## 7.3Inlet 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)
An estimate of at the centre axis of a pipe, see Sec. 6.12 , can be used in conjunction with from of Eq. (7.7 ). For ducts and channels of non-circular cross-section, can be calculated by , where is the cross-sectional area and is the perimeter length. For a partially ﬁlled pipe or duct, corresponds to the wetted region where the ﬂuid is in contact with the boundary.

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)
Values of need to be realistic. Realistic values usually fall within the range of molecular viscosities for common ﬂuids at standard temperature shown below.

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.

4Nils Basse, Turbulence intensity and the friction factor for smooth- and rough-wall pipe ﬂow, 2017.

Notes on CFD: General Principles - 7.3 Inlet turbulence