CFD Online Discussion Forums - Fluid Flow into Still Air from Faucet

I am having difficulties simulating water jetting from a capillary or faucet into still air and breaking up. To me, this should not be so difficult to simulate, but it has proven very time consuming.

I want to simulate the first two regimes of a jet breakup stability curve as shown in the first two boxes of the first attachment (Dumouchel 2008) in 3D. I have simplified the geometry for this with just a cylinder acting as the free space. I have shown the top of the cylinder and meshing I am currently using in the attachments. At the top of the cylinder I have the orifice of the faucet/capillary which is the finer meshed area. I used a parabaloid UDF for the inlet velocity profile profile and set the peak velocity as 2.38m/s. Water is the material that is coming from the faucet and air is what fills the domain. With my current properties I have a Reynolds number = 711 and Weber number of the gas = 0.0286. This falls into the first box of the attachment, Reyleigh regime, but the current simulation (also in attachments) looks more like the second box, first wind-induced regime. It took 10 days to run which is ridiculous and I have yet to see a drop break off, not to mention that I suspect the solution is not correct.

Here is a little more information and settings I used:

Meshing
Total Nodes: 941200
Total Elements: Hexahedrals: 927276; and Quadrilaterals: 26992
**According to ICEM CFD Pre-meshing information before I converted it into mesh**
Minimum Orthogonal Quality = 0.738859
Maximum Ortho Skew = 0.261141
Maximum Aspect Ratio = 16.5582

Setup
General
Pressure-based, Transient, gravity pulling fluid down
Model
VOF, 2 phases
Level Set selected
K-epsilon turbulence, realizable, standard wall functions
Surface tension on (obviously) but no wall adhesion
Boundary Conditions
top of cylinder where orifice inlet is and sides set as free slip wall
bottom of cylinder set as pressure outlet
**Tried setting the free slip walls as pressure outlets as well,
but not much difference to solution**
Solution
PISO scheme
Gradient: Least Squares Cell Based
Pressure: PRESTO!
Momentum: Second Order Upwind
Volume Fraction: Geo-Reconstruct
Turbulent Kinetic Energy, Turbulent Dissipation Rate, and Level-set Function: Second Order Upwind
URF
kept default; did change them before but simulation is too slow to see much difference
Convergence
set to default 1e-3
Initialization
entire cylinder filled with air
Calculation Timestep
Variable method with Global Courant Number = 1 (was set to 0.5 before)
**Courant Number = 2 seemed to diverge sometime after 5000 or so time steps and I ran it over the holidays so I did not want it to diverge.**
Time Step Size = ranges from 2e-7 to 7e-8
max Iteration/Time Step = 50

I have tried looking around to speed up this simulation, but nothings has worked. I have looked at other papers on simulations similar to this (in 2D however) and they usually use similar settings. My computer's processing power is not the issue here I think because I am doing this on a 64GB RAM and 2 Intel Xeon processors workstation.

My main problem right now is that it takes too long to run. Each run of the simulation takes so long I do not have time to diagnose it. I hope I do not have to run a simulation for two weeks and then check to see if it is right, change some minor detail, and run it again for two more weeks.

There are a few things I have considered while looking around but I am not too sure:

My meshing could be too fine leading to errors, so possibly increasing mesh size will lead to a better and faster solution. The problem with this is that I need a fine enough mesh to be able to visualize the thin thread of fluid that attaches the droplet to the stream before breakup.

Maybe Discrete Phase Model might be better? I have read it can model droplet breakups. Might be slower though because it tracks the particles and is useful when there is not a lot of the discrete phase compared to continuous phase. In this case, the flow is continuous and eventually the water will take up a lot more of the domain which is why I do not think it should be used.

Maybe Pseudo-Transient Steady instead of Transient might make things faster? Once the jet and breakup stabilizes, it should have somewhat an oscillating solution since the droplets will periodically fall off and the jet length will increase and decrease because of this. I essentially do not care about the beginning of the flow because I know how it will behave for the most part (gravity will pull the stream down and it will be a growing jet). The problem with this is that I do not know the documentation for it and every time I try to implement it, the jet seems to literally explode upon leaving the orifice and I have no idea why.

I could use two planes of symmetry for the cylinder cutting down the mesh drastically. This would work for the first regime where everything is indeed symmetrical, but for the second regime where the flow gets quite turbulent and not symmetrical, I do not think the physics of the problem elicits the use of symmetry planes.

I am in quite a pickle and I do not know what to do. The only license I have is an academic one which does not allow customer support for this, I think, and I cannot run more than one simulation at a time so I cannot try different things out at the same time. Unfortunately 2D is not an option as I need the results for some other application. If there are any Fluent experts out there that might be able to help or some other post/documentation/resource that would be useful (I swear I tried using the search bar first!) or someone I could contact that would be able to help that would be great! Please let me know or private message me; I have been trying to do this for 3 months with little progress.