Environmental Engineering Reference
In-Depth Information
Laminar
boundary
layer
Typical fully
developed
(laminar)
Developing
Entrance
velocity
V
0
Entrance length,
L
e
,
l
(A)
Typical fully
developed
(turbulent)
Laminar
boundary
layer
Developing
Entrance
velocity
V
0
Entrance length,
L
e
,
t
a
Transition to
turbulent flow
b
c
(a) Turbulent boundary layer
(b) Buffer zone
(c) Laminar sublayer
(B)
FIGURE 3.2
Developing lows and velocity proiles in an idealized airway for laminar and turbulent low
(not to scale).
3.6.3 F
low
in
c
urved
t
ubes
As a laminar, steady low moves though a curved tube, secondary velocity patterns develop in the
transverse plane of the tube.
73
These secondary patterns (Figure 3.3) are a result of the fast-moving
luid in the center of the tube being pushed toward the outside of the bend by inertia. Any distortion
of the velocity proile can be predicted by the Dean number:
1 2
d
R
⎛
⎜
⎞
⎟
De
=
Re
(3.21)
2
where
R
is the radius of curvature of the bend
d
is the tube diameter
The velocity proile will be affected for
De
> 25, and large distortions will occur for
De
> 300.
77
In curved
tubes, velocity proiles are no longer radially symmetric. Instead, in laminar low the proile becomes
M-shaped in the transverse plane and skewed toward the outside wall in the plane of the bend.
78
Search WWH ::
Custom Search