7.3 Inlet turbulence

Expressions are presented in Sec. 7.2 to estimate inlet and initial values of eqn and . They include parameters eqn and eqn which must themselves be estimated sufficiently accurately to calculate eqn and reliably.

The values of eqn and eqn at domain inlets depend on the flow conditions upstream of the inlet. The figure below shows typical ranges of intensity eqn for different upstream flow conditions.

PICT\relax \special {t4ht=

A medium intensity eqn is most commonly specified in CFD problems, in particular for internal flows. For these flows, eqn can be calculated from a power-law function of eqn, fitted to measurements at the central axis in fully developed flow along a smooth-wall pipe, according to4

 0:041 I = 0:055Re : \relax \special {t4ht=
An estimate of eqn at the centre axis of a pipe, see Sec. 6.12 , can be used in conjunction with eqn from of Eq. (7.7 ). For ducts and channels of non-circular cross-section, eqn can be calculated by eqn, where eqn is the cross-sectional area and eqn is the perimeter length. For a partially filled pipe or duct, eqn corresponds to the wetted region where the fluid is in contact with the boundary.

For wall-bounded flows with a boundary layer of thickness eqn, an estimate of eqn is often used. This relation (see also Sec. 6.12 ) requires eqn to be estimated, e.g. from the eqn 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 eqn in terms of length eqn and velocity eqn scales:

 k2in 3 12 1=4 t = c
Values of eqn need to be realistic. Realistic values usually fall within the range of molecular viscosities eqn for common fluids at standard temperature shown below.

PICT\relax \special {t4ht=

The range is presented in terms of kinematic viscosity eqn which governs the rate of momentum diffusion, e.g. the rate of growth of boundary layers. By contrast, forces are governed by dynamic viscosity eqn, 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