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

CHAPTER 5. RESULTS 77
gradient of k + seen in Figures 5.23 & 5.24 is lower than for the low-Reynolds-
number k-ε model. Furthermore, the extent of over- and underprediction of
k + is diminished throughout the cycle. One reason for this may be that
diffusion is not accounted for across the subgrid boundary. Although the
subgrid is constrained to match the main grid value of k + at y/δ = 0.2, there
is no diffusion of k into the main grid from the subgrid. The only information
transmitted from the subgrid to the main grid in the calculation of the model
equation of k is subgrid-averaged Pk and ε.
Two other potential sources of discrepancy between subgrid and low-Reynolds-
number treatments are detalied here. Firstly, greater numerical errors may
occur in the subgrid solution as a result of the averaging process that is used
to apply subgrid results to the main grid as boundary conditions. Secondly,
the subgrid solution may be configured to offer greater near-wall grid refine-
ment because of the fact that the subgrid cell sizes may be set independently
of the main grid cell sizes. In this work, the subgrid solution did employ
smaller cells near the wall than were used in the low-Reynolds-number treat-
ment, because the use of a high-Reynolds-number model in the main grid
allowed the use of fewer nodes in total. However, suitable grid refinement
was employed in all cases so that the computed results may be assumed to
be independent of cell size. It must be highlighted that the potential of
the subgrid treatment to achieve greater near-wall grid refinement without
impacting the refinement of the main grid is a powerful feature of UMIST-N.
Notably, any difference between the subgrid and low-Reynolds-number k-ε
profiles is less discernable in Figures 5.21 & 5.22, where y/δ ≤ 0.2. This
region falls within the subgrid itself, and the calculation there is substan-
tially similar to a standard low-Reynolds-number treatment. The difference