The Mechanism Behind Flow Separation
 

I'd advise everyone to go to the bathroom before you start reading...:p

Simple answer, if you speaka da chinese:

It evens out the momentum of air molecules in the boundary layer, giving kinetic energy to the slowest molecules at the body surface most susceptible to reversing direction due to an adverse pressure gradient.

The long answer, in English please:

I think things will make most sense if I am very thorough…and I’ll have the added benefit of discovering my own shortfalls in understanding! Here are the concepts as I have worked them out in my mind. Let’s start with the fundamentals.

The basic of basics, maybe it will come in handy. Fluid can only act on a body through two types of forces:
1.) Shear forces
2.) Pressure differential

For much of the early history of aerodynamics, people theoretically predicted that all the pressure forces acting on a body would equalize and cancel out. The classic example is the sphere, which seems to be a mainstay in understanding fluid flow.

http://i264.photobucket.com/albums/i...doxResized.jpg

I remember asking in class how that center streamline went through the sphere, but the teacher wasn’t interested in such trivial matters. For those interested in history, the idea was put forth by Jean le Rond D’Alembert, an 18th century mathematician (among other things), who published the concept in 1740. Today, this theoretical anomaly is known as D’Alemberts Paradox. What stumped people for so long was that people didn’t take into account friction and the resulting effect of viscosity. Viscous flow wasn’t fully developed until Prandtl published the boundary layer concept in 1904.

The boundary layer describes the region of fluid around a body that is affected by friction. Specifically, it involves the completely stationary fluid at the body’s surface to the fluid far enough away that has been able to retain 99% of the free stream flow velocity. Essentially, any air that is slowed by the presence of the body is within the boundary layer. An interesting aspect of this phenomenon is that the body essentially grows in size, at least as far as the free air stream is concerned.

http://i264.photobucket.com/albums/i...ndaryLayer.jpg

The boundary layer doesn’t necessarily look like that, but it illustrates that the body has been slightly thickened. Graphically, aerodynamicists represent this slowing of air through a velocity profile. It relates the velocity of the air relative to its height above the body. The further you are away from the body, the closer the air velocity becomes to the free stream air velocity (hence, no drag).

http://i264.photobucket.com/albums/i...ndaryLayer.jpg

First, for those not familiar with these symbols: V∞ = free stream velocity; y = height above body; V = boundary layer velocity. The solid line represents a laminar boundary layer, the dashed represents a turbulent boundary layer. The fundamental difference between laminar and turbulent boundary layers is the presence of streamlines. A streamline can be thought of as a layer of air completely isolated from adjacent layers. In effect, the edges of a streamline act as an impermeable wall. The laminar boundary layer is composed of ordered streamlines, who share no momentum (mass*velocity). These streamlines allow molecules to flow past each other with much less friction, so slow molecules are less likely to speed up and fast molecules are less likely to be slowed down. The turbulent boundary layer has a virtual absence of streamlines, as air molecules freely travel throughout the boundary layer. This allows higher velocity (i.e. higher momentum) air molecules to come into contact with slower molecules and transfer their energy. This sharing of momentum leeches energy from the air molecules already near free stream velocity, since the energy they transfer to slower molecules slows them down. The slowing of these once fast molecules causes the adjacent free air stream to slow, causing the boundary layer to grow in height. All this to come to one conclusion! Laminar boundary layers cause less skin friction drag because there is no sharing of momentum between streamlines, but the velocity profile is not very equalized. Turbulent boundary layers cause more skin friction because there is a free transfer of momentum, but the velocity profile is much more equalized throughout its height.

A couple more ideas, then I’ll get to the “answer.” Generally, the laminar boundary always exists, even in a body immersed in turbulent flow. The reason behind this is the transition point. The free air stream is (usually) orderly, being made up of streamlines, but is subject to the 2nd Law of Thermodyamics (removal of energy = increase disorder). At the front of the body, the flow is laminar because no energy has been dissipated. The further along the body the flow travels, the more it loses kinetic energy to heat through friction. The lower the flow’s energy becomes the greater its disorder becomes, until it becomes so disordered that streamlines are broken and the flow becomes turbulent. The change between laminar and turbulent boundary layers is called the transition point. It can be caused by changes in the Reynold’s number (ρVx/μ; i.e. changes in air density, velocity, viscosity, distance traveled) or by the surface itself. A dimpled golf ball still has a laminar boundary layer, it just simulates a higher Reynold’s number by causing the transition point to occur earlier.

http://i264.photobucket.com/albums/i...itionPoint.jpg

D’Alembert’s paradox, the lack of pressure differential on an object in inviscid (frictionless) flow, failed to account for shear forces. What is so interesting is that shear forces are responsible for pressure differentials even though they are two completely different forces acting on a body. The reason shear forces (friction) account for pressure drag is all due to the transfer of energy into heat.

Prandtl, the man who introduced the boundary layer concept, gave the best analogy. Here it is, modified for clarity by an aerodynamicist named Hoerner. Imagine a rollercoaster car sitting at the top of a drop. When it loses height it picks up speed, until it reaches maximum velocity at the bottom of the drop. According to D’Alembert’s frictionless assumption, you could predict that the rollercoaster car would exchange its speed for height on the other side of the drop and make it to the top.

http://i264.photobucket.com/albums/i.../EnergyMap.jpg

Intuition tells us that the rollercoaster car wouldn’t make it back up to the top, but why? Friction. Some of the kinetic energy of the car is being converted into heat due to friction. What that means is when the car tries to cash in its K.E. for P.E., it is going to come up short and roll backwards. In this system, gravity is the potential energy while velocity is the kinetic energy. In aerodynamic flows, pressure is the potential energy and velocity is the kinetic energy.

Ambient pressure is turned into fast moving air due to a decreasing pressure gradient (pressure going from high to low over a distance). This low pressure is what creates lift in wings, which is great and all, but it needs to turn into ambient pressure again (via an adverse pressure gradient). D’Alembert figured that the fast moving air would slow down and re-pressurize to ambient. Apparently, D’Alembert has never been on a rollercoaster. That fast moving air has already lost some of its energy to heat due to friction, therefore it can’t re-pressurize to its previous state. What happens is that lower pressure air forms in the back of the body, causing a pressure differential. This pressure differential is what is termed pressure drag.

Pressure drag is bad enough at this point, but it goes to hell when the flow separates from the surface. If you remember the velocity profile of the various boundary layers, you notice that the velocity is slowest near the surface because it encounters the most friction. These molecules have essentially changed most of their kinetic energy into heat, so they are going to get royally screwed when it comes time to cash in K.E. for P.E. And royally screwed they get. The slowest of these molecules have so little energy that not only do they stop before reaching the end of the body, they “borrow” potential energy from the free stream flow by traveling backwards. Aerodynamicists have termed this reversed flow as being separated. Of course, air molecules haven’t physically separated from the body (i.e. there isn’t a vacuum), it’s just that flow has stopped in that region. Above this region, the fast moving particles of the more energized boundary layer continue to flow.

http://i264.photobucket.com/albums/i...aratedFlow.jpg

Just like air sucking into a Snapple®, high pressure air wants to suck into the low pressure void. Normally the kinetic energy of the flow would prevent this, but its absence causes some air molecules within the free stream flow to change momentum. This change in momentum, which entails a force, is the pressure drag. Separation causes much more ambient air to change momentum than non-separated flow. Separated flow really is at the limits of my comprehension, because it involves vortexes and extremely complicated flow patterns.

Since separated flow is so bad, aerodynamicists are willing to make some sacrifices to prevent it even if at the cost of some other drag. If you remember the velocity profiles of laminar and turbulent boundary layers, you’ll recall that the turbulent boundary layer has a “fuller” profile. This fullness simply means that air is flowing faster closer to the body surface. This redistribution of momentum means that molecules closer to the surface will have more kinetic energy to cash in when it comes time to re-pressurize. If you recall, this redistribution is at the cost of increased friction due to the removal of streamlines. Turbulent boundary layers increase skin friction, but decrease pressure drag. Laminar turbulent boundary layers decrease skin friction, but increase pressure drag. Neither is better overall, just in certain applications. Horses for courses.

Even turbulent boundary layers run out of steam, losing much of their kinetic energy to heat. In this case, turbulent boundary layers grow larger and the disparity between slow moving and fast moving molecules becomes greater. Even though the proportion of the energy being distributed is roughly constant, the amount of low energy molecules grows (the area under the shallowest part of the exponential line grows). Eventually, even with turbulent flow, you will get separation. To combat this phenomenon, boundary control devices have been created: vortex generators, sucking, blowing, an orgy of methods, really…

They all seek to “re-energize” the boundary layer (aka, reintroduce the kinetic energy lost). Boundary layer blowing and sucking do this artificially through an external pump, but vortex generators act as a grand version of the turbulent boundary layer. Vortex generators force high velocity air molecules near the top of the boundary layer down to the surface by swirling it. Just as the turbulent boundary layer increased the sharing of momentum by breaking up streamlines, vortex generators increase the sharing of momentum by adding a larger vertical velocity component to the boundary layer. The issue with vortex generators is similar to that of the turbulent boundary layer: you increase drag. Vortex generators create drag to produce the swirling action of air. The key is to determine when the benefit of a vortex generator overcomes its pitfalls. It’s a huge balancing act that is usually solved empirically (or semi-empirically via CFD).

If that was a lot to read, imagine typing it. Phew… I hope the article is generally correct, but I am not an aerodynamicist so caveat emptor. I appreciate corrections or improvements…it’s for everyone’s benefit. If there is any vagueness (which I hate in describing/learning aerodynamics, hence the article length) than feel free to contribute. In any case, I hope that answered your question.

- LostCause

My brain hurts!!! At least you didn't include math too!

yeah mine too
oohh brainfroze

Let me see if I can sum it up.

That is why golf balls have dimples (turbulent Flow), they help them go farther. Smooth (Laminar flow) golf balls without dimples come up short.

Pics don't work.

:(, I fix, I fix, ya? Hopefully pictures will make it easier...

I checked the links for the pictures and they are dead, perhaps you copies the wrong url?

Aww, that's the exact opposite of what I intended...:( I realize the article is a freaking book (sorry about that), but the content shouldn't be over any of your guys' heads.

I totally understand if it's too long to read, but I figured for those with a burning desire to learn the topic that it would be a useful resource. I wish the teachers I had took the time to explain things in detail rather than introduce vague concepts, give BS reasons why they occur, and move on. I had to learn that stuff through books, sitting in the library (and I hate reading, :)).

You just explained what happens, the article aims to explain why it happens. I figure if people are willing to buy and read through all 1000 pages of hucho's vehicle aerodynamics that this would be a shortcut (longcut? :)).

Oh, and as far as MetroMPG original question. There is a short, hard answer or a long, simple answer. Take your pick, but no need to ask god :D.

BTW, pics fixed.

- LostCause

the pics seldom work here in the p.o.
gubmint censors & all.
I'll lookit them tonight when i get home.
shhh i'm not really workin.
S.

Not to beat a dead horse here, but if there are any questions I'm willing to give them a go. Such as: What does viscous mean? What is the free air stream? Where do babies come from? :confused:

Hopefully you master this tonight, because tomorrow we derive the Navier-Stokes equation! :eek:

http://i264.photobucket.com/albums/i...vierStokes.jpg

juuuuuuust kidding...

- LostCause

Deriving it is pretty easy, it's analyzing it that sucks. :cool:

Very nice write up :) Bonus points for thoroughness :) And thank you so much for saying:

I've been saying something to that effect since forever that I've been saying something about VGs :D Slapping them anywhere (or everywhere) is no good - hit or miss with a highly chance of miss.

That's what sucks about explaining something as simple as a ribbed piece of plastic... There's a great deal of information one must have a basic understanding of before going into how or why that little piece of plastic does what it does. Alas, it takes a lot of wording to explain this - so a bunch of simple concepts becomes a lot to chew on.

These posts are full of a lot of great information. My head does hurt, but usually I have to go back over it, once I get the general idea. Thanks, to everyone for their sharing.

Great writeup! I admit I only skimmed it tho :rolleyes:

That's only part of the derivation. Maybe using x-y-z coordinate system would be easier. :D

Yeah nice explanation. I liked the qualification of detached flow, I always imagined that the stream of air detached from the car like a ball rolling across it would. The fact that it is stationary or backwards moving air (relative to the car) is useful. That helps me to understand that by taking some of the energy of the faster moving higher up streams the difference in speed is not as great so less air has to move and less force is applied on the vehicle. I'm not sure if I understand the momentum analogy. Did they assume that the high pressure on the front side would equalise with the low pressure on the back side but the surface friction prevents the two pressures from equalising? I'm imagining something like two connected balloons with equal pressures in each (perhaps one at the front and one at the back of the car). The car is effectively pushing air into one of the balloons (the front) leaving less pressure in the other. These pressures can't equalise because the friction between the two balloons slows the transfer of air so it can't 'catch up' to the rate that the car is pushing it. Is that right? You can ignore the balloons that just was to help me consider the two separate areas of pressure...

Your detailed explanation is great. It does lead me to ask this question.
My Honda Insight like most cars today has a camm back.
What type of CD improvements would one expect if I made a tail section that brought it to a point? I guess the terminology would be boat tail?
Mike

Hucho's book provide an example for this.

The back of the insight has roughly the same shape as the Mercedes C 111 III, though shorter and thicker.

http://www.autoblog.com.es/fotos/mercedes/c1113.jpg

On the attached image, the original shape they started with was approximately one third the lenght from the rear wheel skirt.

They tried different lenghts from 0 to 1.5 meters, beyond which there was no improvement in drag.

The function between boat tail lenght and drag reduction in this case was not linear and went up to a 25% reduction in drag.

They settled for roughly 60 cm which lead to roughly 18% in drag reduction.

Just wanted everyone to look at the heat-exchanger outlet at the base of the windshield of the C-111.This is where Kamm did his research and for what he's famous.The radiatior air re-energized the flow over the roof and allowed it to remain attached until he arbitrarily chopped --off the rear.The flow would have otherwise stalled and separated,making the "Kamm-back" a non-starter.The C-111 windshield is also ideal ($3,000 at KIT CAR ).Hucho also says they could have lowered drag even more with extra length,even though graph does not reflect it.Great pic!

Where is the original post?

OfficeLinebacker -

Ibid.

CarloSW2

Good morning Agent Johnson, what you have missed is highly classified information. The original post has self destructed. :p

Interesting this post has been pulled up from the dead, but I removed it because it didn't really seem relevant to the site. In depth discussions/explanations seem a little out of place in a forum. The internet is an ADD person's paradise. :) If anyone is interested, I'll repost it (if I still have it)...if not, into the graveyard it goes with the other stuff I've learned. :o

- LostCause

In.

I vote to bring it back -- good information is good information. :thumbup:

RH77

I can't edit the original post anymore. Here it is, MS Paint graphics and all. I'd advise everyone to go to the bathroom before you start reading...:p

Simple answer, if you speaka da chinese:

It evens out the momentum of air molecules in the boundary layer, giving kinetic energy to the slowest molecules at the body surface most susceptible to reversing direction due to an adverse pressure gradient.

The long answer, in English please:

I think things will make most sense if I am very thorough…and I’ll have the added benefit of discovering my own shortfalls in understanding! Here are the concepts as I have worked them out in my mind. Let’s start with the fundamentals.

The basic of basics, maybe it will come in handy. Fluid can only act on a body through two types of forces:
1.) Shear forces
2.) Pressure differential

For much of the early history of aerodynamics, people theoretically predicted that all the pressure forces acting on a body would equalize and cancel out. The classic example is the sphere, which seems to be a mainstay in understanding fluid flow.

http://i264.photobucket.com/albums/i...doxResized.jpg

I remember asking in class how that center streamline went through the sphere, but the teacher wasn’t interested in such trivial matters. For those interested in history, the idea was put forth by Jean le Rond D’Alembert, an 18th century mathematician (among other things), who published the concept in 1740. Today, this theoretical anomaly is known as D’Alemberts Paradox. What stumped people for so long was that people didn’t take into account friction and the resulting effect of viscosity. Viscous flow wasn’t fully developed until Prandtl published the boundary layer concept in 1904.

The boundary layer describes the region of fluid around a body that is affected by friction. Specifically, it involves the completely stationary fluid at the body’s surface to the fluid far enough away that has been able to retain 99% of the free stream flow velocity. Essentially, any air that is slowed by the presence of the body is within the boundary layer. An interesting aspect of this phenomenon is that the body essentially grows in size, at least as far as the free air stream is concerned.

http://i264.photobucket.com/albums/i...ndaryLayer.jpg

The boundary layer doesn’t necessarily look like that, but it illustrates that the body has been slightly thickened. Graphically, aerodynamicists represent this slowing of air through a velocity profile. It relates the velocity of the air relative to its height above the body. The further you are away from the body, the closer the air velocity becomes to the free stream air velocity (hence, no drag).

http://i264.photobucket.com/albums/i...ndaryLayer.jpg

First, for those not familiar with these symbols: V∞ = free stream velocity; y = height above body; V = boundary layer velocity. The solid line represents a laminar boundary layer, the dashed represents a turbulent boundary layer. The fundamental difference between laminar and turbulent boundary layers is the presence of streamlines. A streamline can be thought of as a layer of air completely isolated from adjacent layers. In effect, the edges of a streamline act as an impermeable wall. The laminar boundary layer is composed of ordered streamlines, who share no momentum (mass*velocity). These streamlines allow molecules to flow past each other with much less friction, so slow molecules are less likely to speed up and fast molecules are less likely to be slowed down. The turbulent boundary layer has a virtual absence of streamlines, as air molecules freely travel throughout the boundary layer. This allows higher velocity (i.e. higher momentum) air molecules to come into contact with slower molecules and transfer their energy. This sharing of momentum leeches energy from the air molecules already near free stream velocity, since the energy they transfer to slower molecules slows them down. The slowing of these once fast molecules causes the adjacent free air stream to slow, causing the boundary layer to grow in height. All this to come to one conclusion! Laminar boundary layers cause less skin friction drag because there is no sharing of momentum between streamlines, but the velocity profile is not very equalized. Turbulent boundary layers cause more skin friction because there is a free transfer of momentum, but the velocity profile is much more equalized throughout its height.

A couple more ideas, then I’ll get to the “answer.” Generally, the laminar boundary always exists, even in a body immersed in turbulent flow. The reason behind this is the transition point. The free air stream is (usually) orderly, being made up of streamlines, but is subject to the 2nd Law of Thermodyamics (removal of energy = increase disorder). At the front of the body, the flow is laminar because no energy has been dissipated. The further along the body the flow travels, the more it loses kinetic energy to heat through friction. The lower the flow’s energy becomes the greater its disorder becomes, until it becomes so disordered that streamlines are broken and the flow becomes turbulent. The change between laminar and turbulent boundary layers is called the transition point. It can be caused by changes in the Reynold’s number (ρVx/μ; i.e. changes in air density, velocity, viscosity, distance traveled) or by the surface itself. A dimpled golf ball still has a laminar boundary layer, it just simulates a higher Reynold’s number by causing the transition point to occur earlier.

http://i264.photobucket.com/albums/i...itionPoint.jpg

D’Alembert’s paradox, the lack of pressure differential on an object in inviscid (frictionless) flow, failed to account for shear forces. What is so interesting is that shear forces are responsible for pressure differentials even though they are two completely different forces acting on a body. The reason shear forces (friction) account for pressure drag is all due to the transfer of energy into heat.

Prandtl, the man who introduced the boundary layer concept, gave the best analogy. Here it is, modified for clarity by an aerodynamicist named Hoerner. Imagine a rollercoaster car sitting at the top of a drop. When it loses height it picks up speed, until it reaches maximum velocity at the bottom of the drop. According to D’Alembert’s frictionless assumption, you could predict that the rollercoaster car would exchange its speed for height on the other side of the drop and make it to the top.

http://i264.photobucket.com/albums/i.../EnergyMap.jpg

Intuition tells us that the rollercoaster car wouldn’t make it back up to the top, but why? Friction. Some of the kinetic energy of the car is being converted into heat due to friction. What that means is when the car tries to cash in its K.E. for P.E., it is going to come up short and roll backwards. In this system, gravity is the potential energy while velocity is the kinetic energy. In aerodynamic flows, pressure is the potential energy and velocity is the kinetic energy.

Ambient pressure is turned into fast moving air due to a decreasing pressure gradient (pressure going from high to low over a distance). This low pressure is what creates lift in wings, which is great and all, but it needs to turn into ambient pressure again (via an adverse pressure gradient). D’Alembert figured that the fast moving air would slow down and re-pressurize to ambient. Apparently, D’Alembert has never been on a rollercoaster. That fast moving air has already lost some of its energy to heat due to friction, therefore it can’t re-pressurize to its previous state. What happens is that lower pressure air forms in the back of the body, causing a pressure differential. This pressure differential is what is termed pressure drag.

Pressure drag is bad enough at this point, but it goes to hell when the flow separates from the surface. If you remember the velocity profile of the various boundary layers, you notice that the velocity is slowest near the surface because it encounters the most friction. These molecules have essentially changed most of their kinetic energy into heat, so they are going to get royally screwed when it comes time to cash in K.E. for P.E. And royally screwed they get. The slowest of these molecules have so little energy that not only do they stop before reaching the end of the body, they “borrow” potential energy from the free stream flow by traveling backwards. Aerodynamicists have termed this reversed flow as being separated. Of course, air molecules haven’t physically separated from the body (i.e. there isn’t a vacuum), it’s just that flow has stopped in that region. Above this region, the fast moving particles of the more energized boundary layer continue to flow.

http://i264.photobucket.com/albums/i...aratedFlow.jpg

Just like air sucking into a Snapple®, high pressure air wants to suck into the low pressure void. Normally the kinetic energy of the flow would prevent this, but its absence causes some air molecules within the free stream flow to change momentum. This change in momentum, which entails a force, is the pressure drag. Separation causes much more ambient air to change momentum than non-separated flow. Separated flow really is at the limits of my comprehension, because it involves vortexes and extremely complicated flow patterns.

Since separated flow is so bad, aerodynamicists are willing to make some sacrifices to prevent it even if at the cost of some other drag. If you remember the velocity profiles of laminar and turbulent boundary layers, you’ll recall that the turbulent boundary layer has a “fuller” profile. This fullness simply means that air is flowing faster closer to the body surface. This redistribution of momentum means that molecules closer to the surface will have more kinetic energy to cash in when it comes time to re-pressurize. If you recall, this redistribution is at the cost of increased friction due to the removal of streamlines. Turbulent boundary layers increase skin friction, but decrease pressure drag. Laminar turbulent boundary layers decrease skin friction, but increase pressure drag. Neither is better overall, just in certain applications. Horses for courses.

Even turbulent boundary layers run out of steam, losing much of their kinetic energy to heat. In this case, turbulent boundary layers grow larger and the disparity between slow moving and fast moving molecules becomes greater. Even though the proportion of the energy being distributed is roughly constant, the amount of low energy molecules grows (the area under the shallowest part of the exponential line grows). Eventually, even with turbulent flow, you will get separation. To combat this phenomenon, boundary control devices have been created: vortex generators, sucking, blowing, an orgy of methods, really…

They all seek to “re-energize” the boundary layer (aka, reintroduce the kinetic energy lost). Boundary layer blowing and sucking do this artificially through an external pump, but vortex generators act as a grand version of the turbulent boundary layer. Vortex generators force high velocity air molecules near the top of the boundary layer down to the surface by swirling it. Just as the turbulent boundary layer increased the sharing of momentum by breaking up streamlines, vortex generators increase the sharing of momentum by adding a larger vertical velocity component to the boundary layer. The issue with vortex generators is similar to that of the turbulent boundary layer: you increase drag. Vortex generators create drag to produce the swirling action of air. The key is to determine when the benefit of a vortex generator overcomes its pitfalls. It’s a huge balancing act that is usually solved empirically (or semi-empirically via CFD).

If that was a lot to read, imagine typing it. Phew… I hope the article is generally correct, but I am not an aerodynamicist so caveat emptor. I appreciate corrections or improvements…it’s for everyone’s benefit. If there is any vagueness (which I hate in describing/learning aerodynamics, hence the article length) than feel free to contribute. In any case, I hope that answered your question.

- LostCause

ah i'll end up printing it

Thanks for reposting! There is a fair bit of hard work here... even more hard work for me to figure it out...:thumbup:

You bet me to it! I was going to say I'm printing it and taking it to the bathroom with me! Ha!

I think I've figured out "Step 1" of understand flow separation, now I'm trying to work on "Step 2." It's akin to learning how to put a computer together, then trying to tackle building one completely from scratch...many orders of magnitude greater in difficulty.

It still boggles my mind to think of this phenomenon at the molecular level. If I can't visualize little atoms passing through the flow, then I don't really believe I understand the concept. In any case, here are a few diagrams I created, borrowed, or assembled from the internet to aid my learning.

Sphere - Laminar Flow
http://i264.photobucket.com/albums/i...aminarfast.gif

The flow around this sphere is completely laminar (note the low Re #). Essentially, the viscosity of the fluid is dominating the flow pattern. Those bubbles you see separate off are called the "Von Karman Vortex Street" since it was Von Karman who first studied the phenomenon. In reality, DaVinci observed them first...

In any case, I've tried paying particular attention to the bubble separation point. It helped me visualize the high pressure, low pressure interaction that occurs during flow separation. To me, it almost seems like high pressure air is finding any weakness to fill the wake bubble. This was a MAJOR pain in the ass to create, by the way. :p

Airfoil - Upper Surface Pressure Distribution
http://i264.photobucket.com/albums/i...Gradient-G.jpg

The shaded graph only represents pressure over the upper surface of the airfoil (which is symmetric). What boggles my mind here is how rapidly high pressure air transforms into low pressure air. It is nearly instantaneous in position. You can also note the re-emergence of high pressure air at the tail section.

CFD Pressure Distribution
http://i264.photobucket.com/albums/i.../cartgrid2.jpg

I found this graph immensely helpful because it showed the pressure distribution around the airfoil, rather than just at its surface. Seeing the gradient from low to high has helped me visualize the total effect of the airfoil on the free airstream. I think its important to understand the action of molecules in the total fluid flow, not just the surface.

Brain Storming
http://i264.photobucket.com/albums/i...radient-PD.jpg

This is just an image I created while brainstorming different ideas. I figured I might as well include it. The upper left was my attempt at understanding the total pressure distribution before I found the CFD plot. The right is my attempt at visualizing molecular changes in pressure. I'm having a hard time separating pressure from density at the molecular level. Lastly, the bottom right was another attempt of mine at developing a total pressure distribution. Those dots are supposed to be molecules, which I intended to use to help me visualize changes in pressure.

Actual Sphere Drag
http://i264.photobucket.com/albums/i...SphereDrag.jpg

This graph goes alongside the one presented in the explanation. This is a generic flow pattern that experiences viscosity. What I found interesting was the pressure distribution around the sphere. The trailing pressure seems directly related to the magnitude of the low pressure.

The lower the pressure the sphere experiences, due to its curvature, the greater its trailing pressure drag will be. It seems that by killing "lift," you also decrease the potential for pressure drag. From an airfoil perspective, it's interesting to see that the wake actually kills potential lift. It should also help some visualize the repressurization of the flow as it slows down.

Good look in your learning endeavors. :)

- LostCause

I've heard that oscillation more commonly referred to as a Von Karman Vortex Street. I prefer that because it sounds like it has more to do with autos.

You are right. Interesting how memory shifts stuff around. :p I've edited the post for the correction.

- LostCause

In terms of how turbulent flow scales down to the molecular level, Kolmogorov's work

http://en.wikipedia.org/wiki/Kolmogorov_microscales

might shed insight into reconciling your thoughts. In a nutshell:

Thank you. I'll take an in depth look at that when I'm in the library again. I love insight. Ideas/clarifications are definately welcome. :)

- LostCause

Deriving them is the easy part. Solving them, or even proving existence and uniqueness of a solution, is worth a cool $1M, see http://www.claymath.org/millennium/. By the way, they look slightly less daunting using vector notation: http://www.see.ed.ac.uk/~johnc/teach...uids4/img3.gif

That hasn't been solved yet by removing time T as a factor and just treating it like another dimension/degree, thus making the 3-D solution quartic and the 2-D solution cubic?

aero-masochizm
 

LostCause,I'm crying "UNCLE------UNCLE!!!!!!!!!! I've been looking at the formula you posted.It's delicious! So good in fact that I poked at both eyes with an ice-pick and put my head in a vise just feel better after viewing it. And as resourceful as I consider myself to be,I've been unable to track down this elusive quarry.I looked at everything I have on fluids,aero,aeroelasticity,dynamics,vibration,phys ics,Calculus,thermo,and aero-mechanics,and can't quite isolate your equation.Some of the symbols are a bit hard to read and some of the subscripts to the symbols are just too small for my aging eyes to discern.My texts are all dated now and I suspect that more current versions would help me,however,I was hoping you could list your source and save me some investigative work.If I can see the text in full-scale,I might be able to deduce whats going on.My silly-wild-___-guess is that it's a differential equation of continuity for steady,incompressible flow,with curvilinear orthogonal coordinates.I see elements of the equation in the work of Euler,Prandtl,Bernoulli,Navier and Stokes.Some of the symbols can have more than one meaning,depending on the discipline.Without a graphic to depict the "system" its hard to know exactly what the context of the equation is,as it makes no reference to boundary layer type or Reynold's numbers.Since Cp,which is a function of Reynold's number, is absent,one can't speculate as to where you'd expect separation to occur (as in a flat plate which has virtually total separated flow).There are so many partial derivatives and symbols which might denote,for instance,velocity potential of irrotational flow or angular displacement,radius or symmetric viscous stress tensor,that its difficult to arrive at a unifying theme.The equation is very exotic and so sophisticated, I'm presuming that its an algorithm for computational fluid dynamics which can deal with flow separation,however for whats shown,a newcomer like me will never be able to crack it.Please expand on this one for us.For the trouble and cost to operate wind-tunnels,there's definitely a big future for CFD and I'd like to at least have a cursory understanding for the code used in the programming,however I'm stuck at top-dead-center.Appreciate you posting it,and hope you can fill in some blanks.Thanks again,Phil.

Partial differential equation ;) So that should clear up the little lowercase delta symbols all over the place :D


That's the sort of thing a professor would show a class to scare everyone :p I can't see all the details, but I'm fairly certain that's in a spherical coordinate system -- note the "r" direction, "theta" direction and "phi" direction (if you don't know where to look for that, let me know and I'll go in detail).... If that's an "r" and I'm not misreading it, that's almost a dead giveaway of some cylindrical or polar or spherical shenanigans :p


That's no algorithm - but you're very right in that it's exotic :D Finite element algorithms will probably have iteration sub or super scripts.

If it really is a spherical coordinate system, it's probably not worth worrying about for car application... Cartesian coordinate systems (x,y,z or whatever letters you prefer) are very practical as you can quickly see forces in intuitive directions - up/back/side --> lift/drag/??? (if you're getting a side force in a symmetric object, there's a problem with your CFD)

Whoa, I posted that image as a joke in reference to the length of my original post.

Trebuchet03 is right as it's the Navier-Stokes equation derived in the spherical coordinate system. I ripped the image from Wikipedia solely because it looked like a jumble of incoherent equations.

I couldn't tell you what the equation meant as I stopped my math at vector calculus. :o It was a joke. I might as well have posted Einstein's derivation of E=mc^2 in tensor calculus...

I don't profess to have mastered aerodynamics or mathematics. After a lot of effort spurred by my own curiousity, I felt I had finally gotten a firm understanding of the boundary layer in layman's terms. My only intent for this post was to help some people save the aggravation of getting a straight, thorough, firm understanding of what had been a question mark in my mind for years.

- LostCause

sphere and vortex sheet
 

I was thinking that in laminar flow,the separation would occur more forward.(are we talking laminar boundary layer here?) For the von Karman Votex Sheet,I was thinking this was only observed in 2-dimensional flow?,and not 3-dimensional,as with the sphere?

The laminar boundary layer does separate earlier.

You are right about the Von Karman Vortex Street. As far as I know, it only applies to two dimensional objects (i.e. cylinder). I have a bad habit of not differentiating between circles, cylinders, and spheres. The point of the image was to visually see the motion of flow separation.

- LostCause

joke
 

Thanks LostCause,trebuchet03,OfficeLinebacker,and PA32R for dragging me into at least the 20th-Century.I only had a year of calc. and I've had to wear an oxygen mask when looking at these rarefied formulas! I want to know where all these things come from,so now,with all your insights,I'll go back to the books(and wikipedia).If I get in trouble,perhaps one of you kind souls can help bale me out.Thanks to all,I think I can sleep now.