Turbulence

Turbulence
Turbulent flow occurs because, in general, rapid fluid motion is unstable.
Suppose fluid is initially flowing through a pipe in the orderly manner, illustrated
by the pathlines . Eventually, something will disturb
the motion, e.g. an obstruction in or a knock on the pipe. Consequently,
elemental volumes, described here as ‘elements’, will alter course and, if
they are moving rapidly enough, fluid friction will not be able to restore
them to their original paths. Moreover the disturbed elements disturb other
elements of fluid from their original path, and soon the entire flow is in the
semi-chaotic state called turbulence, illustrated in Figure 2.5(b).

It is the ratio of fluid momentum (arising from ‘inertia forces’) to viscous
friction which determines whether the flow becomes smooth (i.e. laminar)
or turbulent. This ratio is usually characterised by the non-dimensional
Reynolds number
R_ = uX
Here u is the mean speed of the flow, X is a nominated characteristic length
of the system (in this case the diameter of the pipe) and (/ is the kinematic viscosity of the fluid. The value of _is important for
characterising types of fluid flow, e.g. turbulence. For instance in pipes, flow
will be usually turbulent if _ is larger than about 2300 ___2300_. Criteria
for laminar or turbulent flow in heat transfer are discussed in Chapter 3.
In turbulent flow, random local fluctuations of velocity in three dimensions
are imposed on the mean flow. Thus small elements of fluid moving
along the pipe also move rapidly inwards and outwards across the pipe,
. Since fluid does not slip at the pipe surface
, the mean speed near the surface is smaller than the average
and the mean speed near the centre of the pipe is correspondingly larger.
Therefore the effect of the sideways motions of the fluid elements is to carry
fluid of larger velocity outwards, and fluid of smaller velocity inwards. This
transfer of momentum by elements of fluid is much larger than the corresponding
transfer by molecular motions because
an element of fluid may move significantly across the pipe in a single jump.
In this case with water as the fluid, the mean free path of a molecule in the
liquid is of the order of nanometres.
This transfer of momentum from the fluid to the walls constitutes a
sizeable friction force opposing the motion of the fluid. Thus the presence of
turbulence increases friction as compared with laminar flow; it is important
to appreciate this characteristic of turbulent flow as, for instance