# How to calculate vortex shed frequency curve, versus speed of the incident current

I have a current of air that hits a cylinder, and an hot-wire probe is measuring the velocity behind the cylinder. I have an array of measured velocity and a frequency.

How do I get the vortex shed frequency curve, versus speed of the incident current out of this? I am doing this in MATLAB. Basically I am not sure what any of the two variables are.

• I'm not sure what you're asking... you said you measured velocity and frequency, and said you need to plot frequency vs velocity. But then said you aren't sure "what any of the two variables are." Which two variables don't you know? There are only two variables specified -- velocity and frequency, and you measured both. – tpg2114 May 3 at 14:52
• @tpg2114 Aha... Okey thanks, I guess I just assumed they were different... That the "Vortex frequency sheed" is different from "frequency". – Niklas May 3 at 14:56
• Well, they might still be -- what is the frequency you measured? Do you mean the raw voltage output of the hotwire? Or did you have something else that converted the hotwire voltages into local flow velocities? Your question might still be a good one, but it's unclear what you mean currently. – tpg2114 May 3 at 14:57
• @tpg2114 I am quite sure what I have is the Velocity "of" the hotwire, so it was converted. It was measured at a frequency of 1000 Hz. I have an idea that it might be the frequency of vortexes, how often they develop. – Niklas May 3 at 15:01
• Okay -- I'll try to write up an answer to point you in the right way. – tpg2114 May 3 at 15:03

This sounds like it is something from a fluid dynamics laboratory class, because I recall doing something very similar in mine!

A hotwire measurement is intended to give you a velocity measurement at a location in space. It does this by passing electricity through a thin wire and fancy controllers try to keep the temperature of the wire constant by varying the amount of electricity used. When the air is moving past the hotwire, it cools it off due to convective heat transfer, and so more electricity is needed to hold the temperature. The faster the air, the more electricity required.

So the actual measurement reported by the hotwire directly is the amount of electricity used at each instant in time to hold the temperature constant. This means a few things... first, the hotwire has to be calibrated to a very well-known velocity. Second, it means there is a non-linear transformation from the electricity used to the velocity value, which depends on this calibration.

Depending on your data acquisition system, this mapping of electricity to velocity may be done automatically for you. Or, if your professor is sadistic like mine, we were given the raw voltage vs time outputs and had to do the mapping ourselves. So the first step will be to verify you know what your data is -- either the velocities directly, or the voltages that you need to convert to velocities based on the calibration curves for your particular device.

With that out of the way, let's look at the other parts of the measurement. You mentioned in the comments that the hotwire operated at 1000 Hz. That means it took 1000 data points per second. This means you will not be able to resolve any frequencies above about 500 Hz (due to the Nyquist frequency limits). Not a problem for shedding off of a cylinder, you'll easily resolve that frequency -- but think about what you might be missing at that rate. Is your flow fast enough to be turbulent? If so, will you capture the full turbulent energy spectrum? Not important to answer your specific question, but it's always good to think about what you are measuring and what you can and cannot do with that data.

As a fun side note, we had really long, unshielded wires connecting our hotwire probe to our acquisition system when I did this experiment. We were also sampling at very high frequencies and located rather close to college radio transmitting tower. We forgot all of this and didn't include filters on the lines... We ended up having to redo everything when we analyzed our data and realized that we had captured the radio signal instead of our turbulence.

Anyway, let's assume you have the velocities vs time from your hotwire at a bunch of different inflow velocities. For each inflow velocity, you need to find the shedding frequency. This means you have to take your velocity vs time measurements, and convert it into some kind of frequency measurement. You do this by taking the Fourier Transform of the dataset, which will give you the spectrum of velocities across frequencies. You'll need to lookup how to do this in MATLAB specifically, but if you search for "matlab fft" in your favorite search engine, you should find it.

Once you have your spectrum, you then just need to identify the largest peak (highest amplitude) and see what frequency it occurs at. That will be the frequency with the most energy for your system. That will most likely be the shedding frequency (barring anything strange in your experiment). But think critically about the value you get, because it could be misleading. If it peaks near 0 Hz, what does that mean? Is that actually the shedding cycle, or is there something that should be done to the data first? Repeat this for each inflow velocity and you will get the data you need to plot.

As a fun bonus part -- are there any non-dimensional numbers you can form using this information? You will have the frequency and inflow velocity, and you know some things about the cylinder like it's diameter. If you use this information and make a non-dimensional number, how does that non-dimensional number change with inflow velocity?

• Thank you very much, a lot of good information! – Niklas May 3 at 15:28
• Very helpful, thanks again! Did a hann window on the data as it had an enormous peak at the start of the signal. link does this look good, what do you think? yeah i do also have the diameter, and do have to make a dimensionless number. – Niklas May 3 at 18:16
• @Niklas Well... I'm going to leave it for you to interpret the results... First, note that it's symmetric about 500 Hz. Think about what that means, and look up what the Nyquist frequency limits are. If you sample at 1000 Hz, can you resolve 1000 Hz? Or does a negative frequency look like a positive one? Second, consider what it means when you have a strong peak at very very low frequencies and how that relates to the total signal, keeping in mind that a signal can be decomposed as a mean and a fluctuating component. – tpg2114 May 3 at 18:20
• Also, about non-dimensional numbers... you never have to compute them. But often, the physics takes on nice features when you do. For example, maybe it's constant, or it is linear, or it has some other well-defined shape when non-dimensional that it otherwise wouldn't have. Think about this case -- you have a roughly linear function from your data, which looks okay. If you had a non-dimensional number, maybe it becomes constant? That would be helpful, right? – tpg2114 May 3 at 18:23