Flow over an isolated hill (without dispersion)

Underlying Flow Regime 3-13 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

A fine mesh is needed along both sides of the hill and in the separated region, but when using wall functions one should avoid a near wall cell smaller than 20 wall units to avoid the grey area of ad-hoc matching between log and viscous sublayer (very code dependant).

Near the separation, the mesh step in the streamwise 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.

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.

When using second order convection schemes, instabilities may be due to a tendency towards vortex shedding rather than purely numerical instabilities. This may be an interesting case for TRANS/URANS (Transient/Unsteady RANS). The large value of the turbulent intensity, which none of the models can reproduce, may be an indication of mean flow instability or presence of large-scale vortex shedding

Principal Measured Quantities

As for the backstep flow, an obvious criteria would the 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 as this already eliminates some of the earlier 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 at an early stage of the recirculation, such as X04 located at the foot of the hill, as discrepancies grow downstream. A minimum backflow of U/Uo < - 0.1 should be observed and is a good indication of spatial convergence. Turbulent kinetic energy are already significantly erroneous at the top of the hill (except with RSTM or rapid distortion/stagnation point corrected EVMs) thus any good agreement further downstream would be by pure chance (compensating errors)

Contributors: Frederic Archambeau - EDF - R&D Division