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

CHAPTER 3. CHANNEL FLOW 37
u 2 + = 〈u 2 〉
U 2 τ
v 2 + = 〈v 2 〉
U 2 τ
Sometimes the driving pressure gradient is nondimensionalised by
P + x =
∂〈P 〉
∂x
2
(Uτ ) ρ
δ
(3.30)
(3.31)
(3.32)
Note that 〈u 2 〉 and 〈v 2 〉 may be nondimensionalised as 〈u2 〉
k
also notable that the definitions of Reτ and y + give
y + |y=δ = Reτ
3.4 Steady Channel Flow Data
and 〈v2 〉
. It is
k
(3.33)
Based on the wealth of experimental and DNS results available concerning
the behaviour of steady channel flows, a set of empirical profiles have been
developed to obtain estimates of U + , − 〈uv〉 + , k + , 〈u 2 〉 + , and 〈v 2 〉 + . These
results are compared to DNS and experimental data in the following sections.
Much of the data were found in the AGARD Aerospace Database 1 . The
contributors of specific data sets are cited in the graph legends 2 .
1 Advisory Group for Aerospace Research and Development, France
2 Another excellent source of experimental information may be found at
http://www.efluids.com. Furthermore, at http://torroja.dmt.vpm.es Dr. Javier Jimenez
(School of Aeronautics, University of Madrid) has published full flow fields for channel
flow at Reτ = 180 and Reτ = 550