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

CHAPTER 5. RESULTS 71
match the DNS result for k + .
The subgrid approach with the k-ω turbulence model performs rather well. It
can be seen to underpredict U + in Figures 5.1 & 5.3, although by a relatively
small margin. Away from the wall, the value of k in the k-ω model offers a
good approximation to the DNS result, as seen in Figures 5.2 & 5.4.
All of the solutions underpredict turbulent kinetic energy near the wall, as
is particularly apparent in Figure 5.4. Tracing from the symmetry plane of
the channel towards the wall, the point at which the modelled solutions tend
to depart from the DNS result is y + ≈ 40. This corresponds roughly to the
outer extent of the buffer layer (see Table 2.4).
Overall, the steady channel flow results appear consistent with prior work
and offer credibility to the following calculations involving periodic flow.
5.2 Prescribed Periodic Pressure Gradient
The flow was subjected to the same periodically variable pressure gradient
employed by Kawamura & Homma [29] in their DNS study. This pressure
gradient was defined by
∂ +
〈P 〉
2π
= 1 + 6 sin
∂x
6 t+
where
∂〈P 〉
∂x
(5.3)
and t (time) are nondimensionalised by
+
∂ 〈P 〉
∂x
=
∂〈P 〉
∂x
2
ρ(Uτ ) ss
(5.4)
t + = (Uτ) ss t
δ
δ
(5.5)