I'm trying to find an empirical correlation for obtaining the critical Reynolds number in a 180-degree bend/curve/elbow with a circular cross-section (See the figure). I've searched for a lot of papers with no luck, but I know I’ve seen it somewhere before.
Can you recommend an article or book with a correlation for the critical Reynolds number as a function of tube diameter and curve radius?
Thank you in advance.
In my opinion the critical Reynolds number is only a sensible definition for a tube, not for individual components (vales, bends, orifices etc). If you put an obstruction in an existing tube flow (say a bend, valve etc), this obstruction will of course disturb the flow field of the fluid. Close to the obstruction this might lead to turbulence. But this is not a 'transition' from laminar to turbulent flow, but simply local turbulence. For a 'transition' to occur, the flow has to remain turbulent, up to multiple pipe diameters downstream the disturbance. So the real question is whether the downstream pipe is able to 'dampen out' the disturbance which was created upstream. This ability to dampen out the disturbance is only determined by the Reynolds number in the downstream tube, and not by the origin of the disturbance.
Leander Boer
Thanks for your answer. But how different the flow in these components are from the flow in a straight tube? Obviously, if an obstacle can create turbulence in a bend, it can create turbulence in a straight tube. Maybe the amount of created turbulence is different, but I believe it will be there.
Anyway, my question is about uninterrupted normal fluid flow in a bend, and I don't want to use any kind of turbulator in my simulation. Even the tube walls are considered smooth.
I just want to make sure that the range of my studied flow Reynolds numbers are not exceeding laminar flow regime.
This flow is largely studied in literature, as example I just did a simple search
https://www.google.com/search?client=firefox-b-d&q=transition+flow+in+elbow
I suggest to search in relevant journals such as JFM, PoF, IJHMT and similar
In developing flows Reynolds number is a function of length and so is the arc of bend. If it is developed flow, with arc radius less than 10.33 mts ( atmospheric pressure head) the reynold's number is independent on arc radius and dependent on diameter. As long as dia is constant, there is no variation of reynolds, number.
But if the bend is sharp, the fluid creates a back pressure on the incoming flow, which will mostly make it unsteady flow pattern, where sudden drop in pressure occurs ( can be calculated using darcy-weisch bach relation) and suitable friction factor can be assessed. We can use reynold - calburn analogy to obtain Stanton number, with this we can arrive at reynold's number of the associated flow, at down stream of 180 degrees bend.
Filippo Maria Denaro
Thank you for your response. The problem is most of these studies have focused on the flow in a 90-degrees bend. That is not the case for my simulation. I'm modeling the flow in a 180-degrees bend. I've checked out lots of papers, but there is not any correlation for the critical Reynolds number for a 180-degree bend. I wonder if I can use the 90-degree bend Critical Reynolds number correlation for my case as well since it can be considered as two separate 90-degree bends.
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