Critical Reynolds number and characteristic length

[ntdiemai]

What are the critical Reynolds number for fluid and characteristic length when a cylinder immerses and then rotates in the fluid (The fluid is initially static)?
Please suggest the critical number for the transition from concentric flow to laminar and from laminar to turbulent flow.
I would appreciate your answer!

 

[berkeman]

What are the critical Reynolds number for fluid and characteristic length when a cylinder immerses and then rotates in the fluid (The fluid is initially static)?
Please suggest the critical number for the transition from concentric flow to laminar and from laminar to turbulent flow.
I would appreciate your answer!

Is this for schoolwork?

 

[ntdiemai]

This is for my postgraduate research. I am working on a project which integrates material engineering and fluid dynamics.

 

[berkeman]

Advanced schoolwork is sometimes allowed in the technical PF forums, but only when you show lots of effort and show us your work so far. I'll move this thread to the ME forum where it will get better responses, but please post your research and work so far on this question. Can you post links to the reading you've done so far? What are the Relevant Equations? What simulation software packages do you have available to work on this? Thanks.

 

[ntdiemai]

Ok, I will do that :). Thank you!

 

[boneh3ad]

This smacks of a situation where you've not really dug into the problem too deeply yet. Have you done anything to try to arrive at a solution on your own yet? I don't think most of us would feel particularly compelled to do your postgraduate research for you.

 

[ntdiemai]

Hi, I appreciate your time for reading and replying to my questions. As a postgraduate student, I am aware that it is the most important for myself to learn, understand and solve my problems by myself before I seek help.

At this moment, I am still reading to gain more knowledge about fluid dynamics. Most of the available materials mention flow in pipe or flow past a rotating cylinder, which are not relevant to my problem which is about a cylinder rotating in static fluid (static here means initially static before the cylinder rotates). Also, as I understand, the critical Reynolds numbers come from the combination of practical experiments and theory. So definitely, I need relevant references. So far, I could found only two references relevant to my case [1], [2].

The two references suggested the same characteristic length and formula (shown below) for calculating of Reynolds number. However, they suggested different critical Reynolds numbers to assess the flow pattern which leads to different conclusions in the flow pattern for my problem although the input data, e.g. cylinder radius, fluid viscosity, etc., are the same when I used those critical Reynolds numbers. I am not having a deep enough knowledge in fluid dynamics to decide which reference in the two ones I found is suitable for my problem. That is why I need help from an expert.

The formula for calculating of Reynolds number from the two references which are consistent to each other:

Re = (ρΩ(b)^2)/μ
where ρ fluid density
Ω fluid velocity
b (characteristic length) cylinder radius
μ fluid viscosity

Critical Reynolds numbers from the references:
Reference [1] which was about a rotating disc in a static fluid. The suggested critical Reynolds number for the transition from concentric to laminar is 784, and from laminar to turbulent is 2x10^5.
Reference [2] which mentioned a rotating cylinder in a static fluid. The suggested critical Reynolds number for the transition from laminar to turbulent is 60.

References:
[1] R. I. Olivares, PhD thesis "The effect of sulfur on the dissolution of graphite and carbons in liquid iron-carbon alloys", The University of Newcastle, Australia, 1996.
[2] P. R. N. Childs and P. R. N. Childs, Chapter 6-Rotating Cylinders, Annuli, and Spheres. 2011.

 

[boneh3ad]

The rotating disc is not a great analogue here. Rotating disc have been extensively studied and are subject primarily to the crossflow instability, which dominates transition.

A rotating infinite cylinder, in contrast, is likely to be unstable primarily to Görtler vortices. It's a different physical mechanism so the correlations that work for one flow field won't work for the other.

 

[256bits]

the critical Reynolds number for fluid and characteristic length when a cylinder immerses and then rotates in the fluid

A problem for many.
here is a discussion of it.
https://engineering.stackexchange.c...-length-in-reynolds-number-calculations-in-gePipe flow - easy - everyone "knows" that the diameter( radius ) is the characteristic length.
Other configurations have to be looked up to see what has been used.
And other configurations have no look up, so you have to figure it out yourself, and that it seems is where you stand.

 

[ntdiemai]

I am thankful to bone3ad and 256bits for your kind answers. Also, thanks Berkeman for your kind assistance. Thanks for your helpful answers, I have my problem solved. I will keep learning to understand more about fluid dynamics.
P.S. I already share this forum on my facebook wall :).

 

[boneh3ad]

It's kind of odd to solve something like this so quickly. Generally, finding a simple correlation for transition Reynolds number is not possible. There are, of course, some examples that work out easily, like pipe flow, but this is more of an exception than the rule.

Really, it all depends on your goals here. You could probably concoct an experiment that does a good job of coming up with some decent results for your model. You'd have to take into account the cylinder size and the size of the fluid domain around it (if it becomes too much of an annulus, you'll get Taylor-Couette flow).

However, if you are trying to actually model transition in a situation like this, you'll end up with a pretty big project on your hands. Linear methods don't work well with flows like these because they produce substantial modification of the base flow, which then affects the stability characteristics of that flow. In other words, the problem rapidly becomes nonlinear.