I'd advise everyone to go to the bathroom before you start reading...
Quote:
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Originally Posted by MetroMPG
Here's a question: Is there a simple answer as to why introducing a small amount of turbulence in the boundary layer (ahead of the area where flow would normally separate) moves the separation point further downstream & reduces the size of the wake?
Or does that fall into the category of thinking up questions to ask god? :P
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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.
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.
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).
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.
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.
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.
Just like air sucking into a SnappleŽ, 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