The Mechanism Behind Flow Separation

[OfficeLinebacker]

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:

Turbulence causes the formation of eddies of many different length scales. Most of the kinetic energy of the turbulent motion is contained in the large scale structures. The energy "cascades" from these large scale structures to smaller scale structures by an inertial and essentially inviscid mechanism. This process continues, creating smaller and smaller structures which produces a hierarchy of eddies. Eventually this process creates structures that are small enough that molecular diffusion becomes important and viscous dissipation of energy finally takes place. The scale at which this happens is the Kolmogorov length scale.

[LostCause]

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

[PA32R]

Originally Posted by LostCause

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?

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



juuuuuuust kidding...

- 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:

[OfficeLinebacker]

Originally Posted by PA32R

Solving them, or even proving existence and uniqueness of a solution, is worth a cool $1M, see http://www.claymath.org/millennium/.

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?

[aerohead]

Originally Posted by LostCause

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?

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



juuuuuuust kidding...

- LostCause

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.

[trebuchet03]

My silly-wild-___-guess is that it's a differential equation of continuity for steady,incompressible flow,with curvilinear orthogonal coordinates.

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


That's the sort of thing a professor would show a class to scare everyone 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

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.

That's no algorithm - but you're very right in that it's exotic 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)

[LostCause]

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. 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

[aerohead]

Originally Posted by LostCause

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


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.

Airfoil - Upper Surface Pressure Distribution


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


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


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


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 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?

[LostCause]

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

[aerohead]

Originally Posted by LostCause

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. 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

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.