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

CHAPTER 5. RESULTS 76
more closely resemble the DNS data for τw, except that they exhibit a double-
peak behaviour. τw produced by the k-ω subgrid matches the troughs in the
DNS data effectively, but the peak values are disappointingly overestimated.
The asymmetry in τw suggests that the k-ω model predicts excessively steep
profiles of 〈U〉 + near the wall for most phase angles, as can be seen in Figures
5.31 & 5.32.
The further figures mirror the presentation format employed in the previous
section. Figures 5.21, 5.22, 5.23 & 5.24 display flow variables through time
at y/δ locations of 0.1, 0.2, 0.5 & 0.9, respectively. Figures 5.25, 5.26, 5.27
& 5.28 show snapshots of the channel at various phase angles, and Figures
5.29, 5.30, 5.31 & 5.32 show these against a logarithmic y + scale.
Figures 5.21, 5.22, 5.23 & 5.24 show a tendency for the low-Reynolds-number
k-ε model to exhibit a delay in predicting an increase in k + when the flow
is accelerating. When it appears (for example, at a phase angle of 7π/6
in Figure 5.23), the anticipated increase in k + is sudden and sharp. At
y/δ ≤ 0.5, the peak value of k + through time predicted by the low-Reynolds-
number k-ε model (and indeed by all of the models considered in this work) is
lower than the DNS result, but k + is actually overpredicted throughout most
of the portion of the cycle during which the flow is decelerating. In Figure
5.24, with y/δ = 0.9, the peak value of k + is overpredicted by all except the
k-ω subgrid model and the overprediction of k + during deceleration of the
flow is very pronounced in all of the modelled results.
The use of the UMIST-N subgrid approach with the k-ε model does not ap-
pear to alter the phase position of the suden increase in k + noted above. How-
ever, the subgrid approach does appear to soften this effect. The maximum