Investigating Separation

Nearly a year ago, I was sitting in an incompressible flows class when the professor said something I had never considered before. Loss of lift over an airfoil after stall, she claimed, is caused by a pressure increase due to flow separation over the upper surface.

 
This was contrary to everything I thought I knew about separated and attached flow. Keep flow attached, the conventional wisdom goes, over a tapered shape for greatest pressure recovery and lowest drag (and “zero lift” on a ground vehicle, if you believe some people online, which you shouldn’t); if the flow separates, the pressure drops behind the separation point. Yet in this case, it must be true that separation increases pressure—otherwise, airfoils would not lose lift in stall.
 
Conventional wisdom, as is so often the case, does not tell us the whole story. The effect of separation on surface static pressures and, consequently, lift and drag can be complicated. To investigate, I decided to run some tests.

You might notice that I repurposed the trailing-edge spoiler from my tail testing for this experiment. Reuse materials as much as you can and testing can be quite cheap, often costing just a little of your time after some small initial investment in materials and equipment.

Test 1: Separating Flow Over a Hood
 
First up, I’ll measure pressures down the centerline of the hood of my car. I know from having done this before that I can expect to find negative static gauge pressures here, but what will happen if I use an angled board to separate the flow near the front of the hood, similar to what I did on my truck a few years ago?

Test 2: Separating Flow Over a Curved Roof
 
Like Test 1, in Test 2 I’ll use the same board to separate flow but this time over the roof, just about at the roof peak. I know from having measured pressures here in the past to expect the lowest static gauge pressures anywhere on the car to show up here. Does detaching the flow over this nicely curved surface raise or lower those already strongly negative pressures in the flow downstream of the separation edge?

Test 3: Separating Flow Over a Backlight
 
Finally, for this last test I was inspired by something I’ve noticed on production cars. For a few years now, short overhangs just ahead of and near the outside edge of the backlight have appeared on a number of cars:

Image credit: BMW.

Image credit: Kia.

Image credit: Motor Trend.

Image credit: Toyota.

Image credit: CivicX.com.

What’s going on here?, I wondered. Sometimes these are affixed to cars with backlight angles that are fairly steep (such as the bZ4X) but more often they show up on cars with smoothly tapered glass that should be supporting attached flow and moderate pressure recovery; you can see that the 10^th-generation Civic Type R even included vortex generators in the section between the two fairings, probably to ensure attached flow there. As I thought about it, I came up with a hypothesis. I know from measuring pressures on my Prius’ rear window that there are lower pressures toward the outside of the window than the center (remember, the flow over cars is strongly 3-dimensional). Perhaps separating the flow over just the outside edge of the backlight can increase pressure there, reducing both drag and rear lift? As far as how that might work, my guess is that the trailing vortex that forms along that edge is causing the drop in pressure there; using a fairing to deliberately cause flow separation might move the core of the vortex away from the body and raise pressure.
 
So, for my last test I decided to mock up some fairings and measure pressures along the window with and without them in place. Judging by production cars, these don’t need to be very tall—especially on the Kias and BMW above, they look like they’re not large enough to even poke through the boundary layer. You can estimate boundary layer thickness on your car by

where ρ is air density, v is freestream velocity, L is characteristic length (i.e. the distance from the nose of the car to that spot, measured along the road—about 11.5 ft here), and μ is air viscosity. I can calculate the atmospheric parameters using my known altitude (740 ft) and measured temperature (75° F) in the atmospheric calculator I had to build for a class last fall (alternatively, you can use standard atmosphere tables—although they typically do not account for temperature difference from standard, ΔISA—or an online calculator). This gives a boundary layer thickness there at 65 mph of 2.2 in. I dimensioned my mockups to about half that height (since my car has spent the vast majority of its life at that speed or below, and accounting for the fact that there will be some small area of laminar flow near the front of the car which means this relation for fully turbulent flow overestimates δ—making them slightly smaller ensures they don’t stick out into freestream flow even at highway speeds). Then I took measurements both ahead of and down the window with and without the fairings:

Results and Discussion
 
All pressure measurements above are static gauge pressures, two-way average at 80 kph. Measurement locations are 100mm in front of the leading edge of the spoiler, 100mm behind the trailing edge, and 300mm behind the trailing edge.
 
Look closely at the results and you’ll appreciate why I mentioned that the effect of separation on static pressures can be complicated. By separating flow at three different spots on my car, we can see this firsthand: on the hood, static pressure downstream of separation is increased; on the roof, static pressure downstream of separation is decreased; and finally, on the backlight, static pressure downstream of separation has no measurable change. Clearly, the behavior here is a lot more complicated than “attached flow has higher pressure and separated flow has lower.” It looks like it matters where on the car the flow separates and what the local flow field looks like.
 
Also note that my hypothesis about the effect of backlight fairings on my car was incorrect. It may be that these relatively coarse pressure measurements aren’t sensitive enough to capture whatever change occurred, or it could be that my quick fairing mockups were not dimensioned correctly (maybe they need to be taller? Or wider?), or it could be that the flow over my car simply behaves differently than the cars in the images above due to differences in their shapes. The Prius has an inset rear window, for example, where both those Kias appear to have flush glass.
 
Finally, since I artificially induced flow separation using a spoiler, you probably noticed as well that right behind the spoiler (in its “shadow”), pressure did consistently decrease. However, I was more interested here in observing the behavior further downstream. That said, one major difference between these tests and the airfoil example which prompted this testing is the artificial inducement of separation; the easiest way to do that is with an inclined edge, so the behavior may be different than if I could, say, change the inclination of the entire car body to create separation somewhere that previously supported attached flow. But these quick tests do show that the effect of separating the flow where it was previously attached is not as simple as you might think—something to keep in mind as you investigate the behavior of fairings and spoilers on your own car.