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
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:
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.