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

CHAPTER 5. RESULTS 79
The log law offers predictions of k + in Figures 5.23 & 5.24 that are reasonable.
The log law solution has also been improved greatly by the prescription of U
rather than
∂〈P 〉
. It must once again be noted that the log law only produces
∂x
interesting results away from y/δ = 0.2, where it is applied for this particular
flow.
A ‘kinked’ region of large change in gradient tends to exist in many of the
profiles of 〈U〉 + . This phenomenon can be seen most clearly in Figures 5.25
& 5.26. It is produced by all of the models except for the log law treatment,
and is particularly prevalent in the profiles produced by the low-Reynolds-
number k-ε model. A kink indicates an underprediction of the diffusion of
〈U〉 + within the vicinity of the kink. Deferring to the assumptions of the
EVM, this would suggest a local underprediction of k + . This corollary can
in fact be seen in the figures. Comparing phase angles of 3π/4, π, and 5π/4,
suggests that the location of a kink in 〈U〉 + corresponds to a location of
maximum underprediction of k + . This may be seen by examining Figures
5.25 & 5.26 for velocity and 5.27 & 5.28 for k + .
The same phenomenon of a kinked velocity profile can be observed indirectly
in Figures 5.21, 5.22, 5.23 & 5.24, where 〈U〉 + predicted by the low-Reynolds-
number k-ε model appears to lead the DNS result in phase closer to the wall,
whereas it lags the DNS in phase at higher y/δ. This apparent peculiarity is
in fact a symptom of the changing slope of the 〈U〉 + profile produced by the
k-ε model at different phase angles.
All of the models produce flatter velocity profiles than the DNS, as seen in
Figures 5.25, 5.26, 5.29 & 5.30. This is particularly true just after a phase
angle of π, when the flow is subjected to an adverse pressure gradient and a