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zonexo September 26, 2006 19:48

Feasibility of wind tunnel testing at Re~10^4

I know this is a bit off topic but I believe ppl here should 've the knowledge to help answer this question....

How difficult is it to get cl/cd of airfoils for Re~10^4 in wind tunnel. Currently, the objective is for static case. However, it may be extended to heaving/pitching cases.

I tried to do an approximate calculation using fluent to get the cd of an airfoil at Re~10^4. It's around 3.8e-2. For a wing of 15x3cm, the drag's around a few grams. Are load cells of this range popular? I've not used load cells before but a search on the net seems to give me the impression that they are on the expensive side. Am I right?

Hope someone can help. Thank you.

Jason September 27, 2006 09:32

Re: Feasibility of wind tunnel testing at Re~10^4
Well, it depends on your situation. Based on the model size you listed and the questions you're asking, I'm assuming you're looking to do testing in a university tunnel. Or is this an older, un-instrumented tunnel you're trying to use? (I've been in both situations... self-instrumentation can be difficult)

Load cells can get expensive, and in the "few gram" range, they are rare. Omega puts out an "ultra-low capacity bending beam load cell" that can go as low as +/-2g, but it's a special order and the +/-10g range cell is just under $1000 (US dollars) so I'm guessing the 2g range is at LEAST $1000. Not to mention the lead time for this... since they aren't common, they're typically built to order (the Omega site mentions 14weeks for the 10g cell and doesn't even list an estimate for the 2g cell). And all of that only measures in one axis! Multi axis load cells typically bump the price up, the size up, the lead time up, and the accuracy down.

Another option that I've used is to build my own transducers. All a load cell is, is a strain gauge mounted at a specific location on some material (typically a metal) which has a specific shape and the whole assembly has been tested to give a specific output/input calibration curve (typically mV/lbf or mV/N)). If you're in a university, there's typically some type of structures group, and you could talk to someone there about available strain gauges, and there may be a lab tech that could even mount them for you (that's the hardest part of dealing with strain gauges... it takes a skilled hand to do it right). Strain Gauge Rosettes are a nice option if you have them because you can get all of the principle stresses out of them (and the linear response of metals below their yield stress makes it easier to isolate the components of the force). Once the strain gauges are mounted and the whole thing is installed in the wind tunnel, then you load the system with weights and build your calibration curves. I'm making this sound easier than it is... the metal you use for your load cell (the part that the strain gauges are mounted on) has to be carefully considered based on what you're trying to measure... remember a strain gauge only picks up local strain (best represented by bending stress) so if you're bending on all three axis, then isolating components can become difficult and/or impossible. Look at typical multi-axis load cells and you'll see many internal beams... each of those beams is there to help assist in isolating a component of the force (measuring the 'axial' stress in two beams at different heights lets you isolate the 'axial force' and the pitching moment (difference in parallel forces * distance between mesaured forces = moment).

That's JUST the transducer side of all of this. After this comes the data acquisition side of things. Many (probably most) commercial load cells don't come with data-acq hardware and/or software, so you'd have to get that as well. If you design your own transducer, there's wheatstone bridges to consider, A/D converters, and data acq hardware/software. At a university, you may have all of that available already.

For "steady" measurements you'll have to do some time averaging of the data... there will be noise in the measurements and you'll want to average that out. For "transient" measurements, this becomes more difficult. You're going to want enough points to create a well defined transient curve. For each point, you're going to have to collect several measurements and average them. Lets say you're pitching at 1Hz and you want 20 points/cycle... you're probably going to need at least 10 measurements/point... that means you have to collect data at 200Hz (1Hz * 20points * 10measurements). Those numbers are just guesses... they depend on your pitching cycle, how many points you want to accurately define the pitching curve, and how noisy your signal is.

If you're at a university, it's very important to find someone who's done data acq before so they can help you. Also, find people who've worked with strain gauges for their support, and work along side the people who are going to be building your hardware and mounting your strain gauges to make sure you're designing something that can actually be built.

If this is a university, another good resource is past work. Someone else may have already done all this work for you. Ask around, and do a lot of research.

Hope this helps, and good luck, Jason

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