What is the causality of the higher velocity airflow over the top of an airfoil

Question

In my training as a Certified Flight Instructor, I am required to teach Lift Theory. While simple explanations have sufficed in the past, as I progress in my training and understanding, I want to be able to understand lift in greater detail. During my last lesson, I stumped my Instructor. I asked about the cause of the increased velocity above an airfoil and he could not explain it so I am trying to research it and come to some clear understanding.

I have a hunch described below. Please let me know in semi-layman terms if I am on the right track.

Known:

• As Velocity increases, Pressure decreases and vice versa. (Bernoulli)
• The air moving across the top of an airfoil moves faster than the air below the airfoil. Some have said that this is because the air above has a farther distance to travel but this has been proven untrue.
• Higher pressures below the airfoil and lower pressure above the airfoil create a portion of the lifting force of the airfoil.
• Additional lift forces are created by air being directed down by angle of incidence and the shape of the wing (Newton). This occurs from the air running into the bottom of the wing and being forced downward. Lift is also occurring because the air above is moving at a higher velocity than the air below, and when they meet at the trailing edge, the faster air pushes the slower air downward. (Vortices)
• From the Cambridge University video (see References) showing time-lapse video, we see that the air above the airfoil moves faster such that it reaches the trailing edge sooner than air below the airfoil.

Unknown:

• This proves that the air over the airfoil moves faster but what is the cause for that air to move faster?

My Hypothesis:

• Because of the angle of incidence and angle of attack to the relative wind, a higher pressure is created upon impact at the separation. This upper airfoil high pressure is considered ‘high’ relative only to the air pressure at other areas of the upper airfoil such as the center of pressure or the trailing edge of the wing. (It is not meant to be considered ‘higher’ pressure than the air under the airfoil.

• Also due to angle of incidence and angle of attack, an even lower pressure is created at the trailing edge of the wing.

• Attached is a screen shot of the Cambridge video, with my hypothetical pressures jotted in.

• Because high pressure air always seeks lower pressure air, the air above the airfoil should get an extra push and accelerate to a velocity faster than that of the air under the airfoil.

• I found (see attached) a diagram of Pressure Coefficient distribution across airfoil geometry. This diagram is from an unrelated paper treating a separate subject of shapes of trailing edges. It however is the only graph I could find detailing what pressures occurred where on the airfoil.

References: 1 Cambridge University video https://www.youtube.com/watch?v=UqBmdZ-BNig

2 Morphing Trailing Edges with Shape Memory Alloy Rods. November 2002 URL: https://www.researchgate.net/publication/228531008_Morphing_Trailing_Edges_with_Shape_Memory_Alloy_Rods 1st Silvestro Barbarino 15.46 · Sikorsky Aircraft 2nd Wulf G Dettmer 3rd Michael Ian Friswell 45.16 · Swansea University

Answer 1

Bernoulli and Newton are merely two sides of the same coin. The speed distribution around an airfoil bends the flow such that it leaves the wing in a slightly different direction.

For me to understand aerodynamics, it helped to look at the molecular level. Every air molecule is in a dynamic equilibrium between inertial, pressure and viscous effects.

• Inertial means that the mass of the particle wants to travel on as before and needs force to be convinced otherwise.
• Pressure means that air particles oscillate all the time and bounce into other air particles. The more bouncing, the more force they experience. Pressure and speed move against each other. Pressure corresponds to the potential energy while speed squared corresponds to the kinetic energy of the local flow. In the absence of inertial and viscous effects the sum of both is constant.
• Viscosity means that air molecules, because of this oscillation, tend to assume the speed and direction of their neighbors.

Now to the airflow: When a wing approaches at subsonic speed, the low pressure area over its upper surface will suck in air ahead of it. See it this way: Above and downstream of a packet of air we have less bouncing of molecules (= less pressure), and now the undiminished bouncing of the air below and upstream of that packet will push its air molecules upwards and towards that wing. The packet of air will rise and accelerate towards the wing and be sucked into that low pressure area. Once there, it will "see" that the wing below it curves away from its path of travel, and if that path would remain unchanged, a vacuum between the wing and our packet of air would form. Reluctantly, the packet will change course and follow the wing's contour. This fast-flowing, low-pressure air will in turn suck in new air ahead and below of it, will go on to decelerate and regain its old pressure over the rear half of the wing, and will flow off with its new flow direction.

A packet of air which ends up below the wing will experience less uplift and acceleration, and in the convex part of highly cambered airfoils it will experience a compression. It also has to change its flow path, because the cambered and/or inclined wing will push the air below it downwards, creating more pressure and more bouncing from above for our packet below the wing. When both packets arrive at the trailing edge, they will have picked up some downward speed.

Molecules on a collision course with the wing will be decelerated ahead of the point where they would hit the wing. This point is called stagnation point because here is a very local pressure peak . Once past this point, the molecules will quickly speed up because the lower pressure downstream sucks them away from the stagnation point. If there were no viscosity, there would be a second stagnation point at the trailing edge, but in reality we find some but not a complete pressure recovery there. Below is a plot of the pressure distribution around an airfoil, courtesy of XFOIL. It offers two ways of plotting pressure distributions, one with the chord coordinate on the X axis and the negative pressure coefficient $c_p$ on the Y axis, like that:

The dashed line is for inviscid flow, the solid line for pressure with viscous effects.

Another version plots the pressure as arrows orthogonally on the contour of the airfoil, like that:

Please note that negative values of $c_p$ produce arrows pointing away from the airfoil, and positive values point towards the airfoil. In all cases, the formula for $c_p$ is $$c_p = \frac{p - p_{\infty}}{q_{\infty}}$$ $p$ is the local pressure, $p_{\infty}$ is the pressure far away from the airfoil, and $q_{\infty}$ is the dynamic pressure (= density times speed squared, divided by 2) far away from the airfoil. For incompressible flow at rest $c_p$ equals 1, for flow at ambient speed $c_p$ equals zero, and negative values denote suction.

Behind the wing, both packets will continue along their downward path for a while due to inertia and push other air below them down and sideways. Above them, this air, having been pushed sideways before, will now fill the space above our two packets. Macroscopically, this looks like two big vortices. But the air in these vortices cannot act on the wing anymore, so it will not affect drag or lift.

What is lift?

Following the picture of a pressure field outlined above, lift is the difference of pressure between upper and lower surface of the wing. The molecules will bounce against the wing skin more at the lower side than at the upper side, and the difference is lift.

Or you look at the macroscopic picture: A certain mass of air has been accelerated downwards by the wing, and this required a force to act on that air. This force is what keeps the aircraft up in the air: Lift.

Either way, you will arrive at the same result. By the way: Most of the directional change happens in the forward part of the airfoil, not at the trailing edge!