Page 293 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

248 Fundamentals of Water Treatment Unit Processes: Physical, Chemical, and Biological

formation due to flow past three shapes: (a) a cylin-
der, (b) multiple airfoils, and (c) an inclined flat
5
plate. For each of the three cases, R 10 . Figure
10.8a shows an initial eddy about the size of the
cylinder and just behind it the eddy grows in size as
it is advected downstream. In Figure 10.8b multiple
airfoils cause the same effect but downstream the
adjacent eddies impinge against each other. In
Figure 10.8c the inclined flat plate causes separation
on the underside with intense mixing. As noted,
the fate of the eddies is an ‘‘energy-cascade’’ with
an eventual dissipation of the energy as viscous
(a) forces and heat (Hanson and Cleasby, 1990;
Hanson, 2001).
. Submerged jet: Figure 10.9 illustrates the general
characteristics of a submerged jet as it expands into
the surrounding ambient environment. As seen, the
velocity profile flattens with increasing x-coordinate.
Also, as illustrated, the velocity gradient dv=dr changes
with r at a given x, which means that eddies are created
accordingly and define the mixing zone (seen as a
conical expansion of the jet from the nozzle).

Two notes are relevant at this point: (1) A submerged jet
is also seen in a hydraulic jump, in the plunging nappe
from a weir, and in the flow from an impeller (the jet of an
(b)
axial flow impeller is parallel to the axis of the impeller and is
in the radial direction in a radial-flow impeller). (2) In coagu-
lation with alum, the flow must be distributed in the core of
the jet, before emergence from the orifice, so that the very
small flows of neat alum are carried into the turbulence
zone with its subsequent mixing (which occurs as lateral and
axial dispersion).
(c)
10.3.1.2.3 Energy Spectrum
FIGURE 10.8 Examples of eddy formation due to different For a given mixing volume with a continuous energy
5
disturbances; R 10 . (Courtesy of Professor B. Bienkiewicz, input, such as an impeller, a submerged jet, or flow across a
Colorado State University, Fort Collins, CO, from wind tunnel disturbance, turbulence occurs as vortex tubes in a spectrum
experiments). (a) Cylinder. (b) Multiple airfoils. (c) Flat plate. of sizes that fill the volume in a ‘‘tangle,’’ as described

Nominal boundary of jet
Core of jet
Mixing zone
Nozzle

D x

v(r) x
1
v(r) x
2
x 1 x 2

FIGURE 10.9 Mixing zone in terms of a submerged jet, diameter (D) and velocity profiles as indicated. (Adapted from Albertson, M.L. et al.,
Am. Soc. Civil Eng. Trans., 115, 657, 1950.)