# Evaluation AC5-05

**Boundary layer flow and dispersion over isolated hills and valleys**

**Application Challenge 5-05** © copyright ERCOFTAC 2004

**Comparison of Test data and CFD**

Various comparisons are available in CA and this paper should be consulted for full details. The major comparisons are summarised here for reference. Note that the figures have been scanned from the original AC paper and include the figure numbers in that paper. They will be referred to here by 'local' figure numbers added as captions below the scanned figures.

Figure 1. Velocity profiles at the summit of hill H3 computed with various meshes.

Figure 1 demonstrates that in the severest case (H3 - the steepest hill) results obtained on the standard grid (100 x 80) are very close to those on a grid having four times the number of nodes. Corresponding profiles of, for example, turbulent kinetic energy and locations of the separation and attachment points are also practically coincident; these results gave confidence of both grid independence and the smallness of the truncation errors in the Van Leer scheme used for the convective terms.

Figure 2. Velocity profiles for hill H3 computed with various modifications to the turbulence model.

The computations shown in fig. 2 demonstrate that for this case the 'dissipation modification' (see Section on Overview of CFD Simulations) to the standard k-ε model yields results closest to the experimental data in the downstream region, doing much better in terms of predicting the upslope velocity, the depth of the recirculating region and the sharp velocity gradients in the shear layer.

Figure 3. Kinetic energy profiles over the summit of H3, computed with various turbulence models.

Figure 3 demonstrates that although the curvature modification does not have a major affect on the mean velocity field (fog.2) it does have a significant impact on the turbulence predictions, leading to a k-profile rather closer to the experimental data.

Figure 4. Velocity profiles over H3, computed with fully modified k-ε model and compared with experimental data.

Computations using the fully modified k-ε turbulence model (i.e. including both curvature and dissipation algorithms) yields good agreement with experimental velocity profiles, as shown for hill H3 in fig.4. Similar results were obtained for the more moderate hill slope cases (H5 and H8), confirming the effectiveness of comparatively simple turbulence models in predicting the dominant shear stress and hence the mean flow field in perturbed, deep boundary layers. However, as noted above, turbulence is less well predicted and this has significant affects on the ability of such models to predict scalar concentration fields.

Figure 5. Vertical concentration profiles over flat (i.e. no-hill) terrain, with a source at the hill height.

This is illustrated by the results shown in fig.5, for the (simplest) case of dispersion downwind of a point source over uniform terrain. The (isotropic) diffusivity model predicts vertical spread reasonably well but the concentration levels are significantly overpredicted; this is caused by serious underprediction of the lateral spread (not shown here). Similar behaviour, not unnaturally, occurs for all the calculations of dispersion from sources near the hills, as shown in fig.6, where typically the maximum centreline concentrations are overpredicted by factors of 2-5.

Figure 6. Concentrations downwind of H3, for three source heights at the downwind base of the hill.

Figure 7a.

Figure 7b.

Note that if the concentration values are normalised by their maxima, good agreement is obtained, as illustrated in fig.7a; this was a general feature of the results. An exception was hill H5 (fig.7b), which is an exceptionally difficult case since although there was no separation region in the mean, the experiments indicated that separation occurred intermittently so that material could be advected back towards the hill. Gradient transport models using time-averaged equations cannot be expected to reproduce such behaviour.

© copyright ERCOFTAC 2004

Contributors: Ian Castro - University of Southampton

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