Turbulent Flow in Straight Square Duct - k-ep Validation
 

I am attempting to match the results obtained by Melling and Whitelaw in "Turbulent Flow in a Rectangular Duct" using an anisotropic variant of the k-ep model. There are numerous examples in literature that show the success of various homebrewed anisotropic k-ep models (Wang et al, "Computation of Turb Flow in a Square Duct" and Nisizima, "A Numerical Study of Turbulent Square Duct Flow Using an Anisotropic k-ep Model"). I have yet to accurately predict the secondary velocities and in turn do not see the typical "bulging" of the primary velocity profile towards the corners.

Using Standard k-ep 2 layer, while flagging the quadratic constitutive relation I obtained a mesh independent result that underpredicts the secondary flow by an order of magnitude.

The V2F as well as Realizable 2 layer predict zero secondary flow as expected.

I have also used the RSM and it gives secondary flows that are 50% of those reported in literature. I have returned to the k-ep because I have seen it done before in the literature.

I suppose my questions are:

1. Has anyone run this validation case with success in STAR-CCM+?

2. Is there any way to tweak the k-ep model such that it will predict higher secondary flow?

3. Could you direct me to a source that derives the k-ep model in a way that is understandable to a turbulence modelling beginner?

Thanks,
Darryl

Here is the "bulging" velocity profile seen in experiment.

Does anyone have any insight on how the k-ep model is to be manipulated to give the secondary velocities capable of dispersing the velocity profile so much towards the corners?

The secondary velocities required to do so are in the area of 2-3%. The closest I have got using k-ep with quadratic constitutive relations flagged is 0.1% while RSM gives ~1%.

I have been employing a periodic, fully developed interface. Attached is an image of my geometry. The section is quite thin in the streamwise direction to save computation time. You will notice that only a quarter of the section is modelled as symmetry is exploited.

The mesh is extremely fine and as I have obtained a mesh independent result with each of the "default" k-epsilon models that STAR offers (V2F, standard, realizable 2 layer, AKN) I am in need of some direction as to where to go from here.

As this is my first real validation attempt you can see that I am grasping at straws.

Any help is appreciated.