitch up at the stall.

Swept wings are fitted to full size aircraft to enable them to fly faster before shock waves form on the wing (Raise Mcrit). Your average holiday jet has small shock waves on the wing in the cruise. As long as the shock waves don't get too big they are no big deal. This is obviously not a consideration for our models.

The elliptical planform is the aerodynamic ideal (R.J. Mitchell knew what he was doing) because is generates an elliptical pressure distribution when viewed from the rear. This minimises the generation of tip vortices and gives a nice evenly distributed airflow separation from root to tip. Unfortunately an elliptical planform wing is a pain to manufacture and fit within it all the necessary bits and pieces, so is not widely used. It is still the “Constant” against which the efficiency of any wing planform is measured – even today.

Remember – stalling has nothing to do with speed. You can stall an aerofoil at any speed as soon as the stall angle of attack is reached. Stalling is caused by airflow separation and the amount of separation depends upon the relationship between the adverse pressure gradient and the boundary layer Kinetic Energy. Change the speed and both those characteristics change more or less equally, but their relationship stays the same.
Cheers,
Tony
Principles of Flight instructor (JAA-ATPL)