# Turbulence model for low reynolds problem

I'm simulating the flow in a capillary with a sudden expansion. The small capillary has a diamater of 250 µm. The big capillar has a diamater of 1000 µm. My flow rate ist $1\frac{ml}{min}$. Using standard properties of water I have a Reynolds number of 85 in my small pipe. For my mesh I choose one similar to this case: https://openfoamwiki.net/index.php/Sig_Turbulence_/_Dellenback_Abrupt_Expansion. I am using a low-Re mesh. I simulated it laminar first, but it seems unphysical to me, because I couldn't see any vortex, but because of the high expansion ratio one would expect a vortex after the sudden diameter change. Now I'm using k-omega-SST and getting similar results (no vortex at all). My simulation is converging well.

Do I have to use a special turbulence model for these situation? Or am I wrong in expecting a vortex in this situation?

Best Regards, Gesetzt

• When I used Phoenics, there were several turbulence models - so you have to find out if one that Opefoam has is relevant - I have not used openfoam... Jan 30 '18 at 8:37
• First up, what type of CFD analysis are you doing, RANS? URANS? Given your description it isn't LES. Inferring that this is either RANS or URANS, do you understand the difference between each case? Jan 30 '18 at 8:42
• I'm doing it with RANS, I'm using the simpleFoam-Solver. I know that URANS is for unsteady simulation. Do you think I would need URANS in my case? Jan 30 '18 at 9:28
• If you want to be sure that you are capturing unsteady flow phenomena you need to run some sort of transient simulation, not RANS. URANS can do this, providing the time period for your simulation is long enough to capture the effects, this time period is often not easy to determine. I would argue URANS is not truly unsteady, since it is still using time averaging, but the time averaged quantities vary across time steps. LES and DNS are truly unsteady, but are too computationally expensive for many scenarios. Feb 1 '18 at 17:07
• @Gesetzt from how I understand your set-up I think RANS is sufficient. I suspect you want to see a kind of annular vortex after the diameter-jump. similar to a backward facing step, right?! In order to help you it would be great if you could show some screenshots. If possible I would like to see: 1) your setup, 2) a stream-line-plot, 3) a plot of the turbulent viscosity Feb 2 '18 at 13:17

I solved my problem. I refined the mesh. Part of the problem was the high aspect ratio of my cells, because my tube is very thin in comparison to the length. I have solved the problem laminar and then take this as a starting value for my turbulence model. My results are physical now and the flow is fully developed some time after the expansion. Thanks to everyone who has contributed.

It is likely, in my opinion, that you cannot clearly observe any vortex due to the RANS nature of your simulation. You are seeing a time averaged view of the flow across a single time step. I like this description of RANS in layman's terms:

Let us think about a concept of a time-averaged field calculated by RANS. Imagine a lot of people crossing a diagonal crosswalk in central city at a busy commute time. It may be hard to follow the movement of each person if you look down from the top of a building, but you can tell that most people are walking from the subway station towards the sidewalk on the opposite side. This general view is the “time-averaged field”. That is to say, in RANS, you would not be conscious of detailed movements or routes of each individual; instead, you would calculate how many and in which direction people cross in a fixed amount of time. Nevertheless, time-averaged fields are affected by turbulence as the nature of flow.

You are seeing a general view of your flow field (influenced by turbulence and therefore by your choice of turbulence model), if you want to be sure of capturing the detailed movements, such as a vortex, you may wish to try URANS (although be careful to chose a total simulation time that is long enough to capture everything - URANS still uses time averaging in a given time step) or if you have a very nice PC (and lots of time) LES would do a nice job - maybe overkill for this problem though.

• Saying this, I may be missing the point entirely, since your Reynolds number is well within the laminar flow region you should probably not use a turbulence model at all. Try running a laminar simulation and compare the results to the simulations which included a turbulence model. In such a slow moving flow is a vortex really something you would expect physically? Feb 1 '18 at 17:30