K-ε Model and SIMPLE?
 

Hi Guys,

I wanted to get cleared up about how exactly the k-ε fits into an incompressible solver that doesn't have turbulence handling.

I am reading the Versteeg book Introduction to CFD the Finite Volume Method. In the book he describes pretty thoroughly how to implement the SIMPLE method for a laminar solver, but only has a short chapter giving the transport equations for K and ε but he doesn't tell at all how to implement this turbulence modelling.


My question is how is k-ε implemented? Does it remove all swirling vortexes and eddies from the output? Searching online doesn't yield anything about implementation, only a re-iteration of what the transport equations mean... :(

Thanks!

I hear ya! I am currently trying to implement my own 2D cfd code in MATLAB, i'd like to think that I am 80% of the way there, I'm looking for help with it, but not sure where to go!! If anyone is interested my code is very well annotated, I might not be the strongest programmer, but it is fairly explicit!

Did you find out how to do this in the end? I would GREATLY appreciate any help/advice!

Best regards, Michael

Hey Michael !

Yes I figured out the situation in the end. The RANS model uses modified versions of the NS equations, and in terms of the SIMPLE algorithm you solve the discretized RANS instead of discretized regular NS.

With the RANS you have more variables, and these are simply just scalar variables, so you solve them after you solve momentum, pressure correction ,etc...

Note though that in RANS all eddies and these short-scale transient phenomena will be gone.

May I ask if you are a student in CFD? A master's student perhaps?

Best,
Miz

Why did you choose k-epsilon and not other models such as k-omega or others. What are pros and cons of this model and is it application specific?

Hi Miz,
Those "scalar" variables are in fact the Reynolds stresses, and all zero, one and two equations models use the Boussinesq eddy hypothesis (BEH) to relate the reynolds stresses (basically stresses due to turbulence) to mean flow rates ( since we have 4 equations, continuity and 3 RANS, but now have MEAN unknowns u, v,w, p and 6 independent reynolds stresses (10 unknowns)... therefore, we either need to relate these unknowns back to the mean variables ( which is done through the BEH and a turbulent eddy viscosity mu_t), or solve each REynolds stress with it's own equation to balance the system, which would be the RANS turbulence model, which is more accurate, but computationally expensive.

Therefore, all the zero, one and two equation models attempt to do is to describe the turbulent viscosity mu_t... that's about it, where a zero equation e.g. Pandtl mixing length, uses no additional equations, a one equation model, e.g. Spalart Almaras solve one additional equation to describe mu_t etc... nothing too complicated. See Versteeg and Malalasakera, it's pretty good. Be wary though, as the location of your first cell in the domain from a wall is very important, as turbulence is described differently in different portions of a boundary layer, again, see Versteeg, it's pretty clear cut (after a while!)

yes I am a masters student, in Aeronautical engineering, it is a taught masters with a thesis as well, and mine is on this development of a code... tough going personally as I had to figure matlab out first!

I hope that that clears anything up (if there was anything to be cleared!)

Whilst I haven't incorporated turbulence yet, you are right, PATANKAR does say to calculate the turbulence after correcting the velocities, hopefully it will be as easy as that!

BR, Michael

Luckasz,
I have chosen the Prandtl mixing length, as it is easy to implement, comutationally light, and gives reasonable predictions for velocity gradients in boundary layers. Then I am going to use the k-epsilon as it is described (a little) in Versteeg... as well as being generally fairly well rounded ( not as good as k-omega though). The difference between the two is that there is a term in the epsilon transport equation that cannot be resolved at the wall, and so wall functinos are used to extrapolate the data there, which is a drawback... whereas in the k-omega model, it solve all the way to the wall, but is very sensitive to the assigned freestream values of omega... this problem however is fixed by the Shear Stress Transport (SST) k-omega model, which is essentially a k-epsilon model in freestream and for the outer region of the boundary layer, and then blends into a k-omega model at the wall, baically the best of both worlds! Since I am writing the code, I don't want to make life any more difficult than it already is!!

As for applicability, the k-epsilon is robust, economical, has a fairly wide range of flow, but is not good in: swirling flows, large pressure gradients, separation, jet flows, and with all zero, one, and two equation models, which use the Boussinesq eddy hypothesis, the Reynolds stresses are modelled as being isotropic ( same in all directions), which is not the case in reality.

the k-omega is good external aerodynamic flows, can handle adverse pressure gradients, mixin layers, jet and wake flows, no need for damping functions at the wall, and can be used with or without wall functions!

if you need any more help i'd be happy to help.

BR, Michael