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

CHAPTER 5. RESULTS 75
Figures 5.11, 5.12, 5.13 & 5.14 offer snapshots showing 〈U〉 + and k + , respec-
tively, throughout the channel at various discrete phase positions. Figures
5.15, 5.16, 5.17 & 5.18 show the same again, but plotted against y + rather
than y/δ.
Because of the general inaccuracy of all the models, it is difficult to make
comparisons based on Figures 5.11 to 5.18. Figures 5.13 & 5.14 again high-
light the tendency of the log law solution of k + to generate spurious results
at y/δ = 0.2 where the log law is applied. Furthermore, Figures 5.17 & 5.18
show that all the models produced an underprediction of k + near the wall.
This is similar to the underprediction observed in the steady flow case.
To better facilitate comparisons between the models, and following the pe-
riodic channel flow investigation of Addad [1], a further test case was con-
sidered in which the modelled flows are constrained to exhibit the same bulk
flow rates shown in the DNS study. These results are presented below.
5.3 Prescribed Periodic Bulk Flow Rate
The code was configured to match the bulk flow from the DNS study of
Kawamura & Homma [29], rather than the
∂〈P 〉
∂x
data. Figure 5.19 shows
the resulting pressure variations compared to the pressure variation in the
DNS study. As expected, the resultant pressure variation is higher. The
amplitude on the fluctuation in
∂〈P 〉
∂x is greater than the DNS amplitude by
approximately 100%. Correspondingly, wall shear stress is increased.
As seen in Figure 5.20, the k-ε low-Reynolds-number and subgrid results now