[alexey7783]

Hi Community,

my name is Alex and I'm a PhD student at the University of Erlangen-Nuremberg. Well, my PhD thesis comprises some numerical simulations, namely the outflow of a non-newtonian fluid from a cylindroconical vessel.

My "problem" now is the following. I need the shear rates that occur in this vessel. As this setup is axisymmetric, the best would be to get the shear rates in cylindrical coordinates. The flow in the cylindrical part (like in a tube) only has a axial velocity component, the angular and radial velocities are zero. Only in the conical part radial components occur. I am mostly interested in d(Uz)/dr, which is the shear rate of interest.

Is it possible to transform the cartesian gradient of the velocity into it's corresponding cylindrical counterpart? Does a simple coordinate transformation the job? If yes, how do I do that? I am not a professional programmer, the only thing that helps me is my basic java knowledge.

I searched the forum, and the only things I can find are not useful.

I would really appreciate your help and I am looking forward to your answers!!!

Best regards

Alex

[alexey7783]

Hi again,

perhaps I should concretize my question, so it is easier for you to answer.

So what i need is the shear rate in this vessel with the outflowing non-newtonian fluid. Mainly I am interested in d(Uz)/dr which is the L31 of the gradient tensor of the velocity field in cylindrical coordinates. My simulation yields the velocity in cartesian coordinates. For me the most reasonable way would be to transform the velocity in cartesian to cylindrical coordinates and than take the appropriate definition of the gradient of the velocity vector (meaning in cylindrical coordinates).

My concern is, if I take the transformed velocity vector (which is one thing I need to know how to do it, or better to say if it is already implemented) and then define a volTensorField L with grad(U) than the code uses the definition of the gradient of U in cartesian coordinates. Or is this fear without any reason because I can tell the code that this vector is in cylindrical coordinates and it takes
the right derivation on its own?

After solving this topic I will store the field values in a file to view it with paraView, which is already working (with the L31 entry in cartesian coordinates). Than I want to write a script which extrakts the mean shear stress, the standard deviation, the minimum and maximum value and perhaps the median. Are there already functions implemented that calculate the median and the standard deviation? The others I found already, and for the standard deviation it shouldn't be a big problem to compute this, but if it is already implemented...

Now I hope you get my point. It would be very kind and nice if you are able to help me!

Thanks very much in advance and my best regards!!

Alex