Relationship between body pressures on the rear panels and the base pressure

[JulianEdgar]

Summarising what the experts told me.

There are two main theories used to describe the relationship between body pressures on the rear panels (eg side panels) of a car and the base pressure. One is the jet pump / boundary layer thickness approach, and the other, the trailing vortex approach. Sometimes, the approaches are combined.

Jet pump and boundary layer thickness

This is based on Hoerner’s ‘jet pump’ idea. That is, the flow of air as it leaves the car forms a tube of moving air (the ‘jet’) that surrounds the base area. This moving air mixes with the dead air behind the car and tries to pump it away i.e. entrain it. This reduces pressure on the base, creating drag.

If a thick boundary layer (that is, a layer of air moving more slowly than the freestream) exists on the rear panels of the car, this creates an ‘insulating’ layer between the jet of fast-moving air and the dead air. Thus the thicker the boundary layer, the greater the base pressure, giving less drag.

A thicker boundary layer occurs when there is an adverse pressure gradient, and so there will also be higher pressures on the rear panels when there is a thicker boundary layer. But is the thicker boundary layer caused by the higher pressure or vice versa?

Adrian Gaylard (Jaguar Land Rover) commented:

Which is the chicken and which is the egg? As is often the way with continuum mechanics, it’s a bit of both I think.

Trailing vortices

Different body shapes develop different trailing vortices. Wake pressures reflect these different vortices. For example, a squareback shape has little trailing vortex development and will have pressures on the rear panels that are similar to those in the wake. Conversely, fastbacks and notchbacks will have base pressures that are lower, as the base pressure is strongly influenced by the vortex development.

Thomas Wolf (Porsche) commented:

It is understandable that with a squareback ("shoebox") the pressures on the side surfaces roughly correspond to the base pressure, while this is rather not the case with the fastback. In other words, there is no clear correlation here. Rather, it is a combination of vehicle shape (upper/lower contour, side contour/taper/boat-tailing, cross-sectional shape) and the vortex formation that determine the pressures on the individual surfaces and the base pressure. Thus the flow patterns in the wake result from these relationships and not vice versa.

Combining these approaches

Rob Palin (ex Tesla) combined the above approaches in an earlier communication with me:

There's certainly a complex trade-off when it comes to reducing wake size, and there are strong influences from the surface boundary layer thickness, absolute static pressure, and static pressure gradients at the point of separation. Thick boundary layers and/or weak pressure gradients generally mean weak vortices at the sharper separation edges, and higher overall base pressure.

I asked Rob to expand on this, and he said:

The mechanism here is mainly to weaken any vortices that form around the trailing edges of the vehicle body. I'm sure purists would hate this, but I would describe it as being that thick boundary layers lead to 'fluffier' vortices, which have less intense velocity gradients, thicker cores, and generally much higher pressure. These vortices both pull less hard on the rear-facing surfaces, and burst sooner, meaning that they don't persist for long in either time or space. In aero-acoustic situations that's a bad thing, but for drag it's good.

Behind this is the way that vortices are born from the sudden release of the pinned/slow near-surface air when the air away from the surface is travelling very quickly. This velocity gradient, and the intense viscous shear it causes, rolls the air up into the vortex tube. The steeper the velocity gradient, and/or the more abrupt the disconnection from the surface, the tighter the wrapping of the fluid layers, and the more intense the vortex. Tighter vortices get to lower pressures, and that pressure kind of 'pollutes' the wake around it, lowering the overall pressure.

From the pressure gradient side, as long as you have attached flow, you are aiming to reduce the velocity gradient normal to the surface. You can do so by reducing surface curvature. A secondary option is to try and slow the air down as much as you can before any sharp separation edge, so that the velocity gradient between streamwise flow approaching the edge, and the recirculating flow around the corner of the edge, is minimal. This again leads to less intense vortex generation.

Pressure testing

So it would seem that from either the jet pump / boundary layer thickness idea, or the trailing vortex development idea, having pressures as high as possible towards the rear of the car on the side panels is a good thing. (Remember, they’re still below atmospheric and so it’s sometimes easier to think of them as being “less low” rather than “high”.)

Adrian Gaylard:

This is essentially what is implied by the “pressure recovery” explanation. If you boat tail or extend the flow surface with a spoiler both are generating a thicker boundary layer at separation along with higher pressure.

So anything that you do that increases side pressures is likely to be a good thing. That’s what happened with my Edgarwit air curtains on my Insight, and with my temporary covering of the rear wheel arch with a spat on the Mercedes.

But why do these modifications increase pressure? My guess is that they reduce separation, so leading to the development of a thicker and more stable boundary layer, indicative of a higher pressure (and again there's that chicken and the egg).

[deluxx]

Since I have no tech literature on this subject, and haven't personally tested it, there's a fair amount of misleading information in earlier posts...

[aerohead]

Originally Posted by JulianEdgar

Summarising what the experts told me.

There are two main theories used to describe the relationship between body pressures on the rear panels (eg side panels) of a car and the base pressure. One is the jet pump / boundary layer thickness approach, and the other, the trailing vortex approach. Sometimes, the approaches are combined.

Jet pump and boundary layer thickness

This is based on Hoerner’s ‘jet pump’ idea. That is, the flow of air as it leaves the car forms a tube of moving air (the ‘jet’) that surrounds the base area. This moving air mixes with the dead air behind the car and tries to pump it away i.e. entrain it. This reduces pressure on the base, creating drag.

If a thick boundary layer (that is, a layer of air moving more slowly than the freestream) exists on the rear panels of the car, this creates an ‘insulating’ layer between the jet of fast-moving air and the dead air. Thus the thicker the boundary layer, the greater the base pressure, giving less drag.

A thicker boundary layer occurs when there is an adverse pressure gradient, and so there will also be higher pressures on the rear panels when there is a thicker boundary layer. But is the thicker boundary layer caused by the higher pressure or vice versa?

Adrian Gaylard (Jaguar Land Rover) commented:

Which is the chicken and which is the egg? As is often the way with continuum mechanics, it’s a bit of both I think.

Trailing vortices

Different body shapes develop different trailing vortices. Wake pressures reflect these different vortices. For example, a squareback shape has little trailing vortex development and will have pressures on the rear panels that are similar to those in the wake. Conversely, fastbacks and notchbacks will have base pressures that are lower, as the base pressure is strongly influenced by the vortex development.

Thomas Wolf (Porsche) commented:

It is understandable that with a squareback ("shoebox") the pressures on the side surfaces roughly correspond to the base pressure, while this is rather not the case with the fastback. In other words, there is no clear correlation here. Rather, it is a combination of vehicle shape (upper/lower contour, side contour/taper/boat-tailing, cross-sectional shape) and the vortex formation that determine the pressures on the individual surfaces and the base pressure. Thus the flow patterns in the wake result from these relationships and not vice versa.

Combining these approaches

Rob Palin (ex Tesla) combined the above approaches in an earlier communication with me:

There's certainly a complex trade-off when it comes to reducing wake size, and there are strong influences from the surface boundary layer thickness, absolute static pressure, and static pressure gradients at the point of separation. Thick boundary layers and/or weak pressure gradients generally mean weak vortices at the sharper separation edges, and higher overall base pressure.

I asked Rob to expand on this, and he said:

The mechanism here is mainly to weaken any vortices that form around the trailing edges of the vehicle body. I'm sure purists would hate this, but I would describe it as being that thick boundary layers lead to 'fluffier' vortices, which have less intense velocity gradients, thicker cores, and generally much higher pressure. These vortices both pull less hard on the rear-facing surfaces, and burst sooner, meaning that they don't persist for long in either time or space. In aero-acoustic situations that's a bad thing, but for drag it's good.

Behind this is the way that vortices are born from the sudden release of the pinned/slow near-surface air when the air away from the surface is travelling very quickly. This velocity gradient, and the intense viscous shear it causes, rolls the air up into the vortex tube. The steeper the velocity gradient, and/or the more abrupt the disconnection from the surface, the tighter the wrapping of the fluid layers, and the more intense the vortex. Tighter vortices get to lower pressures, and that pressure kind of 'pollutes' the wake around it, lowering the overall pressure.

From the pressure gradient side, as long as you have attached flow, you are aiming to reduce the velocity gradient normal to the surface. You can do so by reducing surface curvature. A secondary option is to try and slow the air down as much as you can before any sharp separation edge, so that the velocity gradient between streamwise flow approaching the edge, and the recirculating flow around the corner of the edge, is minimal. This again leads to less intense vortex generation.

Pressure testing

So it would seem that from either the jet pump / boundary layer thickness idea, or the trailing vortex development idea, having pressures as high as possible towards the rear of the car on the side panels is a good thing. (Remember, they’re still below atmospheric and so it’s sometimes easier to think of them as being “less low” rather than “high”.)

Adrian Gaylard:

This is essentially what is implied by the “pressure recovery” explanation. If you boat tail or extend the flow surface with a spoiler both are generating a thicker boundary layer at separation along with higher pressure.

So anything that you do that increases side pressures is likely to be a good thing. That’s what happened with my Edgarwit air curtains on my Insight, and with my temporary covering of the rear wheel arch with a spat on the Mercedes.

But why do these modifications increase pressure? My guess is that they reduce separation, so leading to the development of a thicker and more stable boundary layer, indicative of a higher pressure (and again there's that chicken and the egg).

1) Streamlines are isoenergetic.
2) They all contain identical kinetic energy.
3) Velocity can be swapped for low pressure or vice versa.
4) Any cleanup at the front will allow more turbulence-free, kinetic energy to survive to the aft-body.
5) Moderate pressure increase along the side profile will ensure flow attachment, and pressure regain, as the flow decelerates along the sides of the decreasing cross-section, as well as up top ( hopefully ).
6) If flow remains attached all the way, it will be at its slowest velocity, highest pressure, and base pressure will mimic that at the separation line.
7) The presence of the turbulent boundary layer allows for the momentum transfer from the local streamline, down to the lowest strata of the TBL, adjacent to the body 'boundary,' holding it in place.
8) The thickness of the TBL is essentially meaningless, as long as it is present.
9) The shape of the body profile makes or brakes TBL attachment.
10) That's why they call it 'profile' drag.

[JulianEdgar]

Originally Posted by aerohead

8) The thickness of the TBL is essentially meaningless, as long as it is present.

Well unfortunately that isn't what the experts say - including one of your favorite references, Hoerner (section 3-19).

Also refer to https://www.researchgate.net/publica...r_Modification - a paper that specifically addresses the connection between boundary layer thickness and drag.

Again, what you say simply isn't supported by the experts.

[aerohead]

Originally Posted by JulianEdgar

Well unfortunately that isn't what the experts say - including one of your favorite references, Hoerner (section 3-19).

Also refer to https://www.researchgate.net/publica...r_Modification - a paper that specifically addresses the connection between boundary layer thickness and drag.

Again, what you say simply isn't supported by the experts.

1) You have Hoerner's book?
2) You understand that jet pumping action has to do with 'basic, simple, bullets and artillery projectiles, in free-flight? Not an automotive bluff body in ground effect?
3) A streamlined basic body of Cd 0.09 will have the thickest TBL, yet the lowest drag.
4) Can you clarify your remark?

[JulianEdgar]

Originally Posted by aerohead

1) You have Hoerner's book?
2) You understand that jet pumping action has to do with 'basic, simple, bullets and artillery projectiles, in free-flight? Not an automotive bluff body in ground effect?
3) A streamlined basic body of Cd 0.09 will have the thickest TBL, yet the lowest drag.
4) Can you clarify your remark?

1) Yes I have Hoerner's book.

2) You didn't read the paper I cited? Adrian Gaylard suggested it to me as being highly relevant to cars.

3) That's right - you don't seem to understand the original post I made in this thread?

4) Which? Your comment that "The thickness of the TBL is essentially meaningless, as long as it is present." is not supported by the experts.

[aerohead]

Originally Posted by JulianEdgar

1) Yes I have Hoerner's book.

2) You didn't read the paper I cited? Adrian Gaylard suggested it to me as being highly relevant to cars.

3) That's right - you don't seem to understand the original post I made in this thread?

4) Which? Your comment that "The thickness of the TBL is essentially meaningless, as long as it is present." is not supported by the experts.

1) I have Hoerner's 1951 book.
2) There's nothing about jet-pumping action in the chapter on motor vehicles.
3) Only isolated projectiles.
4) What changed that is 'highly relevant'?

[JulianEdgar]

Originally Posted by aerohead

1) I have Hoerner's 1951 book.
2) There's nothing about jet-pumping action in the chapter on motor vehicles.
3) Only isolated projectiles.
4) What changed that is 'highly relevant'?

I am not going to continue joining the merry-go-round.

I am happy to follow the expert advice I receive from the world's top car aerodynamicists, to read the papers they cite, and to read the textbooks they cite.

I pay attention to what professional automotive aerodynamicists say and write. You refuse to do so - and so continue to have a weird set of aerodynamic theories that don't match reality.

That's fine - so long as you don't mislead others.

[aerohead]

Originally Posted by JulianEdgar

I am not going to continue joining the merry-go-round.

I am happy to follow the expert advice I receive from the world's top car aerodynamicists, to read the papers they cite, and to read the textbooks they cite.

I pay attention to what professional automotive aerodynamicists say and write. You refuse to do so - and so continue to have a weird set of aerodynamic theories that don't match reality.

That's fine - so long as you don't mislead others.

That's just it. This is the modus operandi.
Volunteer nothing in your own tongue, such that it's crystal clear, or not, that you understand the topic.
How would you know if anyone's been mislead or not? Nothing you've shared so far overturns anything. Perhaps it obscures.
There's a dividing line between 'basic' and 'complex' bodies. If you work for the Paris Dressmakers, then perhaps it IS a 'black art' to squeeze anything out of something like a Porsche Macan.

[JulianEdgar]

Originally Posted by aerohead

That's just it. This is the modus operandi.
Volunteer nothing in your own tongue, such that it's crystal clear, or not, that you understand the topic.

What an odd thing to write.

I have written well over 100,00 words - two whole books, no less - on modifying and testing car aerodynamics - in "my own tongue".

But you seem to be criticizing me for actually directly quoting experts and text/paper references! Gee, that would never do, would it?

How quite bizarre.