## Simple question on adverse pressure gradients

## Simple question on adverse pressure gradients

(OP)

Hi all,

I have a simple quesiton on the pressure distribution over an aerofoil but I can't seem to conceptually visualise it.

I am starting to convince myself of the flow over a circle such as the image below:

The stagnation point is a region of obvious high pressure (Cp = 1.0) and zero velocity, as the flow moves upwards this is a movement from high -> low pressure (dp/dx < 0) and so is favourable, this translates to an increase in the fluid velocity. At the top of the circle the maximum velocity/lowest pressure is achieved. From the rear of the circle there is also a wake region/seperation region resulting in low pressure.

My question is why does the boundary layer seperate on the right but not the left, i.e why does a downward curve translate to an adverse pressure gradient, from NASA's website:

https://www.grc.nasa.gov/www/k-12/airplane/wrong3....

you cannot think of it as a simple venturi for the bulk flow with the freestream acting as a theoretical wall (although this would make it easier to understand).

Thanks for any info,

Hob

I have a simple quesiton on the pressure distribution over an aerofoil but I can't seem to conceptually visualise it.

I am starting to convince myself of the flow over a circle such as the image below:

The stagnation point is a region of obvious high pressure (Cp = 1.0) and zero velocity, as the flow moves upwards this is a movement from high -> low pressure (dp/dx < 0) and so is favourable, this translates to an increase in the fluid velocity. At the top of the circle the maximum velocity/lowest pressure is achieved. From the rear of the circle there is also a wake region/seperation region resulting in low pressure.

My question is why does the boundary layer seperate on the right but not the left, i.e why does a downward curve translate to an adverse pressure gradient, from NASA's website:

https://www.grc.nasa.gov/www/k-12/airplane/wrong3....

you cannot think of it as a simple venturi for the bulk flow with the freestream acting as a theoretical wall (although this would make it easier to understand).

Thanks for any info,

Hob

## RE: Simple question on adverse pressure gradients

However, your premise about left and right being symmetrical is incorrect. You have a higher than nominal pressure on the left where the air is being compressed, so flow separation is impossible, but a lower than nominal pressure on the right, where the air is expanding. Separation is a fancy word for when all the air cannot follow the curve of the surface as it's expanding. There is a Wikipedia article: https://en.wikipedia.org/wiki/Flow_separation

TTFN

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## RE: Simple question on adverse pressure gradients

For the flow regieme pictured I believe the flow is incompressible, I guess the confusing part is the low pressure on the rear of the circle. Via Bernoulli this would translate to a high velocity, but in reality it is seperated flow:

Is it that Bernoulli cannot be applied in the wake region due to the rotation of the flow?

## RE: Simple question on adverse pressure gradients

You can think of it as a "stickiness" of the boundary layer that breaks down and results in flow separation

TTFN

I can do absolutely anything. I'm an expert!

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## RE: Simple question on adverse pressure gradients

## RE: Simple question on adverse pressure gradients

Why is point (4) adverse?, the flow is recirculating due to the pressure gradient, but why does downward curvature result in an adverse gradient in the first place?

The only theory on the subject I have seen is based on potential flow, but this would give rise to inviscid lift surely?

## RE: Simple question on adverse pressure gradients

## RE: Simple question on adverse pressure gradients

from: https://www.grc.nasa.gov/www/k-12/airplane/wrong3....

"The part of the theory about Bernoulli's equation and a difference in pressure existing across the airfoil is correct. In fact, this theory is very appealing because there are parts of the theory that are correct. In our discussions on pressure-area integration to determine the force on a body immersed in a fluid, we mentioned that if we knew the velocity, we could obtain the pressure and determine the force. The problem with the "Venturi" theory is that it attempts to provide us with the velocity based on an incorrect assumption (

the constriction of the flow produces the velocity field). We can calculate a velocity based on this assumption, and use Bernoulli's equation to compute the pressure, and perform the pressure-area calculation and the answer we get does not agree with the lift that we measure for a given airfoil."So I am still at a loss as to the pressure gradient if the venturi effect for an aerofoil is incorrect.

## RE: Simple question on adverse pressure gradients

~~the dangle~~Attack, bound vortices, circulation, kutta condition, lifting line theory...We had a full term class on fluid dynamics at uni that culminated in 'why a wing produced lift' and some members of the class still didn't understand (although they probably got better grades on the exam than me).

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## RE: Simple question on adverse pressure gradients

## RE: Simple question on adverse pressure gradients

TTFN

I can do absolutely anything. I'm an expert!

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## RE: Simple question on adverse pressure gradients

another day in paradise, or is paradise one day closer ?

## RE: Simple question on adverse pressure gradients

IRstuff - Lift as far as I can see arises due to the stagnation point on the lower surface of the wing and the curvature of the wing downwards, from momentum conservation there must be a resulting net upwards force. This is about the most qualitative accepted explination I can find.

The classical argument is simply there is a pressure difference resulting in an upwards pressure force 'lift', we can relate this to Bernoulli and state the velocity on the upper surface must be faster than the velocity on the lower surface, this arises due to the geometry of the wing. I haven't yet seen the reason as to how the geometry generates this velocity difference. Most state Bernoulli and the effective change in area giving rise to the velocity (the freestream and the wing surface acting as a venturi).

For a while I have been trying to see why more aerodynamicists haven't run into this problem, about the closest is Doug McLean and his book (I found yesterday), he gives an explination to the problem in his Youtube video:

https://www.youtube.com/watch?v=QKCK4lJLQHU (from 15:11 to 27:56).

For me it is the arising of an adverse pressure gradient from the point of maximum wing thickness.

## RE: Simple question on adverse pressure gradients

A relatively thin flat plate at an angle to the air flow will generate lift and display most of the same basic characteristics as a tear drop airfoil shape. In fact most initial labs at uni used flat plates not airfoil sections.

Likewise, symmetrical airfoils also generate lift and even asymmetric ones will generate 'lift' if the airplane is flown upside down.

(There are secondary characteristics which are impacted, just not fundamentally if they'll generate lift.)

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