How does CFX 5.5 handle flow that is initially laminar but goes turbulent? Case in point is turbulent flow over a smooth flat plate, which of course has an initial laminar region at the leading edge. I've simulated this with k-e and SST turbulence models and with 1st order, full second order (blend factor=1) and high resolution advection on both structured and unstructured meshes.

I'm comparing the numerically determined values for Cf with the following equation, valid for turbulent flow:

Cf=0.455/(ln^2(0.06 Re_x)) (Eq.1)

as given in White, Viscous Fluid Flow, Chapter 6.

On the structured mesh, Cf compares well with theory for Re_x>4.7e6 (which is the "highest" value for transition according to White) and not good at all for Re_x<4.7e6. They do not follow a typical transition curve, or a laminar solution at these low Re_x though.

On the unstrutured mesh, the numerical values follow Eq. 1 closely, even to Re_x<1e6, which is supposed to be strictly laminar. The question therefore is what happens during a turbulent solution when the flow is supposed to be laminar? Does the eddy viscosity just become very small, in which case turbulent effects become negligible (which does not seem to be the case) or does it "enforce" turbulence, almost like one would do experimentally using a trip wire at the leading edge?

Hi Louwrens,

I won't claim to be an expert on laminar to turbulent transition, but I have done a small amount of work here which involved flows in a pipe assembly, which happened to be right on the laminar to turbulent transition. My application is for pipe flows rather than flat plate boundary layer stuff, but hopefully it will still be useful.

The k-omega turbulence models handle turbulence better then the epsilon based ones as they can naturally let k head towards zero in the laminar region, and revert to a laminar solution. I chose the SST turbulence model for my application.

I only did a simple check of the accuracy of this model for my application. I ran a simulation with a low flow which would have been laminar in the entire domain with both the laminar and SST models, and the results were within about 5% for overall pressure drop, and the flow fields looked pretty similar. When I viewed the k field of the solution, it was pretty small values, and the turbulent viscosity was mainly orders of magnitude less than the molecular viscosity (ie the simulation had reverted to a laminar simulation), but there was small areas where the turbulent viscosity was approaching the molecular viscosity (this would have been the areas where the small discrepency in the two simulations came from).

Hope that helps. Glenn Horrocks

Thanx for the response Glenn. What still bugs me though is why my results (for both k-e and SST) follow the turbulent solution in the laminar region, rather than the laminar solution. I understand transition is very complex, and my application is not to predict transition but I need to understand how the modelling of turbulence affects the answers at lower-than-turbulent reynolds numbers. I like the idea to plot the k distribution though, that might give me some insight...

Any more possible answers?? Keep them rolling in!

Hi Louwrens,

As I said previously, as far as I understand k-omega based models can model laminar flows by making the turbulent viscosity small compared to the molecular viscosity. It might be better to look at the turbulent viscosity rather than the k values - that will give you a better idea of the relative contribution of the turbulence model to the solution.

I think I need to refer you to a higher authority. Can I recommend "Turbulence modelling for CFD" by DC Wilcox. It has an extensive discussion on the modelling of laminar to turbulent transitions. (Everything I have is from this book anyway)

Regards, Glenn Horrocks

Hi Louwrens,

to answer your question, most turbulence models (i.e. k-e, k-w) treat the boundary layer as having been tripped from the leading edge and are designed only to predict fully turbulent flows. As you correctly pointed out, this does not actually occur in reality. If the turbulence model does predict a small region of laminar (i.e. low eddy viscosity) this is by accident, not by design. Laminar to turbulent transition has been largely neglected in turbulence modelling. My personal feeling is that this is because until recently, we havn't really been able to bridge the gap between theoretical transition predicted by linear stability theory as well as observed in experiments and actual statistical turbulence models. There have been some attempts to improve the transition predictions of turbulence models and these are often referred to as "low-Reynolds number turbulence models". Unfortunately, in practice most of these models have extremely poor convergence behavior and have not been proven to predict transition very accurately. They also suffer from a rather nasty little quirk whereby they are quite sensitive to small differences in code implemenation and numerics. As a result the same transition model implemented in two different Navier-Stokes codes can produce significantly different results. That said we've been doing some work on this area at CFX and as a beta feature their will be a laminar-turbulent transition model in the next release of TASCflow.

Thanx Robin. I'm not worried as such by the "correctness" of the results in the laminar region, but what's important is to know what happens in the code, and your post confirms my hunch.

why would the code give different trends for structured and unstructured meshes? The unstructured mesh results follows the theory closely, while the stuctured grid results is only close to the theory in the fully turbulent region?

My first hunch would be that for the structured mesh your doing a better job capturing the results and your seeing the true prediction from the turbulence model. For the unstructured mesh you are probably not grid independent and it's just a coincidence that the result matches what you expect from experiment. If you refine the unstructured grid it should be comparable to the structured result.