# If an aerofoil is placed in a narrow wind tunnel, how will that affect the lift it produces?

## This is NACA 0000 aerofoil:

This is just a straight line - roughly what a paper plane's aerofoil section looks like (I chose this aerofoil for its simplicity). If we put this aerofoil in a wind tunnel, then this is my approximation of what the air-flow around it might look like:

(Infinite wind tunnel - ignore ground effect) $$(AoA=12°)$$

The air-flow isn't ideal; there is flow seperation already at the leading edge. But still, the aerofoil will produce a net positive lift.

But what happens if we put this aerofoil in a narrow wind tunnel? The pressure distribution appears to have been reversed: high pressure above and low pressure below.

This is explained as follows: through a convergent duct, the air-flow velocity (and thus dynamic pressure) increases. This is accompanied by a reduction in static pressure, such that the total pressure remains constant (the opposite is true for a divergent duct).

Is this true? and so will the aerofoil produce a downforce instead of lift in the narrow wind tunnel?

You need to consider more than just the static pressure. In the usual demonstrations of the Bernoulli effect, the pressure tap is placed perpendicular to the streamlines, which means it only "feels" the static pressure, but an object placed directly in the middle of the streamlines acts as a "stagnation point," and feels an additional pressure associated with actually forcing the streamlines to take a different path.

A small hole perpendicular to the streamlines can be used to measure the static pressure. A small hole placed parallel to the streamlines at a point where the streamlines are forced to stop can be used to measure the stagnation pressure. In this case, the airfoil is neither parallel nor perpendicular to the streamlines, and the resultant pressure will be somewhere in between the two.

• Yes, but what will be the net effect? will the lift reduce due to change in pressure distribution? will it stay same? (or will it increase due to ground effect?) Commented May 28, 2023 at 3:24
• @AdityaSharma The lower wall should increase the lift due to ground effect. The upper wall should decrease the lift. The net effect probably depends on the actual distances. Commented May 28, 2023 at 3:26
• Alright, so if we remove the lower wall, the lift should reduce. By the way, I believe that the upper wall will also contribute towards "ground" effect, since it is also limiting the downwash, just like the lower wall (think of a Formula 1 car that uses ground effect to improve downforce - this is a similar case, just inverted). So if the F1 car with the same setup achieves an increase in lift (downforce), why would our setup suffer from a decrease in lift? Commented May 28, 2023 at 3:36
• @AdityaSharma Hmm, I think you're right, actually. (The bit about the upper wall I was not so sure about to begin with). In that case, both the floor and the ceiling would increase the lift and it makes the overall effect much easier to figure out. Commented May 28, 2023 at 3:43
• Yes, that is exactly what I thought when I first came across this problem, but then I thought: How would the apparent "reversal" of pressure distribution (as explained by Bernoulli's principle) affect the lift? - This is something I was never able to understand. Commented May 28, 2023 at 3:47

This is a case where working backwards from actual wind tunnel data may be more helpful.

A higher pressure stagnation zone will form underneath the plate. This is the ground effect, increasing lift. Air velocity will increase at the exit of this area (at the trailing edge).

A lower pressure area forms above the plate, with a lower (or even reverse) air flow at its exit. This will increase lift.

The Formula 1 car is producing downforce (or a reverse ground effect).

So, Bernoulli can't explain everything. Local pressure may be a more accurate way to predict lifting effects.

However, if a more smoothly cambered airfoil is chosen, interference with upper airflow may indeed reduce lift, especially at higher Reynolds numbers.

• Read on about biplane wing interference effects. Commented May 28, 2023 at 4:31
• "A higher pressure stagnation zone will form underneath the plate." - but the pressure never increases at the entrance of a Venturi, it only decreases, there is no stagnation (based on my limited knowledge of the Venturi effect). What would make this setup different from a Venturi? Commented May 28, 2023 at 6:37
• @AdityaSharma it may be that the trailing edge is where velocity increases, and pressure decreases. The upper wall may indeed reduce lift (even with the flat plate). I think the upper wall may cause a stall at a lower AoA. Commented May 28, 2023 at 10:32
• "It may be that the trailing edge is where velocity increases, and pressure decreases." - In my opinion, that shouldn't be the case. To justify my opinion, I would first like to summarise why the velocity increases and pressure decreases in a Venturi. There are two principles in action: 1) Law of conservation of mass, and 2) Bernoulli's principle. Law 1 tells us that mass flow rate (of an ideal fluid) through a streamtube will always be equal at every section of the tube. This implies that if the section area decreases, velocity must increase for the mass flow rate to remain constant. Commented May 28, 2023 at 11:33
• Law 2 tells us that the increase in velocity produces an increase in dynamic pressure. Now, the static pressure must reduce for the total pressure to remain constant. Based on this description of the venturi effect, the increase in dynamic pressure and decrease in static pressure must take place gradually as the section area reduces, not suddenly at the choke (trailing edge). Commented May 28, 2023 at 11:33