The UMIST-N Near-Wall Treatment Applied to Periodic Channel Flow

CHAPTER 5. RESULTS 78
between the subgrid and standard low-Reynolds-number treatments is in the
averaging used within the subgrid to apply subgrid results as a boundary con-
dition to the main grid. Therefore, the impact of using a subgrid treatment
manifests itself beyond y/δ = 0.2.
The subgrid k-ω model predicts k + admirably well in Figures 5.21, 5.22, 5.23
& 5.24. It does not exhibit the sudden increase in k + noted above, and actual
predicted values of k + appear to be at least as accurate as those of other
models at each of the traverse points shown. However, careful examination
of the DNS data suggests that a slightly greater slope of k + with time is
to be expected when k + is increasing than when it is decreasing. At lower
values of y/δ, the k-ω model appears to fail to capture this effect, suggesting
a qualitative error. Such a criticism would be harsh, however, in light of
Figure 5.24 (y/δ = 0.9), in which the k-ω model does exhibit a greater slope
on the increase of k + than on the decrease. On the whole, the model appears
to offer good qualitative and quantitative accuracy.
The favourable performance of the k-ω subgrid in predicting k + is most ap-
parent at large y + , as seen in Figures 5.27, 5.28, 5.31 & 5.32. The k-ω
prediction matches the DNS almost perfectly for y = δ and phase angles of
5π/4 and 3π/2, and the model produces good results at y = δ for other phase
angles. Near the wall, the behaviour of k + is more accurately reproduced by
the k-ω subgrid for phase angles of π/2 and 3π/4 (favourable pressure gradi-
ent) than by the k-ε subgrid. However, the k-ω model’s near-wall predictions
are less favourable at phase angles of 3π/2 and 7π/4, under the influence of
an adverse pressure gradient. At phase angles of 0 and π, there is little
discernible difference among the near-wall predictions of the various models.