Page 134 - Analysis and Design of Energy Geostructures

106 Analysis and Design of Energy Geostructures

When reference is made to real fluids, viscosity causes the insurgence of shear forces
against the direction of the motion, involving the conversion of mechanical energy
into heat and a consequent variation of the total head (cf. Fig. 3.18B).
An essential component in the description of mass transfer problems is the relation-
ship between the total head and the characteristic velocity of the fluid that gives rise
to the flow of mass. This characteristic velocity is the mean macroscopic relative velocity of
the fluid and is defined with reference to a relevant volume. This volume coincides
with the REV and allows simplifying the local velocity field characterising every point
of the fluid in motion that may be too complex to be analysed rigorously, especially
in the context of seepage flows (Vulliet et al., 2016).

3.10 Laminar and turbulent flows

A critical feature of convection mass transfer phenomena is the flow regime (or flow

condition). There are two fundamental convection mass transfer regimes: laminar flow
and turbulent flow. Laminar flow is a type of mass transfer in which the trajectories of
the single particles constituting the fluid in motion coincide with the effective trajecto-
ries of the average fluid motion. Turbulent flow is a type of mass transfer in which the
trajectories of the single particles constituting the fluid in motion are random and no
more coincident with the effective trajectories of the average fluid motion.
The distinction between laminar and turbulent flows is usually based on the
knowledge of the Reynolds number. The Reynolds number is a dimensionless num-
ber that can be determined as

Re x 5 ρ v N x ð3:33Þ
f
μ
f
where v N is the characteristic velocity of the fluid (i.e. typically the mean relative
velocity), x is the characteristic length of the considered problem (i.e. typically the
hydraulic diameter for a flow within a circular pipe) and μ is the dynamic viscosity of
f
the fluid. The Reynolds number represents the ratio of the inertia to viscous forces: if
the Reynolds number is relatively small, inertia forces are insignificant relative to
viscous forces and the flow is laminar; the opposite is true if the Reynolds number is
significant, that is viscous forces are negligible relative to inertia forces and the flow is
turbulent.
In many flow processes both laminar and turbulent conditions occur, with laminar
conditions preceding turbulent conditions. In between these conditions a transition
zone is evidenced, in which a conversion from laminar flow conditions to turbulent
flow conditions occurs. A critical Reynolds number is often employed to delimit the
transition zone between laminar and turbulent flow conditions. For lower values of