2D flow over backward facing step

Underlying Flow Regime 3-15 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

Key Physics

The key physics of the problem, as mentioned, include first a fixed separation of a boundary layer determined by the geometry and then a shear layer that bifurcates at the reattachment. The prediction of the reattachment position and the pattern of the streamlines are the first features to predict. The prediciton of the turbulence structure around the reattachment (i.e. velocity and length scales) is important, particularly for heat transfer calculations. The first advice is that a wall-law should not be used because of the absence of local equilibrium in the recirculation zone. In this region it is difficult to predict the peak values of turbulence kinetic energy and shear stress. Another feature of the problem is the presence of a secondary bubble near the bottom corner. Also difficult to predict is the recovery of the boundary layer downstream of the reattachment.

Numerical Issues

The grid must be more refined near the step; a 100x100 grid is considered to be sufficiently refined. Several RANS calculations have been performed using 120x120 and refinement studies have been performed. For LES calculations Alkselvol and Moin (1993) have used a 192x48x32 grid.

The use of wall functions together with high Reynolds number models is not recommended. If this approach is used, the implementation should be carefully performed. In a work presented by Gotjans and Menter (1998) a strong sensitivity to grid refinement was found when using standard wall functions. Modified wall functions were proposed in that work, that make the calculation more stable allowing grid independency to be achieved. It is particularly important to use a zero flux boundary condition for k, and to use k to compute the friction velocity. In the reattachment region, if the velocity scale (the friction velocity) is calculated from the standard log-law, then the mean velocity vanishes and so does the shear stress.

Computational domain and boundary conditions

Some studies presented have taken the domain to be the same to that used in DNS simulations. The domain in that case extended from 10H prior to the step to 20H downwards. It should be noted that in those studies an outflow convective condition was applied to avoid numerical problems due to the boundary condition. Otherwise it is advised to use a longer domain downstream. The choice of 10H prior to the step allows to have a developed boundary layer with the momentum thickness Reynolds number corresponding to each experiment (5000 for DS and 600 for JD), so that the inlet conditions of the experiments and DNS are reproduced as close as possible.

Physical modelling

It should be advised that the k-ε model gives poor results in this test case. Other two equation models, the SST for instance, give much better results. Even the one equation model of Menter performs better, at least in the mean flow prediction. The ASM provides slightly better results especially with the modification in the P equation, something that also is observed in second moment models, which give in general much better results, as expected. In between, the k-ε-χ² model of Durbin (1995) shows a very good performance, the only underprediction being the recovery of the boundary layer downstream and a small shift in the peaks of turbulent kinetic energy profiles.

A step beyond could be the use of two layer models, as in Rodi (1991). They are more expensive, but they require less points in the boundary layers than low Re number models. This could be specially important when performing heat transfer calculations, because the Nusselt number distribution (and so the heat flux to the surface) is very sensitive to the prediction of the length scale near the wall, in the recirculation and (especially) in the reattachment zones.

A common problem to all RANS calculations is that they predict a slower recovery of the boundary layer downstream the reattachment than that observed in the experiments. Even second moment closure models have this problem although the results presented by Hanjalic and Jakirlic (1998) have shown an improvement. On the other hand LES calculations reported in Akselvol and Moin (1993) have shown a very good agreement with the DNS profiles even in the recovery region.

Recommendations for future work

As mentioned before this problem has been calculated using a wide range of turbulence models and many different codes have been used to solve it with different implementations. Even the modern RANS models, like the SST model or the V2F model have been tested for this case.

It would be interesting to have updated LES calculations, as those presented by Akselvol and Moin (1993) are based on an earlier version of the experiment.

Contributors: Arnau Duran - CIMNE