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

CHAPTER 3. CHANNEL FLOW 45
The profiles quoted above for 〈u 2 〉 + , 〈v 2 〉 + , − 〈uv〉 + , and k + near the wall do
not adequately satisfy the relationships in 3.46 and 3.50. Therefore, in the
interest of completeness, values of A, B, C, and D are found as functions of
Reynolds number based on DNS results 3 . [30, 44]
The functions are:
A = 1.060 × 10 −4 Reτ + (0.1107)
B = 1.757 × 10 −7 Reτ + 4.546 × 10 −5
C = 9.005 × 10 −7 Reτ + 5.855 × 10 −4
D = 9.362 × 10 −5 Reτ + (0.0680) (3.52)
The Reynolds-number dependent near-wall proportionalities indicated above
are consistent with the DNS results of Antonia & Kim [4], who analyzed
the near-wall behaviour of u + , v + , − 〈uv〉 + , and other parameters at two
Reynolds numbers.
3.5 Local Nondimensionalisation
When examining computed results, it is often more straightforward to nor-
malise y by k, rather than by τw. In a complex, multidimensional mesh, it is
not possible, in general, to relate modelled flow parameters to friction at a
corresponding point along the wall.
When y is normalised by k, the customary notation is y ∗ . The method of
3 It is notable that the relationships A = a 2 , B = b 2 , and C = 〈ab〉 do not imply
C = √ AB.