Page 333 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

2. Kinematic similarity: Paths of fluid motion are Turbulence intensity: In general, the higher the amount of
geometrically similar and the ratios of velocities energy dissipated as random fluid motion with a
at corresponding points are equal to the ratios at given volume, the higher the turbulence intensity.
other corresponding points. Also, the higher the R, the higher the velocity gra-
3. Dynamic similarity: The ratio of masses and dient as G, the higher the turbulence intensity.
q ffiffiffiffiffiffiffiffiffi
forces at corresponding points are equal to the 0 2
(v ) =v (see
ratios and other corresponding points, and geo- A mathematical definition is: I ¼
Section 10.3.1.2).
metric and kinematic similarity exist.
Turbulence, isotropic: (1) The turbulence characteristics are
Other parameters of similarity include detention
not dependent on the direction of the axes of refer-
time, u; power per unit volume, P=V; average vel-
ocity gradient, G; tip velocity, nD; etc. ence. Isotropic turbulence can exist only when
Static mixer: Ordinarily a static mixer is considered as one homogeneous turbulence already exists (Batchelor,
of the proprietary elements placed in a pipe that 1953, p. 3). (2) Isotropic turbulence occurs if its
has blades causing a flow bifurcation and helical statistical features do not change with rotation or
twist to the next element where another bifurcation reflection of a set of coordinate axes; all three com-
occurs. In a broader sense, a static mixer may be ponents of the root mean square velocity variations
considered any obstruction placed in a flow that must be equal, based on a rectangular coordinate
causes bifurcations or turbulence, e.g., wake turbu- system; in isotropic turbulence there is no shear
stress and no gradients of mean velocity (Stenquist
lence, or a jet.
and Kaufman, 1972, p. 12).
Submerged jet: A high-velocity fluid flow that enters a large
Velocity field: (1) The description of velocity vectors in
mass of stagnant fluid such that a characteristic vel-
space for a given system at a given time. (2) Velocity
ocity profile with associated turbulence zone is cre-
field: The configuration of velocity vectors for
ated (see Albertson et al., 1950). In practice the jet
a given set of boundaries. Thus the geometry of a
may enter a larger flow of fluid (as opposed to a
basin and the impeller act as a system to result in
stagnant fluid mass) and the velocity profile and
a particular velocity field. Any changes in such a
turbulence zone may deviate somewhat from those
system will result in a different velocity field.
for the stagnant fluid mass.
Vortex: (1) Curvature of surface in vessel caused by tangen-
Tank: Adefined volume having defined geometric propor-
tial velocity component induced by the rotation of
tions. See basin.
impeller in center. At high impeller velocities, the
Tracer: Dye or salt injected into a flow stream for the pur-
vortex may reach the impeller. (2) Same as eddy (see
pose of downstream detection to discern the shape of
eddy). Generally, a vortex is a rotational motion of
C(t) curve.
fluid that decreases in diameter with length. (3) A
Turbine: The term, turbine, is not defined explicitly,
although it seems to be used in chemical engineering vortex tube, i.e., an ‘‘eddy.’’
as a radial-flow-type impeller. In this sense, turbines Vortex stretching: A vortex tube that extends in length; its
have a variety of shapes, e.g., flat blade, six vanes diameter decreases as its length increases.
normal to flow, flat blades mounted on a plate, Wake: The whole region of nonzero vorticity on the down-
curved blades with surface normal to flow, flat stream side of a body in an otherwise uniform stream
blades with surface at an angle to plane of rotation. of fluid (Batchelor, 1967, p. 348).
Flow is both radial and tangential to the impeller Wave number: A mathematically defined characteristic
circle. The currents persist throughout the vessel of turbulence given the symbol, k, and defined
and are effective in penetrating what would other- as k ¼ 1=l, in which l is the length scale of the
turbulence.
wise be stagnant zones. High shear occurs in the
vicinity of the impeller. Baffles are necessary to
impede fluid rotation (McCabe et al., 1993, p. 237).
[Axial flow impellers seem to be excluded from the REFERENCES
definition of a turbine by McCabe et al.] Albertson, M. L., Dai, Y. B., Jensen, R. A., and Rouse, H., Diffusion
Turbulence: Random velocities of fluid superimposed on the of submerged jets, Paper 2409, American Society of Civil
general advective velocity vector. Engineers Transactions, 115:639–697, 1950.
Turbulence, homogeneous: Random velocities whose Amirtharajah, A., Design of rapid mix units, in: Sanks, R. L. (Ed.),
average properties are independent of position in Water Treatment Plant Design, Ann Arbor Science Publishers,
the fluid (Batchelor, 1953, p. 1). Homogeneous Ann Arbor, MI, 1979.
Amirtharajah, A. and Mills, K. M., Rapid-mix design for mechan-
turbulence is difficult to attain in laboratory situ-
isms of alum coagulation, Journal of the American Water
ations but may be approached by a grid. Usually,
Works Association, 74(4):210–216, April 1982.
real-world turbulence is more complex than homo- Amirtharajah, A. and Tambo, N., Mixing in water treatment, in:
geneous turbulence (p. 2). Amirtharajah, A., Clark, M. M., and Trussell, R. R. (Eds.),