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turbomachinery coordinates m', theta vs m, r*theta

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Old   April 27, 2011, 16:34
Default turbomachinery coordinates m', theta vs m, r*theta
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Hi,

I am currently writing a small tool which helps me to set up blade geometries in a turbomachine.
In order to define the blade camberlines, I am using either a m' / theta (m' = m_prime) or a m/r*theta (m = meridional coordinate) coordinate system. I found both definitions in the handbook of Mises (Drela).

Now, I am asking myself which coordinate system is more senseful. I know that some "comercial" tools prefer the m'/theta-definition because it shell be angle-preserving - but why is this not the case with m/r*theta? Can this be proven mathematically?

Is the m'/theta coordinate-system senseful if the fluid is _not_ following a streamline (e.g. in a deswirler which turns the flow from radial to axial), as described in the mises manual?

Thx for the help.
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Old   September 1, 2013, 22:01
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Hi,

My reply is very late, but may be helpful. Based on my mapping experience based on both m-rtheta and m'-theta. I found that m'-theta is indeed angle preserving and m-rtheta was more dimension preserving. Recently I can across a paper that mentions m-theta transform also. But for my purpose I have used m'-theta for mean-line and m-rtheta for adding thickness and preserving absolute dimensions of LE , max thickness and TE.

Best Regards

Apoorv
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Old   April 20, 2015, 02:58
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Hi Apoorv,

This post is a while ago but hopefully you could help me. I am intrested in that coordinate tranformation. After searching a lot in the internet I could not find any usefull decriptions. The most of them only provide the formula m'=dm/r. But all my tries doesent seem to reach any success. Could you help me we that mapping process. Maybe with an simple example. I am very greatfull for your help.

Thanks
Kam

Hi,

My reply is very late, but may be helpful. Based on my mapping experience based on both m-rtheta and m'-theta. I found that m'-theta is indeed angle preserving and m-rtheta was more dimension preserving. Recently I can across a paper that mentions m-theta transform also. But for my purpose I have used m'-theta for mean-line and m-rtheta for adding thickness and preserving absolute dimensions of LE , max thickness and TE.

Best Regards

Apoorv[/QUOTE]
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