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

CHAPTER 5. RESULTS 80
sudden increase in k + occurs for y/δ ≥ 0.5 (Figures 5.23 & 5.24). When the
pressure gradient diminishes and becomes adverse, the effect on velocity is
expected to manifest itself first near the wall and then propagate outwards.
This happens because the laminar layer near the wall contains less kinetic
energy and therefore less momentum. All of the modelled results exhibit
this preferential slowing of the fluid near the wall when the pressure gradient
becomes adverse, but they do so later in phase and to a lesser extent than
what is seen in the DNS data. This can be seen in Figures 5.25 & 5.26.
It is interesting to compare the snapshots for the phase angles of π/2, 3π/4,
and π found in Figures 5.29 & 5.30. The excessive flatness of the 〈U〉 +
profiles is apparent in all of these snapshots, but particularly at the phase
angle of π, where the flattening occurs at a lower value of y + for all the models
than at the phase angle of π/2. Between these two, the snapshot at phase
angle 3π/4 shows the subgrid k-ω model already flattening at lower y + , while
the low-Reynolds-number k-ε model persists in flattening only at higher y + .
The subgrid k-ε modelled results follow the low-Reynolds-number solution
for lower y + , but the 〈U〉 + profile flattens at y/δ ≈ 0.2 earlier to join the
subgrid k-ω results for higher y + . The point at which the subgrid solution
flattens corresponds roughly to the outer extent of the subgrid. Thus, at this
transitional snapshot in time, when the 〈U〉 + profile is undergoing a change
of shape, the solutions appears to be particularly sensitive to the averaging
procedure used to calculate main grid boundary condition from the subgrid
solution.
An interesting feature of the UMIST-N subgrid approach is highlighted by
the k-ω prediction of k + at phase angles of π/2 and 3π/4. Here, the k +
profiles predicted by the subgrid k-ω model exhibit a double peak (two local