Flow over an isolated hill (without dispersion)

Underlying Flow Regime 3-13 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

Key Physics

The key physics are separation from a smooth surface due to an adverse pressure gradient, leading to a free shear layer which reattaches further downstream. A recirculating flow is created in the lee of the hill, bounded by the separation point, the free shear layer, and its reattachment location. The location of the separation point and the angle of the separation streamline determine the length of the recirculation region.

Numerical Modelling issues

A fine mesh is needed along both sides of the hill and in the separated region. However, when using wall functions one should avoid near wall cells leading to a a y+ smaller than 20; to avoid the transitional region between log and viscous sublayer - which is very code dependent.

Near the separation point, the mesh step in the stream-wise direction also needs to be reasonably small.

The profile of the vertical velocity component on the hill summit is a good indicator of sensitivity to mesh refinement.

The intensity of the backflow is a good indicator of pressure solver convergence.

Physical Modelling

Inlet conditions imposed at 3 hill heights upstream of the hill summit is probably a minimum, but acceptable if these are defined as fully developed channel flow profiles. Results are quite sensitive to the dissipation inlet profile.

As for flow over a backward-facing step, the most obvious performance criterion is the predicted size of the recirculation bubble. The separation point varies in a narrow range of abscissa but this has a large effect on the angle of the separation streamline and in turn the reattachment point. A reattachment point in the range x/h_max = 4.5 and 5.5 can be considered a success, and this already eliminates some of the earlier (under-resolved?) k-epsilon simulations which fall very short of this value (see Fig. 2) and even most k-omega models which reattach after x/h_max = 6.

Axial velocity profiles should be compared well downstream from the hill summit, such as at station X04 located at the foot of the hill, since any discrepancies between prediction and measurement will be more obvious at such downstream locations.

A minimum backflow of U/Uo < - 0.1 should be observed in the recirculation region and this parameter is a good indication of spatial convergence.

In the case of k-epsilon simulations, the turbulent kinetic energy is spuriously high at the top of the hill, thus any general good agreement found further downstream with such approaches is essentially fortuitous and probably due to compensating errors. Reynolds Stress Transport or rapid distortion/stagnation point-corrected Eddy Viscosity models are able to capture the turbulent kinetic energy at the top of the hill.

Application Uncertainties

When using second order convection schemes, instabilities may be due to a tendency towards vortex shedding, rather than purely numerical instabilities.

Recommendations for Future Work

Instabilities, which may be a characteristic of vortex shedding, would be interesting to examine using TRANS/URANS (Transient/Unsteady RANS): The large value of the turbulent intensity close to reattachment, which none of the models can reproduce, may be an indication of mean flow instability or the presence of large-scale vortex shedding.

Contributors: Frederic Archambeau - EDF - R&D Division