# Vortex in a pipe / Solutions or approximations?

I want to study a vortex flow in a pipe; in other words helical flow.

A couple introductory texts on fluid mechanics (e.g. Shames, Mechanics of Fluids) describe the solution to vortex flow in 2D:

$$V_{\theta} = \frac \Gamma {(2 \pi r)}$$

(with a singularity at the center). However, what about a vortex in a pipe?

• If I assume irrotational flow down a pipe, can I establish a helical vortex (e.g. $$V_r = 0$$; $$V_z > 0$$; $$V_\theta> 0$$)?
• Is it merely superposition (e.g. irrotational 2D + parabolic laminar or irrotational 2D + plug flow)?

If this is solved using CFD, then how do I identify which types of CFD are appropriate? Is this still merely a potential flow? What is the simplest CFD that would solve this type of problem?

• What is your objective here? If you just want to see a vortex move down a pipe, you can get by with potential flow probably. But if you want to look at vortex bubble breakdown, or heat transfer, or.... just about anything else, you'll need more. Can you explain what the objective of your study is and what you are hoping to learn? Feb 10 '16 at 17:16
• The objective is to design a structure that would intentionally cause a vortex to form in a pipe. The goal is to cause a fluid to pass by a series of illuminators and enable uniform illumination (dose) of the fluid by averaging around in circumference. Flow is turbulent, but simply plug flow, going into the vortexing structure. It is single phase flow (no cavitation, one species). I suspect potential flow is adequate, but all examples I've seen in texts are 2D. What is the difference between pot'l flow and laminar flow? Feb 11 '16 at 17:34
• If the flow is turbulent, you have to go all-in with Navier-Stokes, RANS or LES. Potential flow is inviscid and irrotational -- both of which are defining characteristics of turbulent flows. So if you need to simulate creating a vortex, you will absolutely need viscosity and vorticity and so potential flow will definitely not work. Feb 11 '16 at 18:31
• What is the "test" for inviscid or irrotational? Is it a question of simulate with various conditions and see what matches experiment or is there a test that you can apply to see which approximations must be made? Feb 11 '16 at 20:18
• The only "test" I know of is to understand A) What you are interested in, B) What the different approximations throw out and C) What physics processes will occur in your problem of interest. As soon as you have turbulence, you must have both viscosity and vorticity (so no more potential equations and no Euler equations). It sounds like you have a swirler (your vortex generator) which will only work through viscosity, just like a wing, and so you pretty much have to solve the full set of equations. Feb 12 '16 at 0:31

It is fully non-sense to treat potantial flow as non-viscous. In fluid, theare only two flows are non-viscous. First flow is a constant velocity (m/s) one. Second one is quasi-rigid rotation (in vortex core) with constant angular (radian/s) velocity. People of even age of 80 y.o. make errors treating irrotational flows as non-viscous ones and rotational flows as viscouse (second type flow is rotational but non-viscous).

For discussion, write to Pavlo_Lukianov@nau.edu.ua

This depending on the velocity and dimensions is a most probably turbulent flow which can be solved by finite volume and a simple turbulence model such as k-omega or k-epsilon. I do not know what you mena by which type of CFD should I use. You can use a pre-existing library or a commercial solver such as ANSYS Fluent.

The geometry of the pipe is not known, but if it is an elbow there would be cavity flow as well. However, the equations are all the same (Navier-Stokes) and the best and easiest numerical scheme is finite volume.

These are 2 references explaining this phenomenon to some extent:

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– JMac
Apr 24 '19 at 16:34