Page 357 - Dust Explosions in the Process Industries

326 Dust Explosions in the Process Industries

definition of turbulent$uid$ow is “an irregular condition of flow in which the various
quantities show a random variation with time and space coordinates, so that statistically
distinct average values can be discerned.”Turbulencecan be generated by friction forces
at fixed walls (flow through conduits, flow past bodies) or by the flow of layers of fluids
with different velocities past or over one another. There is a distinct difference between
the kinds of turbulence generated in the two ways. Therefore, it is convenient to clas-
sify turbulence generated and continuously affected by fixed walls as “wall turbulence”
and turbulence in the absence of walls as “free turbulence.”
In the case of real viscous fluids, viscosity effects result in the kinetic energy of flow
being converted into heat. If there is no continual external source of energy to maintain
the turbulent motion, the motion decays. Other effects of viscosity are to make the tur-
bulence more homogeneous and less dependent on direction. Turbulence is called
isotropic if its statistical features have no preference for any direction, so that perfect dis-
order exists. In this case, which is seldom encounteredin practice, no average shear stress
can occur and, consequently,no gradient of the mean velocity. The mean velocity, if any,
is constant throughout the field.
In all other cases, where the mean velocity shows a gradient, the turbulence is non-
isotropic (or anisotropic). Sincethis gradient in mean velocity is associated with the occur-
rence of an average shear stress, the expression shear-$ow turbulence is often used to
designate this class of flow. Most real turbulent flows, such as wall turbulence and
anisotropic free turbulence, fall into this class.
If one compares different turbulent flows, each having its distinct “pattern,” one may
observe differences, for instance, in the size of the patterns. Therefore, to describe a tur-
bulent motion quantitatively, it is necessary to introduce the concept of scale of turbu-
lence. There is a certain scale in time and a certain scale in space. The magnitude of these
scales are determined by the geometry of the environment in which the flow occurs and
the flow velocities. For example, for turbulent flow in a pipe, one may expect a time scale
on the order of the ratio between pipe diameter and average flow velocity, that is, the
average time required for a flow to move the length of one pipe diameter, and a space
scale on the order of magnitude of the diameter of the pipe.
However, it is insufficient to characterize a turbulent motion by its scales alone,
because neither the scales nor the average velocity tell anything about the violence of
the motion. The motion violence is related to the fluctuation of the momentary velocity,
not to its average value. If the momentary velocity is
v=v+v (4.80)

where v isae average velocity and v the momentary deviation. v is zero by definition.
However, vz is positive and it is customaryto define the violence of the turbulent motion,
often called the intensity of the turbulence by

(4.81)
The relative turbulence intensity is then defined by the ratio v’l v.
As discussed by Beer, Chomiak, and Smoot (1984) in the context of pulverized coal
combustion, it is customary to distinguish among three main domains of turbulence: