Flow over an isolated hill (without dispersion)

Underlying Flow Regime 3-13 © copyright ERCOFTAC 2004

Description

Introduction

The flow separation behind a smooth hill is the logical extension to the most widespread and basic CFD test case of the backstep-flow. It allows testing of body-fitted or unstructured discretisations, and from the turbulence modelling point of view, it adds the difficulty of predicting the point of flow separation, as this one is no longer imposed by a geometrical singularity. Obtaining the correct length of recirculation, or re-attachment point, is further complicated by the fact that this strongly depends on the separation point position and resulting angle of the separating streamline. The case is not only very relevant to the environmental sector but also to all areas in need of refined modelling of fully developed turbulent flows, and in a nutshell, it exhibits the severe limitations of standard RANS models for separated flows.

Review of UFR studies and choice of test case

The flow over a steep hill leads to highly turbulent free shear layers which are well documented, see e.g. Snyder & Hunt (1980), Castro & Haque (1987). The case considered here and described in Almeida et al. (1992), has the advantage of being confined in a channel that limits the extend of the computational domain, and furthermore the fully developed channel flow upstream of the hill is easy to use as inlet conditions.

The hill, 28 mm high, is located about 6 m downstream of the tunnel inlet where a fully developed channel flow is achieved in the absence of the obstacle(s). The flow separates in the region of unfavourable pressure gradient on the downstream surface of the hill and, in the case of multiple hills, reattaches at an oblique angle on the upstream surface of the next hill. Very high levels of velocity fluctuations have been measured in the shear layers surrounding the recirculation bubbles.

The single hill case was considered at the 4th Workshop ERCOFTAC refined Flow modelling workshop organised by University of Karlsruhe, IFH, April 1995. Streamlines obtained at the time of the workshop are shown on Fig. 1. Predictions of the re-circulation originating from the top of the hill, were found to be very dispersed even for users of identical models. General conclusions on the performance of the various models were difficult to find, partly because there was a large amount of data to be compared and because different contributors obtained quite different results with nominally the same turbulence models. However some general trends could be drawn from the workshop for the k-ε model and the Reynolds-stress model (RSM).

The more complex Reynolds-stress model is not consistently better than the k-ε model concerning the practical relevant mean quantities. It performs slightly better for the predictions of the turbulence quantities.

In Almeida et al. (1992) the authors also presented measurements for a series of 10 hills, which is believed even more challenging if one attempts a periodic flow simulation. Detailed LES data for a similar periodic case was recently produced by 2 independent groups: Jang, Temmerman, Leschziner (2001); and Mellen, Fröhlich, Rodi (2000). In this case the RANS simulation is no longer tied down by fixed inlet conditions and in some cases the differences even for the mean flow streamlines are so large that it becomes impossible to separate cause from consequence when analysing the discrepancies.

Contributors: Frederic Archambeau - EDF - R&D Division