by Steve Smith
February 18, 1998
This project is an effort to resolve a problem with
two different sets of wind tunnel data for the same airplane, using computer
flow simulations of the airplane model inside the tunnel and also flying
in free air.
Last year, I worked on a project to design a new,
better winglet to put on the wing tips of the MD-11 jetliner. I got to
test my winglets on a small wind tunnel model (4.7% scale) of the MD-11
in the Ames 12 foot wind tunnel. At the same time, I tested the original
winglets so I could compare them.
Later on, after the test was over, I got the idea
that I should have tested the model with a standard wingtip ( no winglets)
for comparison. It turned out that a bigger model (7.25% scale) of the
MD-11 was going to be tested soon, so I arranged to make the comparison
of the original winglet with a normal wingtip during that test. So now,
I have one comparison on the small model, and one comparison on the big
model. I want to combine the results so I can compare everything together.
But the wind tunnel effects on the two models were different, and the
comparison doesn't work well unless I can correct for this size difference.
When air flows over an object, it can tell how big
the object is by how long it takes to flow past it. To compensate for
the difference in size, you can just make the flow go faster. This becomes
a problem because the speed gets close to the speed of sound, and the
flow is distorted by compressibility effects. It turns out that you can
also compensate for the model size by changing the air density. The relationship
of model size, flow speed, and density that is used to compare similar
flows is called Reynolds number. Theoretically, the flow over two objects
of different size is the same if the Reynolds number is the same.
For the two different scale models that were tested, the tunnel conditions were adjusted so that the Reynolds number and the Mach number were the same. If the influence of the wind tunnel itself can be compensated for, both these models should produce the same force coefficients. Force coefficients are basically the forces divided by the wing area of the airplane model. It is customary to compare force coefficients instead of actual forces, because the basic effect of size (a bigger wing makes more lift) is compensated for. This correction is not the same as the more subtle effect of Reynolds number, which affects the details of the fluid motion. Without the tunnel wall effects corrections, a comparison of lift and drag characteristics for the two models showed about 20% difference in drag for the same lift. This is a huge difference! I hope the wall corrections will compensate enough to make the results for the two models the same, as they should. We will see!