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

CHAPTER 5. RESULTS 74
where y/δ = 0.2, the log law produces results for k + that are in phase with the
results for 〈U〉 + . This is to be expected from the log law equations. Further
from the wall, where the k-ε model equations are applied, the generated
result is improved, but still offers little encouragement as to the applicability
of the log law to this flow.
Examining turbulent kinetic energy, k + in Figures 5.7, 5.8, 5.9 & 5.10, it
appears that the subgrid k-ε treatment closely matches the low-Reynolds-
number k-ε solution for y/δ ≤ 0.2, within the subgrid region. Outside of the
subgrid region (Figures 5.9 & 5.10), the subgrid solution appears to capture
the effects of variations in
∂〈P 〉
∂x
slightly less effectively than the low-Reynolds-
number counterpart. This suggests that the process of averaging the subgrid
solution to be applied as a boundary condition to the main grid introduces
some discernible measure of inaccuracy. The subgrid solution can therefore
produce different results than a calculation that is continuous throughout the
flow field (standard low-Reynolds-number treatment), even when the same
turbulence model is used in each case.
The k-ω solution produces and amplitude of oscillation of τw that more closely
matches the DNS than that produced by the k-ε subgrid solution (Figure
5.6). Correspondingly, the k-ω model produces fluctuations in bulk velocity
that are also slightly improved (Figure 5.5). This is an indication of the
applicability of the k-ω model to boundary layer flow. The k-ω model exhibits
a less prominent peak in turbulent kinetic energy than is produced by the
k-ε model (Figures 5.7, 5.8, 5.9 & 5.10). This may be compounded by the
general tendency of the k-ω model to offer lower values of k, as observed in
the steady flow results.