I've simulated the turbulent flow inside a hydrocyclone using an axisymmetric model (swirling velocity is calculated as a scalar field ). A subgrid scale model has been used to account for turbulent effects. The problem is: the finer the grid, the higher the swirling velocity, so that the agreement between the numerical solution and the experiments becomes worse as the grid is refined. Whose fault might this be?

Thank you.

(1). When you refine the mesh, I think you are also changing the inlet swirl velocity profiles?

What is meant precisely by subgrid scale model? Presumably, it does not mean that the sgs model is part of a LES, as otherwise the calculation should be three-dimensional and time dependent. In LES, as the mesh is refined the sgs viscosity tends to zero.

Strictly speaking, I'm not doing LES yet because the model is 2D. Actually, I use the Smagorinsky model to account for turbulent effects and the grid is refined as much as possible. The sgs viscosity actually tends to zero as the grid is refined, but the swirl velocity profiles depart from the experiments considerably. The axisymmetry assumption is quite reasonable, especially if the experimental profiles throughout the theta coordinate are compared (many authors claim to have obtained good results under this assumption). With regard to the inlet profile, I have performed a number of experiments and it does not seem to affect the core flow significantly (i.e. the swirl profiles are still overpredicted).

Thanks for your replies. Francisco

For these flows when using a statistically-averaged turbulence model the computed flow field is very sensitive to the turbulence closure model. I still do not understand the rationale behind your modelling. If you are not doing LES, then I do not know why you are using a sgs model, as this model scales with grid size and not eddy size. Thus, in the limit of a very fine mesh there is no turbulence.

The axisymmetric assumptions is reasonable for these flows when using a statistical turbulence model. However, the turbulence is always 3d, and a true LES should be 3d even if the mean flow is axisymmetric. The idea of the sgs model when used in LES is that more of large scale motion will be resolved when the grid size is reduced.

Indeed, our ultimate goal is to simulate the full 3D flow inside the hydrocyclone. However, this would be too costly for the moment and we decided to start with a 2D model. Your comments have really clarified some of my doubts and perhaps you could help me more. In numerical terms, it has never been clear to me the difference between classical turbulence modelling and LES. The conceptual difference is obvious, but if the same numerical scheme is used (pv coupling and numerical scheme), the only difference would be in the calculation of the turbulent viscosity. I have used second order schemes for both the convective terms and the time derivative in a projection method in my code. I could have used a Prandtl mixing length model, for instance, instead of the Smagorinsky model, and in that case, I would have obtained reasonable(?) results. So, why would it be wrong to use an sgs model? Thanks for your response. Francisco.

The Smagorinsky model is essentially an adaptation of the Prandtl mixing length model, except for the crucial difference that it uses the grid size as the local length scale rather than the mixing length. The grid size is reasonable for LES as explained in my last message, but for a statistical turbulence model this length scale it is not meaningful as one is not trying to resolve the large-scale motion directly.

With an eddy-viscosity turbulence model, the equations are statistically averaged and the resulting unknown turbulence correlations are usually closed by means of the Boussinesq stress-strain relationship. The eddy viscosity that appears in this relationship scales with a velocity and length scale that is representative of the large-scale turbulent motion. Therefore, I think you should use the Prandtl mixing length rather than the grid size in the eddy-viscosity relationship.

Note that with LES the instantaneous motion is decomposed into resolved and unresolved scales, whereas in conventional turbulence modelling it is resolved into a mean and fluctuating component.

(1). It is good to be creative. (2). But sometimes, one needs to follow the correct approach "first", then do "your own thing" next. (3). "DIY" is fine, but for safety reasons, follow the correct instruction first. (4). It is hard for readers to interpret and answer question about your creative results. (that is doing things in parallel) I am not asking you to change your approach. I am saying that we are talking about different things.

It is good to get your comments. I believe the responses I have been sent have clarified many of my doubts. I have just started my tests with the full 3D model and I hope to improve the results I obtained with the 2D model (at the expense of computer time).