Page 276 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

246 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Fig. 6.1.2.1 The energy cascade of turbulence.

flow U. The high wavenumber range or small scales is the dissipation range where we
find the smallest eddies and where viscosity is playing an important role. Between
these two zones is the inertial range where the energy transfers from the larger scales
to the smallest ones. The extent of this zone is function of the Reynolds number as its
gives an idea of the difference between the largest scales and the smallest scales pre-
sent in the flow. Actually, as the Reynolds increase the smallest scales become even
smaller while the large scales are not significantly modified because more related to
the geometry. The largest eddies of this range (inertial range) are proportional to the
physical geometry, while the smallest are determined by the viscous dissipation and
viscosity. Along the inertial range, under an equilibrium assumption, the transfer rate
of energy between scales equals the dissipation rate E. Based on a dimensional reason-
ing and assuming that the length scale of the smallest eddies is determined by the vis-
cosity ν and the dissipation E, Kolmogorov (1941) determined:
η
¼ Re 3=4 , (6.1.2.1)
l 0
u η 1=4
¼ Re , (6.1.2.2)
u 0