7.3 Inlet turbulence
Expressions are presented in Sec. 7.2
to estimate inlet and
initial values of and
. They include parameters
and
which must
themselves be estimated sufficiently accurately to calculate
and
reliably.
The values of and
at domain inlets
depend on the flow conditions upstream of the inlet. The figure below
shows typical ranges of intensity
for different upstream
flow conditions.
A medium intensity is most commonly
specified in CFD problems, in particular for internal flows. For
these flows,
can be calculated from a power-law function of
,
fitted to measurements at the central axis in fully developed flow
along a smooth-wall pipe, according to4
![]() |
(7.7) |







For wall-bounded flows with a boundary layer of
thickness , an estimate of
is often used. This relation (see also
Sec. 6.12
) requires
to be estimated,
e.g. from the
expression for
a turbulent layer at the end of Sec. 6.4
.
Verifying turbulent viscosity
Combining Eq. (7.4
), Eq. (7.6
) and Eq. (6.31
) gives the following
expression for in terms of length
and velocity
scales:
![]() |
(7.8) |


The range is presented in terms of kinematic viscosity which governs the
rate of momentum
diffusion, e.g. the rate of growth of boundary
layers. By contrast, forces
are governed by dynamic viscosity
, which make liquids
“feel” more viscous.