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Power output of vertical axis water turbine

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Old   March 16, 2015, 05:17
Default Power output of vertical axis water turbine
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Allan L.
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Hi all,

I'm currently a 4th year Naval Architecture student, and for my individual thesis I've been running simulations on a 3-blade water stream turbine at different design tip-speed ratios, measuring the moment on the shaft.

My question is how to calculate the power output, and henceforth the Cp from the measured moment.

Do i integrate the moment over 1 revolution, or average moment over 1 second, or something else? Really struggling to know which is the correct way forward.

Would appreciate any comments, thank you!
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Old   March 16, 2015, 10:07
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You will want to create a report and monitor to pull out your moment (toruqe) as well as the rotational speed (if you don't already know it). Then create an expression report that is the the product of the two to give you power. Same for Cp, this is a function of your operating condition and rotor area, right? Not sure if your naval definitions are different from my aero definitions. Make sure to set the correct units on the expression reports, too.

With the power and cp expression reports defined you can then right click and create a plot and monitor, (I would do separate plots since there is going to be a huge difference in magnitude betwen them. Now, run your analysis.

I will assume for now that you are doing steady state and you are seeing an oscillating power and cp plot. When the oscilations are stable, your residuals look converged, and your other values of interest (rpm, thrust, flow rate, etc...) have converged then stop. Right click the plots in the tree and select tabulate. This will display a table of the plot values that you can export to excel. Then just average several oscillations, do more than one, and make sure you capture full peak-peak periods. The average is basically the same as integrating over time. Do this several different times to make sure that your selection isn't significantly impacting your averaged value.

That being said, you would be better off not doing steady state analysis and resolving each time step fully. However, that may be beyond the scope of an undergrad project.
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Old   March 18, 2015, 07:11
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MBdonCFD, thanks for answering.

Yes you're correct the equations are the same, and we've realised this.

There is one thing i forgot to mention which i think you have assumed our turbine is under free motion... However right now we're running it under forced motion, as we are looking to find a curve by genetic algorithm to optimise the turbine efficiency by individual blade pitch control.

This is where most of my worries lie, because the turbine is rotating forcibly at a fixed speed, we're not sure exactly how this is impeding our resulting moment and hence our power output... Obviously the turbine is steadily rotating, but the moment calculated in 1 revolution ranges (for an example tip-speed ratio of 2.4) from 100 - 2500 Nm. For lower TSR there is partly negative moment on some section of rotation. Residuals converged.
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Old   March 18, 2015, 08:13
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My reply was a little misleading. I didn't assume free motion, but I see how you could have thought so. Sorry for any confusion.

I haven't ever worked a any water turbines, but I have done more than my fair share of vertical axis wind turbines. In my experience we typically ran a range of TSR's to get a cp curve, then you determine what your optimal TSR is. To really simulate 'free motion' you need to use a multi physics package. I think star-ccm+ will couple with some of them, but we never went that far. There is more at play than just mass distribution in the blades, you have to consider generator resistance, bearing losses, etc...

For a horizontal axis there are some great codes that couple BEM theory with basic dynamics to give you these kinds of answers. (Look at NREL codes, Aerodyn I think). However, I haven't ever seen one for vertical axis. That would have to couple double multi stream tube theory and the same kinds of dynamics.

Is this something you designed, or are you just analyzing?
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Old   March 18, 2015, 08:27
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Ah ok my bad, yes we're doing a very similar thing to yourself then in that respect so i have to thank you for your detailed first post.

As you said the free motion will need plenty of more considerations, would love to get some of this done but my deadline is fast approaching. Thanks for the codes you mentioned for horizontal-axis will definitely check these out.

The turbine is our own design, but it's based on a couple of previous designs to try and prove efficiency improvements.


Going back to my initial problem, to confirm what you're saying is to take the average Cp value over 1 revolution? And then do this for multiple revs and get the average of all that?
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Old   March 18, 2015, 09:12
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I would just do it all in one swoop. No need to eaxtract multiple revs, average each one, then average the averages. Just average over several revolutions to begin with. Just be sure to capture several full periods.
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Old   March 18, 2015, 10:16
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Yeah that's the way i've done it.

Now forgive me if i'm being completely stupid here, but i'm coming up with average Cp of around 0.7 doing the power output / (0.5*rho*V^3*A)
Do i then multiply this by the Betz limit because otherwise the Cp is too high...
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Old   March 18, 2015, 10:50
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Ah... You have stumbled on to an area of great debate. Luckily, I had a VERY good professor for my wind energy class. If you examine the classic Betz derivaiton, you will notice that it is specific to HAWT class. You will indeed find that there are several situations where this is seemingly violated. I ran in to this issue working with ducted HAWT. I found that if I just did my own derivation keeping in line with Betz's assumptions I got a more appropriate answer. I would imagine the same is true for VAWT, although, I cannot say for sure. Do the derivation or maybe google vertical axis betz limit and see what comes back.

Most people would just look at that and say, 'SEE?!? Betz was full of it.' Don't be that guy.
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Old   September 15, 2021, 16:15
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Edgar Alejandro Martínez Ojeda
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I made a code in C++, it's based on the double multiple stream tube model by Paraschivou, you can use water as a working fluid: https://www.youtube.com/watch?v=S64VQ1UgH18
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